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Construction Mathematics


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Contents

Preface xi

About the authors xiii

Acknowledgements xv

1 Using a scientific calculator 1

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 19

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 27

4.1 Indices 27

4.2 Laws of indices 27

vi Contents

4.2.1 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 33

5.1 Standard form 33

5.2 Significant figures 34

5.3 Estimation 36

6 Transposition and evaluation of formulae 38

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 45

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

7.2.2 Value added tax (VAT) 54

7.3 Bulking of sand 54

8 Graphs 59

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 72

9.1 Introduction 72

9.2 Length 73

9.2.1 Conversion factors 73

9.2.2 Use of the graphical method 74

percentage 53

Contents vii

9.3 Mass 76

9.4 Area, volume and capacity 78

9.5 Temperature 80

10 Geometry 82

10.1 Angles 82

10.2 Polygons 86

10.3 Triangles 86

9.3.1 Conversion factors 76

9.3.2 Graphical method 76

10.1.1 Types of angle 84

10.3.1 Types of triangle 86

10.3.2 Theorem of Pythagoras 87

10.3.3 Similar triangles 89

10.4 Quadrilaterals 92

10.5 Sum of the angles in a polygon 95

10.6 The circle 96

11 Areas (1) 101

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

12 Volumes (1) 115

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 (1) 132

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 155

14.1 Introduction 155

14.2 Setting out a simple building site 155

14.3 Bay windows and curved brickwork 158

11.5.1 Cavity walls 109

viii Contents

14.4 Checking a building for square corners 160

14.5 Circular arches 163

14.6 Elliptical arches 166

15 Costing – materials and labour 171

15.1 Introduction 171

15.2 Foundations 171

15.3 Cavity walls 173

15.4 Flooring 176

15.5 Painting 177

16 Statistics 183

16.1 Introduction 183

16.2 Tally charts 183

16.3 Tables 184

16.4 Types of data 184

16.5 Averages 186

16.4.1 Discrete data 184

16.4.2 Continuous data 184

16.4.3 Raw data 184

16.4.4 Grouped data 185

16.5.1 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

16.8 Frequency distributions 193

16.7.1 Pictograms 189

16.7.2 Bar charts 189

16.7.3 Pie charts 190

16.7.4 Line graphs 190

16.8.1 Histograms 193

16.8.2 Frequency polygons 194

16.8.3 Cumulative frequency distribution 196

17 Areas and volumes (2) 201

17.1 Introduction 201

17.2 Surface area of a pyramid 201

17.3 Surface area of a cone 204

18 Areas and volumes (3) 208

18.1 Introduction 208

18.2 Mid-ordinate rule 208

17.2.1 Frustum of a pyramid 202

17.3.1 Frustum of a cone 205

Contents ix

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 (2) 220

19.1 The sine rule and the cosine rule 220

19.2 Area of triangles 228

20 Computer techniques 233

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

19.1.1 The sine rule 220

19.1.2 The cosine rule 225

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