Construction Mathematics – Surinder Singh Virdi (KTE0018)

Construction Mathematics – Surinder Singh Virdi, Contents:  

1 Using a scientific calculator

1.1 Introduction

1.2 Keys of a scientific calculator

2 Numbers

2.1 Introduction

2.2 History of numbers

2.3 Positive numbers, negative numbers and integers

2.4 Prime and composite numbers

2.5 Square numbers

2.6 Addition and subtraction

2.7 Decimal numbers

2.7.1 Place value

2.7.2 Adding, subtracting and multiplying decimals

2.7.3 Multiplication and division by the powers of 10

2.8 Order of operations

2.8.1 Brackets

3 Basic algebra

3.1 Introduction

3.2 Addition and subtraction

3.3 Multiplication and division

3.4 Brackets

3.5 Simple equations

3.6 Application of linear equations

4 Indices and logarithms

4.1 Indices

4.2 Laws of indices

4.2.1 Multiplication

4.2.2 Division

4.2.3 Power of a power

4.2.4 Negative powers

4.2.5 Zero index

4.3 Logarithms

5 Standard form, significant figures and estimation

5.1 Standard form

5.2 Significant figures

5.3 Estimation

6 Transposition and evaluation of formulae

6.1 Transposition of formulae

6.1.1 Type 1 formulae

6.1.2 Type 2 formulae

6.1.3 Type 3 formulae

6.2 Evaluation of formulae

7 Fractions and percentages

7.1 Fractions

7.1.1 Simplification of fractions

7.1.2 Equivalent fractions

7.1.3 Addition and subtraction of fractions

7.1.4 Multiplication and division of fractions

7.1.5 Conversion of fractions to decimals

7.2 Percentages

7.2.1 Conversion of fractions and decimals into percentage

7.2.2 Value added tax (VAT)

7.3 Bulking of sand

8 Graphs

8.1 Introduction

8.2 Cartesian axes and coordinates

8.3 Straight-line graphs

8.4 The law of the straight line

8.4.1 The gradient (m)

8.4.2 The intercept (c)

9 Units and their conversion

9.1 Introduction

9.2 Length

9.2.1 Conversion factors

9.2.2 Use of the graphical method

9.3 Mass

9.3.1 Conversion factors

9.3.2 Graphical method

9.4 Area, volume and capacity

9.5 Temperature

10 Geometry

10.1 Angles

10.1.1 Types of angle

10.2 Polygons

10.3 Triangles

10.3.1 Types of triangle

10.3.2 Theorem of Pythagoras

10.3.3 Similar triangles

10.4 Quadrilaterals

10.5 Sum of the angles in a polygon

10.6 The circle

11 Areas (1)

11.1 Introduction

11.2 Area of triangles

11.3 Area of quadrilaterals

11.4 Area of circles

11.5 Application of area to practical problems

11.5.1 Cavity walls

12 Volumes (1)

12.1 Introduction

12.2 Volume of prisms, cylinders, pyramids and cones

12.3 Mass, volume and density

12.4 Concrete mix and its constituents

13 Trigonometry (1)

13.1 Introduction

13.2 The trigonometrical ratios

13.3 Trigonometric ratios for 30°, 45°, 60°

13.4 Angles of elevation and depression

13.5 Stairs

13.6 Roofs

13.7 Excavations and embankments

14 Setting out

14.1 Introduction

14.2 Setting out a simple building site

14.3 Bay windows and curved brickwork

14.4 Checking a building for square corners

14.5 Circular arches

14.6 Elliptical arches

15 Costing – materials and labour

15.1 Introduction

15.2 Foundations

15.3 Cavity walls

15.4 Flooring

15.5 Painting

16 Statistics

16.1 Introduction

16.2 Tally charts

16.3 Tables

16.4 Types of data

16.4.1 Discrete data

16.4.2 Continuous data

16.4.3 Raw data

16.4.4 Grouped data

16.5 Averages

16.5.1 The mean

16.5.2 The mode

16.5.3 The median

16.5.4 Comparison of mean, mode and median

16.6 The range

16.7 Statistical diagrams

16.7.1 Pictograms

16.7.2 Bar charts

16.7.3 Pie charts

16.7.4 Line graphs

16.8 Frequency distributions

16.8.1 Histograms

16.8.2 Frequency polygons

16.8.3 Cumulative frequency distribution

17 Areas and volumes (2)

17.1 Introduction

17.2 Surface area of a pyramid

17.2.1 Frustum of a pyramid

17.3 Surface area of a cone

17.3.1 Frustum of a cone

18 Areas and volumes (3)

18.1 Introduction

18.2 Mid-ordinate rule

18.3 Trapezoidal rule

18.4 Simpson’s rule

18.5 Volume of irregular solids

18.6 Prismoidal rule

19 Trigonometry (2)

19.1 The sine rule and the cosine rule

19.1.1 The sine rule

19.1.2 The cosine rule

19.2 Area of triangles

20 Computer techniques

20.1 Introduction

20.2 Microsoft Excel 2000

Assignment 1

Assignment 2

Appendix 1 Concrete mix

Appendix 2 Answers to exercises

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