GCSE Maths Revision Higher - ELITE Tuition

Revision

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GCSE Mathematics

Higher Tier

Stafford Burndred

Consultant Editor: Brian Seager, Chairman of Examiners

Easingwold School

GCSE Mathematics

Name....................................................................................................................................

Address ................................................................................................................................

..............................................................................................................................................

..............................................................................................................................................

Date of exams:

(1) ..............................................................................

(2) ................................................................................

Aural .........................................................................

Coursework deadline dates:

(1) ..............................................................................

(2) ................................................................................

Exam board ..........................................................................................................................

Syllabus number ...................................................................................................................

Candidate number ...............................................................................................................

Centre number .....................................................................................................................

Further copies of this publication, as well as the guides for Foundation and Intermediate tiers may be obtained from:

Pearson Publishing

Chesterton Mill, French¡¯s Road, Cambridge CB4 3NP

Tel 01223 350555 Fax 01223 356484

Email info@pearson.co.uk

Web site

ISBN: 1 84070 272 9

Published by Pearson Publishing 2003

? Pearson Publishing

No part of this publication may be copied or reproduced, stored in a retrieval system or

transmitted in any form or by any means electronic, mechanical, photocopy, recording or

otherwise without the prior permission of the publisher.

Easingwold School

Contents

Introduction

...........................................................................................

vi

Examiner¡¯s tips

...........................................................................................

vii

Number skills

Rational and irrational numbers .........................................

1

Calculator skills

Using a calculator: Brackets, memory and fractions ..........

Using a calculator: Powers, roots and memory .................

Standard form ....................................................................

2

3

4

Fractions, decimals and

percentages

Percentages and fractions..................................................

Calculating growth and decay rates ..................................

5

6

Number patterns

Patterns you must recognise..............................................

Product of primes, highest common factor,

lowest common multiple and reciprocals ..........................

7

8

Trial and improvement .......................................................

Equations ...........................................................................

Rewriting formulae .............................................................

9

10

11

Iteration ..............................................................................

12

Variation

Direct and inverse variation ...............................................

13

Algebraic skills

Using algebraic formulae ...................................................

Rules for indices (powers) ..................................................

Expansion of brackets ........................................................

Factorisation ¨C 1.................................................................

Factorisation ¨C 2.................................................................

Factorisation ¨C 3.................................................................

Solving quadratic equations ..............................................

Simultaneous equations: Solving using algebra ................

Simplifying algebraic fractions ¨C 1 .....................................

Simplifying algebraic fractions ¨C 2 .....................................

14

15

16

17

18

19

20

21

22

23

Graphs

Drawing lines......................................................................

Simultaneous equations: Solving by drawing a graph ......

Solving equations using graphical methods......................

The straight line equation y = mx + c ...............................

Using tangents to find gradients .......................................

Expressing general rules in symbolic form ¨C 1 ..................

Expressing general rules in symbolic form ¨C 2 ..................

Drawing graphs..................................................................

Sketching graphs ¨C 1..........................................................

Sketching graphs ¨C 2..........................................................

Speed, time and distance graphs ......................................

Area under a curve.............................................................

24

25

26

27

28

29

30

31

32

33

34

35

Equations

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Contents

Angles

Intersecting and parallel lines ............................................

Bearings .............................................................................

36

37

Similarity

Similarity.............................................................................

38

Congruency

Congruent triangles ¨C 1 .....................................................

Congruent triangles ¨C 2 .....................................................

39

40

Transformations

Combined and inverse transformations.............................

Enlargement by a fractional scale factor............................

Enlargement by a negative scale factor.............................

41

42

43

Measurement

Compound measures.........................................................

Time ...................................................................................

Upper and lower bounds of numbers ¨C 1..........................

Upper and lower bounds of numbers ¨C 2..........................

44

45

46

47

Circles

Length, area and volume of shapes with curves................

Angle and tangent properties of circles ¨C 1 ......................

Angle and tangent properties of circles ¨C 2 ......................

Angle and tangent properties of circles ¨C 3 ......................

48

49

50

51

Perimeter, area and volume

Calculating length, area and volume ¨C 1 ...........................

Calculating length, area and volume ¨C 2 ...........................

Calculating length, area and volume ¨C 3 ...........................

Formulae for length, area and volume ..............................

Ratio for length, area and volume .....................................

52

53

54

55

56

Pythagoras¡¯ theorem

and trigonometry

Pythagoras¡¯ theorem ..........................................................

Trigonometry: Finding an angle.........................................

Trigonometry: Finding a side .............................................

Trigonometry: Solving problems........................................

Trigonometry and Pythagoras¡¯ theorem for 3-D shapes....

Sine, cosine and tangent of any angle ¨C 1 ........................

Sine, cosine and tangent of any angle ¨C 2 ........................

Sine, cosine and tangent of any angle ¨C 3 ........................

Sine rule, cosine rule, area of a triangle ¨C 1 ......................

Sine rule, cosine rule, area of a triangle ¨C 2 ......................

57

58

59

60

61

62

63

64

65

66

Vectors

Vectors

Vectors

Vectors

Vectors

1..........................................................................

2..........................................................................

3..........................................................................

4..........................................................................

67

68

69

70

Locus

Locus (plural loci) ...............................................................

71

¨C

¨C

¨C

¨C

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Contents

Questionnaires

Designing questionnaires...................................................

Sampling ............................................................................

Hypotheses ........................................................................

72

73

74

Tables and graphs

Comparing data .................................................................

Histograms .........................................................................

Grouped data.....................................................................

75

76

77

Cumulative frequency

Cumulative frequency ........................................................

Using cumulative frequency diagrams

to compare distributions ....................................................

78

Standard deviation

Standard deviation .............................................................

The normal distribution......................................................

80

81

Scatter diagrams

Line of best fit ....................................................................

82

Probability

Estimation of probability by experiment ...........................

Tree diagrams.....................................................................

Conditional and independent probability .........................

Probability (and, or)............................................................

Probability (at least)............................................................

83

84

85

86

87

Supplementary material

3-D co-ordinates ................................................................

Inequalities .........................................................................

Critical path analysis ..........................................................

Linear programming...........................................................

Transformations (matrices) ¨C 1 ...........................................

Transformations (matrices) ¨C 2 ...........................................

88

89

90

91

92

93

Important facts you are expected to know .............................................................................

94

Diagnostic tests

Index

Easingwold School

79

Diagnostic tests .........................................................................

Answers......................................................................................

98

111

...........................................................................................

116

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