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    • Grade 10 >
      • Grade 10 Answers
      • Algebraic Expressions
      • Algebraic Functions
      • Analytical Geometry
      • Exponents
      • Equations and Inequalities
      • Euclidean Geometry
      • Finance and Growth
      • Numbers and Patterns
      • Measurement
      • Probability
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      • Trigonometry
      • Trigonometric Functions
    • Grade 11 >
      • Grade 11 Answers
      • Algebraic Functions
      • Analytical Geometry
      • Equations and Inequalities
      • Exponents and Surds
      • Euclidean Geometry
      • Finance, Growth and Decay
      • Measurement
      • Numbers and Patterns
      • Probability
      • Statistics
      • Trigonometry
      • Trig Functions
    • Grade 12 >
      • Grade 12 Answers
      • Analytical Geometry
      • Calculus
      • Euclidean Geometry
      • Finance, Growth and Decay
      • Functions
      • Functions: Exponential and Logarithmic
      • Functions: Polynomials
      • Patterns, Sequences and Series
      • Probability
      • Statistics
      • Trigonometry

Check list:

  1. Revise the effect of the parameters \(a\) and \(q\) and investigate the effect of \(p\) on the graphs of the functions defined by: 
    1.1.  \(y = f\left( x \right) = a{\left( {x + p} \right)^2} + q\)
    1.2.  \(y = f\left( x \right) = \frac{a}{{x + p}} + q\)
    1.3.  \(y = f\left( x \right) = a{b^{x + p}} + q\) where \(b > 0\,,\quad b \ne 1\).
  2. Investigate numerically the average gradient between two points on a curve and develop an intuitive understanding of the concept of the gradient of a curve at a point.
  3. Investigate the effect of the parameter \(k\) on the graphs of the functions defined by \(y = \sin \left( {kx} \right)\), \(y = \cos \left( {kx} \right)\) and \(y = \tan \left( {kx} \right)\).
  4. Investigate the effect of the parameter \(p\) on the graphs of the functions defined by \(y = \sin \left( {x + p} \right)\), \(y = \cos \left( {x + p} \right)\) and \(y = \tan \left( {x + p} \right)\).
  5. Draw sketch graphs defined by:
    \(y = a\sin k\left( {x + p} \right)\) 
    \(y = a\cos k\left( {x + p} \right)\) and
    \(y = a\tan k\left( {x + p} \right)\) at most two parameters at a time.

Learn the concepts:

Well, Grade 11s, we're finally at the last section for this term and it's a big one. I really like functions. Like conventional algebra (solving equations, factorising, etc) it's easy to do when you know the steps. In other words, you can get full marks for this section IF you practice, and practice, and practice. Work hard in these next 4 weeks!

Algebraic Functions:

Recapping Grade 10 Algebraic Functions

Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Mixed Revision Exercise from Grade 10 textbook
Exercise 1 Page 87 
Still want to learn more? Try these links:
  • This website has various examples to help learners understand by the word function.
  • YouTube video explaining functions, input and output with an example.
  • A resource for teachers who want to brush up on their personal knowledge regarding functions.
Videos from learn.mindset.co.za

The Quadratic Function    \(y = a{\left( {x + p} \right)^2} + q\)

Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 2 Page 94 
Exercise 3 Page 98 
Relevant sections in Everything Maths:
  • Quadratic functions
  • Average gradient
Still want to learn more? Try these links:
  • How to draw a parabola using basic knowledge.
  • A good resource, as one can generate multiple questions on an applet for finding the equation of parabola graphs.

The Hyperbolic Function    \(y = f\left( x \right) = \frac{a}{{x + p}} + q\)

Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:
  • Hyperbolic functions
Still want to learn more? Try these links:
  • Learning Channel PDF note on the parabola and hyperbola.

The Exponential Function    \(y = f\left( x \right) = a{b^{x + p}} + q\)  where  \(b > 0\,,\quad b \ne 1\)

Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:
  • Exponential functions
Still want to learn more? Try these links:
  • An introductory resource that explores the different shapes of the exponential graph by investigating the variables in the equation.
  • A resource that is in a simple format that can be used with the learners for them to further understand the exponential function. 
  • A resource that provides a step by step tutorial on sketching the exponential graph. 
  • Find the equation of exponential graphs

Mixed Algebraic Functions

Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:
  • Average gradient
Still want to learn more? Try these links:
  • Various transformation are explored and investigated in this online note.
  • This shows the transformation graphs by colour coding each function.
  • This resource can be used to revise the concept of gradient before moving onto gradient between two points. 

Trigonometric Functions:

Recapping Grade 10 Trigonometric Functions

Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Videos from learn.mindset.co.za

The Sine Function    \(y = a\sin k\left( {x + p} \right)\)

Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:
  • The sine function

The Cosine Function    \(y = a\cos k\left( {x + p} \right)\)

Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:
  • The cosine function

The Tangent Function    \(y = a\tan k\left( {x + p} \right)\)     

Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:
  • The tangent function

Practice the concepts:

Check out that sexy teacher!
Download the note.
Download the note.
Download the note.
Download the note.
Download the note.
Download the note.
Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:
  • Summary
  • End of chapter exercises
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  • High School
    • Grade 10 >
      • Grade 10 Answers
      • Algebraic Expressions
      • Algebraic Functions
      • Analytical Geometry
      • Exponents
      • Equations and Inequalities
      • Euclidean Geometry
      • Finance and Growth
      • Numbers and Patterns
      • Measurement
      • Probability
      • Statistics
      • Trigonometry
      • Trigonometric Functions
    • Grade 11 >
      • Grade 11 Answers
      • Algebraic Functions
      • Analytical Geometry
      • Equations and Inequalities
      • Exponents and Surds
      • Euclidean Geometry
      • Finance, Growth and Decay
      • Measurement
      • Numbers and Patterns
      • Probability
      • Statistics
      • Trigonometry
      • Trig Functions
    • Grade 12 >
      • Grade 12 Answers
      • Analytical Geometry
      • Calculus
      • Euclidean Geometry
      • Finance, Growth and Decay
      • Functions
      • Functions: Exponential and Logarithmic
      • Functions: Polynomials
      • Patterns, Sequences and Series
      • Probability
      • Statistics
      • Trigonometry