Contents
Preface
ix
Acknowledgements
x
Instructor’s Manual
xi
1 Basic arithmetic
1
1.1 Introduction
1
1.2 Revision of addition and subtraction
1
1.3 Revision of multiplication and division
3
1.4 Highest common factors and lowest
common multiples
5
1.5 Order of precedence and brackets
6
2 Fractions
9
2.1 Introduction
9
2.2 Adding and subtracting fractions
10
2.3 Multiplication and division of fractions
12
2.4 Order of precedence with fractions
13
Revision Test 1
15
3 Decimals
16
3.1 Introduction
16
3.2 Converting decimals to fractions and
vice-versa
16
3.3 Significant figures and decimal places
17
3.4 Adding and subtracting decimal numbers
18
3.5 Multiplying and dividing decimal numbers 19
4 Using a calculator
22
4.1 Introduction
22
4.2 Adding, subtracting, multiplying and
dividing
22
4.3 Further calculator functions
23
4.4 Evaluation of formulae
28
5 Percentages
33
5.1 Introduction
33
5.2 Percentage calculations
33
5.3 Further percentage calculations
35
5.4 More percentage calculations
36
Revision Test 2
39
6 Ratio and proportion
40
6.1 Introduction
40
6.2 Ratios
40
6.3 Direct proportion
42
6.4 Inverse proportion
45
7 Powers, roots and laws of indices
47
7.1 Introduction
47
7.2 Powers and roots
47
7.3 Laws of indices
48
8 Units, prefixes and engineering notation
53
8.1 Introduction
53
8.2 SI units
53
8.3 Common prefixes
53
8.4 Standard form
56
8.5 Engineering notation
57
Revision Test 3
60
9 Basic algebra
61
9.1 Introduction
61
9.2 Basic operations
61
9.3 Laws of indices
64
10 Further algebra
68
10.1 Introduction
68
10.2 Brackets
68
10.3 Factorization
69
10.4 Laws of precedence
71
11 Solving simple equations
73
11.1 Introduction
73
11.2 Solving equations
73
11.3 Practical problems involving simple
equations
77
Revision Test 4
82
12 Transposing formulae
83
12.1 Introduction
83
12.2 Transposing formulae
83
12.3 Further transposing of formulae
85
12.4 More difficult transposing of formulae
87
13 Solving simultaneous equations
90
13.1 Introduction
90
13.2 Solving simultaneous equations in two
unknowns
90
13.3 Further solving of simultaneous equations 92
Preface
ix
Acknowledgements
x
Instructor’s Manual
xi
1 Basic arithmetic
1
1.1 Introduction
1
1.2 Revision of addition and subtraction
1
1.3 Revision of multiplication and division
3
1.4 Highest common factors and lowest
common multiples
5
1.5 Order of precedence and brackets
6
2 Fractions
9
2.1 Introduction
9
2.2 Adding and subtracting fractions
10
2.3 Multiplication and division of fractions
12
2.4 Order of precedence with fractions
13
Revision Test 1
15
3 Decimals
16
3.1 Introduction
16
3.2 Converting decimals to fractions and
vice-versa
16
3.3 Significant figures and decimal places
17
3.4 Adding and subtracting decimal numbers
18
3.5 Multiplying and dividing decimal numbers 19
4 Using a calculator
22
4.1 Introduction
22
4.2 Adding, subtracting, multiplying and
dividing
22
4.3 Further calculator functions
23
4.4 Evaluation of formulae
28
5 Percentages
33
5.1 Introduction
33
5.2 Percentage calculations
33
5.3 Further percentage calculations
35
5.4 More percentage calculations
36
Revision Test 2
39
6 Ratio and proportion
40
6.1 Introduction
40
6.2 Ratios
40
6.3 Direct proportion
42
6.4 Inverse proportion
45
7 Powers, roots and laws of indices
47
7.1 Introduction
47
7.2 Powers and roots
47
7.3 Laws of indices
48
8 Units, prefixes and engineering notation
53
8.1 Introduction
53
8.2 SI units
53
8.3 Common prefixes
53
8.4 Standard form
56
8.5 Engineering notation
57
Revision Test 3
60
9 Basic algebra
61
9.1 Introduction
61
9.2 Basic operations
61
9.3 Laws of indices
64
10 Further algebra
68
10.1 Introduction
68
10.2 Brackets
68
10.3 Factorization
69
10.4 Laws of precedence
71
11 Solving simple equations
73
11.1 Introduction
73
11.2 Solving equations
73
11.3 Practical problems involving simple
equations
77
Revision Test 4
82
12 Transposing formulae
83
12.1 Introduction
83
12.2 Transposing formulae
83
12.3 Further transposing of formulae
85
12.4 More difficult transposing of formulae
87
13 Solving simultaneous equations
90
13.1 Introduction
90
13.2 Solving simultaneous equations in two
unknowns
90
13.3 Further solving of simultaneous equations 92