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Quadratic Equations (view source)

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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Mathematics:_History The Story of Mathematics]
 
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[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]
 
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[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]
 
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[http://www.karnatakaeducation.org.in/KOER/en/index.php/Maths:_Question_Papers Question Bank]
 
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= Concept Map =
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== Concept Map ==
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<mm>[[Quadratic_Equations.mm|Flash]]</mm>
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[[File:Quadratic_Equations.mm|Flash]]
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__FORCETOC__
 
__FORCETOC__
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= Textbook =
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== Textbook ==
 
Please click here for Karnataka and other text books.
 
Please click here for Karnataka and other text books.
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#[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]
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#[http://nimsdxb.com/wp-content/uploads/Unit-4_Quadratic_Equations_Core.pdf/ cbse text book]
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==Additional Information==
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{{#widget:Iframe |url=http://www.slideshare.net/slideshow/embed_code/10549763|width=450 |height=360 |border=1 }}
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=Additional Information=
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===Useful websites===
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==Useful websites==
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==Reference Books==
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= Teaching Outlines =
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[https://in.ixl.com/search?q=quadratic+equation/ For more information about quadratic equation]
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===Reference Books===
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[[Text_Books| relevent references]]
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=== Resources ===
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==== Resource Title ====
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[http://www.mathopenref.com/quadraticexplorer.html Quadratic Function Explorer]
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==== Description ====
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This interactive activity helps you realize the action of the three coefficients a, b, c in a quadratic equation.
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 +
== Teaching Outlines ==
    
==Concept #1 - Introduction to quadratic equations==
 
==Concept #1 - Introduction to quadratic equations==
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An equation of the form  ax^2+bx+c = 0 where a ≠ 0 and a, b, c belongs to R.
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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===
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===Notes for teachers===
 
===Notes for teachers===
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#Basic knowledge of equations, linear equations,general form of linear equation, finding the rooots of equation, graphical representation of linear equations.<br>
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''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.''
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#More importance to be given for signs while transforming the equations.
    
===Activities===
 
===Activities===
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#Activity No #1 '''introduction to quadratic equation '''
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#Activity No 1 '''[[Quadratic_equations_introduction_to_quadratic_equation_activity_1|Introduction to quadratic equation]]'''
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Please use this link:
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#Activity No 2 '''[[Quadratic_equations_introduction_to_quadratic_equation_actvity 2| Making a rectangular garden]]'''
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http://www.youtube.com/watch?v=NbmVOVal3qA
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#Activity No 3 '''[[Quadratic_equations_introduction_to_quadratic_equation_activity 3| Understanding<math> ax^2+bx+c=0</math> geometrically]]'''
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----
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#Activity No #2 '''Concept Name - Activity No.'''
      
==Concept #2 - Types of equations==
 
==Concept #2 - Types of equations==
 
===Pure Quadratic Equation & Adfected Quadratic Equation===
 
===Pure Quadratic Equation & Adfected Quadratic Equation===
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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.
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===Learning objectives===
 
===Learning objectives===
 
#To distinguish between pure & adfected equations among the given equations.
 
#To distinguish between pure & adfected equations among the given equations.
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===Notes for teachers===
 
===Notes for teachers===
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''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.''
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#Knowledge of general form of quadratic equations<br>
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#roots of equation<br>
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#proper use of signs.
    
===Activities===
 
===Activities===
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#Activity No #1 '''Concept Name - Activity No.'''
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'''[[Identifying pure and adfected ouadratic equations- Activity No1]]'''
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#Activity No #2 '''Concept Name - Activity No.'''
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'''[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==  
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===Notes for teachers===
 
===Notes for teachers===
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''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.''
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#different methods of solving quadratic equation
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#knowledge of suitable formula to be used to solve specific problem.
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===Activities===
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#identify the type of quadratic equation.
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#Activity No #1 '''Concept Name - Activity No.'''
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#Activity No #2 '''Concept Name - Activity No.'''
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===Notes for teachers===
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''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===
 
===Activities===
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#Activity No #1 '''Concept Name - Activity No.'''
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#Activity No #1 #Activity No 3-[http://www.projectmaths.ie/students/strand4JC/student-activity-quadratic-formula.pdf| quadratic formula]<br>
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#Activity No #2 '''Concept Name - Activity No.'''
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#Activity No #2 '''Concept Name - Activity No'''
    
==Concept #4Methods of solution==
 
==Concept #4Methods of solution==
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#Solving quadratic equation by completing the square method
 
#Solving quadratic equation by completing the square method
 
#Deriving formula to find the roots of quadratic equation.
 
#Deriving formula to find the roots of quadratic equation.
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#Solving quadratic equation by using formula.
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#Solving quadratic equation by using formula.<br>
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#Solving quadratic equation graphically.
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#Solving quadratic equation graphically.<br>
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#To find the sum and product of the roots of the quadratic equations.
    
===Notes for teachers===
 
===Notes for teachers===
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''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.''
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*Students need to know factorisation
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*substitution of values and simplification
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*Identifying suitable method
    
===Activities===
 
===Activities===
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#Activity No #1 '''Concept Name - Activity No.'''
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#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]       
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<iframe scrolling="no" src="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" width="968px" height="487px" style="border:0px;"> </iframe>
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#Activity No 2-[http://www.wikihow.com/Solve-Quadratic-Equations/ learn more how to solve Q.E]
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#Activity No #2 '''Concept Name - Activity No.'''
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#Activity 3-[http://www.learnnc.org/lp/pages/2981| learn quadratics]
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#Activity 4- [[Quadratic Equation solution activity1|Quadratic Equation solution]]
    
==Concept #5'''Nature of roots'''==
 
==Concept #5'''Nature of roots'''==
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===Notes for teachers===
 
===Notes for teachers===
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''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.''
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Guiding in Identifying the nature based on the value of discriminant
    
===Activities===
 
===Activities===
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#Activity No #1 '''Concept Name - Activity No.'''
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#Activity No #1 '''Concept Name - Activity No.'''[http://interpret the nature of roots/ interpret the nature of the roots]
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<iframe scrolling="no" src="https://www.geogebratube.org/material/iframe/id/30041/width/1936/height/886/border/888888/rc/false/ai/false/sdz/true/smb/true/stb/true/stbh/true/ld/false/sri/true/at/preferhtml5" width="1936px" height="886px" style="border:0px;"> </iframe>
      
#Activity No #2 '''Concept Name - Activity No.'''
 
#Activity No #2 '''Concept Name - Activity No.'''
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===Learning objectives===
 
===Learning objectives===
 
By applying the methods of solving quadratic equations, finding the solutions to real life situations.
 
By applying the methods of solving quadratic equations, finding the solutions to real life situations.
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===Notes for teachers===
 
===Notes for teachers===
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''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.''
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Help the students in Identifying parameters and suitable methods for solving application problems.
    
===Activities===
 
===Activities===
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#Activity No #1 '''applications - .'''
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#Activity No #1 [https://www.youtube.com/watch?v=IGGnn9oa4QYz| more word problems]
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__FORCETOC__
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#Activity 2:[http://www.ehow.com/info_8502727_applications-quadratic-equations.html| quadratics in real life]
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=Activity - Name of Activity=
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==Estimated Time==
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==Materials/ Resources needed==
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==Prerequisites/Instructions, if any==
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==Multimedia resources==
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==Website interactives/ links/ simulations/ Geogebra Applets==
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==Process (How to do the activity)==
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==Developmental Questions (What discussion questions)==
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==Evaluation (Questions for assessment of the child)==
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==Question Corner==
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==Activity Keywords==
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'''To link back to the concept page'''
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[[Topic Page Link]]
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#Activity No #2 '''Concept Name - Activity No.'''
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=Assessment activities for CCE=
 
=Assessment activities for CCE=
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.[Http://Tube.geogebra.org/m/105393c|quadratic quiz]
    
=Hints for difficult problems =
 
=Hints for difficult problems =
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#If P & q are the roots of the equation 2a^-4a+1=0 find the value of
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1.If P & q are the roots of the equation <math>2a^2-4a+1=0</math> find the value of  
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p^3+q^3<br>
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<math>p^3+q^3</math><br>
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Pre requisites:
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[[solution]]<br>
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#Standard form of quadratic equation
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2.The altitude of a triangle is 6cm greter than its base. If its area is 108cmsq .Find its base.<br>
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#Formula to find the sum & product of quadratic equation
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[[solution]]<br>
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#Knowledge of using appropriate identity
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3.Solve <math>x^2-4x-8=0</math> By completing the square. <br>
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Interpretation of the Problem:
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[[solution]]
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#Compare the equation with standard form and identify the values of a,b,c
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#To find the sum of the roots of the quadratic equation using the formula
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#To find the product of the roots of the equation
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# Using the identity & rewriting p^3+q^3 as (p+q)^3-3pq(p+q)
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#Substitute the values of m+n & mn in (p+q)^3-3pq(p+q)
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#Simplification
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Concepts:
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#Formula to find the sum and product of the roots of the quadratic equation
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#Identity (a+b)^3=a^3+b^3+3ab(a+b)
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Algorithm: <br>
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Consider the equation 2a^2-4a+1=0<br>
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Here a=2,b=-4 & c=1<br>
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If p & q are the roots of the quadratic equation then<br>
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p+q=-b/a=-(-4)/2=2<br>
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pq=c/a=1/2<br>
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Therefore,<br>
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p^3+q^3=(p+q)^3-3pq(p+q)<br>
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      =(2)^3-3(1/2)(2)<br>
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      =8-3<br>
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      =5
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=Ex.no.9.11 /problem no.9=
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The altitude of a triangle is 6cm greter than its base. If its area is 108cmsq .Find its base.<br>
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Statement: Solving problem based on quadratic equations.<br>
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*Interpretation  of the problem:<br> * Converting data in to eqn.<br> *Knowledge about area of a triangle.<br>*knowledge of the formula of area of triangle.<br>*Methods of finding the roots of the eqn.<br> *Methods of finding the roots of the
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*Different approches to solve the problem: <br>*Factorisation
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*Using formula
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*using graph
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*Concept used:Forming the eqn. 216=x(x+6)
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216=x2+6x<br>
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x2 +6x -216=0<br>
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Substitution:  x 2 +18x-12x -216=0<br>
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Simplification:  x(x+18)-12(x+18)=0<br>
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(x+18)( x-12)=0<br>
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(x+18)=0 (x-12)=0<br>
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x=-18, x=12<br>.
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# Base=12cm,  <br> Altitude=x+6
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=12+6=18cm.<br>
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'''Prior Knowledge''' -<br>
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*Methods of solving the Eqn<br>
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*Factorisation<br>
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*Using Formula<br>
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*Using Graph<br>
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= Project Ideas =
     −
= Math Fun =
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[[Category:Class 10]]
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[[Category:Quadratic Equations]]
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