Automotive_Science_and_Mathematics

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1 Arithmetic 1
1.1 Terminology of number systems 1
1.2 The decimal system 1
Addition and subtraction of decimals 2
Multiplication and division – decimals 2
1.3 Degrees of accuracy 4
Rounding numbers 4
1.4 Accuracy in calculation 4
1.5 Powers and roots and standard form 4
General rules for indices 5
1.6 Standard form 5
Multiplying and dividing numbers in standard form 5
1.7 Factors 6
1.8 Fractions 6
Addition and subtraction 6
Fractions and whole numbers 6
Combined addition and subtraction 7
Multiplication and division of fractions 7
Order of performing operations in problems involving fractions 7
1.9 Ratio and proportion. Percentages 8
Examples of ratios in vehicle technology 8
1.10 The binary system 10
Most significant bit (MSB) 10
Hexadecimal 10
Converting base 10 numbers to binary 10
Uses of binary numbers in vehicle systems 10
1.11 Directed numbers 11
Rules for dealing with directed numbers 11
1.12 Summary of main points 12
1.13 Exercises 12
2 Statistics – An introduction 16
2.1 Definition 16
2.2 Collecting and sorting raw data 17
2.3 Making sense of data 17
Discrete variables 17
Continuous variables 17
2.4 Descriptive statistics – pictographs 18
Pie charts 18
2.5 Interpreting data. Statistical inference 19
Frequency and tally charts 19
The tally chart and frequency distribution 19
2.6 Importance of the shape of a frequency distribution 20
The histogram 20
The frequency polygon 20
Cumulative frequency 21
2.7 Interpreting statistics 22
Sampling 22
2.8 Features of the population that are looked for in a sample 22
Average 22
2.9 The normal distribution 23
Importance of the normal distribution 24
Other ways of viewing frequency distributions – quartiles, deciles,
percentiles 25
2.10 Summary of main points 26
2.11 Exercises 26
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vi Contents
2 Statistics – An introduction 16
2.1 Definition 16
2.2 Collecting and sorting raw data 17
2.3 Making sense of data 17
Discrete variables 17
Continuous variables 17
2.4 Descriptive statistics – pictographs 18
Pie charts 18
2.5 Interpreting data. Statistical inference 19
Frequency and tally charts 19
The tally chart and frequency distribution 19
2.6 Importance of the shape of a frequency distribution 20
The histogram 20
The frequency polygon 20
Cumulative frequency 21
2.7 Interpreting statistics 22
Sampling 22
2.8 Features of the population that are looked for in a sample 22
Average 22
2.9 The normal distribution 23
Importance of the normal distribution 24
Other ways of viewing frequency distributions – quartiles, deciles,
percentiles 25
2.10 Summary of main points 26
2.11 Exercises 26
3 Algebra and graphs 29
3.1 Introduction 29
3.2 Formulae 29
3.3 Evaluating formulae 29
3.4 Processes in algebra 30
Brackets 30
3.5 Algebraic expressions and simplification 30
Expression 30
3.6 Factorising 31
3.7 Equations 31
Solving equations 31
3.8 Transposition of formulae 33
3.9 Graphs 34
Variables 34
Scales 34
Coordinates 35
3.10 Graphs and equations 36
The straight-line graph 36
3.11 Summary of main points
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3.12 Exercises 38
Exercises – Section 3.3 38
Exercises – Section 3.4 38
Exercises – Section 3.5 38
Exercises – Section 3.6 38
Exercises – Section 3.7 38
Exercises – Section 3.8 38
Exercises – Section 3.10 38
4 Geometry and trigonometry 41
4.1 Angles 41
Angular measurement 41
Angles and rotation 41
4.2 Examples of angles in automotive work 42
Angles and lines 43
Adding and subtracting angles 43
4.3 Types of angle 44
Adjacent angles 44
Opposite angles 44
Corresponding angles 44
Alternate angles 44
Supplementary angles 44
Complementary angles 44
4.4 Types of triangle 45
Acute angled triangle 45
Obtuse angled triangle 45
Equilateral triangle 45
Isosceles triangle 45
Scalene triangle 45
Right angled triangle 46
Labelling sides and angles of a triangle 46
Sum of the three angles of a triangle 46
4.5 Pythagoras’ theorem 46
4.6 Circles 46
Ratio of diameter and circumference 47
Length of arc 47
4.7 Timing marks 47
4.8 Wheel revolutions and distance travelled 48
4.9 Valve opening area 48
4.10 Trigonometry 48
4.11 Using sines, cosines and tangents 49
Sines 49
Cosines 50
Tangents 51
4.12 Summary of formulae 52
4.13 Exercises 52
Exercises – Section 4.2 53
Exercises – Section 4.3 53
Exercises – Section 4.4 54
Exercises – Section 4.5 55
Exercises – Section 4.6 55

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