Quadratic Equations

From Karnataka Open Educational Resources

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Concept Map

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Textbook

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

Additional Information

Useful websites

click here

  • [1]
  • wikipedia link for quadratic equation [2]

Reference Books

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 [[Quadratic_equations_introduction_to_quadratic_equation_activity 3| Understanding Failed to parse (syntax error): {\displaystyle ax^2+bx+c=0,/math> geometrically]] ==Concept #2 - Types of equations== ===Pure Quadratic Equation & Adfected Quadratic Equation=== ===Learning objectives=== #To distinguish between pure & adfected equations among the given equations. #Standard forms of pure & adfected quadratic equations. ===Notes for teachers=== #Knowledge of general form of quadratic equations<br> #roots of equation<br> #proper use of signs. ===Activities=== #Activity No #1 '''[[Identifying pure and adfected ouadratic equations- Activity No1]]''' #Activity No #2 '''[[http://in.ask.com/youtube?q=quadratic+equations+class+10&v=ViblRRhFamA&qsrc=472%7C]] ==Concept #3 What is the solution of a quadratic equation== The roots of the Quadratic Equation which satisfy the equation ===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=== #different methods of solving quadratic equation #knowledge of suitable formula to be used to solve specific problem. #identify the type of quadratic equation. ===Activities=== #Activity No #1 '''Concept Name - Activity No.'''[http://in.ask.com/youtube?q=quadratic+equations+class+10&v=ViblRRhFamA&qsrc=472| solution to Q.E] #Activity No #2 '''Concept Name - Activity No.'''[[Quadratic_equations_introduction_to_quadratic_equation_activity_1|Quadratic_equations_introduction_to_quadratic_equation_activity_1]] [['''PROBLEM SOLVING ABILITY''']] ==Estimated Time==20 Minutes ==Materials/ Resources needed== paper and pen<br> ==Prerequisites/Instructions, if any==knowledge of formulas related to the topic.<br> ==ie,general form of quadratic equation <math>ax^2+bx+c=0<math><br> 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=== #Activity No #1 '''Concept Name - Activity No.''' #Activity No #2 '''Concept Name - Activity No.''' ==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=== #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> [http://en.wikipedia.org/wiki/Quadratic_equation] #Solving quadratic equation graphically.<br>To find the sum and product of the roots of the quadratic equations. [https://www.geogebratube.org/student/m8358] ===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=== #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.projectmaths.ie/students/strand4JC/student-activity-quadratic-formula.pdf| quadratic formula]<br> #Activity 3 [http://www.learnnc.org/lp/pages/2981| learn quadratics] ==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=== #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=== #Activity No #1 '''Concept Name - Activity No.'''[http://interpret the nature of roots/ interpret the nature of the roots] <ggb_applet width="968" height="487" version="4.2" 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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] #Activity No #2 '''Concept Name - Activity No.''' ==Concept #6'''applications'''== 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=== #Activity No #1 '''applications - .''' [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] '''to link back to content page''' =Activity - Name of Activity= ==Estimated Time== ==Materials/ Resources needed== ==Prerequisites/Instructions, if any== ==Multimedia resources== ==Website interactives/ links/ simulations/ Geogebra Applets== ==Process (How to do the activity)== ==Developmental Questions (What discussion questions)== ==Evaluation (Questions for assessment of the child)== ==Question Corner== ==Activity Keywords== '''To link back to the concept page''' [[Topic Page Link]] #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 <math>2a^2-4a+1=0} 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

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.

[3]

  1. Solving quadratic equation graphically. [4]
    To find the sum and product of the roots of the quadratic equations.

[5]

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

  1. Activity 3

learn quadratics

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

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

| interpret the nature of roots]

  1. Activity No #2 Concept Name - Activity No.[6]

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

  1. Activity No #1 applications - .

more word problems

  1. Activity 2:quadratics in real life

to link back to content page

Activity - Name of Activity

Multimedia resources

Website interactives/ links/ simulations/ Geogebra Applets

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

Developmental Questions (What discussion questions)

Evaluation (Questions for assessment of the child)

Question Corner

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   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

Project Ideas

quiz

Math Fun

play with Q.E
fun with Q.E [7]

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