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Via Afrika
Mathematics
Grade 10 Study Guide

M. Pillay, L.J. Schalekamp, G. du Toit, C.R. Smith, L. Bruce, M.L. Botsane,
J. Bouman, N.S. Muthige, S.F. Carletti

,Authors • Authors • Authors • Authors

S tu d y G u i d e

Mathematics
Grade 10

,Contents
Introduction to Mathematics.......................................................................................5

Chapter 1 Algebraic expressions�� 6
Overview��6
Unit 1 The number system��7
Unit 2 Multiplying algebraic expressions��8
Unit 3 Factorisation��10
Unit 4 Algebraic fractions��13
Questions��15

Chapter 2 Exponents�� 16
Overview��16
Unit 1 Laws of exponents��17
Unit 2 Simplifying exponents��18
Unit 3 Solving equations that contain exponents��20
Questions��23

Chapter 3 Number patterns�� 24
Overview��24
Unit 1 Linear number patterns��25
Unit 2 More complicated linear number patterns��27
Questions��29

Chapter 4 Equations and inequalities�� 30
Overview��30
Unit 1 Linear equations��31
Unit 2 Quadratic equations��34
Unit 3 Literal equations��35
Unit 4 Simultaneous equations��37
Unit 5 Linear inequalities��38
Questions��40

Chapter 5 Trigonometry�� 41
Overview��41
Unit 1 Right-angled triangles��42
Unit 2 Definitions of the trigonometric ratios��43

, Unit 3 Special triangles��44
Unit 4 Using your calculator��45
Unit 5 Solving trigonometric equations��46
Unit 6 Extending the ratios to 0° ≤ θ ≤ 360°��48
Unit 7 Graphs of the trigonometric functions��53
Questions��55

Chapter 6 Functions�� 57
Overview��57
Unit 1 What is a function?��58
Unit 2 Graphs of functions��60
Unit 3 The graph of y = ax2 + q ��63
Unit 4 The graph of y =  __ax + q��64
Unit 5 The graph of y = abx + q, b > 0 and b ≠ 1��66
Unit 6 Sketching graphs��68
Unit 7 Finding the equations of graphs��71
Unit 8 The effect of a and q on trigonometric graphs��72
Questions��74

Chapter 7 Polygons�� 75
Overview��75
Unit 1 Similar triangles��76
Unit 2 Congruent triangles��78
Unit 3 Quadrilaterals��80
Questions��83

Chapter 8 Analytical geometry�� 84
Overview��84
Unit 1 The distance formula��85
Unit 2 The gradient formula��86
Unit 3 The midpoint formula��88
Questions��89

Chapter 9 Finance, growth and decay�� 91
Overview��91
Unit 1 Simple interest��92
Unit 2 Compound growth��94
Questions��97

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Schooljaar: 200
Uploaded on: April 4, 2023
Number of pages: 168
Written in: 2022/2023
Type: Exam (elaborations)
Contains: Answers

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