Difference between revisions of "Quadratic Equations"

From Karnataka Open Educational Resources
Jump to navigation Jump to search
 
(23 intermediate revisions by 3 users not shown)
Line 6: Line 6:
 
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"
 
{| id="mp-topbanner" style="width:100%;font-size:100%;border-collapse:separate;border-spacing:20px;"
 
|-
 
|-
|style="width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| 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:_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]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| 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:_Pedagogy Teaching of Mathematics]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Pedagogy Teaching of Mathematics]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| 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/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Curriculum_and_Syllabus Curriculum and Syllabus]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| 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:_Topics Topics in School Mathematics]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_Topics Topics in School Mathematics]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| 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/Text_Books#Mathematics_-_Textbooks Textbooks]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Text_Books#Mathematics_-_Textbooks Textbooks]
|style=" width:10%; border:none; border-radius:5px;box-shadow: 10px 10px 10px #888888; background:#f9f9ff; vertical-align:middle; text-align:center; "|
+
| 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/Maths:_Question_Papers Question Bank]
 
[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
|}
 
|}
 
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 ==
<mm>[[Quadratic_Equations.mm|Flash]]</mm>
+
[[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://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]
 
#[http://nimsdxb.com/wp-content/uploads/Unit-4_Quadratic_Equations_Core.pdf/ cbse text book]
  
=Additional Information=
+
==Additional Information==
 
{{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/10549763|width=450 |height=360 |border=1 }}  
 
{{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/10549763|width=450 |height=360 |border=1 }}  
  
==Useful websites==
+
===Useful websites===
  
 
[https://in.ixl.com/search?q=quadratic+equation/ For more information about quadratic equation]
 
[https://in.ixl.com/search?q=quadratic+equation/ For more information about quadratic equation]
  
==Reference Books==
+
===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 =
+
== Teaching Outlines ==
  
 
==Concept #1 - Introduction to quadratic equations==
 
==Concept #1 - Introduction to quadratic equations==
Line 55: Line 65:
  
 
#Activity No 1 '''[[Quadratic_equations_introduction_to_quadratic_equation_activity_1|Introduction to quadratic equation]]'''
 
#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 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]]
+
#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==
 
==Concept #2 - Types of equations==
 
===Pure Quadratic Equation & Adfected Quadratic Equation===
 
===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 affected. The letters a, b, and c are called coefficients: and c is the constant coefficient.
+
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===
Line 72: Line 82:
  
 
===Activities===
 
===Activities===
#Activity No #1 '''[[Identifying pure and adfected ouadratic equations- Activity No1]]'''
+
'''[[Identifying pure and adfected ouadratic equations- Activity No1]]'''
  
#Activity No #2 '''
+
'''[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==  
Line 89: Line 99:
  
 
===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==
Line 103: Line 113:
 
#Deriving formula to find the roots of quadratic equation.
 
#Deriving formula to find the roots of quadratic equation.
 
#Solving quadratic equation by using formula.<br>
 
#Solving quadratic equation by using formula.<br>
 
+
#Solving quadratic equation graphically.<br>
#Solving quadratic equation graphically.<br>To find the sum and product of the roots of the quadratic equations.
+
#To find the sum and product of the roots of the quadratic equations.
[https://www.geogebratube.org/student/m8358]
 
  
 
===Notes for teachers===
 
===Notes for teachers===
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
+
*Students need to know factorisation
 +
*substitution of values and simplification
 +
*Identifying suitable method
  
 
===Activities===
 
===Activities===
#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 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-[http://www.wikihow.com/Solve-Quadratic-Equations/ learn more how to solve Q.E]
 
#Activity No 2-[http://www.wikihow.com/Solve-Quadratic-Equations/ learn more how to solve Q.E]
#Activity No 3-[http://www.projectmaths.ie/students/strand4JC/student-activity-quadratic-formula.pdf| quadratic formula]<br>
+
#Activity 3-[http://www.learnnc.org/lp/pages/2981| learn quadratics]
#Activity 4-[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'''==
Line 123: Line 134:
  
 
===Notes for teachers===
 
===Notes for teachers===
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
+
Guiding in Identifying the nature based on the value of discriminant
  
 
===Activities===
 
===Activities===
Line 136: Line 147:
  
 
===Notes for teachers===
 
===Notes for teachers===
''These are short notes that the teacher wants to share about the concept, any locally relevant information, specific instructions on what kind of methodology used and common misconceptions/mistakes.''
+
Help the students in Identifying parameters and suitable methods for solving application problems.
  
 
===Activities===
 
===Activities===
#Activity No #1 '''applications - .'''
+
#Activity No #1 [https://www.youtube.com/watch?v=IGGnn9oa4QYz| more word problems]
[https://www.youtube.com/watch?v=IGGnn9oa4QYz| more word problems]
 
 
#Activity 2:[http://www.ehow.com/info_8502727_applications-quadratic-equations.html| quadratics in real life]
 
#Activity 2:[http://www.ehow.com/info_8502727_applications-quadratic-equations.html| quadratics in real life]
'''to link back to content page'''
+
=Assessment activities for CCE=
 
 
'''To link back to the concept page'''
 
[[Topic Page Link]]
 
#Activity No #2 '''Concept Name - Activity No.'''
 
 
 
Assessment activities for CCE=
 
 
.[Http://Tube.geogebra.org/m/105393c|quadratic quiz]
 
.[Http://Tube.geogebra.org/m/105393c|quadratic quiz]
  
Line 160: Line 164:
 
[[solution]]
 
[[solution]]
  
'''back to the concept page'''
+
[[Category:Class 10]]
[[Quadratic_Equations]]
+
[[Category:Quadratic Equations]]

Latest revision as of 14:30, 19 December 2020

ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

The Story of Mathematics

Philosophy of Mathematics

Teaching of Mathematics

Curriculum and Syllabus

Topics in School Mathematics

Textbooks

Question Bank

While creating a resource page, please click here for a resource creation checklist.

Concept Map

[maximize]


Textbook

Please click here for Karnataka and other text books.

  1. Karnataka text book for Class 10, Chapter 09 - Quadratic Equations
  2. cbse text book

Additional Information

Useful websites

For more information about quadratic equation

Reference Books

relevent references

Resources

Resource Title

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 where a ≠ 0 and a, b, c belongs to R.

Learning objectives

converting verbal statement into equations.

Notes for teachers

  1. Basic knowledge of equations, linear equations,general form of linear equation, finding the rooots of equation, graphical representation of linear equations.
  2. More importance to be given for signs while transforming the equations.

Activities

  1. Activity No 1 Introduction to quadratic equation
  2. Activity No 2 Making a rectangular garden
  3. Activity No 3 Understanding geometrically

Concept #2 - Types of equations

Pure Quadratic Equation & Adfected Quadratic Equation

Quadratic equation,in the form , is termed as quadratic expression and the equation of the form , 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

  1. To distinguish between pure & adfected equations among the given equations.
  2. Standard forms of pure & adfected quadratic equations.

Notes for teachers

  1. Knowledge of general form of quadratic equations
  2. roots of equation
  3. proper use of signs.

Activities

Identifying pure and adfected ouadratic equations- Activity No1

work sheet Activity No2

Concept #3 What is the solution of a quadratic equation

The roots of the Quadratic Equation which satisfy the equation

Learning objectives

  1. x=k is a solution of the quadratic equation if k satisfies the quadratic equation
  2. Any quadratic equation has at most two roots.
  3. The roots form the solution set of quadratic equation.

Notes for teachers

  1. different methods of solving quadratic equation
  2. knowledge of suitable formula to be used to solve specific problem.
  3. identify the type of quadratic equation.

Activities

  1. Activity No #1 #Activity No 3-quadratic formula
  2. Activity No #2 Concept Name - Activity No

Concept #4Methods of solution

Different methods of finding the solution to a quadratic equation

  1. Factorisation method
  2. Completing the square method
  3. Formula method
  4. Graphical method.

Learning objectives

  1. Solving quadratic equation by factorisation method
  2. Solving quadratic equation by completing the square method
  3. Deriving formula to find the roots of quadratic equation.
  4. Solving quadratic equation by using formula.
  5. Solving quadratic equation graphically.
  6. To find the sum and product of the roots of the quadratic equations.

Notes for teachers

  • Students need to know factorisation
  • substitution of values and simplification
  • Identifying suitable method

Activities

  1. Activity No 1 -geogebra
  2. Activity No 2-learn more how to solve Q.E
  3. Activity 3-learn quadratics
  4. Activity 4- Quadratic Equation solution

Concept #5Nature 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

  1. To find the discriminant & interpret the nature of the roots of the given quadratic equation.

Notes for teachers

Guiding in Identifying the nature based on the value of discriminant

Activities

  1. Activity No #1 Concept Name - Activity No.the nature of roots/ interpret the nature of the roots
  1. Activity No #2 Concept Name - Activity No.

Concept #6applications

Solving problems based on quadratic equations.

Learning objectives

By applying the methods of solving quadratic equations, finding the solutions to real life situations.

Notes for teachers

Help the students in Identifying parameters and suitable methods for solving application problems.

Activities

  1. Activity No #1 more word problems
  2. Activity 2:quadratics in real life

Assessment activities for CCE

.quiz

Hints for difficult problems

1.If P & q are the roots of the equation find the value of
solution
2.The altitude of a triangle is 6cm greter than its base. If its area is 108cmsq .Find its base.
solution
3.Solve By completing the square.
solution