FabuMaths
  • 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

Check list:

  1. The concept of a function, where a certain quantity (output value) uniquely depends on another quantity (input value). Work with relationships between variables using tables, graphs, words and formulae. Convert flexibly between these representations. Note that the graph defined by \(y=x\) should be known from Grade 9.
  2. Point by point plotting of basic graphs defined by \(y=x^2\), \(y = \frac{1}{x}\) and \(y=b^x\), \(b>0\), \(b \ne 1\) to discover shape, domain (input values), range (output values), asymptotes, axes of symmetry, turning points and intercepts on the axes (where applicable).
  3. Investigate the effect of \(a\) and \(q\) on the graphs defined by \(y=a.f(x)+q\), where \(f(x)=x\), \(f(x)=x^2\), \(f(x)=\frac{1}{x}\) and \(f(x)=b^x\), \(b>0\), \(b \ne 1\).
  4. Point by point plotting of basic graphs defined by \(y = \sin \theta \), \(y=\cos\theta\) and \(y=\tan\theta\) for \(\theta  \in \left[ {{0^o};{{360}^o}} \right]\).
  5. Study the effect of \(a\) and \(q\) on the graphs defined by \(y=a\sin\theta+q\), \(y=a\cos\theta+q\); and \(y=a\tan\theta+q\) where \(a\), \(q \in \mathbb{Q}\) for \(\theta  \in \left[ {{0^o};{{360}^o}} \right]\).
  6. Sketch graphs, find the equations of given graphs and interpret graphs. Note: Sketching of the graphs must be based on the observation of number 3 and 5.

Learn the concepts:

Hello there Grade 10s. There is a part of me that is dreading this section. There is just so much content to cover and a small amount of time to get it done in. By the end of this section, you are going to be so sick of plotting functions! Plotting functions is a really important skill and when you master it, you will find the other, more complicated questions, far easier.

Grade 10s, you will work hard in this section. Make sure you are getting enough sleep and don't fall behind on your daily work!

Algebraic Functions:

Introduction to Functions

Videos from learn.mindset.co.za
Mind Action Series: Mathematics 10 Textbook & Workbook (2011)
Exercise 1 Page 126
Relevant sections in Everything Maths:
  • Functions in the real world
Still want to learn more? Try these links:
  • This website explains the concept of a function and the concepts domain and range of a function in the simplest possible way.

The Linear Function

Videos from learn.mindset.co.za
Mind Action Series: Mathematics 10 Textbook & Workbook (2011)
Exercise 2 Page 130 
Exercise 3 Page 134 
Exercise 4 Page 137 
Exercise 5 Page 139 
Exercise 6 Page 140 
Exercise 7 Page 141
Relevant sections in Everything Maths:
  • Linear functions
Still want to learn more? Try these links:
  • Step by step instructions on plotting linear functions.

The Quadratic Function

Mind Action Series: Mathematics 10 Textbook & Workbook (2011)
Exercise 8 Page 145 
Exercise 9 Page 147 
Exercise 10 Page 150 
Exercise 11 Page 151
Relevant sections in Everything Maths:
  • Quadratic functions
Still want to learn more? Try these links:
  • Step by step instructions on plotting quadratic functions.
Videos from learn.mindset.co.za

The Hyperbolic Function

Mind Action Series: Mathematics 10 Textbook & Workbook (2011)
Exercise 12 Page 156 
Exercise 13 Page 160 
Exercise 14 Page 162
Relevant sections in Everything Maths:
  • Hyperbolic functions
Videos from learn.mindset.co.za

The Exponential Function

Mind Action Series: Mathematics 10 Textbook & Workbook (2011)
Exercise 15 Page 165 
Exercise 16 Page 169 
Exercise 17 Page 172 
Exercise 18 Page 174
Relevant sections in Everything Maths:
  • Exponential functions
Still want to learn more? Try these links:
  • Step by step instructions on plotting exponential functions.
  • A note on the parent function of an exponential function.
Videos from learn.mindset.co.za

Interpreting Functions:

Videos from learn.mindset.co.za
Mind Action Series: Mathematics 10 Textbook & Workbook (2011)
Exercise 19 Page 175
Relevant sections in Everything Maths:
  • Interpretation of graphs

Practice the concepts:

Download the note.
Download the note.
Download the note.
Videos from learn.mindset.co.za
Mind Action Series: Mathematics 10 Textbook & Workbook (2011)
Mixed Revision Exercise Page 176 
Some Challenges Page 180
Relevant sections in Everything Maths:
  • Chapter 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