Difference between revisions of "Quadratic Equations"
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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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− | = 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=== | ||
+ | |||
+ | [https://in.ixl.com/search?q=quadratic+equation/ For more information about quadratic equation] | ||
+ | |||
+ | ===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 | + | #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 | + | #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 | + | #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== | + | ==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'''== | ||
+ | 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=== | |
− | + | #Activity No #1 [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] | ||
=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 | |
− | = | + | <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]] |
Latest revision as of 14:30, 19 December 2020
Philosophy of Mathematics |
While creating a resource page, please click here for a resource creation checklist.
Concept Map
Textbook
Please click here for Karnataka and other text books.
Additional Information
Useful websites
For more information about quadratic equation
Reference Books
Resources
Resource Title
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
- Basic knowledge of equations, linear equations,general form of linear equation, finding the rooots of equation, graphical representation of linear equations.
- More importance to be given for signs while transforming the equations.
Activities
- Activity No 1 Introduction to quadratic equation
- Activity No 2 Making a rectangular garden
- 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
- 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
- roots of equation
- proper use of signs.
Activities
Identifying pure and adfected ouadratic equations- Activity No1
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 #Activity No 3-quadratic formula
- 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.
- Solving quadratic equation graphically.
- 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
- Activity No 1 -geogebra
- Activity No 2-learn more how to solve Q.E
- Activity 3-learn quadratics
- 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
- 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
- Activity No #1 Concept Name - Activity No.the nature of roots/ interpret the nature of the roots
- 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
- Activity No #1 more word problems
- 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