Transcription of Via Afrika Maths Study Guide Gr10
1 Authors Authors Authors Authors St udy Guide MathematicsGrade 10 Via Afrika Maths Study Guide Gr10 116/01/2012 12:43 ContentsIntroduction 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
2 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
3 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 Via Afrika Maths Study Guide Gr10 216/01/2012 12.
4 43 Unit 3 Special triangles 44 Unit 4 Using your calculator 45 Unit 5 Solving trigonometric equations 46 Unit 6 Extending the ratios to 0 360 48 Unit 7 Graphs of the trigonometric functions 53 Questions 55 Chapter 6 Functions 57 Overview 57 Unit 1 What is a function?
5 58 Unit 2 Graphs of functions 60 Unit 3 The graph of y = ax2 + q 63 Unit 4 The graph of y = a __ x + 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
6 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.
7 Growth and decay 91 Overview 91 Unit 1 Simple interest 92 Unit 2 Compound growth 94 Questions 97 Via Afrika Maths Study Guide Gr10 316/01/2012 12:43 Chapter 10 Statistics 98 Overview 98 Unit 1 Measures of central tendency.
8 Ungrouped data 99 Unit 2 Measures of dispersion 101 Unit 3 Box-and-whisker plot 103 Unit 4 Grouped data 104 Questions 107 Chapter 11 Measurement 110 Overview 110 Units 1 and 2 Right prisms and cylinders 111 Unit 3 The volume and surface area of complex-shaped solids 113 Questions 116 Chapter 12 Probability 117 Overview 117 Unit 1 Probability 118 Unit 2 Combination of events 120 Questions
9 122 Exam Papers ..123 Answers to questions ..133 Answers to exam papers ..152 Glossary ..162 Via Afrika Maths Study Guide Gr10 416/01/2012 12:43 Via Afrika Mathematics5 Introduction to mathematics There once was a magnificent mathematical horse. You could teach it arithmetic, which it learned with no difficulty, and algebra was a breeze. It could even prove theorems in Euclidean geometry. But when it tried to learn analytic geometry, it would rear back on its hind legs, and make violent head motions in resistance. The moral of this story is that you can t put Descartes before the horse. If you have a Study routine that you are happy with and you are getting the grade you want from your mathematics class you might benefit from comparing your Study habits to the tips presented is Not a Spectator SportIn order to learn mathematics you must be actively involved in the doing and feeling of mathematics .
10 Work to Understand the Principles LISTEN During Class. No the Study Guide is not enough. In order to get something out of the class you need to listen while in class. Sometimes important ideas will not be written down, but instead be spoken by the teacher. Learn the (proper) Notation. Bad notation can jeopardise your results. Pay attention to them in the worked examples in this Study Guide , Practise, Practise, Practise. Practise as much as possible. The only way to really learn how to do problems is work through lots of them. The more you work, the better prepared you will be come exam time. There are extra practise opportunities in this Study Guide . Persevere. You might not instantly understand every topic covered in a mathematics class. There might be some topics that you will have to work at before you completely understand them.
