文件名称:
Construction Mathematics
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文件大小: 10mb
下载次数: 0
上传时间: 2009-05-26
详细说明： 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 percentage 53 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 Contents vii 9.3 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 82 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 10.4 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 11.5.1 Cavity walls 109 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 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 16.4.1 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 (2) 201 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 (3) 208 18.1 Introduction 208 18.2 Mid-ordinate rule 208 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 19.1.1 The sine rule 220 19.1.2 The cosine rule 225 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 ...展开收缩
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