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Maths Grade 12 Learner Support STEP Ahead 2021


Mathematics (University of Johannesburg)




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CURRICULUM GRADE 10 -12 DIRECTORATE




NCS (CAPS)


TEACHER SUPPORT DOCUMENT


GRADE 12


MATHEMATICS
STEP AHEAD PROGRAMME


2021




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PREFACE
This support document serves to assist Mathematics learners on how to deal with curriculum gaps and learning
losses as a result of the impact of COVID-19 in 2020. It also captures the challenging topics in the Grade 10
-12 work. Activities should serve as a guide on how various topics are assessed at different cognitive levels
and also preparing learners for informal and formal tasks in Mathematics. It will cover the following topics:

Table of contents

3 – 25
1. FUNCTIONS
26 – 45
2. FINANCE
45 – 74
3. STATISTICS
75 – 100
4. PROBABILITY
100 – 137
5 TRIGONOMETRY
138 – 145
6. ANSWERS TO ALL ACTIVITIES




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1. FUNCTIONS

TOPIC: Revision of grade 11 functions ( Lesson 1)
RELATED CONCEPTS/ TERMS/VOCABULARY

Function – A relationship for which each element of the domain (𝑥) corresponds to exactly one
element of the range(𝑦). For every 𝑥- value there is only one possible 𝑦-value.
 Increasing function - A function that is going upwards when looking at it from left to right.
 Decreasing function – A function that is going ‘downwards when looking at it from left to right. N.B
if a function has a turning point, this is the point at which a function could change from decreasing
to increasing
 Horizontal shift – A translation of the graph either to the left or the right
 Vertical shift – A translation of the graph either up or down
 Average gradient – The gradient between two points on a curved graph.
 Domain – All the possible 𝑥 values that are covered by the function/ graph (to find the domain
always study the graph from left to right)
 Range – All the possible 𝑦 values that are covered by the function/ graph ( to find the range always
study the graph from bottom to top)
 𝑥- intercept- Where a function cuts the 𝑥- axis
 𝑦- intercept- where a function cuts the 𝑦- axis
 Axis of symmetry – A line that cuts the function exactly in half
 A parabola has a vertical line of symmetry (𝑥 =…..)
 A hyperbola has 2 axes of symmetry which form a cross͢͢͢͢. These are in the
form
𝑦 = 𝑚𝑥 + 𝑐
 An exponential graph does not have an axis of symmetry
 Asymptote – A straight line that a curved graph gets closer to but never touches
 Turning point – the point at which a function (parabola, sin or cos graph) changes from increasing to
decreasing or from decreasing
 Maximum – The highest the graph can be and is always the 𝑦-value of the turning point
 Minimum – The lowest the graph can be and is always the 𝑦-value of the turning point. N.B Min
and Max only involves functions that have a turning point.
RESOURCES
 Grade 11 Textbooks
NOTES
𝑎
In Grade 10 we discussed hyperbolic function of the form 𝑦 = + 𝑞. We will now focus on hyperbolic
𝑥
𝑎
functions of the form 𝑦 = + 𝑞 where 𝑥 + 𝑝 ≠ 0
𝑥+𝑝

Consider the example:
2
Given 𝑓(𝑥) = +1
𝑥−2
2
It is clear that from the revision of Grade 10 hyperbolas that the graph of 𝑦 = + 1 has a horizontal
𝑥−2

asymptote at y = 1.
It is also the case that 𝑥 − 2 ≠ 0, i.e. 𝑥 ≠ 2 because then the denominator will be zero and the expression
2
𝑥−2
would be undefined.




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