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 15 Chapter 2 Exponents 16 Overview
2 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
3 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 12:43 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?
4 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 76 Unit 2 Congruent triangles
5 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 Via Afrika Maths Study Guide Gr10 316/01/2012 12:43 Chapter 10 Statistics 98 Overview 98 Unit 1 Measures of central tendency.
6 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 122 Exam Papers.
7 123 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. Work to Understand the Principles LISTEN During Class. No the Study Guide is not enough.
8 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. Think about these topics and work through problems from this Study Guide . You will often find that, after a little work, a topic that initially baffled you will suddenly make sense. Have the Proper Attitude.
9 Always do the best that you can. The AMA of Mathematics ABILITY is what you re capable of doing. MOTIVATION determines what you do. ATTITUDE determines how well you do is not pure intellectual power that counts, it s commitment. Dana Scott Via Afrika Maths Study Guide Gr10 516/01/2012 12:43 Via Afrika Mathematics6 Chapter1 Algebraic expressionsOverviewIn this unit, we discuss real numbers, which are divided into rational and irrational numbers. Here, you will also learn about surds, and how to round off real numbers. You will also learn how to multiply integers, monomials and binomials by a polynomial. Finally, we discuss factorisation and how to work with algebraic 1 Page 6 Algebraic expressions Real numbers Surds Rounding offUNIT 1 Page 7 The number system Multiply integers and monomials by polynomials The product of two binomials Multiplying a binomial by a trinomial The sum and difference of two cubesUNIT 2 Page 8 Multiplying algebraic expressions Common factors Difference between two squares Perfect squares Trinomials of the form x2 + bx + c Trinomials of the form ax2 + bx + c Factorising by grouping Factorising the sum and difference of cubesUNIT 3 Page 10 Factorisation Simplifying fractions Products of algebraic fractions Adding and subtracting algebraic fractionsUNIT 4 Page 13 Algebraic fractions Via Afrika Maths Study Guide Gr10 616/01/2012 12:43 Via Afrika Mathematics7 Unit1 The number Real numbers Real numbers are divided into rational and irrational numbers.
10 Natural numbers (N)ZeroWhole numbers (N0)Negative numbersReal numbers (R)Rational numbers (Q)Irrational numbers (Q )Fractions of the form a __ b , a, b Z, b 0 Integers (Z) We can write a rational number as a fraction, a __ b , where a and b Z, and b 0. We cannot express an irrational number as a Surds A surd is a root of an integer that we cannot express as a fraction. Surds are irrational numbers. Examples of surds are __ 3 and __ 2 . Rounding off If the number after the cut-off point is 4 or less, then we leave the number before it as it is. If the number is equal to 5 or more, then increase the value of the number before it by 1. Via Afrika Maths Study Guide Gr10 716/01/2012 12:43 Via Afrika Mathematics8 Unit2 Multiplying algebraic Multiply integers and monomials by polynomials Each term inside the bracket is multiplied by the term in front of the bracket. 1 __ 6 a2b(6abc 12ac + 18b) = ( 1 __ 6 a2b 6abc) ( 1 __ 6 a2b 12ac) + ( 1 __ 6 a2b 18b) = a3b2c + 2a3bc The product of two binomials Each term inside the first set of brackets is multiplied by each term inside the second set of brackets.
