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Summary Maths Grade 12 Final Revision (Paper 1 & 2)
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Summary of 39 pages for the course Maths at 12th Grade
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Matric RevisionGetting a different perspective
on Mathematics exams
Prepared and presented
by Sarel van Greunen
©Sarel van Greunen All Rights Reserved.
, -2-
Table of Contents
Functions, relations and inverses ...................................................................................................... 3
Sequences and Series ....................................................................................................................... 6
Differentiation ................................................................................................................................. 7
Exponents ........................................................................................................................................ 9
Logarithms ..................................................................................................................................... 10
Financial Mathematics ................................................................................................................... 11
Trigonometry ................................................................................................................................. 13
Euclidean Geometry ....................................................................................................................... 15
Analytical Geometry ....................................................................................................................... 21
Statistics and linear regression ....................................................................................................... 23
Exercises
Functions, relations and inverses - Questions.................................................................................. 25
Sequences and series - Questions ................................................................................................... 27
Differentiation - Questions ............................................................................................................. 29
Exponents and logarithms - Questions ............................................................................................ 31
Financial Mathematics - Questions ................................................................................................. 31
Trigonometry - Questions ............................................................................................................... 32
Euclidean Geometry – Questions .................................................................................................... 33
Analytical Geometry - Questions .................................................................................................... 36
Statistics - Questions ...................................................................................................................... 39
©Sarel van Greunen
All rights reserved. No part of this publication may be reproduced, distributed, or transmitted in any form or
by any means, including photocopying, recording, or other electronic or mechanical methods, without the
prior written permission of the publisher, except in the case of brief quotations embodied in critical reviews
and certain other noncommercial uses permitted by copyright law.
©Sarel van Greunen English Summer School Sep 2017 All rights reserved
, -3-
Functions, relations and inverses
Definition: A relation is when a variable gets related to another variable by use of any formulae or
equation, ie x gets related to y. How y reacts to x gives us the different graphs.
A function is a special relation for which each x only has one y. The moment that that is
not the case, we have a non-function.
There are 9 different graphs you have to be able to analyse, interpret and sketch:
• Straight line
• Parabola
• Cubic
• Hyperbola
• Exponential
• Logarithmic
• Sine
• Cosine
• Tangent
There are certain questions, which you must be able to answer for all 9 graphs:
1. 𝒙-intercept:
o Let 𝑦 = 0.
2. y-intercept:
o Let 𝑥 = 0.
3. Definition/Domain:
o All 𝑥-values for which the function is defined.
4. Rang
o All y-values for which the function is defined.
5. Intersection between graphs:
o Set the y-values equal to each other or
o Use substitution to solve simultaneously.
6. Inverse relations:
o An inverse function is a reflection of a graph over the line 𝑦 = 𝑥.
o Determining the equation of an inverse: Swop the 𝑥 and y’s around in your equation,
then, preferrably, you make y the subject.
o Sketching an inverse: Take the original graph’s coordinates and swop the 𝑥 and y values
around and draw the sketch.
o REMEMBER: Domain of original is Range of inverse and Range of original is Domain of
the inverse.
©Sarel van Greunen English Summer School Sep 2017 All rights reserved
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