Construction Mathematics Book

## Contents

### 1    Using a scientiﬁc calculator

1.1    Introduction 1
1.2    Keys of a scientiﬁc calculator 1

### 2    Numbers 8

2.1    Introduction 8
2.2    History of numbers 8
2.3    Positive numbers, negative numbers and integers 9
2.4    Prime and composite numbers 10
2.5    Square numbers 10
2.6    Addition and subtraction 10
2.7    Decimal numbers 12
2.7.1    Place value 12
2.7.2    Adding, subtracting and multiplying decimals        13
2.7.3    Multiplication and division by the powers of 10     14
2.8    Order of operations 16
2.8.1    Brackets 16

### 3    Basic algebra

3.1    Introduction 19
3.2    Addition and subtraction 19
3.3    Multiplication and division 20
3.4    Brackets 21
3.5    Simple equations 22
3.6    Application of linear equations 23

### 4    Indices and logarithms

4.1    Indices 27
4.2    Laws of indices 274.2.1    Multiplication 28
4.2.2    Division 28
4.2.3    Power of a power 29
4.2.4    Negative powers 30
4.2.5    Zero index 31
4.3    Logarithms 31

### 5    Standard form, signiﬁcant ﬁgures and estimation

5.1    Standard form 33
5.2    Signiﬁcant ﬁgures 34
5.3    Estimation 36

### 6    Transposition and evaluation of formulae

6.1    Transposition of formulae 38
6.1.1    Type 1 formulae 38
6.1.2    Type 2 formulae 39
6.1.3    Type 3 formulae 39
6.2    Evaluation of formulae 42

### 7    Fractions and percentages

7.1    Fractions 45
7.1.1    Simpliﬁcation of fractions 48
7.1.2    Equivalent fractions 49
7.1.3    Addition and subtraction of fractions 50
7.1.4    Multiplication and division of fractions 51
7.1.5    Conversion of fractions to decimals 52
7.2    Percentages 52
7.2.1    Conversion of fractions and decimals into
percentage 53
7.2.2    Value added tax (VAT) 54
7.3    Bulking of sand 54

### 8    Graphs

8.1    Introduction 59
8.2    Cartesian axes and coordinates 59
8.3    Straight-line graphs 63
8.4    The law of the straight line 65
8.4.1    The gradient (m) 66
8.4.2    The intercept (c) 67

### 9    Units and their conversion

9.1    Introduction 72
9.2    Length 73
9.2.1    Conversion factors 73
9.2.2    Use of the graphical method 74
vi Contents9.3     Mass 76
9.3.1      Conversion factors 76
9.3.2      Graphical method 76
9.4     Area, volume and capacity 78
9.5     Temperature 80

### 10    Geometry

10.1     Angles 82
10.1.1    Types of angle 84
10.2     Polygons 86
10.3     Triangles 86
10.3.1    Types of triangle 86
10.3.2    Theorem of Pythagoras 87
10.3.3    Similar triangles 89
10.5     Sum of the angles in a polygon 95
10.6     The circle 96

### 11    Areas

11.1     Introduction 101
11.2     Area of triangles 102
11.3     Area of quadrilaterals 103
11.4     Area of circles 104
11.5     Application of area to practical problems 105
11.5.1    Cavity walls 109

### 12    Volumes

12.1     Introduction 115
12.2     Volume of prisms, cylinders, pyramids and cones        116
12.3     Mass, volume and density 123
12.4     Concrete mix and its constituents 124

### 13    Trigonometry

13.1     Introduction 132
13.2     The trigonometrical ratios 132
13.3     Trigonometric ratios for 30°, 45°, 60° 134
13.4     Angles of elevation and depression 138
13.5     Stairs 140
13.6     Roofs 144
13.7     Excavations and embankments 149

### 14    Setting out

14.1     Introduction 155
14.2     Setting out a simple building site 155
14.3     Bay windows and curved brickwork 158
4.4     Checking a building for square corners 160
14.5     Circular arches 163
14.6     Elliptical arches 166

### 15    Costing – materials and labour

15.1     Introduction 171
15.2     Foundations 171
15.3     Cavity walls 173
15.4     Flooring 176
15.5     Painting 177

### 16    Statistics

16.1     Introduction 183
16.2     Tally charts 183
16.3     Tables 184
16.4     Types of data 184
16.4.1    Discrete data 184
16.4.2    Continuous data 184
16.4.3    Raw data 184
16.4.4    Grouped data 185
16.5     Averages 186
16.5.1    The mean 186
16.5.2    The mode 187
16.5.3    The median 187
16.5.4    Comparison of mean, mode and median        187
16.6     The range 187
16.7     Statistical diagrams 189
16.7.1    Pictograms 189
16.7.2    Bar charts 189
16.7.3    Pie charts 190
16.7.4    Line graphs 190
16.8     Frequency distributions 193
16.8.1    Histograms 193
16.8.2    Frequency polygons 194
16.8.3    Cumulative frequency distribution 196

### 17    Areas and volumes

17.1     Introduction 201
17.2     Surface area of a pyramid 201
17.2.1    Frustum of a pyramid 202
17.3     Surface area of a cone 204
17.3.1    Frustum of a cone 205

### 18    Areas and volumes

18.1     Introduction 208
18.2     Mid-ordinate rule 208
18.3     Trapezoidal rule 209
18.4     Simpson’s rule 210
18.5     Volume of irregular solids 212
18.6     Prismoidal rule 214

### 19    Trigonometry

19.1     The sine rule and the cosine rule 220
19.1.1    The sine rule 220
19.1.2    The cosine rule 225
19.2     Area of triangles 228

### 20    Computer techniques

20.1     Introduction 233
20.2     Microsoft Excel 2000 233
Assignment 1 247
Assignment 2 252
Appendix 1 Concrete mix 257
Appendix 2 Answers to exercises 259
Index 279

### Note:

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