Quadratic Equations

 ಕನ್ನಡದಲ್ಲಿ ನೋಡಿ

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

= Concept Map = Flash

= Textbook = Please click here for Karnataka and other text books.
 * 1) Karnataka text book for Class 10, Chapter 09 - Quadratic Equations

=Additional Information=

Useful websites
click here
 * 
 * wikipedia link for quadratic equation

Reference Books
= Teaching Outlines =

Concept #1 - Introduction to quadratic equations
An equation of the form $$ax^2+bx+c = 0$$ 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 ax^2+bx+c=0 geometrically

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

 * 1) Activity No #1 Identifying pure and adfected ouadratic equations- Activity No1


 * 1) Activity No #2 '''[]

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
PROBLEM SOLVING ABILITY
 * 1) Activity No #1 Concept Name - Activity No.| solution to Q.E
 * 2) Activity No #2 Concept Name - Activity No.Quadratic_equations_introduction_to_quadratic_equation_activity_1

Estimated Time
20 Minutes

Materials/ Resources needed
paper and pen

Prerequisites/Instructions, if any
knowledge of formulas related to the topic. ==ie,general form of quadratic equation ax^2+bx+c=0 roots of the equation ax^2+bx+c=0 is x=+}

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.

Activities

 * 1) Activity No #1 Concept Name - Activity No.
 * 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.
 * 1) Solving quadratic equation graphically. To find the sum and product of the roots of the quadratic equations.

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.

Activities

 * 1) Activity No 1 | geogebra


 * 1) Activity No 2

| quadratic formula |     learn quadratics
 * 1) Activity 3

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
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.

Activities
<ggb_applet width="968" height="487" version="4.2" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="true" showToolBar="true" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />| interpret the nature of roots]
 * 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
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.

Activities
| more word problems to link back to content page
 * 1) Activity No #1 applications - .
 * 1) Activity 2:| quadratics in real life

=Activity - Name of Activity=

Activity Keywords
To link back to the concept page Topic Page Link
 * 1) Activity No #2 Concept Name - Activity No.

=Assessment activities for CCE=

=Hints for difficult problems = 1.If P & q are the roots of the equation $$2a^2-4a+1=0$$ find the value of $$p^3+q^3$$ solution 2.The altitude of a triangle is 6cm greter than its base. If its area is 108cmsq .Find its base. solution 3.Solve $$x^2-4x-8=0$$ By completing the square. solution

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.
 * 1) Solving quadratic equation graphically. To find the sum and product of the roots of the quadratic equations.

Notes for teachers

 * 1) guide the students in using suitable method of solution.
 * 2) instruct the students to reduce the given equation to standard form.

Activities

 * 1) Activity No 1 | geogebra


 * 1) Activity No 2

| quadratic formula |     learn quadratics
 * 1) Activity 3

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
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.

Activities
<ggb_applet width="968" height="487" version="4.2" ggbBase64="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" enableRightClick="false" showAlgebraInput="false" enableShiftDragZoom="true" showMenuBar="true" showToolBar="true" showToolBarHelp="true" enableLabelDrags="false" showResetIcon="true" />| interpret the nature of roots]
 * 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
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.

Activities
| more word problems to link back to content page
 * 1) Activity No #1 applications - .
 * 1) Activity 2:| quadratics in real life

=Activity - Name of Activity=

Process (How to do the activity)
students are given some gradation problems, and asked to solve using appropriate method.

Activity Keywords
To link back to the concept page Topic Page Link
 * 1) Activity No #2 Concept Name - Activity No.

=Assessment activities for CCE=

=Hints for difficult problems = 1.If P & q are the roots of the equation $$2a^2-4a+1=0$$ find the value of $$p^3+q^3$$ solution 2.The altitude of a triangle is 6cm greter than its base. If its area is 108cmsq .Find its base. solution 3.Solve $$x^2-4x-8=0$$ By completing the square. solution

= Project Ideas = | quiz

= Math Fun = | play with Q.E | fun with Q.E