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''[http://karnatakaeducation.org.in/KOER/index.php/೧೦ನೇ_ತರಗತಿಯ_ವರ್ಗ_ಸಮೀಕರಣಗಳು ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ]''</div>
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
| style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; " |[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Philosophy Philosophy of Mathematics]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
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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'''].
While creating a resource page, please click here for a resource creation [http://karnatakaeducation.org.in/KOER/en/index.php/Resource_Creation_Checklist '''checklist'''].
= Concept Map =
== Concept Map ==
[[File:Quadratic_Equations.mm|Flash]]
__FORCETOC__
__FORCETOC__
= Textbook =
== Textbook ==
Please click here for Karnataka and other text books.
Please click here for Karnataka and other text books.
#[http://ktbs.kar.nic.in/New/Textbooks/class-x/english/maths/class-x-english-maths-chapter09.pdf Karnataka text book for Class 10, Chapter 09 - Quadratic Equations]
#[http://nimsdxb.com/wp-content/uploads/Unit-4_Quadratic_Equations_Core.pdf/ cbse text book]
==Additional Information==
{{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/10549763|width=450 |height=360 |border=1 }}
===Useful websites===
=Additional Information=
[https://in.ixl.com/search?q=quadratic+equation/ For more information about quadratic equation]
= Teaching Outlines =
===Reference Books===
[[Text_Books| relevent references]]
=== Resources ===
==== Resource Title ====
[http://www.mathopenref.com/quadraticexplorer.html Quadratic Function Explorer]
==== Description ====
This interactive activity helps you realize the action of the three coefficients a, b, c in a quadratic equation.
== Teaching Outlines ==
==Concept #1 - Introduction to quadratic equations==
An equation of the form <math>ax^2+bx+c = 0</math> where a ≠ 0 and a, b, c belongs to R.
===Learning objectives===
===Learning objectives===
converting verbal statement into equations.
===Notes for teachers===
===Notes for teachers===
#Basic knowledge of equations, linear equations,general form of linear equation, finding the rooots of equation, graphical representation of linear equations.<br>
#More importance to be given for signs while transforming the equations.
===Activities===
===Activities===
#Activity No 1 '''[[Quadratic_equations_introduction_to_quadratic_equation_activity_1|Introduction to quadratic equation]]'''
#Activity No 2 '''[[Quadratic_equations_introduction_to_quadratic_equation_actvity 2| Making a rectangular garden]]'''
#Activity No 3 '''[[Quadratic_equations_introduction_to_quadratic_equation_activity 3| Understanding<math> ax^2+bx+c=0</math> geometrically]]'''
==Concept #2 - Types of equations==
===Pure Quadratic Equation & Adfected Quadratic Equation===
Quadratic equation,in the form <math>ax^2+bx+c = 0</math>, is termed as quadratic expression and the equation of the form <math>ax^2+bx+c = 0</math>, a≠0 is called quadratic equation in x. This equation is also known to be pure quadratic equation if the value of b is zero i.e. b=0. Otherwise it is said to be adfected. The letters a, b, and c are called coefficients: and c is the constant coefficient.
===Learning objectives===
===Learning objectives===
#To distinguish between pure & adfected equations among the given equations.
#Standard forms of pure & adfected quadratic equations.
===Notes for teachers===
===Notes for teachers===
#Knowledge of general form of quadratic equations<br>
#roots of equation<br>
#proper use of signs.
===Activities===
===Activities===
'''[[Identifying pure and adfected ouadratic equations- Activity No1]]'''
'''[http://mathworksheets4kids.com/equations/quadratic.html/ work sheet Activity No2]'''
==Concept #3 What is the solution of a quadratic equation?==
==Concept #3 What is the solution of a quadratic equation==
The roots of the Quadratic Equation which satisfy the equation
===Learning objectives===
===Learning objectives===
#x=k is a solution of the quadratic equation if k satisfies the quadratic equation
#Any quadratic equation has at most two roots.
#The roots form the solution set of quadratic equation.
===Notes for teachers===
===Notes for teachers===
#different methods of solving quadratic equation
#knowledge of suitable formula to be used to solve specific problem.
#identify the type of quadratic equation.
===Activities===
===Activities===
#Activity No #1 '''Concept Name - Activity No.'''
#Activity No #1 #Activity No 3-[http://www.projectmaths.ie/students/strand4JC/student-activity-quadratic-formula.pdf| quadratic formula]<br>
#Activity No #2 '''Concept Name - Activity No.'''
#Activity No #2 '''Concept Name - Activity No'''
==Concept #4Methods of solution==
==Concept #4Methods of solution==
Different methods of finding the solution to a quadratic equation
#Factorisation method
#Completing the square method
#Formula method
#Graphical method.
===Learning objectives===
===Learning objectives===
#Solving quadratic equation by factorisation method
#Solving quadratic equation by completing the square method
#Deriving formula to find the roots of quadratic equation.
#Solving quadratic equation by using formula.<br>
#Solving quadratic equation graphically.<br>
#To find the sum and product of the roots of the quadratic equations.
===Notes for teachers===
===Notes for teachers===
*Students need to know factorisation
*substitution of values and simplification
*Identifying suitable method
===Activities===
===Activities===
#Activity No #1 '''Concept Name - Activity No.'''
#Activity No 1 -[https://www.geogebratube.org/material/iframe/id/8357/width/968/height/487/border/888888/rc/false/ai/false/sdz/true/smb/false/stb/false/stbh/true/ld/false/sri/true/at/preferhtml5| geogebra]
#Activity No #2 '''Concept Name - Activity No.'''
#Activity No 2-[http://www.wikihow.com/Solve-Quadratic-Equations/ learn more how to solve Q.E]
#Activity 3-[http://www.learnnc.org/lp/pages/2981| learn quadratics]
#Activity 4- [[Quadratic Equation solution activity1|Quadratic Equation solution]]
==Concept #5'''Nature of roots'''==
==Concept #5'''Nature of roots'''==
The roots of a quadratic equation can be real & equal, real & distinct or imaginary.
Nature of roots depends on the values of b^-4ac.
===Learning objectives===
===Learning objectives===
#To find the discriminant & interpret the nature of the roots of the given quadratic equation.
===Notes for teachers===
===Notes for teachers===
Guiding in Identifying the nature based on the value of discriminant
===Activities===
===Activities===
#Activity No #1 '''Concept Name - Activity No.'''
#Activity No #1 '''Concept Name - Activity No.'''[http://interpret the nature of roots/ interpret the nature of the roots]
#Activity No #2 '''Concept Name - Activity No.'''
#Activity No #2 '''Concept Name - Activity No.'''
==Concept #6'''applications'''==
==Concept #6'''applications'''==
Solving problems based on quadratic equations.
===Learning objectives===
===Learning objectives===
By applying the methods of solving quadratic equations, finding the solutions to real life situations.
===Notes for teachers===
===Notes for teachers===
Help the students in Identifying parameters and suitable methods for solving application problems.
===Activities===
===Activities===
#Activity No #1 '''Concept Name - Activity No.'''
#Activity No #1 [https://www.youtube.com/watch?v=IGGnn9oa4QYz| more word problems]
#Activity No #2 '''Concept Name - Activity No.'''
#Activity 2:[http://www.ehow.com/info_8502727_applications-quadratic-equations.html| quadratics in real life]
=Assessment activities for CCE=
=Assessment activities for CCE=
.[Http://Tube.geogebra.org/m/105393c|quadratic quiz]
= Hints for difficult problems =
=Hints for difficult problems =
1.If P & q are the roots of the equation <math>2a^2-4a+1=0</math> find the value of
= Project Ideas =
<math>p^3+q^3</math><br>
[[solution]]<br>
2.The altitude of a triangle is 6cm greter than its base. If its area is 108cmsq .Find its base.<br>
[[solution]]<br>
3.Solve <math>x^2-4x-8=0</math> By completing the square. <br>
[[solution]]
[[Category:Class 10]]
[[Category:Quadratic Equations]]
