https://karnatakaeducation.org.in/KOER/en/api.php?action=feedcontributions&user=Shobhit&feedformat=atomKarnataka Open Educational Resources - User contributions [en]2024-03-29T09:41:25ZUser contributionsMediaWiki 1.35.6https://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmShobhit3.drawio.svg&diff=36531File:MmShobhit3.drawio.svg2022-07-06T06:48:12Z<p>Shobhit: </p>
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<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=User:Shobhit&diff=36530User:Shobhit2022-07-06T06:47:53Z<p>Shobhit: </p>
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<div>{{#drawio:mmShobhit3|interactive}}</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmShobhit2.drawio.svg&diff=36529File:MmShobhit2.drawio.svg2022-07-06T06:40:10Z<p>Shobhit: </p>
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<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=User:Shobhit&diff=36528User:Shobhit2022-07-06T06:39:55Z<p>Shobhit: </p>
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<div>{{#drawio:mmShobhit2|interactive}}</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmShobhit1.drawio.svg&diff=36527File:MmShobhit1.drawio.svg2022-07-06T06:38:09Z<p>Shobhit: </p>
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<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=User:Shobhit&diff=36526User:Shobhit2022-07-06T06:37:52Z<p>Shobhit: </p>
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<div>{{#drawio:mmShobhit1|interactive}}</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmShobhit.drawio.svg&diff=36525File:MmShobhit.drawio.svg2022-07-06T06:35:41Z<p>Shobhit: </p>
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<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=User:Shobhit&diff=36524User:Shobhit2022-07-06T06:35:19Z<p>Shobhit: </p>
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<div>{{#drawio:mmShobhit|interactive}}</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=User:Shobhit&diff=36523User:Shobhit2022-07-06T06:34:53Z<p>Shobhit: Created page with "{{#drawio:mmPolygons|interactive}}"</p>
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<div>{{#drawio:mmPolygons|interactive}}</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmQuadrilaterals1.drawio.svg&diff=36522File:MmQuadrilaterals1.drawio.svg2022-07-06T05:11:58Z<p>Shobhit: Shobhit uploaded a new version of File:MmQuadrilaterals1.drawio.svg</p>
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<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmPolygons.drawio.svg&diff=36521File:MmPolygons.drawio.svg2022-07-06T04:58:34Z<p>Shobhit: Shobhit uploaded a new version of File:MmPolygons.drawio.svg</p>
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<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmPolygons.drawio.svg&diff=36520File:MmPolygons.drawio.svg2022-07-06T04:57:26Z<p>Shobhit: Shobhit uploaded a new version of File:MmPolygons.drawio.svg</p>
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<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmQuadrilaterals1.drawio.svg&diff=36512File:MmQuadrilaterals1.drawio.svg2022-07-05T08:43:54Z<p>Shobhit: </p>
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<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Quadrilaterals&diff=36511Quadrilaterals2022-07-05T08:43:34Z<p>Shobhit: /* Concept Map */</p>
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''[http://karnatakaeducation.org.in/KOER/index.php/ಬಹು_ಭುಜಾಕೃತಿಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].<br />
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<br />
=== Concept Map ===<br />
{{#drawio:mmQuadrilaterals1}}<br />
<br />
==Textbook==<br />
To add textbook links, please follow these instructions to: ([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])<br />
==Additional Information==<br />
This videos is related to classification and properties of quadrilaterals.<br />
<br />
{{#widget:YouTube|id=0OW2bU0So-4}} {{#widget:YouTube|id=udS3nkj2cfg}}<br />
===Useful websites===<br />
#[http://www.shodor.org/ihnteractivate/discussions/Quadrilaterals/ click here] : For effective introduction to quadrilaterals.<br />
#[http://www.mathopenref.com/quadrilateral.html click here] : Simple explanation about quadrilaterals.<br />
#[http://www.slideshare.net/muzzu1999/types-of-quadrilaterals-and-its-properties-group-4 click here] : This website has a very good activity on properties of quadrilaterals.<br />
#[http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i1/bk8_1i3.htm click here] This is a very good website for students to understand classification of quadrilaterals as per their properties.<br />
===Reference Books===<br />
*Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer the page 89 [http://www.textbooksonline.tn.nic.in/Std9.htm click here]<br />
*Refer 9th standard mathematics ncert textbook from the following link [http://www.ncert.nic.in/ncerts/textbook/textbook.htm?iemh1=8-15 click here]<br />
=== Additional Resources ===<br />
<br />
==== Resource Title ====<br />
[http://www.mathopenref.com/tocs/quadrilateraltoc.html Quadrilaterals]<br />
<br />
==== OER ====<br />
# List web resources with a brief description of what it contains; how it can be used and whether it can be by teacher/ student or both<br />
# Books and journals<br />
# Textbooks<br />
# Syllabus documents<br />
<br />
==== Non-OER ====<br />
# List web resources with a brief description of what it contains; how it can be used and whether it can be by teacher/ student or both<br />
#* http://www.mathopenref.com/quadrilateral.html : Simple explanation about quadrilaterals.<br />
#* http://www.slideshare.net/muzzu1999/types-of-quadrilaterals-and-its-properties-group-4 : This website has a very good activity on properties of quadrilaterals.<br />
#* http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i1/bk8_1i3.htm This is a very good website for students to understand classification of quadrilaterals as per their properties.<br />
#* http://www.shodor.org/ihnteractivate/discussions/Quadrilaterals/ click here : For effective introduction to quadrilaterals.<br />
# Books and journals<br />
#* Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer to page 89 [http://www.textbooksonline.tn.nic.in/Std9.htm click here]<br />
#* Refer 9th standard mathematics NCERT textbook from the following link [http://www.ncert.nic.in/ncerts/textbook/textbook.htm?iemh1=8-15 click here]<br />
# Textbooks : Karnataka State Text book of mathematics [http://ktbs.kar.nic.in/new/website%20textbooks/class9/9th%20standard/9th-english-maths-1.pdf Class 9-Chapter 8:Quadrilaterals]<br />
# Syllabus documents (CBSE, ICSE, IGCSE etc)<br />
<br />
= Additional Information =<br />
An Ortho-diagonal quadrilateral i.e., any quadrilateral whose diagonals are perpendicular to each other possesses certain interesting properties. This article [http://azimpremjiuniversity.edu.in/SitePages/pdf/quadrilaterals-with-perpendicular-diagonals.pdf 'Quadrilaterals with Perpendicular Diagonals'] by Shailesh Shirali (published in ''<nowiki/>'At Right Angles''' | Vol. 6, No. 2, August 2017) discusses a few of them. <br />
<br />
''<nowiki/>''<br />
<br />
=== Learning Objectives ===<br />
* Introduction to polygons <br />
* The meaning of quadrilateral<br />
* Identification of various types of quadrilaterals<br />
* Different properties of special quadrilaterals<br />
* Construction of quadrilaterals to given suitable data <br />
* Finding area of quadrilaterals<br />
* Introduction to cyclic quadrilaterals<br />
<br />
=== Teaching Outlines ===<br />
====Concept 1: Introduction to Quadrilaterals====<br />
The word quadrilateral comes from two latin words "quadri" which means a "variant of 4" and 'latera' which means 'side'. A quadrilateral is a 4 sided figure with 4 sides, 4 angles and 4 vertices.<br />
<br />
This topic has its basics in polygons. Try to elicit live examples for quadrilaterals from within classroom, starting from the shape of a textbook. Show the vertices of a rectangular page. Mark three sets of four points on the blackboard, one set being collinear and other non-collinear. Call students to join the points of each set of points. This activity will introduce them to the concept of quadrilateral. <br />
<br />
===== Activities # =====<br />
<br />
====== [[Introduction to quadrilaterals]] ======<br />
This activity explores formation of a quadrilateral and elements related with the shape.<br />
<br />
======[[Identifying quadrilaterals]]======<br />
This is an exploration into quadrilaterals. A specific type of quadrilateral can be selected with the checkboxes, and any blue dots on each quadrilateral can be dragged to change the shape.<br />
<br />
====== Concept 3: Types of quadrilaterals ======<br />
Quadrilaterals are of different types. Grouping is made based on the four angle measures and/or sides. Each type is recognized with its characteristic properties. The types include regular, non-regular; convex, concave; parallelogram (square, rectangle, rhombus,) and non-parallelograms (trapezium and kite).<br />
<br />
===== Activities # =====<br />
<br />
====== [[Quadrilaterals "I have - Who has?"|"I have - Who has ?"]]======<br />
A hands on group activity that helps in identifying and building vocabulary related to quadrilaterals.<br />
<br />
====== [[Venn diagrams of quadrilaterals]] ======<br />
Classifying quadrilaterals based on their properties and identifying related quadrilaterals with ven-diagram.<br />
<br />
==== Concept 2: Properties of quadrilaterals ====<br />
There are certain characteristic properties by which a quadrilateral is identified. A quadrilateral is a plane closed figure having 4 sides and 4 angles. The sum of all 4 interior angles of any quadrilateral always equals to 360 degrees. This is called the interior angle sum property of a quadrilateral. The sum of all 4 exterior angles of any quadrilateral equals 360 degrees. This is called the exterior angle sum property of the quadrilateral. If any 3 angles of a quadrilateral are known the fourth angle can be found using the angle sum property.<br />
<br />
===== Activities # =====<br />
<br />
====== [[Angle sum property of a quadrilateral]]======<br />
Showing the sum of angles of quadrilaterals by placing the angles of the quadrilateral adjacent to each other with a hand on activity.<br />
<br />
====== [[Sum of the interior angles of a quadrilateral]] ======<br />
The sum of the measures of the angles in any quadrilateral is 4 right angles.<br />
<br />
====== [[Sum of angles at point of intersection of diagonals in a quadrilateral]] ======<br />
A diagonal is the line segment that joins a vertex of a polygon to any of its non-adjacent vertices. These two diagonals of a quadrilateral form angle, this activity explores the property of these angles.<br />
<br />
====== [[Area of a quadrilateral]] ======<br />
A diagonal divides a quadrilateral into 2 triangles. Understanding the area of a quadrilateral in terms of triangles is done with this activity.<br />
<br />
==== [[Properties of Parallelogram]] ====<br />
<br />
==== [[Parallelogram on same base and between same parallels have equal area]] ====<br />
<br />
==== [[Mid point of sides of a Quadrilateral forms parallelogram]] ====<br />
<br />
==== Concept 3 : Properties of Rhombus ====<br />
A rhombus is a quadrilateral with all sides of equal length. The opposite angles of a rhombus are equal and its diagonals are perpendicular bisectors of one another. Since the opposite sides and opposite angles of a rhombus have the same measures, it is also a parallelogram. Hence, a rhombus has all properties of a parallelogram and also that of a kite. [[Properties of Rhombus|(click here)]]<br />
<br />
==== Concept 3: Construction of quadrilaterals ====<br />
<br />
==== Concept 4: Square ====<br />
A square is a 4-sided regular polygon with all sides equal and all internal angles 90. A square is the only regular quadrilateral. It can also be considered as a special rectangle with both adjacent sides equal. Its opposite sides are parallel. The diagonals are congruent and bisect each other at right angles. The diagonals bisect the opposite angles. Each diagonal divides the square into two congruent isosceles right angled triangles. A square can be inscribed in a circle. A circle can be inscribed in a square touching all its sides.<br />
<br />
[[Introduction to a square and its properties|Click here : Introduction to a square and its properties]]<br />
<br />
Four sides of a square are equal. Adjacent sides are at right angles with each other. The area of a square is side x side sq units. The perimeter of a square is the length of distance around its boundary which is 4 times its side.<br />
<br />
====== [[Pull me to see if I still remain a square]] ======<br />
<br />
====== [[Area of a square]] ======<br />
[[Constructing a square|'''Constructing a square''']]<br />
<br />
==== Concept 5: Cyclic Quadrilaterals ====<br />
<br />
==== [[Cyclic Quadrilaterals]] ====<br />
<br />
====== [[Theorems on cyclic quadrilaterals]] ======<br />
<br />
==== Concept : Kite ====<br />
A kite has two pairs of congruent sides. Its diagonals intersect at right angles. The sum of its four sides would be its perimeter. Its area is given by the formula <math>(1/2) (product of its diagnols)</math><br />
<br />
====== [[A Kite and its properties]] ======<br />
<br />
====== [[Construction of a kite]] ======<br />
<br />
====== [[Deriving formula for area of a kite]] ======<br />
<br />
==== Concept : Trapezium ====<br />
<br />
======[[A Trapezium and its properties]]======<br />
<br />
====== [[Deriving formula for area of a trapezium]] ======<br />
<br />
====== [[Construction of Trapezium]] ======<br />
<br />
====== [[Construct an isosceles trapezium and study its properties]] ======<br />
A trapezium in which non-parallel sides are equal is called as an Isosceles Trapezium. The diagonals of an isosceles trapezium are equal. An isosceles trapezium has one line of reflection symmetry. This line connects the midpoints of the two bases. Both pairs of base angles of an isosceles trapezium are congruent. Pairs of angles in an isosceles trapezium that do not share a base are supplementary. The area of an isosceles trapezium is given by<math>(a+b)/2 x h</math> , where a and b are the lengths of the parallel sides and h is the distance (height) between the parallel sides.<br />
<br />
===== Solved problems/ key questions (earlier was hints for problems).[edit | edit source] =====<br />
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=== Projects (can include math lab/ science lab/ language lab)[edit | edit source] ===<br />
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[[Category:Class 9]]<br />
[[Category:Quadrilaterals]]</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Quadrilaterals&diff=36510Quadrilaterals2022-07-05T08:43:17Z<p>Shobhit: /* Concept Map */</p>
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''[http://karnatakaeducation.org.in/KOER/index.php/ಬಹು_ಭುಜಾಕೃತಿಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]<br />
| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]<br />
| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |<br />
[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]<br />
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]<br />
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]<br />
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[http://karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]<br />
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]<br />
|}<br />
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].<br />
<br />
<br />
=== Concept Map ===<br />
{{#drawio:mmQuadrilaterals}}<br />
<br />
==Textbook==<br />
To add textbook links, please follow these instructions to: ([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])<br />
==Additional Information==<br />
This videos is related to classification and properties of quadrilaterals.<br />
<br />
{{#widget:YouTube|id=0OW2bU0So-4}} {{#widget:YouTube|id=udS3nkj2cfg}}<br />
===Useful websites===<br />
#[http://www.shodor.org/ihnteractivate/discussions/Quadrilaterals/ click here] : For effective introduction to quadrilaterals.<br />
#[http://www.mathopenref.com/quadrilateral.html click here] : Simple explanation about quadrilaterals.<br />
#[http://www.slideshare.net/muzzu1999/types-of-quadrilaterals-and-its-properties-group-4 click here] : This website has a very good activity on properties of quadrilaterals.<br />
#[http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i1/bk8_1i3.htm click here] This is a very good website for students to understand classification of quadrilaterals as per their properties.<br />
===Reference Books===<br />
*Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer the page 89 [http://www.textbooksonline.tn.nic.in/Std9.htm click here]<br />
*Refer 9th standard mathematics ncert textbook from the following link [http://www.ncert.nic.in/ncerts/textbook/textbook.htm?iemh1=8-15 click here]<br />
=== Additional Resources ===<br />
<br />
==== Resource Title ====<br />
[http://www.mathopenref.com/tocs/quadrilateraltoc.html Quadrilaterals]<br />
<br />
==== OER ====<br />
# List web resources with a brief description of what it contains; how it can be used and whether it can be by teacher/ student or both<br />
# Books and journals<br />
# Textbooks<br />
# Syllabus documents<br />
<br />
==== Non-OER ====<br />
# List web resources with a brief description of what it contains; how it can be used and whether it can be by teacher/ student or both<br />
#* http://www.mathopenref.com/quadrilateral.html : Simple explanation about quadrilaterals.<br />
#* http://www.slideshare.net/muzzu1999/types-of-quadrilaterals-and-its-properties-group-4 : This website has a very good activity on properties of quadrilaterals.<br />
#* http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i1/bk8_1i3.htm This is a very good website for students to understand classification of quadrilaterals as per their properties.<br />
#* http://www.shodor.org/ihnteractivate/discussions/Quadrilaterals/ click here : For effective introduction to quadrilaterals.<br />
# Books and journals<br />
#* Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer to page 89 [http://www.textbooksonline.tn.nic.in/Std9.htm click here]<br />
#* Refer 9th standard mathematics NCERT textbook from the following link [http://www.ncert.nic.in/ncerts/textbook/textbook.htm?iemh1=8-15 click here]<br />
# Textbooks : Karnataka State Text book of mathematics [http://ktbs.kar.nic.in/new/website%20textbooks/class9/9th%20standard/9th-english-maths-1.pdf Class 9-Chapter 8:Quadrilaterals]<br />
# Syllabus documents (CBSE, ICSE, IGCSE etc)<br />
<br />
= Additional Information =<br />
An Ortho-diagonal quadrilateral i.e., any quadrilateral whose diagonals are perpendicular to each other possesses certain interesting properties. This article [http://azimpremjiuniversity.edu.in/SitePages/pdf/quadrilaterals-with-perpendicular-diagonals.pdf 'Quadrilaterals with Perpendicular Diagonals'] by Shailesh Shirali (published in ''<nowiki/>'At Right Angles''' | Vol. 6, No. 2, August 2017) discusses a few of them. <br />
<br />
''<nowiki/>''<br />
<br />
=== Learning Objectives ===<br />
* Introduction to polygons <br />
* The meaning of quadrilateral<br />
* Identification of various types of quadrilaterals<br />
* Different properties of special quadrilaterals<br />
* Construction of quadrilaterals to given suitable data <br />
* Finding area of quadrilaterals<br />
* Introduction to cyclic quadrilaterals<br />
<br />
=== Teaching Outlines ===<br />
====Concept 1: Introduction to Quadrilaterals====<br />
The word quadrilateral comes from two latin words "quadri" which means a "variant of 4" and 'latera' which means 'side'. A quadrilateral is a 4 sided figure with 4 sides, 4 angles and 4 vertices.<br />
<br />
This topic has its basics in polygons. Try to elicit live examples for quadrilaterals from within classroom, starting from the shape of a textbook. Show the vertices of a rectangular page. Mark three sets of four points on the blackboard, one set being collinear and other non-collinear. Call students to join the points of each set of points. This activity will introduce them to the concept of quadrilateral. <br />
<br />
===== Activities # =====<br />
<br />
====== [[Introduction to quadrilaterals]] ======<br />
This activity explores formation of a quadrilateral and elements related with the shape.<br />
<br />
======[[Identifying quadrilaterals]]======<br />
This is an exploration into quadrilaterals. A specific type of quadrilateral can be selected with the checkboxes, and any blue dots on each quadrilateral can be dragged to change the shape.<br />
<br />
====== Concept 3: Types of quadrilaterals ======<br />
Quadrilaterals are of different types. Grouping is made based on the four angle measures and/or sides. Each type is recognized with its characteristic properties. The types include regular, non-regular; convex, concave; parallelogram (square, rectangle, rhombus,) and non-parallelograms (trapezium and kite).<br />
<br />
===== Activities # =====<br />
<br />
====== [[Quadrilaterals "I have - Who has?"|"I have - Who has ?"]]======<br />
A hands on group activity that helps in identifying and building vocabulary related to quadrilaterals.<br />
<br />
====== [[Venn diagrams of quadrilaterals]] ======<br />
Classifying quadrilaterals based on their properties and identifying related quadrilaterals with ven-diagram.<br />
<br />
==== Concept 2: Properties of quadrilaterals ====<br />
There are certain characteristic properties by which a quadrilateral is identified. A quadrilateral is a plane closed figure having 4 sides and 4 angles. The sum of all 4 interior angles of any quadrilateral always equals to 360 degrees. This is called the interior angle sum property of a quadrilateral. The sum of all 4 exterior angles of any quadrilateral equals 360 degrees. This is called the exterior angle sum property of the quadrilateral. If any 3 angles of a quadrilateral are known the fourth angle can be found using the angle sum property.<br />
<br />
===== Activities # =====<br />
<br />
====== [[Angle sum property of a quadrilateral]]======<br />
Showing the sum of angles of quadrilaterals by placing the angles of the quadrilateral adjacent to each other with a hand on activity.<br />
<br />
====== [[Sum of the interior angles of a quadrilateral]] ======<br />
The sum of the measures of the angles in any quadrilateral is 4 right angles.<br />
<br />
====== [[Sum of angles at point of intersection of diagonals in a quadrilateral]] ======<br />
A diagonal is the line segment that joins a vertex of a polygon to any of its non-adjacent vertices. These two diagonals of a quadrilateral form angle, this activity explores the property of these angles.<br />
<br />
====== [[Area of a quadrilateral]] ======<br />
A diagonal divides a quadrilateral into 2 triangles. Understanding the area of a quadrilateral in terms of triangles is done with this activity.<br />
<br />
==== [[Properties of Parallelogram]] ====<br />
<br />
==== [[Parallelogram on same base and between same parallels have equal area]] ====<br />
<br />
==== [[Mid point of sides of a Quadrilateral forms parallelogram]] ====<br />
<br />
==== Concept 3 : Properties of Rhombus ====<br />
A rhombus is a quadrilateral with all sides of equal length. The opposite angles of a rhombus are equal and its diagonals are perpendicular bisectors of one another. Since the opposite sides and opposite angles of a rhombus have the same measures, it is also a parallelogram. Hence, a rhombus has all properties of a parallelogram and also that of a kite. [[Properties of Rhombus|(click here)]]<br />
<br />
==== Concept 3: Construction of quadrilaterals ====<br />
<br />
==== Concept 4: Square ====<br />
A square is a 4-sided regular polygon with all sides equal and all internal angles 90. A square is the only regular quadrilateral. It can also be considered as a special rectangle with both adjacent sides equal. Its opposite sides are parallel. The diagonals are congruent and bisect each other at right angles. The diagonals bisect the opposite angles. Each diagonal divides the square into two congruent isosceles right angled triangles. A square can be inscribed in a circle. A circle can be inscribed in a square touching all its sides.<br />
<br />
[[Introduction to a square and its properties|Click here : Introduction to a square and its properties]]<br />
<br />
Four sides of a square are equal. Adjacent sides are at right angles with each other. The area of a square is side x side sq units. The perimeter of a square is the length of distance around its boundary which is 4 times its side.<br />
<br />
====== [[Pull me to see if I still remain a square]] ======<br />
<br />
====== [[Area of a square]] ======<br />
[[Constructing a square|'''Constructing a square''']]<br />
<br />
==== Concept 5: Cyclic Quadrilaterals ====<br />
<br />
==== [[Cyclic Quadrilaterals]] ====<br />
<br />
====== [[Theorems on cyclic quadrilaterals]] ======<br />
<br />
==== Concept : Kite ====<br />
A kite has two pairs of congruent sides. Its diagonals intersect at right angles. The sum of its four sides would be its perimeter. Its area is given by the formula <math>(1/2) (product of its diagnols)</math><br />
<br />
====== [[A Kite and its properties]] ======<br />
<br />
====== [[Construction of a kite]] ======<br />
<br />
====== [[Deriving formula for area of a kite]] ======<br />
<br />
==== Concept : Trapezium ====<br />
<br />
======[[A Trapezium and its properties]]======<br />
<br />
====== [[Deriving formula for area of a trapezium]] ======<br />
<br />
====== [[Construction of Trapezium]] ======<br />
<br />
====== [[Construct an isosceles trapezium and study its properties]] ======<br />
A trapezium in which non-parallel sides are equal is called as an Isosceles Trapezium. The diagonals of an isosceles trapezium are equal. An isosceles trapezium has one line of reflection symmetry. This line connects the midpoints of the two bases. Both pairs of base angles of an isosceles trapezium are congruent. Pairs of angles in an isosceles trapezium that do not share a base are supplementary. The area of an isosceles trapezium is given by<math>(a+b)/2 x h</math> , where a and b are the lengths of the parallel sides and h is the distance (height) between the parallel sides.<br />
<br />
===== Solved problems/ key questions (earlier was hints for problems).[edit | edit source] =====<br />
<br />
=== Projects (can include math lab/ science lab/ language lab)[edit | edit source] ===<br />
<br />
=== Assessments - question banks, formative assessment activities and summative assessment activities[edit | edit source] ===<br />
[[Category:Class 9]]<br />
[[Category:Quadrilaterals]]</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Quadrilaterals&diff=36509Quadrilaterals2022-07-05T08:40:43Z<p>Shobhit: /* Concept Map */</p>
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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].<br />
<br />
<br />
=== Concept Map ===<br />
{{#drawio:mmQuadrilaterals|interactive}}<br />
<br />
==Textbook==<br />
To add textbook links, please follow these instructions to: ([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])<br />
==Additional Information==<br />
This videos is related to classification and properties of quadrilaterals.<br />
<br />
{{#widget:YouTube|id=0OW2bU0So-4}} {{#widget:YouTube|id=udS3nkj2cfg}}<br />
===Useful websites===<br />
#[http://www.shodor.org/ihnteractivate/discussions/Quadrilaterals/ click here] : For effective introduction to quadrilaterals.<br />
#[http://www.mathopenref.com/quadrilateral.html click here] : Simple explanation about quadrilaterals.<br />
#[http://www.slideshare.net/muzzu1999/types-of-quadrilaterals-and-its-properties-group-4 click here] : This website has a very good activity on properties of quadrilaterals.<br />
#[http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i1/bk8_1i3.htm click here] This is a very good website for students to understand classification of quadrilaterals as per their properties.<br />
===Reference Books===<br />
*Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer the page 89 [http://www.textbooksonline.tn.nic.in/Std9.htm click here]<br />
*Refer 9th standard mathematics ncert textbook from the following link [http://www.ncert.nic.in/ncerts/textbook/textbook.htm?iemh1=8-15 click here]<br />
=== Additional Resources ===<br />
<br />
==== Resource Title ====<br />
[http://www.mathopenref.com/tocs/quadrilateraltoc.html Quadrilaterals]<br />
<br />
==== OER ====<br />
# List web resources with a brief description of what it contains; how it can be used and whether it can be by teacher/ student or both<br />
# Books and journals<br />
# Textbooks<br />
# Syllabus documents<br />
<br />
==== Non-OER ====<br />
# List web resources with a brief description of what it contains; how it can be used and whether it can be by teacher/ student or both<br />
#* http://www.mathopenref.com/quadrilateral.html : Simple explanation about quadrilaterals.<br />
#* http://www.slideshare.net/muzzu1999/types-of-quadrilaterals-and-its-properties-group-4 : This website has a very good activity on properties of quadrilaterals.<br />
#* http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i1/bk8_1i3.htm This is a very good website for students to understand classification of quadrilaterals as per their properties.<br />
#* http://www.shodor.org/ihnteractivate/discussions/Quadrilaterals/ click here : For effective introduction to quadrilaterals.<br />
# Books and journals<br />
#* Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer to page 89 [http://www.textbooksonline.tn.nic.in/Std9.htm click here]<br />
#* Refer 9th standard mathematics NCERT textbook from the following link [http://www.ncert.nic.in/ncerts/textbook/textbook.htm?iemh1=8-15 click here]<br />
# Textbooks : Karnataka State Text book of mathematics [http://ktbs.kar.nic.in/new/website%20textbooks/class9/9th%20standard/9th-english-maths-1.pdf Class 9-Chapter 8:Quadrilaterals]<br />
# Syllabus documents (CBSE, ICSE, IGCSE etc)<br />
<br />
= Additional Information =<br />
An Ortho-diagonal quadrilateral i.e., any quadrilateral whose diagonals are perpendicular to each other possesses certain interesting properties. This article [http://azimpremjiuniversity.edu.in/SitePages/pdf/quadrilaterals-with-perpendicular-diagonals.pdf 'Quadrilaterals with Perpendicular Diagonals'] by Shailesh Shirali (published in ''<nowiki/>'At Right Angles''' | Vol. 6, No. 2, August 2017) discusses a few of them. <br />
<br />
''<nowiki/>''<br />
<br />
=== Learning Objectives ===<br />
* Introduction to polygons <br />
* The meaning of quadrilateral<br />
* Identification of various types of quadrilaterals<br />
* Different properties of special quadrilaterals<br />
* Construction of quadrilaterals to given suitable data <br />
* Finding area of quadrilaterals<br />
* Introduction to cyclic quadrilaterals<br />
<br />
=== Teaching Outlines ===<br />
====Concept 1: Introduction to Quadrilaterals====<br />
The word quadrilateral comes from two latin words "quadri" which means a "variant of 4" and 'latera' which means 'side'. A quadrilateral is a 4 sided figure with 4 sides, 4 angles and 4 vertices.<br />
<br />
This topic has its basics in polygons. Try to elicit live examples for quadrilaterals from within classroom, starting from the shape of a textbook. Show the vertices of a rectangular page. Mark three sets of four points on the blackboard, one set being collinear and other non-collinear. Call students to join the points of each set of points. This activity will introduce them to the concept of quadrilateral. <br />
<br />
===== Activities # =====<br />
<br />
====== [[Introduction to quadrilaterals]] ======<br />
This activity explores formation of a quadrilateral and elements related with the shape.<br />
<br />
======[[Identifying quadrilaterals]]======<br />
This is an exploration into quadrilaterals. A specific type of quadrilateral can be selected with the checkboxes, and any blue dots on each quadrilateral can be dragged to change the shape.<br />
<br />
====== Concept 3: Types of quadrilaterals ======<br />
Quadrilaterals are of different types. Grouping is made based on the four angle measures and/or sides. Each type is recognized with its characteristic properties. The types include regular, non-regular; convex, concave; parallelogram (square, rectangle, rhombus,) and non-parallelograms (trapezium and kite).<br />
<br />
===== Activities # =====<br />
<br />
====== [[Quadrilaterals "I have - Who has?"|"I have - Who has ?"]]======<br />
A hands on group activity that helps in identifying and building vocabulary related to quadrilaterals.<br />
<br />
====== [[Venn diagrams of quadrilaterals]] ======<br />
Classifying quadrilaterals based on their properties and identifying related quadrilaterals with ven-diagram.<br />
<br />
==== Concept 2: Properties of quadrilaterals ====<br />
There are certain characteristic properties by which a quadrilateral is identified. A quadrilateral is a plane closed figure having 4 sides and 4 angles. The sum of all 4 interior angles of any quadrilateral always equals to 360 degrees. This is called the interior angle sum property of a quadrilateral. The sum of all 4 exterior angles of any quadrilateral equals 360 degrees. This is called the exterior angle sum property of the quadrilateral. If any 3 angles of a quadrilateral are known the fourth angle can be found using the angle sum property.<br />
<br />
===== Activities # =====<br />
<br />
====== [[Angle sum property of a quadrilateral]]======<br />
Showing the sum of angles of quadrilaterals by placing the angles of the quadrilateral adjacent to each other with a hand on activity.<br />
<br />
====== [[Sum of the interior angles of a quadrilateral]] ======<br />
The sum of the measures of the angles in any quadrilateral is 4 right angles.<br />
<br />
====== [[Sum of angles at point of intersection of diagonals in a quadrilateral]] ======<br />
A diagonal is the line segment that joins a vertex of a polygon to any of its non-adjacent vertices. These two diagonals of a quadrilateral form angle, this activity explores the property of these angles.<br />
<br />
====== [[Area of a quadrilateral]] ======<br />
A diagonal divides a quadrilateral into 2 triangles. Understanding the area of a quadrilateral in terms of triangles is done with this activity.<br />
<br />
==== [[Properties of Parallelogram]] ====<br />
<br />
==== [[Parallelogram on same base and between same parallels have equal area]] ====<br />
<br />
==== [[Mid point of sides of a Quadrilateral forms parallelogram]] ====<br />
<br />
==== Concept 3 : Properties of Rhombus ====<br />
A rhombus is a quadrilateral with all sides of equal length. The opposite angles of a rhombus are equal and its diagonals are perpendicular bisectors of one another. Since the opposite sides and opposite angles of a rhombus have the same measures, it is also a parallelogram. Hence, a rhombus has all properties of a parallelogram and also that of a kite. [[Properties of Rhombus|(click here)]]<br />
<br />
==== Concept 3: Construction of quadrilaterals ====<br />
<br />
==== Concept 4: Square ====<br />
A square is a 4-sided regular polygon with all sides equal and all internal angles 90. A square is the only regular quadrilateral. It can also be considered as a special rectangle with both adjacent sides equal. Its opposite sides are parallel. The diagonals are congruent and bisect each other at right angles. The diagonals bisect the opposite angles. Each diagonal divides the square into two congruent isosceles right angled triangles. A square can be inscribed in a circle. A circle can be inscribed in a square touching all its sides.<br />
<br />
[[Introduction to a square and its properties|Click here : Introduction to a square and its properties]]<br />
<br />
Four sides of a square are equal. Adjacent sides are at right angles with each other. The area of a square is side x side sq units. The perimeter of a square is the length of distance around its boundary which is 4 times its side.<br />
<br />
====== [[Pull me to see if I still remain a square]] ======<br />
<br />
====== [[Area of a square]] ======<br />
[[Constructing a square|'''Constructing a square''']]<br />
<br />
==== Concept 5: Cyclic Quadrilaterals ====<br />
<br />
==== [[Cyclic Quadrilaterals]] ====<br />
<br />
====== [[Theorems on cyclic quadrilaterals]] ======<br />
<br />
==== Concept : Kite ====<br />
A kite has two pairs of congruent sides. Its diagonals intersect at right angles. The sum of its four sides would be its perimeter. Its area is given by the formula <math>(1/2) (product of its diagnols)</math><br />
<br />
====== [[A Kite and its properties]] ======<br />
<br />
====== [[Construction of a kite]] ======<br />
<br />
====== [[Deriving formula for area of a kite]] ======<br />
<br />
==== Concept : Trapezium ====<br />
<br />
======[[A Trapezium and its properties]]======<br />
<br />
====== [[Deriving formula for area of a trapezium]] ======<br />
<br />
====== [[Construction of Trapezium]] ======<br />
<br />
====== [[Construct an isosceles trapezium and study its properties]] ======<br />
A trapezium in which non-parallel sides are equal is called as an Isosceles Trapezium. The diagonals of an isosceles trapezium are equal. An isosceles trapezium has one line of reflection symmetry. This line connects the midpoints of the two bases. Both pairs of base angles of an isosceles trapezium are congruent. Pairs of angles in an isosceles trapezium that do not share a base are supplementary. The area of an isosceles trapezium is given by<math>(a+b)/2 x h</math> , where a and b are the lengths of the parallel sides and h is the distance (height) between the parallel sides.<br />
<br />
===== Solved problems/ key questions (earlier was hints for problems).[edit | edit source] =====<br />
<br />
=== Projects (can include math lab/ science lab/ language lab)[edit | edit source] ===<br />
<br />
=== Assessments - question banks, formative assessment activities and summative assessment activities[edit | edit source] ===<br />
[[Category:Class 9]]<br />
[[Category:Quadrilaterals]]</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Quadrilaterals&diff=36508Quadrilaterals2022-07-05T08:40:27Z<p>Shobhit: /* Concept Map */</p>
<hr />
<div><div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/KOER/index.php/ಬಹು_ಭುಜಾಕೃತಿಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]<br />
| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]<br />
| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |<br />
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]<br />
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[http://karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]<br />
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[http://karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]<br />
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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].<br />
<br />
<br />
=== Concept Map ===<br />
<br />
==Textbook==<br />
To add textbook links, please follow these instructions to: ([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])<br />
==Additional Information==<br />
This videos is related to classification and properties of quadrilaterals.<br />
<br />
{{#widget:YouTube|id=0OW2bU0So-4}} {{#widget:YouTube|id=udS3nkj2cfg}}<br />
===Useful websites===<br />
#[http://www.shodor.org/ihnteractivate/discussions/Quadrilaterals/ click here] : For effective introduction to quadrilaterals.<br />
#[http://www.mathopenref.com/quadrilateral.html click here] : Simple explanation about quadrilaterals.<br />
#[http://www.slideshare.net/muzzu1999/types-of-quadrilaterals-and-its-properties-group-4 click here] : This website has a very good activity on properties of quadrilaterals.<br />
#[http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i1/bk8_1i3.htm click here] This is a very good website for students to understand classification of quadrilaterals as per their properties.<br />
===Reference Books===<br />
*Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer the page 89 [http://www.textbooksonline.tn.nic.in/Std9.htm click here]<br />
*Refer 9th standard mathematics ncert textbook from the following link [http://www.ncert.nic.in/ncerts/textbook/textbook.htm?iemh1=8-15 click here]<br />
=== Additional Resources ===<br />
<br />
==== Resource Title ====<br />
[http://www.mathopenref.com/tocs/quadrilateraltoc.html Quadrilaterals]<br />
<br />
==== OER ====<br />
# List web resources with a brief description of what it contains; how it can be used and whether it can be by teacher/ student or both<br />
# Books and journals<br />
# Textbooks<br />
# Syllabus documents<br />
<br />
==== Non-OER ====<br />
# List web resources with a brief description of what it contains; how it can be used and whether it can be by teacher/ student or both<br />
#* http://www.mathopenref.com/quadrilateral.html : Simple explanation about quadrilaterals.<br />
#* http://www.slideshare.net/muzzu1999/types-of-quadrilaterals-and-its-properties-group-4 : This website has a very good activity on properties of quadrilaterals.<br />
#* http://www.cimt.plymouth.ac.uk/projects/mepres/book8/bk8i1/bk8_1i3.htm This is a very good website for students to understand classification of quadrilaterals as per their properties.<br />
#* http://www.shodor.org/ihnteractivate/discussions/Quadrilaterals/ click here : For effective introduction to quadrilaterals.<br />
# Books and journals<br />
#* Please download 9th standard mathematics textbook of Tamil Nadu state syllabus from the following link and refer to page 89 [http://www.textbooksonline.tn.nic.in/Std9.htm click here]<br />
#* Refer 9th standard mathematics NCERT textbook from the following link [http://www.ncert.nic.in/ncerts/textbook/textbook.htm?iemh1=8-15 click here]<br />
# Textbooks : Karnataka State Text book of mathematics [http://ktbs.kar.nic.in/new/website%20textbooks/class9/9th%20standard/9th-english-maths-1.pdf Class 9-Chapter 8:Quadrilaterals]<br />
# Syllabus documents (CBSE, ICSE, IGCSE etc)<br />
<br />
= Additional Information =<br />
An Ortho-diagonal quadrilateral i.e., any quadrilateral whose diagonals are perpendicular to each other possesses certain interesting properties. This article [http://azimpremjiuniversity.edu.in/SitePages/pdf/quadrilaterals-with-perpendicular-diagonals.pdf 'Quadrilaterals with Perpendicular Diagonals'] by Shailesh Shirali (published in ''<nowiki/>'At Right Angles''' | Vol. 6, No. 2, August 2017) discusses a few of them. <br />
<br />
''<nowiki/>''<br />
<br />
=== Learning Objectives ===<br />
* Introduction to polygons <br />
* The meaning of quadrilateral<br />
* Identification of various types of quadrilaterals<br />
* Different properties of special quadrilaterals<br />
* Construction of quadrilaterals to given suitable data <br />
* Finding area of quadrilaterals<br />
* Introduction to cyclic quadrilaterals<br />
<br />
=== Teaching Outlines ===<br />
====Concept 1: Introduction to Quadrilaterals====<br />
The word quadrilateral comes from two latin words "quadri" which means a "variant of 4" and 'latera' which means 'side'. A quadrilateral is a 4 sided figure with 4 sides, 4 angles and 4 vertices.<br />
<br />
This topic has its basics in polygons. Try to elicit live examples for quadrilaterals from within classroom, starting from the shape of a textbook. Show the vertices of a rectangular page. Mark three sets of four points on the blackboard, one set being collinear and other non-collinear. Call students to join the points of each set of points. This activity will introduce them to the concept of quadrilateral. <br />
<br />
===== Activities # =====<br />
<br />
====== [[Introduction to quadrilaterals]] ======<br />
This activity explores formation of a quadrilateral and elements related with the shape.<br />
<br />
======[[Identifying quadrilaterals]]======<br />
This is an exploration into quadrilaterals. A specific type of quadrilateral can be selected with the checkboxes, and any blue dots on each quadrilateral can be dragged to change the shape.<br />
<br />
====== Concept 3: Types of quadrilaterals ======<br />
Quadrilaterals are of different types. Grouping is made based on the four angle measures and/or sides. Each type is recognized with its characteristic properties. The types include regular, non-regular; convex, concave; parallelogram (square, rectangle, rhombus,) and non-parallelograms (trapezium and kite).<br />
<br />
===== Activities # =====<br />
<br />
====== [[Quadrilaterals "I have - Who has?"|"I have - Who has ?"]]======<br />
A hands on group activity that helps in identifying and building vocabulary related to quadrilaterals.<br />
<br />
====== [[Venn diagrams of quadrilaterals]] ======<br />
Classifying quadrilaterals based on their properties and identifying related quadrilaterals with ven-diagram.<br />
<br />
==== Concept 2: Properties of quadrilaterals ====<br />
There are certain characteristic properties by which a quadrilateral is identified. A quadrilateral is a plane closed figure having 4 sides and 4 angles. The sum of all 4 interior angles of any quadrilateral always equals to 360 degrees. This is called the interior angle sum property of a quadrilateral. The sum of all 4 exterior angles of any quadrilateral equals 360 degrees. This is called the exterior angle sum property of the quadrilateral. If any 3 angles of a quadrilateral are known the fourth angle can be found using the angle sum property.<br />
<br />
===== Activities # =====<br />
<br />
====== [[Angle sum property of a quadrilateral]]======<br />
Showing the sum of angles of quadrilaterals by placing the angles of the quadrilateral adjacent to each other with a hand on activity.<br />
<br />
====== [[Sum of the interior angles of a quadrilateral]] ======<br />
The sum of the measures of the angles in any quadrilateral is 4 right angles.<br />
<br />
====== [[Sum of angles at point of intersection of diagonals in a quadrilateral]] ======<br />
A diagonal is the line segment that joins a vertex of a polygon to any of its non-adjacent vertices. These two diagonals of a quadrilateral form angle, this activity explores the property of these angles.<br />
<br />
====== [[Area of a quadrilateral]] ======<br />
A diagonal divides a quadrilateral into 2 triangles. Understanding the area of a quadrilateral in terms of triangles is done with this activity.<br />
<br />
==== [[Properties of Parallelogram]] ====<br />
<br />
==== [[Parallelogram on same base and between same parallels have equal area]] ====<br />
<br />
==== [[Mid point of sides of a Quadrilateral forms parallelogram]] ====<br />
<br />
==== Concept 3 : Properties of Rhombus ====<br />
A rhombus is a quadrilateral with all sides of equal length. The opposite angles of a rhombus are equal and its diagonals are perpendicular bisectors of one another. Since the opposite sides and opposite angles of a rhombus have the same measures, it is also a parallelogram. Hence, a rhombus has all properties of a parallelogram and also that of a kite. [[Properties of Rhombus|(click here)]]<br />
<br />
==== Concept 3: Construction of quadrilaterals ====<br />
<br />
==== Concept 4: Square ====<br />
A square is a 4-sided regular polygon with all sides equal and all internal angles 90. A square is the only regular quadrilateral. It can also be considered as a special rectangle with both adjacent sides equal. Its opposite sides are parallel. The diagonals are congruent and bisect each other at right angles. The diagonals bisect the opposite angles. Each diagonal divides the square into two congruent isosceles right angled triangles. A square can be inscribed in a circle. A circle can be inscribed in a square touching all its sides.<br />
<br />
[[Introduction to a square and its properties|Click here : Introduction to a square and its properties]]<br />
<br />
Four sides of a square are equal. Adjacent sides are at right angles with each other. The area of a square is side x side sq units. The perimeter of a square is the length of distance around its boundary which is 4 times its side.<br />
<br />
====== [[Pull me to see if I still remain a square]] ======<br />
<br />
====== [[Area of a square]] ======<br />
[[Constructing a square|'''Constructing a square''']]<br />
<br />
==== Concept 5: Cyclic Quadrilaterals ====<br />
<br />
==== [[Cyclic Quadrilaterals]] ====<br />
<br />
====== [[Theorems on cyclic quadrilaterals]] ======<br />
<br />
==== Concept : Kite ====<br />
A kite has two pairs of congruent sides. Its diagonals intersect at right angles. The sum of its four sides would be its perimeter. Its area is given by the formula <math>(1/2) (product of its diagnols)</math><br />
<br />
====== [[A Kite and its properties]] ======<br />
<br />
====== [[Construction of a kite]] ======<br />
<br />
====== [[Deriving formula for area of a kite]] ======<br />
<br />
==== Concept : Trapezium ====<br />
<br />
======[[A Trapezium and its properties]]======<br />
<br />
====== [[Deriving formula for area of a trapezium]] ======<br />
<br />
====== [[Construction of Trapezium]] ======<br />
<br />
====== [[Construct an isosceles trapezium and study its properties]] ======<br />
A trapezium in which non-parallel sides are equal is called as an Isosceles Trapezium. The diagonals of an isosceles trapezium are equal. An isosceles trapezium has one line of reflection symmetry. This line connects the midpoints of the two bases. Both pairs of base angles of an isosceles trapezium are congruent. Pairs of angles in an isosceles trapezium that do not share a base are supplementary. The area of an isosceles trapezium is given by<math>(a+b)/2 x h</math> , where a and b are the lengths of the parallel sides and h is the distance (height) between the parallel sides.<br />
<br />
===== Solved problems/ key questions (earlier was hints for problems).[edit | edit source] =====<br />
<br />
=== Projects (can include math lab/ science lab/ language lab)[edit | edit source] ===<br />
<br />
=== Assessments - question banks, formative assessment activities and summative assessment activities[edit | edit source] ===<br />
[[Category:Class 9]]<br />
[[Category:Quadrilaterals]]</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Polygons&diff=36507Polygons2022-07-05T07:31:50Z<p>Shobhit: /* Angle sum property */</p>
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==Concept map==<br />
<br />
{{#drawio:mmPolygons|interactive}}<br />
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== Textbook ==<br />
To add textbook links, please follow these instructions to: <br />
([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])<br />
<br />
==Additional Information==<br />
=== Resources ===<br />
<br />
==== Resource Title ====<br />
[http://www.mathopenref.com/tocs/polygontoc.html Polygons]<br />
<br />
===Useful websites===<br />
1. http://www.wyzant.com/resources/lessons/math/geometry/quadrilaterals/polygons . This website is good for referring to the theory regarding polygons.<br />
===Reference Books===<br />
<br />
== Teaching Outlines ==<br />
<br />
# Introduction to polygon<br />
# Naming the polygons<br />
# Characteristics of polygons.<br />
# Types of polygons.<br />
<br />
==Building prior competencies==<br />
Many student are entering Class 9 without adequate understanding of prior concepts like angles, line, etc.<br />
Therefore, the following sequence of lessons has been suggested with a combination of hands-on activities, Geogebra work to build those concepts in students.<br />
[[File:Polygon_prior_competencies_upload.mm|flash]]<br />
<br />
The following Geogebra files are used with associated lessons:<br />
#[[:File:0. Angles introduction.ggb|Angles introduction]]<br />
#[[:File:1. Complementary angles demonstration.ggb|Complementary angles]]<br />
#[[:File:2. Supplementary angles demonstration.ggb|Supplementary angles]]<br />
#[[:File:3. parallellines-2.ggb|Activity with parallel line]]<br />
#[[:File:4. Introduction to a triangle.ggb|Demonstration of triangle]]<br />
#[[:File:5. Introduction to a polygon.ggb|Polygon]]<br />
<br />
==Concept #1. Introduction to polygons and nomenclature.==<br />
===Learning objectives===<br />
# Lines intersect to form figures.<br />
# Two dimensional closed figures can be of varied shapes.<br />
# Plane closed figures with ≥ 3 sides are known as polygons.<br />
# They can be defined as two-dimensional, closed, plane shapes composed of a finite number of straight sides that meet at points called vertices.<br />
# There are a countless number of polygons. <br />
# Because they all differ in the number of sides that they have, this results in different angle measures at their vertices. <br />
# With the exception of the triangle and quadrilateral, all polygon names end with "gon."<br />
# Generally polygons are named with their number of sides as prefixes. The prefix for the word "hexagon" is "hexa," which essentially means "six."<br />
<br />
==Notes for teachers==<br />
Source: This information has been taken from the website :http://www.wyzant.com/resources/lessons/math/geometry/quadrilaterals/polygons<br><br />
Summary: There are a countless number of polygons. Because they all differ in the number of sides that they have, this results in different angle measures at their vertices. Listed below are the names and number of sides of some polygons. The "Interior Angle Measure" column of the table only applies to regular polygons, in which all the interior angles are equal.<br><br />
With the exception of the triangle and quadrilateral, notice that all polygon names end with "gon." What sets regular polygon names apart from each other are their prefixes, which speak to the number of sides that they have. For instance, the prefix for the word "hexagon" is "hexa," which essentially means "six." However, as we move down our list and the names for polygons becomes quite confusing, we need a more efficient way of naming polygons. One way is by not calling a polygon by its real name, but rather by just saying the number of sides it has, and attaching "-gon" at the end. For instance, rather than calling an 18-sided polygon an "octdecagon," we can just call it an 18-gon. Thus, a polygon with n sides is simply called an n-gon.<br />
<br />
[[File:naming polygons.jpeg|400px]]<br />
<br />
<br />
<br />
===Activity No # 1. Which polygon am I ? ===<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div><br />
|}<br />
*Estimated Time: 30 minutes.<br />
*Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.<br />
*Prerequisites/Instructions, if any:<br />
# Lines intersect to form figures.<br />
# Plane closed figures have atleast 3 sides. <br />
# The intersecting points of two lines is known as a vertex and the lines are the edges/sides.<br />
# Meaning of greek numerals uni, bi, tri ....etc.<br />
*Multimedia resources: Laptop<br />
*Website interactives/ links/ / Geogebra Applets: This geogebra file has been created by '''Smt Sarah Zakiya Madam, GUHS, Yellagondapalya.'''<br />
<span> </span><br />
<br />
<span></span><div id="ggbContainerfbad5ae84c119793e6125f6c6fe3c642"></div><span></span><br />
*Process: <br />
# The teacher can tell the students that they are surrounded by many different kinds of shapes every day. <br />
# Many of these shapes are two-dimensional plane figures. <br />
# Plane figures are flat. They can be closed or not closed. <br />
# Plane figures made up of three or more closed line segments are polygons. <br />
# Each line segment of a polygon is a side. Polygons are classified and named based on the number of sides. <br />
*Developmental Questions:<br />
# How many vertices, sides and angles does this figure have ? Name the figure.<br />
# What is the point of intersection of two lines called ?<br />
# What parameters do you identify in each figure ? (side, vertex, angle, plane surface and area )<br />
# What can you say about the number of vertices and the number of sides in each figure ?<br />
# Which figure would you think will be formed if the number of sides is increased indefinately.<br />
*Evaluation:<br />
# What determines the side or edge of the figure ?<br />
# Are the students able to corelate the names with the number of sides ?<br />
# Are the students able to appreciate the nature of shapes formed with each increasing side?<br />
# Students can discuss angle sum property in each case by dividing the figure into triangles or quadrilaterals.<br />
*Question Corner:<br />
# A hexagon is a polygon with _________ angles.<br />
# Is circle a polygon ?<br />
# What is a polygon with 12 sides called ?<br />
# You have a collection of sides from triangles and decagons. The total number of sides is 100 and you have 4 decagons. How many triangles do you have ?<br />
<br />
===Activity No # ===<br />
{| style="height:10px; float:right; align:center;"<br />
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''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div><br />
|}<br />
*Estimated Time<br />
*Materials/ Resources needed<br />
*Prerequisites/Instructions, if any<br />
*Multimedia resources<br />
*Website interactives/ links/ / Geogebra Applets<br />
*Process/ Developmental Questions<br />
*Evaluation<br />
*Question Corner<br />
<br />
==Concept #2. Properties and measurements of polygons==<br />
===Learning objectives===<br />
# The sum of the interior angle measures of an n-sided, convex polygon is <math>(n-2).180</math><br />
# A regular polygon has all sides and angles equal.<br />
# All exterior angles of a polygon add upto 360 degrees.<br />
# Each exterior angle must be <math>360/n</math><br />
# Each of the exterior angle and interior angles are measured from the same line. hence they add upto 180 degrees.<br />
# Area of Polygon = perimeter × apothem / 2 [[File:Apothem.jpeg|150px]]<br />
<br />
<br />
(This image has been taken from:http://www.mathsisfun.com/geometry/regular-polygons.html)<br />
<br />
===Notes for teachers===<br />
===Activity No # 1. Polygon's table of values.===<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]</div><br />
|}<br />
*Estimated Time: 90 minutes.<br />
*Materials/ Resources needed:<br />
# Sheets of paper, scale, compass, protractor, pencil.<br />
*Prerequisites/Instructions, if any:<br />
# Knowledge of different polygons and their names.<br />
# Requisite formulae needed to do the calculations.<br />
# Skills to perform and tabulate calculations accurately. <br />
*Multimedia resources:<br />
*Website interactives/ links/ / Geogebra Applets:<br />
Please refer to this website for more clarity on this activity : http://www.mathsisfun.com/geometry/regular-polygons.html<br />
*Process:<br />
# Use the formulas listed in learning objectives above to make a table of Side, Apothem and Area, compared to a Radius of "1":<br />
# Let the table have the following columns.<br />
<br />
[[File:Table.jpeg|800px]]<br />
<br />
*Developmental Questions:<br />
# Name the types of polygons based on their sides.<br />
# What is a regular polygon ?<br />
# How many sides does a ______________ have ?<br />
# What is an interior angle ?<br />
# Is there any relationship between the number of sides and number of angles ?<br />
# What radius has been mentioned here as common for all ?<br />
# What is an apothem ?<br />
# How do you get the central point of a polygon ?<br />
# What is the formula to find the area of a polygon ?<br />
*Evaluation:<br />
# Which measuring parameter do you think is the deciding factor for the area of a polygon ?<br />
*Question Corner<br />
# Can you find the listed measures like interior angle, area without using the formula ? How ? Discuss.<br />
<br />
===Activity No # ===<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div><br />
|}<br />
*Estimated Time<br />
*Materials/ Resources needed<br />
*Prerequisites/Instructions, if any<br />
*Multimedia resources<br />
*Website interactives/ links/ / Geogebra Applets<br />
*Process/ Developmental Questions<br />
*Evaluation<br />
*Question Corner<br />
<br />
==Concept #3. Types of polygons==<br />
===Learning objectives===<br />
# There are several polygons. <br />
# Polygons are classified by considering their angle measures and side length measures. <br />
# If a polygon's angles and sides are equal, then the polygon is called a regular polygon. <br />
# If the measures of a polygon's angles or side lengths differ, then the polygon is called an irregular polygon.<br />
# Primary shapes can be combined to form composite polygons. (This knowledge will help while deducing area formulae for complex figures which would be derived by splitting them into primary figures.)<br />
===Notes for teachers===<br />
===Activity No # Tangram - Building polygons===<br />
This activity has been taken from the website :http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bs7act1.pdf<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div><br />
|}<br />
[[File:Tangram.jpg|300px]]<br />
<br />
*Estimated Time : 40 minutes.<br />
*Materials/ Resources needed: Chart papers, scissors, pencil, scale.<br />
*Prerequisites/Instructions, if any<br />
# An understanding of basic shapes like square, rectangle, parallelogram, triangle and trapezium.<br />
# Ability to draw mentioned shapes accurately and cut exactly on boundaries.<br />
*Multimedia resources<br />
*Website interactives/ links/ / Geogebra Applets<br />
*Process:<br />
# This is a very old Chinese puzzle known as a tangram.<br />
# Cut out the square below into 7 shapes.<br />
# Cut out the 7 shapes and rearrange them to form:<br><br />
(a) a square from two triangles, and then change it to a parallelogram;<br><br />
(b) a rectangle using three pieces, and then change it into a parallelogram;<br><br />
(c) a trapezium with three pieces;<br><br />
(d) a parallelogram with four pieces;<br><br />
(e) a trapezium from the square, parallelogram and the two small triangles;<br><br />
(f) a triangle with three pieces;<br><br />
(g) a rectangle with all seven pieces.<br><br />
(h) a kite with two traingles.<br><br />
4. Finally, put the pieces back together to form the original square.<br><br />
*Developmental Questions:<br />
# Were you all able to read and follow the instructions.<br />
# Name and point the different shapes in the figure.<br />
# Name the dimensions of each shape. <br />
*Evaluation:<br />
# Were the students able to identify the types of polygons based on the number of sides.<br />
# What type of two triangles would you need to form a square ?<br />
*Question Corner:<br />
# What are the characteristic properties of each shape: square, rectangle, triangle, parallelogram and trapezium ?<br />
# What did you learn from this activity ?<br />
<br />
===Activity No #===<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div><br />
|}<br />
*Estimated Time:<br />
*Materials/ Resources needed:<br />
*Prerequisites/Instructions, if any:<br />
*Multimedia resources:<br />
*Website interactives/ links/ / Geogebra Applets:<br />
*Process/ Developmental Questions:<br />
*Evaluation:<br />
*Question Corner:<br />
<br />
===Activity No # ===<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div><br />
|}<br />
*Estimated Time<br />
*Materials/ Resources needed<br />
*Prerequisites/Instructions, if any<br />
*Multimedia resources<br />
*Website interactives/ links/ / Geogebra Applets<br />
*Process/ Developmental Questions<br />
*Evaluation<br />
*Question Corner<br />
<br />
= Hints for difficult problems =<br />
[[:File:polygon problem.odt]]<br />
==Angle sum property==<br />
CLASS IX TOPIC POLYGONS<br />
ADDITIONAL PROBLEMS (problem no 3 )<br />
A polygon has 'n' sides .Two of it's angles are right angles and each of remaining angle isFind the value of 'n'.<br />
Step 1;(Students must understand the problem)<br />
In a polygon of side 'n' two angles are and other angles are each. We must find out value of 'n'.<br />
Step 2(Students know the formula for sum of angles of polygon of side 'n')<br />
(2n-4)right angles.<br />
Step 3(Sum of the angles is equal to what?)<br />
There are 'n' angles in a polygon of side 'n'.Out of 'n' angles 2 angles are right anles and other (n-2) angles are each.<br />
<br />
(2n-4) <math>90^0</math> = (n-2)<nowiki><math>\144^0+(2)(90^0)how to open the bracket and substitute the values)</nowiki><br />
<br />
2n x - 4 x = <br />
<br />
= (Brings similar terms at one side of the equation)<br />
<br />
= (Add and substract and simplify) <br />
<br />
= <br />
<br />
n = (Devide and simplify)<br />
<br />
n = 7<br />
<br />
= Project Ideas =<br />
<br />
= Math Fun =<br />
<br />
'''Usage''' <br />
<br />
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template<br />
<br />
[[Category:Polygons]]</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmQuadrilaterals.drawio.svg&diff=36506File:MmQuadrilaterals.drawio.svg2022-07-05T06:31:11Z<p>Shobhit: Shobhit uploaded a new version of File:MmQuadrilaterals.drawio.svg</p>
<hr />
<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmQuadrilaterals.drawio.svg&diff=36505File:MmQuadrilaterals.drawio.svg2022-07-05T06:31:09Z<p>Shobhit: Shobhit uploaded a new version of File:MmQuadrilaterals.drawio.svg</p>
<hr />
<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmQuadrilaterals.drawio.svg&diff=36504File:MmQuadrilaterals.drawio.svg2022-07-05T06:30:32Z<p>Shobhit: Shobhit uploaded a new version of File:MmQuadrilaterals.drawio.svg</p>
<hr />
<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmQuadrilaterals.drawio.svg&diff=36503File:MmQuadrilaterals.drawio.svg2022-07-05T06:29:27Z<p>Shobhit: Shobhit uploaded a new version of File:MmQuadrilaterals.drawio.svg</p>
<hr />
<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:MmPolygons.drawio.svg&diff=36502File:MmPolygons.drawio.svg2022-07-04T11:26:19Z<p>Shobhit: </p>
<hr />
<div></div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Polygons&diff=36501Polygons2022-07-04T11:25:33Z<p>Shobhit: /* concept map */</p>
<hr />
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While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].<br />
<br />
==Concept map==<br />
<br />
{{#drawio:mmPolygons|interactive}}<br />
<br />
== Textbook ==<br />
To add textbook links, please follow these instructions to: <br />
([{{fullurl:{{FULLPAGENAME}}/textbook|action=edit}} Click to create the subpage])<br />
<br />
==Additional Information==<br />
=== Resources ===<br />
<br />
==== Resource Title ====<br />
[http://www.mathopenref.com/tocs/polygontoc.html Polygons]<br />
<br />
===Useful websites===<br />
1. http://www.wyzant.com/resources/lessons/math/geometry/quadrilaterals/polygons . This website is good for referring to the theory regarding polygons.<br />
===Reference Books===<br />
<br />
== Teaching Outlines ==<br />
<br />
# Introduction to polygon<br />
# Naming the polygons<br />
# Characteristics of polygons.<br />
# Types of polygons.<br />
<br />
==Building prior competencies==<br />
Many student are entering Class 9 without adequate understanding of prior concepts like angles, line, etc.<br />
Therefore, the following sequence of lessons has been suggested with a combination of hands-on activities, Geogebra work to build those concepts in students.<br />
[[File:Polygon_prior_competencies_upload.mm|flash]]<br />
<br />
The following Geogebra files are used with associated lessons:<br />
#[[:File:0. Angles introduction.ggb|Angles introduction]]<br />
#[[:File:1. Complementary angles demonstration.ggb|Complementary angles]]<br />
#[[:File:2. Supplementary angles demonstration.ggb|Supplementary angles]]<br />
#[[:File:3. parallellines-2.ggb|Activity with parallel line]]<br />
#[[:File:4. Introduction to a triangle.ggb|Demonstration of triangle]]<br />
#[[:File:5. Introduction to a polygon.ggb|Polygon]]<br />
<br />
==Concept #1. Introduction to polygons and nomenclature.==<br />
===Learning objectives===<br />
# Lines intersect to form figures.<br />
# Two dimensional closed figures can be of varied shapes.<br />
# Plane closed figures with ≥ 3 sides are known as polygons.<br />
# They can be defined as two-dimensional, closed, plane shapes composed of a finite number of straight sides that meet at points called vertices.<br />
# There are a countless number of polygons. <br />
# Because they all differ in the number of sides that they have, this results in different angle measures at their vertices. <br />
# With the exception of the triangle and quadrilateral, all polygon names end with "gon."<br />
# Generally polygons are named with their number of sides as prefixes. The prefix for the word "hexagon" is "hexa," which essentially means "six."<br />
<br />
==Notes for teachers==<br />
Source: This information has been taken from the website :http://www.wyzant.com/resources/lessons/math/geometry/quadrilaterals/polygons<br><br />
Summary: There are a countless number of polygons. Because they all differ in the number of sides that they have, this results in different angle measures at their vertices. Listed below are the names and number of sides of some polygons. The "Interior Angle Measure" column of the table only applies to regular polygons, in which all the interior angles are equal.<br><br />
With the exception of the triangle and quadrilateral, notice that all polygon names end with "gon." What sets regular polygon names apart from each other are their prefixes, which speak to the number of sides that they have. For instance, the prefix for the word "hexagon" is "hexa," which essentially means "six." However, as we move down our list and the names for polygons becomes quite confusing, we need a more efficient way of naming polygons. One way is by not calling a polygon by its real name, but rather by just saying the number of sides it has, and attaching "-gon" at the end. For instance, rather than calling an 18-sided polygon an "octdecagon," we can just call it an 18-gon. Thus, a polygon with n sides is simply called an n-gon.<br />
<br />
[[File:naming polygons.jpeg|400px]]<br />
<br />
<br />
<br />
===Activity No # 1. Which polygon am I ? ===<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div><br />
|}<br />
*Estimated Time: 30 minutes.<br />
*Materials/ Resources needed: Laptop, geogebra file, projector and a pointer.<br />
*Prerequisites/Instructions, if any:<br />
# Lines intersect to form figures.<br />
# Plane closed figures have atleast 3 sides. <br />
# The intersecting points of two lines is known as a vertex and the lines are the edges/sides.<br />
# Meaning of greek numerals uni, bi, tri ....etc.<br />
*Multimedia resources: Laptop<br />
*Website interactives/ links/ / Geogebra Applets: This geogebra file has been created by '''Smt Sarah Zakiya Madam, GUHS, Yellagondapalya.'''<br />
<span> </span><br />
<br />
<span></span><div id="ggbContainerfbad5ae84c119793e6125f6c6fe3c642"></div><span></span><br />
*Process: <br />
# The teacher can tell the students that they are surrounded by many different kinds of shapes every day. <br />
# Many of these shapes are two-dimensional plane figures. <br />
# Plane figures are flat. They can be closed or not closed. <br />
# Plane figures made up of three or more closed line segments are polygons. <br />
# Each line segment of a polygon is a side. Polygons are classified and named based on the number of sides. <br />
*Developmental Questions:<br />
# How many vertices, sides and angles does this figure have ? Name the figure.<br />
# What is the point of intersection of two lines called ?<br />
# What parameters do you identify in each figure ? (side, vertex, angle, plane surface and area )<br />
# What can you say about the number of vertices and the number of sides in each figure ?<br />
# Which figure would you think will be formed if the number of sides is increased indefinately.<br />
*Evaluation:<br />
# What determines the side or edge of the figure ?<br />
# Are the students able to corelate the names with the number of sides ?<br />
# Are the students able to appreciate the nature of shapes formed with each increasing side?<br />
# Students can discuss angle sum property in each case by dividing the figure into triangles or quadrilaterals.<br />
*Question Corner:<br />
# A hexagon is a polygon with _________ angles.<br />
# Is circle a polygon ?<br />
# What is a polygon with 12 sides called ?<br />
# You have a collection of sides from triangles and decagons. The total number of sides is 100 and you have 4 decagons. How many triangles do you have ?<br />
<br />
===Activity No # ===<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div><br />
|}<br />
*Estimated Time<br />
*Materials/ Resources needed<br />
*Prerequisites/Instructions, if any<br />
*Multimedia resources<br />
*Website interactives/ links/ / Geogebra Applets<br />
*Process/ Developmental Questions<br />
*Evaluation<br />
*Question Corner<br />
<br />
==Concept #2. Properties and measurements of polygons==<br />
===Learning objectives===<br />
# The sum of the interior angle measures of an n-sided, convex polygon is <math>(n-2).180</math><br />
# A regular polygon has all sides and angles equal.<br />
# All exterior angles of a polygon add upto 360 degrees.<br />
# Each exterior angle must be <math>360/n</math><br />
# Each of the exterior angle and interior angles are measured from the same line. hence they add upto 180 degrees.<br />
# Area of Polygon = perimeter × apothem / 2 [[File:Apothem.jpeg|150px]]<br />
<br />
<br />
(This image has been taken from:http://www.mathsisfun.com/geometry/regular-polygons.html)<br />
<br />
===Notes for teachers===<br />
===Activity No # 1. Polygon's table of values.===<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]</div><br />
|}<br />
*Estimated Time: 90 minutes.<br />
*Materials/ Resources needed:<br />
# Sheets of paper, scale, compass, protractor, pencil.<br />
*Prerequisites/Instructions, if any:<br />
# Knowledge of different polygons and their names.<br />
# Requisite formulae needed to do the calculations.<br />
# Skills to perform and tabulate calculations accurately. <br />
*Multimedia resources:<br />
*Website interactives/ links/ / Geogebra Applets:<br />
Please refer to this website for more clarity on this activity : http://www.mathsisfun.com/geometry/regular-polygons.html<br />
*Process:<br />
# Use the formulas listed in learning objectives above to make a table of Side, Apothem and Area, compared to a Radius of "1":<br />
# Let the table have the following columns.<br />
<br />
[[File:Table.jpeg|800px]]<br />
<br />
*Developmental Questions:<br />
# Name the types of polygons based on their sides.<br />
# What is a regular polygon ?<br />
# How many sides does a ______________ have ?<br />
# What is an interior angle ?<br />
# Is there any relationship between the number of sides and number of angles ?<br />
# What radius has been mentioned here as common for all ?<br />
# What is an apothem ?<br />
# How do you get the central point of a polygon ?<br />
# What is the formula to find the area of a polygon ?<br />
*Evaluation:<br />
# Which measuring parameter do you think is the deciding factor for the area of a polygon ?<br />
*Question Corner<br />
# Can you find the listed measures like interior angle, area without using the formula ? How ? Discuss.<br />
<br />
===Activity No # ===<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div><br />
|}<br />
*Estimated Time<br />
*Materials/ Resources needed<br />
*Prerequisites/Instructions, if any<br />
*Multimedia resources<br />
*Website interactives/ links/ / Geogebra Applets<br />
*Process/ Developmental Questions<br />
*Evaluation<br />
*Question Corner<br />
<br />
==Concept #3. Types of polygons==<br />
===Learning objectives===<br />
# There are several polygons. <br />
# Polygons are classified by considering their angle measures and side length measures. <br />
# If a polygon's angles and sides are equal, then the polygon is called a regular polygon. <br />
# If the measures of a polygon's angles or side lengths differ, then the polygon is called an irregular polygon.<br />
# Primary shapes can be combined to form composite polygons. (This knowledge will help while deducing area formulae for complex figures which would be derived by splitting them into primary figures.)<br />
===Notes for teachers===<br />
===Activity No # Tangram - Building polygons===<br />
This activity has been taken from the website :http://www.cimt.plymouth.ac.uk/projects/mepres/allgcse/bs7act1.pdf<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div><br />
|}<br />
[[File:Tangram.jpg|300px]]<br />
<br />
*Estimated Time : 40 minutes.<br />
*Materials/ Resources needed: Chart papers, scissors, pencil, scale.<br />
*Prerequisites/Instructions, if any<br />
# An understanding of basic shapes like square, rectangle, parallelogram, triangle and trapezium.<br />
# Ability to draw mentioned shapes accurately and cut exactly on boundaries.<br />
*Multimedia resources<br />
*Website interactives/ links/ / Geogebra Applets<br />
*Process:<br />
# This is a very old Chinese puzzle known as a tangram.<br />
# Cut out the square below into 7 shapes.<br />
# Cut out the 7 shapes and rearrange them to form:<br><br />
(a) a square from two triangles, and then change it to a parallelogram;<br><br />
(b) a rectangle using three pieces, and then change it into a parallelogram;<br><br />
(c) a trapezium with three pieces;<br><br />
(d) a parallelogram with four pieces;<br><br />
(e) a trapezium from the square, parallelogram and the two small triangles;<br><br />
(f) a triangle with three pieces;<br><br />
(g) a rectangle with all seven pieces.<br><br />
(h) a kite with two traingles.<br><br />
4. Finally, put the pieces back together to form the original square.<br><br />
*Developmental Questions:<br />
# Were you all able to read and follow the instructions.<br />
# Name and point the different shapes in the figure.<br />
# Name the dimensions of each shape. <br />
*Evaluation:<br />
# Were the students able to identify the types of polygons based on the number of sides.<br />
# What type of two triangles would you need to form a square ?<br />
*Question Corner:<br />
# What are the characteristic properties of each shape: square, rectangle, triangle, parallelogram and trapezium ?<br />
# What did you learn from this activity ?<br />
<br />
===Activity No #===<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div><br />
|}<br />
*Estimated Time:<br />
*Materials/ Resources needed:<br />
*Prerequisites/Instructions, if any:<br />
*Multimedia resources:<br />
*Website interactives/ links/ / Geogebra Applets:<br />
*Process/ Developmental Questions:<br />
*Evaluation:<br />
*Question Corner:<br />
<br />
===Activity No # ===<br />
{| style="height:10px; float:right; align:center;"<br />
|<div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#f5f5f5; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/?q=node/305 Click to Comment]''</div><br />
|}<br />
*Estimated Time<br />
*Materials/ Resources needed<br />
*Prerequisites/Instructions, if any<br />
*Multimedia resources<br />
*Website interactives/ links/ / Geogebra Applets<br />
*Process/ Developmental Questions<br />
*Evaluation<br />
*Question Corner<br />
<br />
= Hints for difficult problems =<br />
[[:File:polygon problem.odt]]<br />
==Angle sum property==<br />
CLASS IX TOPIC POLYGONS<br />
ADDITIONAL PROBLEMS (problem no 3 )<br />
A polygon has 'n' sides .Two of it's angles are right angles and each of remaining angle isFind the value of 'n'.<br />
Step 1;(Students must understand the problem)<br />
In a polygon of side 'n' two angles are and other angles are each.We must find out value of 'n'.<br />
Step 2(Students know the formula for sum of angles of polygon of side 'n')<br />
(2n-4)right angles.<br />
Step 3(Sum of the angles is equal to what?)<br />
There are 'n' angles in a polygon of side 'n'.Out of 'n' angles 2 angles are right anles and other (n-2) angles are each.<br />
<br />
(2n-4) <math>90^0</math> = (n-2)<nowiki><math>\144^0+(2)(90^0)how to open the bracket and substitute the values)</nowiki><br />
<br />
2n x - 4 x = <br />
<br />
= (Brings similar terms at one side of the equation)<br />
<br />
= (Add and substract and simplify) <br />
<br />
= <br />
<br />
n = (Devide and simplify)<br />
<br />
n = 7<br />
<br />
= Project Ideas =<br />
<br />
= Math Fun =<br />
<br />
'''Usage''' <br />
<br />
Create a new page and type <nowiki>{{subst:Math-Content}}</nowiki> to use this template<br />
<br />
[[Category:Polygons]]</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Need_for_limits&diff=36349Need for limits2022-06-17T12:10:18Z<p>Shobhit: </p>
<hr />
<div>Limits help us understand the behavior of a function at points even when its not explicitly defined. \<br />
<br />
=== Activity ===<br />
'''Consider the function <math>f(x)=e^{\frac{-1}{x^2}}</math>'''<br />
<br />
We want to know about the behavior of function at <math>x=0</math>however <math>f(0)</math>is not defined since <math>\frac{1}{0}</math>can't be operated upon. To solve this dilemma we will look at the behavior of <math>f(x)</math>when x is near to 0. <br />
<br />
'''In a spreadsheet, plot the values of f(x) as x is the 'neighborhood' of 0. Then plot the function and mark your observations.''' <br />
<br />
=== Solution ===<br />
{{Geogebra|frydyff2}}<br />
We can see that as the values approach 0, <math>f(x)</math>get really really small and really close to 0 however at no point, does it touch 0. And as the values go away from 0 <math>f(x)</math>starts getting bigger. <br />
{{Geogebra|bqh7e9dj}}<br />
The same can be observed from the plot.</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Need_for_limits&diff=36348Need for limits2022-06-17T12:06:04Z<p>Shobhit: Created page with "Limits help us understand the behavior of a function at points even when its not explicitly defined. \ === Activity === '''Consider the function <math>f(x)=e^{\frac{-1}{x^2}..."</p>
<hr />
<div>Limits help us understand the behavior of a function at points even when its not explicitly defined. \<br />
<br />
=== Activity ===<br />
'''Consider the function <math>f(x)=e^{\frac{-1}{x^2}}</math>'''<br />
<br />
We want to know about the behavior of function at <math>x=0</math>however <math>f(0)</math>is not defined since <math>\frac{1}{0}</math>can't be operated upon. To solve this dilemma we will look at the behavior of <math>f(x)</math>when x is near to 0. <br />
<br />
'''In a spreadsheet, plot the values of f(x) as x is the 'neighborhood' of 0. Then plot the function and mark your observations.'''</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Limits&diff=36342Limits2022-06-17T10:55:40Z<p>Shobhit: /* Activity */</p>
<hr />
<div>== Learning Objectives ==<br />
* Having an intuitionistic understanding of Limits of a function. <br />
* Understanding algebra of limits.<br />
* Working out limits of various types of functions. <br />
* Identifying various indeterminate forms. <br />
<br />
== Concept 1: Understanding Limits of a function ==<br />
<br />
=== Activity ===<br />
<br />
===== [https://karnatakaeducation.org.in/KOER/en/index.php/Need_for_limits Understanding the need for limits.] =====<br />
<br />
=== Theory ===<br />
'''Limits''' : Its surprisingly hard to rigorously define limits but we can deduce an intuitive explanation from various examples. We say that the limit of function <math>f(x)</math> as <math>x</math> tends to ''a'' is ''L'' , if <math>f(x)</math> approaches (gets closer to) ''L'' , as <math>x</math> gets closer to ''a''. If such a number does not exist, we say that the limit does not exist. <br />
<br />
This is expressed mathematically as <math>\lim_{x \to a} f(x) = L </math><br />
<br />
=== Activity ===<br />
<br />
==== [https://karnatakaeducation.org.in/KOER/en/index.php/definition_of_limits Understanding the definition of limits.] ====<br />
<br />
=== Important Point ===<br />
What is <math>\lim_{x \to 2} f(x) </math>where <math>f(x) = \left\{<br />
\begin{array}{ll}<br />
x & \quad x \in \R - [2] \\<br />
6 & \quad x = 2<br />
\end{array}<br />
\right.</math>?<br />
<br />
Since as <math>x</math> approaches 2, <math>f(x)</math>approaches 2 , <math>\lim_{x \to 2} f(x) </math>= 2. <br />
<br />
This shows that <math>\lim_{x \to a} f(x) </math>need not be equal to <math>f(a)</math>even when <math>f(a)</math> is explicitly defined. <br />
<br />
== Concept 2 : Limit laws ==<br />
In this section we will learn the algebra of limit of functions. <br />
<br />
=== Theory ===<br />
Before delving into more complex theorems, let us establish the basic ones. <br />
<br />
Limit of a constant function is same at each point. <br />
<br />
i.e. <math> \lim _{x \rightarrow a} c=c <br />
</math><br />
<br />
Also limit of <math> f(x) = x <br />
</math>at <math> a <br />
</math>is <math> a <br />
</math>.<br />
<br />
i.e. <math> \lim _{x \rightarrow a} x=a <br />
</math>. This makes sense since the function is defined at all points and is continuous.<br />
<br />
Now we are prepared to move forward with the algebra of limits. <br />
<br />
<math>\begin{aligned}<br />
&\lim _{x \rightarrow p}(f(x)+g(x))=\lim _{x \rightarrow p} f(x)+\lim _{x \rightarrow p} g(x) \\<br />
&\lim _{x \rightarrow p}(f(x)-g(x))=\lim _{x \rightarrow p} f(x)-\lim _{x \rightarrow p} g(x) \\<br />
&\lim _{x \rightarrow p}(f(x) \cdot g(x))=\lim _{x \rightarrow p} f(x) \cdot \lim _{x \rightarrow p} g(x) \\<br />
&\lim _{x \rightarrow p}(f(x) / g(x))=\lim _{x \rightarrow p} f(x) / \lim _{x \rightarrow p} g(x) \\<br />
&\lim _{x \rightarrow p} \quad f(x)^{g(x)}=\lim _{x \rightarrow p} f(x)^{\lim _{x \rightarrow p} g(x)}<br />
\end{aligned}</math><br />
<br />
=== Activity ===<br />
[https://karnatakaeducation.org.in/KOER/en/index.php/Understanding_limit_laws '''Intuitively understanding limit laws.'''] <br />
<br />
== Concept 3 : Working out limits of functions algebraically ==<br />
Using the limit laws we studied in the last section, we can manipulate functions and try to solve them algebraically instead of using graphs or tables like we did before.</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Linear_programming&diff=36341Linear programming2022-06-17T10:52:07Z<p>Shobhit: </p>
<hr />
<div>== Concept 1 : Mathematical modelling ==<br />
One of the most important applications of mathematics in life is to find a optimal solution for problems. For example, what goods should a shopkeeper buy to get the most amount of profit or what is the optimal combination of food you should eat to get maximum amount of nutrients? <br />
<br />
To solve these questions, we need to mathematize them i.e. make equations out of those which can be solved. For example we need to write down how much profit does the shopkeeper get on each good, how much budget does he have, which goods sell more, which goods might go bad etc and then using this data, devise equations which will help us in finding the optimal combination of goods the shopkeeper should buy. <br />
<br />
This process of converting a real life problem in a mathematical fashion is called '''mathematical modelling.''' <br />
<br />
== Concept 2 : Linear Programming ==<br />
As the name suggests, '''Linear Programming''' is a method of optimizing a mathematical model which is represent by linear constraints only i.e. it does not contain any second order terms. Only equations of form <math>a_1 x_1+a_2x_2+a_3 x_3......=a_0</math>are allowed where <math>a_n</math>are constants and <math>x_n</math>are variables. <br />
<br />
== Concept 2 : Finding optimal solutions ==<br />
Now we will solve a real life optimization problem using linear programming. <br />
<br />
=== '''Question''' ===<br />
One kind of cake (Cake A) requires 200g of flour and 25g of fat, and another kind of cake (Cake B) requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes. (From NCERT) <br />
<br />
Let <math>x </math>be the number of cake A and <math>y</math>be the number of cake B. <br />
<br />
According to the question we have to maximize <math>x+y</math>in limited number of ingredients (5 kg flour and 1 kg fat) <br />
<br />
Before moving ahead we should set a baseline. We know that <math>x<br />
</math>and <math>y</math>cant be less than 0. <br />
<br />
Hence <math>x , y \geq 0 </math><br />
<br />
For flour : <br />
<br />
<math>200 x + 100 y \leq 5000</math> <br />
<br />
What this basically means is that if we make <math>x</math>cake A , we will use <math>200x<br />
</math>grams of flour. Similarly for <math>y<br />
</math> cake B, we will use <math>100y<br />
</math> grams of flour. The total flour used in all the cakes should be less than 5000g. <br />
<br />
Similarly for fat : <br />
<br />
<math>25x + 50y \leq 1000</math><br />
<br />
Now we have four linear inequalities. There are multiple ways to solve these inequalities. The method we will look here is the graphical method which is easier to visualize and understand. <br />
<br />
==== Activity ====<br />
Plot the following inequalities on geogebra. <br />
<br />
<math>x \geq 0 </math><br />
<br />
<math>y \geq 0 </math><br />
<br />
<math>200 x + 100 y \leq 5000</math><br />
<br />
<math>25x + 50y \leq 1000</math><br />
<br />
{{Geogebra|shvcc7wh}}<br />
<br />
The area in which all the colors are overlapping represents the region where all these inequalities are satisfied. <br />
==== Activity ====<br />
Plot the area in which all the four inequalities overlap and plot all the vertices of the resulting polygon. <br />
<br />
{{Geogebra|qvjg3ntd}}<br />
<br />
==== Solution ====<br />
Now we have four bounds of this polygon inside of which all the four inequalities are satisfied. All we need to do now is find a point in this set, where <math>x+y</math>is maximised. <br />
<br />
Simply looking at the the second plot, we can see that at A , <math>x+y</math>= 0, at C its 20, at D its 25 and finally at B its 30. <br />
<br />
This gives us our solution that '''''x = 20''''' and '''''y = 30''''' . <br />
<br />
What this means in real life is that if the baker bakes 20 of the first type of cakes and 30 of the second type, they will end up with the most possible amount of cakes using 5kg flour and 1kg fat. <br />
<br />
== Recap ==<br />
From above we can conclude that solving a optimisation problem using linear programming has following steps: <br />
* Make a system linear inequalities using the constrains of the real life scenario. (For example we only had 5kg flour and 1kg fat and we used it to device the model) <br />
* Plot the system of linear inequalities<br />
* Plot the area which contains all the points that satisfy the inequalities. <br />
* Among those points, find the point which maximizes or minimizes the the variables (depending on your need). This point will always be one of the vertex of the polygon plotted by the linear equations. For example in our question, it was the vertex B(20,10) which maximized <math>x+y</math><br />
* And you are done!<br />
<br />
== Additional Material ==<br />
{{Youtube<br />
| 1 = K7TL5NMlKIk<br />
}}{{Youtube|Bzzqx1F23a8<br />
}}</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Linear_programming&diff=36340Linear programming2022-06-17T10:51:30Z<p>Shobhit: </p>
<hr />
<div>== Concept 1 : Mathematical modelling ==<br />
One of the most important applications of mathematics in life is to find a optimal solution for problems. For example, what goods should a shopkeeper buy to get the most amount of profit or what is the optimal combination of food you should eat to get maximum amount of nutrients? <br />
<br />
To solve these questions, we need to mathematize them i.e. make equations out of those which can be solved. For example we need to write down how much profit does the shopkeeper get on each good, how much budget does he have, which goods sell more, which goods might go bad etc and then using this data, devise equations which will help us in finding the optimal combination of goods the shopkeeper should buy. <br />
<br />
This process of converting a real life problem in a mathematical fashion is called '''mathematical modelling.''' <br />
<br />
== Concept 2 : Linear Programming ==<br />
As the name suggests, '''Linear Programming''' is a method of optimizing a mathematical model which is represent by linear constraints only i.e. it does not contain any second order terms. Only equations of form <math>a_1 x_1+a_2x_2+a_3 x_3......=a_0</math>are allowed where <math>a_n</math>are constants and <math>x_n</math>are variables. <br />
<br />
== Concept 2 : Finding optimal solutions ==<br />
Now we will solve a real life optimization problem using linear programming. <br />
<br />
=== '''Question''' ===<br />
One kind of cake (Cake A) requires 200g of flour and 25g of fat, and another kind of cake (Cake B) requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes. (From NCERT) <br />
<br />
Let <math>x </math>be the number of cake A and <math>y</math>be the number of cake B. <br />
<br />
According to the question we have to maximize <math>x+y</math>in limited number of ingredients (5 kg flour and 1 kg fat) <br />
<br />
Before moving ahead we should set a baseline. We know that <math>x<br />
</math>and <math>y</math>cant be less than 0. <br />
<br />
Hence <math>x , y \geq 0 </math><br />
<br />
For flour : <br />
<br />
<math>200 x + 100 y \leq 5000</math> <br />
<br />
What this basically means is that if we make <math>x</math>cake A , we will use <math>200x<br />
</math>grams of flour. Similarly for <math>y<br />
</math> cake B, we will use <math>100y<br />
</math> grams of flour. The total flour used in all the cakes should be less than 5000g. <br />
<br />
Similarly for fat : <br />
<br />
<math>25x + 50y \leq 1000</math><br />
<br />
Now we have four linear inequalities. There are multiple ways to solve these inequalities. The method we will look here is the graphical method which is easier to visualize and understand. <br />
<br />
==== Activity ====<br />
Plot the following inequalities on geogebra. <br />
<br />
<math>x \geq 0 </math><br />
<br />
<math>y \geq 0 </math><br />
<br />
<math>200 x + 100 y \leq 5000</math><br />
<br />
<math>25x + 50y \leq 1000</math><br />
<br />
{{Geogebra|shvcc7wh}}<br />
<br />
The area in which all the colors are overlapping represents the region where all these inequalities are satisfied. <br />
==== Activity ====<br />
Plot the area in which all the four inequalities overlap and plot all the vertices of the resulting polygon. <br />
<br />
{{Geogebra|qvjg3ntd}}<br />
<br />
==== Solution ====<br />
Now we have four bounds of this polygon inside of which all the four inequalities are satisfied. All we need to do now is find a point in this set, where <math>x+y</math>is maximised. <br />
<br />
Simply looking at the the second plot, we can see that at A , <math>x+y</math>= 0, at C its 20, at D its 25 and finally at B its 30. <br />
<br />
This gives us our solution that '''''x = 20''''' and '''''y = 30''''' . <br />
<br />
What this means in real life is that if the baker bakes 20 of the first type of cakes and 30 of the second type, they will end up with the most possible amount of cakes using 5kg flour and 1kg fat. <br />
<br />
== Recap ==<br />
From above we can conclude that solving a optimisation problem using linear programming has following steps: <br />
* Make a system linear inequalities using the constrains of the real life scenario. (For example we only had 5kg flour and 1kg fat and we used it to device the model) <br />
* Plot the system of linear inequalities<br />
* Plot the area which contains all the points that satisfy the inequalities. <br />
* Among those points, find the point which maximizes or minimizes the the variables (depending on your need). This point will always be one of the vertex of the polygon plotted by the linear equations. For example in our question, it was the vertex B(20,10) which maximized <math>x+y</math><br />
* And you are done!<br />
<br />
== Additional Material ==<br />
{{Youtube<br />
| 1 = v=K7TL5NMlKIk<br />
}}{{Youtube|Bzzqx1F23a8<br />
}}</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Linear_programming&diff=36339Linear programming2022-06-17T10:27:41Z<p>Shobhit: </p>
<hr />
<div>== Concept 1 : Mathematical modelling ==<br />
One of the most important applications of mathematics in life is to find a optimal solution for problems. For example, what goods should a shopkeeper buy to get the most amount of profit or what is the optimal combination of food you should eat to get maximum amount of nutrients? <br />
<br />
To solve these questions, we need to mathematize them i.e. make equations out of those which can be solved. For example we need to write down how much profit does the shopkeeper get on each good, how much budget does he have, which goods sell more, which goods might go bad etc and then using this data, devise equations which will help us in finding the optimal combination of goods the shopkeeper should buy. <br />
<br />
This process of converting a real life problem in a mathematical fashion is called '''mathematical modelling.''' <br />
<br />
== Concept 2 : Linear Programming ==<br />
As the name suggests, '''Linear Programming''' is a method of optimizing a mathematical model which is represent by linear constraints only i.e. it does not contain any second order terms. Only equations of form <math>a_1 x_1+a_2x_2+a_3 x_3......=a_0</math>are allowed where <math>a_n</math>are constants and <math>x_n</math>are variables. <br />
<br />
== Concept 2 : Finding optimal solutions ==<br />
Now we will solve a real life optimization problem using linear programming. <br />
<br />
=== '''Question''' ===<br />
One kind of cake (Cake A) requires 200g of flour and 25g of fat, and another kind of cake (Cake B) requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes. (From NCERT) <br />
<br />
Let <math>x </math>be the number of cake A and <math>y</math>be the number of cake B. <br />
<br />
According to the question we have to maximize <math>x+y</math>in limited number of ingredients (5 kg flour and 1 kg fat) <br />
<br />
Before moving ahead we should set a baseline. We know that <math>x<br />
</math>and <math>y</math>cant be less than 0. <br />
<br />
Hence <math>x , y \geq 0 </math><br />
<br />
For flour : <br />
<br />
<math>200 x + 100 y \leq 5000</math> <br />
<br />
What this basically means is that if we make <math>x</math>cake A , we will use <math>200x<br />
</math>grams of flour. Similarly for <math>y<br />
</math> cake B, we will use <math>100y<br />
</math> grams of flour. The total flour used in all the cakes should be less than 5000g. <br />
<br />
Similarly for fat : <br />
<br />
<math>25x + 50y \leq 1000</math><br />
<br />
Now we have four linear inequalities. There are multiple ways to solve these inequalities. The first method we will look at is the graphical method which is easier to visualize and understand. <br />
<br />
==== Activity ====<br />
Plot the following inequalities on geogebra. <br />
<br />
<math>x \geq 0 </math><br />
<br />
<math>y \geq 0 </math><br />
<br />
<math>200 x + 100 y \leq 5000</math><br />
<br />
<math>25x + 50y \leq 1000</math><br />
<br />
{{Geogebra|shvcc7wh}}<br />
<br />
The area in which all the colors are overlapping represents the region where all these inequalities are satisfied. <br />
==== Activity ====<br />
Plot the area in which all the four inequalities overlap and plot all the vertices of the resulting polygon. <br />
<br />
{{Geogebra|qvjg3ntd}}<br />
<br />
==== Observation ====<br />
Now we have four bounds of this polygon inside of which all the four inequalities are satisfied. All we need to do now is find a point in this set, where <math>x+y</math>is maximised. <br />
<br />
Simply looking at the</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Linear_programming&diff=36338Linear programming2022-06-17T08:06:27Z<p>Shobhit: </p>
<hr />
<div>{{Geogebra|qvjg3ntd}}<br />
<br />
== Concept 1 : Mathematical modelling ==<br />
One of the most important applications of mathematics in life is to find a optimal solution for problems. For example, what goods should a shopkeeper buy to get the most amount of profit or what is the optimal combination of food you should eat to get maximum amount of nutrients? <br />
<br />
To solve these questions, we need to mathematize them i.e. make equations out of those which can be solved. For example we need to write down how much profit does the shopkeeper get on each good, how much budget does he have, which goods sell more, which goods might go bad etc and then using this data, devise equations which will help us in finding the optimal combination of goods the shopkeeper should buy. <br />
<br />
This process of converting a real life problem in a mathematical fashion is called '''mathematical modelling.''' <br />
<br />
== Concept 2 : Linear Programming ==<br />
As the name suggests, '''Linear Programming''' is a method of optimizing a mathematical model which is represent by linear constraints only i.e. it does not contain any second order terms. Only equations of form <math>a_1 x_1+a_2x_2+a_3 x_3......=a_0</math>are allowed where <math>a_n</math>are constants and <math>x_n</math>are variables. <br />
<br />
== Concept 2 : Finding optimal solutions ==<br />
Now we will solve a real life optimization problem using linear programming. <br />
<br />
=== '''Question''' ===<br />
One kind of cake (Cake A) requires 200g of flour and 25g of fat, and another kind of cake (Cake B) requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes. (From NCERT) <br />
<br />
Let <math>x </math>be the number of cake A and <math>y</math>be the number of cake B. <br />
<br />
According to the question we have to maximize <math>x+y</math>in limited number of ingredients (5 kg flour and 1 kg fat) <br />
<br />
Before moving ahead we should set a baseline. We know that <math>x<br />
</math>and <math>y</math>cant be less than 0. <br />
<br />
Hence <math>x , y \geq 0 </math><br />
<br />
For flour : <br />
<br />
<math>200 x + 100 y \leq 5000</math> <br />
<br />
What this basically means is that if we make <math>x</math>cake A , we will use <math>200x<br />
</math>grams of flour. Similarly for <math>y<br />
</math> cake B, we will use <math>100y<br />
</math> grams of flour. The total flour used in all the cakes should be less than 5000g. <br />
<br />
Similarly for fat : <br />
<br />
<math>25x + 50y \leq 1000</math><br />
<br />
Now we have four linear inequalities. There are multiple ways to solve these inequalities. The first method we will look at is the graphical method which is easier to visualize and understand. <br />
<br />
==== Activity ====<br />
Plot the following inequalities on geogebra. <br />
<br />
<math>x \geq 0 </math><br />
<br />
<math>y \geq 0 </math><br />
<br />
<math>200 x + 100 y \leq 5000</math><br />
<br />
<math>25x + 50y \leq 1000</math><br />
<br />
Geogebra file : https://www.geogebra.org/calculator/qvjg3ntd<br />
<br />
The area in which all the colors are overlapping represents the region where all these inequalities are satisfied. <br />
[[File:Linear programming question 1.png|Geogebra plot|center|frameless|777x777px]]<br />
<br />
==== Activity ====<br />
Plot the area in which all the four inequalities overlap and plot all the vertices of the resulting polygon. <br />
<br />
Geogebra file : https://www.geogebra.org/calculator/qvjg3ntd<br />
<br />
[[File:Linear Programming plot 2 .png|center|frameless|700x700px]]<br />
<br />
==== Observation ====<br />
Now we have four bounds of this polygon inside of which all the four inequalities are satisfied. All we need to do now is find a point in this set, where <math>x+y</math>is maximised. <br />
<br />
Simply looking at the</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Linear_programming&diff=36337Linear programming2022-06-17T08:02:51Z<p>Shobhit: </p>
<hr />
<div>== Concept 1 : Mathematical modelling ==<br />
One of the most important applications of mathematics in life is to find a optimal solution for problems. For example, what goods should a shopkeeper buy to get the most amount of profit or what is the optimal combination of food you should eat to get maximum amount of nutrients? <br />
<br />
To solve these questions, we need to mathematize them i.e. make equations out of those which can be solved. For example we need to write down how much profit does the shopkeeper get on each good, how much budget does he have, which goods sell more, which goods might go bad etc and then using this data, devise equations which will help us in finding the optimal combination of goods the shopkeeper should buy. <br />
<br />
This process of converting a real life problem in a mathematical fashion is called '''mathematical modelling.''' <br />
<br />
== Concept 2 : Linear Programming ==<br />
As the name suggests, '''Linear Programming''' is a method of optimizing a mathematical model which is represent by linear constraints only i.e. it does not contain any second order terms. Only equations of form <math>a_1 x_1+a_2x_2+a_3 x_3......=a_0</math>are allowed where <math>a_n</math>are constants and <math>x_n</math>are variables. <br />
<br />
== Concept 2 : Finding optimal solutions ==<br />
Now we will solve a real life optimization problem using linear programming. <br />
<br />
=== '''Question''' ===<br />
One kind of cake (Cake A) requires 200g of flour and 25g of fat, and another kind of cake (Cake B) requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes. (From NCERT) <br />
<br />
Let <math>x </math>be the number of cake A and <math>y</math>be the number of cake B. <br />
<br />
According to the question we have to maximize <math>x+y</math>in limited number of ingredients (5 kg flour and 1 kg fat) <br />
<br />
Before moving ahead we should set a baseline. We know that <math>x<br />
</math>and <math>y</math>cant be less than 0. <br />
<br />
Hence <math>x , y \geq 0 </math><br />
<br />
For flour : <br />
<br />
<math>200 x + 100 y \leq 5000</math> <br />
<br />
What this basically means is that if we make <math>x</math>cake A , we will use <math>200x<br />
</math>grams of flour. Similarly for <math>y<br />
</math> cake B, we will use <math>100y<br />
</math> grams of flour. The total flour used in all the cakes should be less than 5000g. <br />
<br />
Similarly for fat : <br />
<br />
<math>25x + 50y \leq 1000</math><br />
<br />
Now we have four linear inequalities. There are multiple ways to solve these inequalities. The first method we will look at is the graphical method which is easier to visualize and understand. <br />
<br />
==== Activity ====<br />
Plot the following inequalities on geogebra. <br />
<br />
<math>x \geq 0 </math><br />
<br />
<math>y \geq 0 </math><br />
<br />
<math>200 x + 100 y \leq 5000</math><br />
<br />
<math>25x + 50y \leq 1000</math><br />
<br />
Geogebra file : https://www.geogebra.org/calculator/qvjg3ntd<br />
<br />
The area in which all the colors are overlapping represents the region where all these inequalities are satisfied. <br />
[[File:Linear programming question 1.png|Geogebra plot|center|frameless|777x777px]]<br />
<br />
==== Activity ====<br />
Plot the area in which all the four inequalities overlap and plot all the vertices of the resulting polygon. <br />
<br />
Geogebra file : https://www.geogebra.org/calculator/qvjg3ntd<br />
<br />
[[File:Linear Programming plot 2 .png|center|frameless|700x700px]]<br />
<br />
==== Observation ====<br />
Now we have four bounds of this polygon inside of which all the four inequalities are satisfied. All we need to do now is find a point in this set, where <math>x+y</math>is maximised. <br />
<br />
Simply looking at the</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:Linear_Programming_plot_2_.png&diff=36335File:Linear Programming plot 2 .png2022-06-17T07:43:54Z<p>Shobhit: </p>
<hr />
<div>plot 2 of question 1 - Linear Programming</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Linear_programming&diff=36334Linear programming2022-06-17T07:20:48Z<p>Shobhit: /* Concept 1 : Linear inequalities */</p>
<hr />
<div>== Concept 1 : Mathematical modelling ==<br />
One of the most important applications of mathematics in life is to find a optimal solution for problems. For example, what goods should a shopkeeper buy to get the most amount of profit or what is the optimal combination of food you should eat to get maximum amount of nutrients? <br />
<br />
To solve these questions, we need to mathematize them i.e. make equations out of those which can be solved. For example we need to write down how much profit does the shopkeeper get on each good, how much budget does he have, which goods sell more, which goods might go bad etc and then using this data, devise equations which will help us in finding the optimal combination of goods the shopkeeper should buy. <br />
<br />
This process of converting a real life problem in a mathematical fashion is called '''mathematical modelling.''' <br />
<br />
== Concept 2 : Linear Programming ==<br />
As the name suggests, '''Linear Programming''' is a method of optimizing a mathematical model which is represent by linear constraints only i.e. it does not contain any second order terms. Only equations of form <math>a_1 x_1+a_2x_2+a_3 x_3......=a_0</math>are allowed where <math>a_n</math>are constants and <math>x_n</math>are variables. <br />
<br />
== Concept 2 : Finding optimal solutions ==<br />
Now we will solve a real life optimization problem using linear programming. <br />
<br />
=== '''Question''' ===<br />
One kind of cake (Cake A) requires 200g of flour and 25g of fat, and another kind of cake (Cake B) requires 100g of flour and 50g of fat. Find the maximum number of cakes which can be made from 5kg of flour and 1 kg of fat assuming that there is no shortage of the other ingredients used in making the cakes. (From NCERT) <br />
<br />
Let <math>x </math>be the number of cake A and <math>y</math>be the number of cake B. <br />
<br />
According to the question we have to maximize <math>x+y</math>in limited number of ingredients (5 kg flour and 1 kg fat) <br />
<br />
Before moving ahead we should set a baseline. We know that <math>x<br />
</math>and <math>y</math>cant be less than 0. <br />
<br />
Hence <math>x , y \geq 0 </math><br />
<br />
For flour : <br />
<br />
<math>200 x + 100 y \leq 5000</math> <br />
<br />
What this basically means is that if we make <math>x</math>cake A , we will use <math>200x<br />
</math>grams of flour. Similarly for <math>y<br />
</math> cake B, we will use <math>100y<br />
</math> grams of flour. The total flour used in all the cakes should be less than 5000g. <br />
<br />
Similarly for fat : <br />
<br />
<math>25x + 50y \leq 1000</math><br />
<br />
Now we have four linear inequalities. There are multiple ways to solve these inequalities. The first method we will look at is the graphical method which is easier to visualize and understand. <br />
<br />
==== Activity ====<br />
Plot the following inequalities on geogebra. <br />
<br />
<math>x \geq 0 </math><br />
<br />
<math>y \geq 0 </math><br />
<br />
<math>200 x + 100 y \leq 5000</math><br />
<br />
<math>25x + 50y \leq 1000</math><br />
<br />
Geogebra file : https://www.geogebra.org/calculator/qvjg3ntd<br />
[[File:Linear programming question 1.png|thumb|Geogebra plot]]</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=File:Linear_programming_question_1.png&diff=36333File:Linear programming question 1.png2022-06-17T07:20:11Z<p>Shobhit: </p>
<hr />
<div>geogebra activity for linear programming</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Linear_programming&diff=36332Linear programming2022-06-16T11:59:57Z<p>Shobhit: Made Linear Programming page</p>
<hr />
<div>== Foundations of Linear Programming ==<br />
Linear Programming is a way to find optimal solutions for a mathematical model defined by the linear constraints. <br />
<br />
== Concept 1 : Linear inequalities ==<br />
<br />
== Concept 2 : Finding optimal solutions ==</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Maths_topics_by_class&diff=36331Maths topics by class2022-06-16T11:41:54Z<p>Shobhit: /* Class 11 topics */</p>
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<div><div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/KOER/index.php/ತರಗತಿವಾರು_ಗಣಿತ_ವಿಷಯಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
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[[Portal-Mathematics|Back to Mathematics Portal]]<br />
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<br />
=='''Class 11 topics'''==<br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Limits Limits]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/linear_programming Linear Programming]<br />
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=='''Class 10 topics'''==<br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Real Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Progressions Progressions]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Permutations_And_Combinations Permutations And Combinations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability Probability]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surds Surds]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polynomials Polynomials]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quadratic_Equations Quadratic Equations]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Pythogoras_Theorem Pythogoras Theorem]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Trigonometry Trigonometry]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Basic_Geometry Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Circles Chord Properties]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Circles Tangent Properties]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra Graphs and Polyhedra] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Co-ordinate_geometry Co-ordinate geometry]<br />
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==Class 9 topics==<br />
{| <br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Square_Root Square Root]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Number Systems]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surds Surds]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Banking Banking]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Compound_Interest Compound Interest]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Hire_purchase_and_installment_buying Hire Purchase and Installment Buying]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Ratio_and_Proportion Ratio and Proportion]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |P[http://karnatakaeducation.org.in/KOER/en/index.php/Multiplication_of_polynomials olynomials]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Factorisation Factorisation] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/HCF_and_LCM HCF and LCM]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Simultaneous_Linear_Equations Simultaneous Linear Equations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Variation Variation]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polygons Polygons]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quadrilaterals Quadrilaterals]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Theorems_and_problems_on_parallelograms Theorems and problems on parallelograms] <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles Circles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Concurrency_in_triangles Concurrency in triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_to_Euclid's_Geometry Introduction to Euclid's Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Lines_and_Angles Lines and Angles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surface_Areas_and_Volumes Surface Areas and Volumes]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Area_of_parallelograms_and_triangles Area of parallelograms and triangles] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Coordinate_Geometry Coordinate Geometry] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Triangles] <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Construction Constructions] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Heron's_Formula Heron's Formula] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability Probability]<br />
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==Class 8 topics==<br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Playing_With_Numbers Playing With Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Squares,_Square-_Roots,_Cubes_And_Cube-_Roots Squares,Square-Roots,Cubes And Cube-Roots]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Rational_Numbers Rational Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Commercial_Arithmetic Commercial Arithmetic]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Algebraic_Expressions Algebraic Expressions]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Factorisation Factorisation]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Linear_Equations_In_One_ Linear Equations In One Variable]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Exponents Exponents]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_To_Graphs Introduction To Graphs]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Axioms,_Postulates_And_ Axioms,Postulates And Theorems]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Theorems_On_Triangles Theorems On Triangles]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Congruency_Of_Triangles Congruency Of Triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Construction_Of_Triangles Construction Of Triangles]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quardilaterals Quardilaterals]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_to_Algebra Introduction to Algebra]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Basic_Geometry Basic Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Fraction Fraction]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Number_Systems Number Systems]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles Circles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Graph_Theory Graph Theory]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polygons Polygons]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability,_Permutations_and_Combinations Probability,Permutations and Combinations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Triangles]<br />
|}<br />
<br />
[[Category:Mathematics]]</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Limits&diff=36330Limits2022-06-16T11:38:55Z<p>Shobhit: Added Limits page</p>
<hr />
<div>== Learning Objectives ==<br />
* Having an intuitionistic understanding of Limits of a function. <br />
* Understanding algebra of limits.<br />
* Working out limits of various types of functions. <br />
* Identifying various indeterminate forms. <br />
<br />
== Concept 1: Understanding Limits of a function ==<br />
<br />
=== Activity ===<br />
<br />
===== Understanding the need for limits. =====<br />
<br />
=== Theory ===<br />
'''Limits''' : Its surprisingly hard to rigorously define limits but we can deduce an intuitive explanation from various examples. We say that the limit of function <math>f(x)</math> as <math>x</math> tends to ''a'' is ''L'' , if <math>f(x)</math> approaches (gets closer to) ''L'' , as <math>x</math> gets closer to ''a''. If such a number does not exist, we say that the limit does not exist. <br />
<br />
This is expressed mathematically as <math>\lim_{x \to a} f(x) = L </math><br />
<br />
=== Activity ===<br />
<br />
==== Understanding the definition of limits. ====<br />
<br />
=== Important Point ===<br />
What is <math>\lim_{x \to 2} f(x) </math>where <math>f(x) = \left\{<br />
\begin{array}{ll}<br />
x & \quad x \in \R - [2] \\<br />
6 & \quad x = 2<br />
\end{array}<br />
\right.</math>?<br />
<br />
Since as <math>x</math> approaches 2, <math>f(x)</math>approaches 2 , <math>\lim_{x \to 2} f(x) </math>= 2. <br />
<br />
This shows that <math>\lim_{x \to a} f(x) </math>need not be equal to <math>f(a)</math>even when <math>f(a)</math> is explicitly defined. <br />
<br />
== Concept 2 : Limit laws ==<br />
In this section we will learn the algebra of limit of functions. <br />
<br />
=== Theory ===<br />
Before delving into more complex theorems, let us establish the basic ones. <br />
<br />
Limit of a constant function is same at each point. <br />
<br />
i.e. <math> \lim _{x \rightarrow a} c=c <br />
</math><br />
<br />
Also limit of <math> f(x) = x <br />
</math>at <math> a <br />
</math>is <math> a <br />
</math>.<br />
<br />
i.e. <math> \lim _{x \rightarrow a} x=a <br />
</math>. This makes sense since the function is defined at all points and is continuous.<br />
<br />
Now we are prepared to move forward with the algebra of limits. <br />
<br />
<math>\begin{aligned}<br />
&\lim _{x \rightarrow p}(f(x)+g(x))=\lim _{x \rightarrow p} f(x)+\lim _{x \rightarrow p} g(x) \\<br />
&\lim _{x \rightarrow p}(f(x)-g(x))=\lim _{x \rightarrow p} f(x)-\lim _{x \rightarrow p} g(x) \\<br />
&\lim _{x \rightarrow p}(f(x) \cdot g(x))=\lim _{x \rightarrow p} f(x) \cdot \lim _{x \rightarrow p} g(x) \\<br />
&\lim _{x \rightarrow p}(f(x) / g(x))=\lim _{x \rightarrow p} f(x) / \lim _{x \rightarrow p} g(x) \\<br />
&\lim _{x \rightarrow p} \quad f(x)^{g(x)}=\lim _{x \rightarrow p} f(x)^{\lim _{x \rightarrow p} g(x)}<br />
\end{aligned}</math><br />
<br />
=== Activity ===<br />
Intuitively understanding limit laws. <br />
<br />
== Concept 3 : Working out limits of functions algebraically ==<br />
Using the limit laws we studied in the last section, we can manipulate functions and try to solve them algebraically instead of using graphs or tables like we did before.</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Maths_topics_by_class&diff=36329Maths topics by class2022-06-16T09:24:17Z<p>Shobhit: </p>
<hr />
<div><div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/KOER/index.php/ತರಗತಿವಾರು_ಗಣಿತ_ವಿಷಯಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
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[[Portal-Mathematics|Back to Mathematics Portal]]<br />
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=='''Class 11 topics'''==<br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Limits Limits]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Progressions Progressions]<br />
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=='''Class 10 topics'''==<br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Real Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Progressions Progressions]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Permutations_And_Combinations Permutations And Combinations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability Probability]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surds Surds]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polynomials Polynomials]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quadratic_Equations Quadratic Equations]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Similar Triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Pythogoras_Theorem Pythogoras Theorem]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Trigonometry Trigonometry]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Basic_Geometry Geometry]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Circles Tangent Properties]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra Graphs and Polyhedra] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Co-ordinate_geometry Co-ordinate geometry]<br />
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==Class 9 topics==<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polygons Polygons]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Area_of_parallelograms_and_triangles Area of parallelograms and triangles] <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Triangles] <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Construction Constructions] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Heron's_Formula Heron's Formula] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability Probability]<br />
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==Class 8 topics==<br />
{| <br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Playing_With_Numbers Playing With Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Squares,_Square-_Roots,_Cubes_And_Cube-_Roots Squares,Square-Roots,Cubes And Cube-Roots]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Rational_Numbers Rational Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Commercial_Arithmetic Commercial Arithmetic]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Algebraic_Expressions Algebraic Expressions]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Factorisation Factorisation]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Linear_Equations_In_One_ Linear Equations In One Variable]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Exponents Exponents]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_To_Graphs Introduction To Graphs]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Axioms,_Postulates_And_ Axioms,Postulates And Theorems]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Theorems_On_Triangles Theorems On Triangles]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Congruency_Of_Triangles Congruency Of Triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Construction_Of_Triangles Construction Of Triangles]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quardilaterals Quardilaterals]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
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'''More topics'''<br />
{| <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_to_Algebra Introduction to Algebra]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Basic_Geometry Basic Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Fraction Fraction]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Number_Systems Number Systems]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles Circles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Graph_Theory Graph Theory]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polygons Polygons]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability,_Permutations_and_Combinations Probability,Permutations and Combinations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Triangles]<br />
|}<br />
<br />
[[Category:Mathematics]]</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Maths_topics_by_class&diff=36328Maths topics by class2022-06-16T09:12:21Z<p>Shobhit: /* Class 11 topics */</p>
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<div><div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/KOER/index.php/ತರಗತಿವಾರು_ಗಣಿತ_ವಿಷಯಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
{|<br />
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[[Portal-Mathematics|Back to Mathematics Portal]]<br />
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=='''Class 11 topics'''==<br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Limits]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Progressions Progressions]<br />
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=='''Class 10 topics'''==<br />
{| <br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Real Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Progressions Progressions]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Permutations_And_Combinations Permutations And Combinations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability Probability]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surds Surds]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polynomials Polynomials]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quadratic_Equations Quadratic Equations]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Similar Triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Pythogoras_Theorem Pythogoras Theorem]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Trigonometry Trigonometry]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Basic_Geometry Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Circles Chord Properties]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Circles Tangent Properties]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra Graphs and Polyhedra] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Co-ordinate_geometry Co-ordinate geometry]<br />
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==Class 9 topics==<br />
{| <br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Square_Root Square Root]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Number Systems]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surds Surds]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Banking Banking]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Compound_Interest Compound Interest]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Hire_purchase_and_installment_buying Hire Purchase and Installment Buying]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Ratio_and_Proportion Ratio and Proportion]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |P[http://karnatakaeducation.org.in/KOER/en/index.php/Multiplication_of_polynomials olynomials]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Factorisation Factorisation] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/HCF_and_LCM HCF and LCM]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Division Division]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Simultaneous_Linear_Equations Simultaneous Linear Equations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Variation Variation]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polygons Polygons]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quadrilaterals Quadrilaterals]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Theorems_and_problems_on_parallelograms Theorems and problems on parallelograms] <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles Circles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Concurrency_in_triangles Concurrency in triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_to_Euclid's_Geometry Introduction to Euclid's Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Lines_and_Angles Lines and Angles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surface_Areas_and_Volumes Surface Areas and Volumes]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Area_of_parallelograms_and_triangles Area of parallelograms and triangles] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Coordinate_Geometry Coordinate Geometry] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Triangles] <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Construction Constructions] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Heron's_Formula Heron's Formula] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability Probability]<br />
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==Class 8 topics==<br />
{| <br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Playing_With_Numbers Playing With Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Squares,_Square-_Roots,_Cubes_And_Cube-_Roots Squares,Square-Roots,Cubes And Cube-Roots]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Rational_Numbers Rational Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Commercial_Arithmetic Commercial Arithmetic]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Algebraic_Expressions Algebraic Expressions]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Factorisation Factorisation]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Linear_Equations_In_One_ Linear Equations In One Variable]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Exponents Exponents]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_To_Graphs Introduction To Graphs]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Axioms,_Postulates_And_ Axioms,Postulates And Theorems]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Theorems_On_Triangles Theorems On Triangles]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Congruency_Of_Triangles Congruency Of Triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Construction_Of_Triangles Construction Of Triangles]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quardilaterals Quardilaterals]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
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'''More topics'''<br />
{| <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_to_Algebra Introduction to Algebra]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Basic_Geometry Basic Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Fraction Fraction]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Number_Systems Number Systems]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles Circles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Graph_Theory Graph Theory]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polygons Polygons]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability,_Permutations_and_Combinations Probability,Permutations and Combinations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Triangles]<br />
|}<br />
<br />
[[Category:Mathematics]]</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Maths_topics_by_class&diff=36327Maths topics by class2022-06-16T09:11:43Z<p>Shobhit: Added Class 11 section</p>
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<div><div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/KOER/index.php/ತರಗತಿವಾರು_ಗಣಿತ_ವಿಷಯಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
{|<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |<br />
[[Portal-Mathematics|Back to Mathematics Portal]]<br />
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=='''Class 10 topics'''==<br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Limits]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Progressions Progressions]<br />
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=='''Class 10 topics'''==<br />
{| <br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Real Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Progressions Progressions]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Permutations_And_Combinations Permutations And Combinations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability Probability]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surds Surds]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polynomials Polynomials]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quadratic_Equations Quadratic Equations]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Similar Triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Pythogoras_Theorem Pythogoras Theorem]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Trigonometry Trigonometry]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Basic_Geometry Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Circles Chord Properties]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Circles Tangent Properties]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra Graphs and Polyhedra] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Co-ordinate_geometry Co-ordinate geometry]<br />
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==Class 9 topics==<br />
{| <br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Square_Root Square Root]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Number Systems]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surds Surds]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Banking Banking]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Compound_Interest Compound Interest]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Hire_purchase_and_installment_buying Hire Purchase and Installment Buying]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Ratio_and_Proportion Ratio and Proportion]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |P[http://karnatakaeducation.org.in/KOER/en/index.php/Multiplication_of_polynomials olynomials]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Factorisation Factorisation] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/HCF_and_LCM HCF and LCM]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Division Division]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Simultaneous_Linear_Equations Simultaneous Linear Equations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Variation Variation]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polygons Polygons]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quadrilaterals Quadrilaterals]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Theorems_and_problems_on_parallelograms Theorems and problems on parallelograms] <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles Circles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Concurrency_in_triangles Concurrency in triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_to_Euclid's_Geometry Introduction to Euclid's Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Lines_and_Angles Lines and Angles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surface_Areas_and_Volumes Surface Areas and Volumes]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Area_of_parallelograms_and_triangles Area of parallelograms and triangles] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Coordinate_Geometry Coordinate Geometry] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Triangles] <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Construction Constructions] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Heron's_Formula Heron's Formula] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability Probability]<br />
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==Class 8 topics==<br />
{| <br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Playing_With_Numbers Playing With Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Squares,_Square-_Roots,_Cubes_And_Cube-_Roots Squares,Square-Roots,Cubes And Cube-Roots]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Rational_Numbers Rational Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Commercial_Arithmetic Commercial Arithmetic]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Algebraic_Expressions Algebraic Expressions]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Factorisation Factorisation]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Linear_Equations_In_One_ Linear Equations In One Variable]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Exponents Exponents]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_To_Graphs Introduction To Graphs]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Axioms,_Postulates_And_ Axioms,Postulates And Theorems]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Theorems_On_Triangles Theorems On Triangles]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Congruency_Of_Triangles Congruency Of Triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Construction_Of_Triangles Construction Of Triangles]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quardilaterals Quardilaterals]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
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'''More topics'''<br />
{| <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_to_Algebra Introduction to Algebra]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Basic_Geometry Basic Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Fraction Fraction]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Number_Systems Number Systems]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles Circles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Graph_Theory Graph Theory]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polygons Polygons]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability,_Permutations_and_Combinations Probability,Permutations and Combinations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Triangles]<br />
|}<br />
<br />
[[Category:Mathematics]]</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Maths_topics_by_class&diff=36326Maths topics by class2022-06-16T06:36:25Z<p>Shobhit: removed Category:Class 11 topics using HotCat</p>
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<div><div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/KOER/index.php/ತರಗತಿವಾರು_ಗಣಿತ_ವಿಷಯಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
{|<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |<br />
[[Portal-Mathematics|Back to Mathematics Portal]]<br />
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=='''Class 10 topics'''==<br />
{| <br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Real Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Progressions Progressions]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Permutations_And_Combinations Permutations And Combinations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability Probability]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surds Surds]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polynomials Polynomials]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quadratic_Equations Quadratic Equations]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Similar Triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Pythogoras_Theorem Pythogoras Theorem]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Trigonometry Trigonometry]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Basic_Geometry Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Circles Chord Properties]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Circles Tangent Properties]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra Graphs and Polyhedra] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Co-ordinate_geometry Co-ordinate geometry]<br />
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==Class 9 topics==<br />
{| <br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Square_Root Square Root]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Number Systems]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surds Surds]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Banking Banking]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Compound_Interest Compound Interest]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Hire_purchase_and_installment_buying Hire Purchase and Installment Buying]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Ratio_and_Proportion Ratio and Proportion]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |P[http://karnatakaeducation.org.in/KOER/en/index.php/Multiplication_of_polynomials olynomials]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Factorisation Factorisation] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/HCF_and_LCM HCF and LCM]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Division Division]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Simultaneous_Linear_Equations Simultaneous Linear Equations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Variation Variation]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polygons Polygons]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quadrilaterals Quadrilaterals]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Theorems_and_problems_on_parallelograms Theorems and problems on parallelograms] <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles Circles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Concurrency_in_triangles Concurrency in triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_to_Euclid's_Geometry Introduction to Euclid's Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Lines_and_Angles Lines and Angles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surface_Areas_and_Volumes Surface Areas and Volumes]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Area_of_parallelograms_and_triangles Area of parallelograms and triangles] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Coordinate_Geometry Coordinate Geometry] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Triangles] <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Construction Constructions] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Heron's_Formula Heron's Formula] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability Probability]<br />
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==Class 8 topics==<br />
{| <br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Playing_With_Numbers Playing With Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Squares,_Square-_Roots,_Cubes_And_Cube-_Roots Squares,Square-Roots,Cubes And Cube-Roots]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Rational_Numbers Rational Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Commercial_Arithmetic Commercial Arithmetic]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Algebraic_Expressions Algebraic Expressions]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Factorisation Factorisation]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Linear_Equations_In_One_ Linear Equations In One Variable]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Exponents Exponents]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_To_Graphs Introduction To Graphs]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Axioms,_Postulates_And_ Axioms,Postulates And Theorems]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Theorems_On_Triangles Theorems On Triangles]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Congruency_Of_Triangles Congruency Of Triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Construction_Of_Triangles Construction Of Triangles]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quardilaterals Quardilaterals]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
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'''More topics'''<br />
{| <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_to_Algebra Introduction to Algebra]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Basic_Geometry Basic Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Fraction Fraction]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Number_Systems Number Systems]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles Circles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Graph_Theory Graph Theory]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polygons Polygons]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability,_Permutations_and_Combinations Probability,Permutations and Combinations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Triangles]<br />
|}<br />
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[[Category:Mathematics]]</div>Shobhithttps://karnatakaeducation.org.in/KOER/en/index.php?title=Maths_topics_by_class&diff=36325Maths topics by class2022-06-16T06:36:04Z<p>Shobhit: /* Class 10 topics */</p>
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<div><div style="width:150px;border:none; border-radius:10px;box-shadow: 5px 5px 5px #888888; background:#ffffff; vertical-align:top; text-align:center; padding:5px;"><br />
''[http://karnatakaeducation.org.in/KOER/index.php/ತರಗತಿವಾರು_ಗಣಿತ_ವಿಷಯಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div><br />
{|<br />
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[[Portal-Mathematics|Back to Mathematics Portal]]<br />
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=='''Class 10 topics'''==<br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Real Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Progressions Progressions]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Permutations_And_Combinations Permutations And Combinations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability Probability]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surds Surds]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polynomials Polynomials]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quadratic_Equations Quadratic Equations]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Similar Triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Pythogoras_Theorem Pythogoras Theorem]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Trigonometry Trigonometry]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Basic_Geometry Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Circles Chord Properties]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles_and_lines Circles Tangent Properties]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Graphs_And_Polyhedra Graphs and Polyhedra] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Co-ordinate_geometry Co-ordinate geometry]<br />
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==Class 9 topics==<br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Square_Root Square Root]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Real_Numbers Number Systems]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surds Surds]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Sets Sets]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Banking Banking]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Compound_Interest Compound Interest]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Hire_purchase_and_installment_buying Hire Purchase and Installment Buying]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Ratio_and_Proportion Ratio and Proportion]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |P[http://karnatakaeducation.org.in/KOER/en/index.php/Multiplication_of_polynomials olynomials]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Factorisation Factorisation] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/HCF_and_LCM HCF and LCM]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Division Division]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Simultaneous_Linear_Equations Simultaneous Linear Equations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Variation Variation]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polygons Polygons]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quadrilaterals Quadrilaterals]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Theorems_and_problems_on_parallelograms Theorems and problems on parallelograms] <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles Circles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Concurrency_in_triangles Concurrency in triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_to_Euclid's_Geometry Introduction to Euclid's Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Lines_and_Angles Lines and Angles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Surface_Areas_and_Volumes Surface Areas and Volumes]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Area_of_parallelograms_and_triangles Area of parallelograms and triangles] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Coordinate_Geometry Coordinate Geometry] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Triangles] <br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Construction Constructions] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Heron's_Formula Heron's Formula] <br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability Probability]<br />
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==Class 8 topics==<br />
{| <br />
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| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Playing_With_Numbers Playing With Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Squares,_Square-_Roots,_Cubes_And_Cube-_Roots Squares,Square-Roots,Cubes And Cube-Roots]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Rational_Numbers Rational Numbers]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Commercial_Arithmetic Commercial Arithmetic]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Statistics Statistics]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Algebraic_Expressions Algebraic Expressions]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Factorisation Factorisation]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Linear_Equations_In_One_ Linear Equations In One Variable]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Exponents Exponents]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_To_Graphs Introduction To Graphs]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Axioms,_Postulates_And_ Axioms,Postulates And Theorems]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Theorems_On_Triangles Theorems On Triangles]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Congruency_Of_Triangles Congruency Of Triangles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Construction_Of_Triangles Construction Of Triangles]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Quardilaterals Quardilaterals]<br />
| style="width:5%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Mensuration Mensuration]<br />
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'''More topics'''<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Introduction_to_Algebra Introduction to Algebra]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Basic_Geometry Basic Geometry]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Fraction Fraction]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Number_Systems Number Systems]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Circles Circles]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Graph_Theory Graph Theory]<br />
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| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Polygons Polygons]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Probability,_Permutations_and_Combinations Probability,Permutations and Combinations]<br />
| style="width:10%; border:none; border-radius:5px;box-shadow: 5px 5px 5px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://karnatakaeducation.org.in/KOER/en/index.php/Triangles Triangles]<br />
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[[Category:Mathematics]]<br />
[[Category:Class 11 topics]]</div>Shobhit