Preface |
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xiii | |
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SECTION 1 APPLIED MATHEMATICS |
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1 | (166) |
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3 | (7) |
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3 | (1) |
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1.2 Revision of addition and subtraction |
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4 | (1) |
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1.3 Revision of multiplication and division |
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5 | (2) |
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1.4 Highest common factors and lowest common multiples |
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7 | (1) |
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1.5 Order of operation and brackets |
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8 | (2) |
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2 Fractions, decimals and percentages |
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10 | (14) |
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11 | (4) |
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15 | (1) |
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16 | (3) |
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19 | (3) |
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Revision Test 1 Arithmetic, fractions, decimals and percentages |
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22 | (2) |
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3 Indices, units, prefixes and engineering notation |
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24 | (18) |
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25 | (1) |
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26 | (2) |
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3.3 Introduction to engineering units |
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28 | (1) |
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28 | (2) |
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30 | (1) |
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31 | (1) |
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32 | (2) |
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34 | (3) |
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3.9 Metric -- US/Imperial conversions |
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37 | (5) |
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4 Calculations and evaluation of formulae |
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42 | (8) |
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42 | (1) |
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42 | (4) |
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4.3 Evaluation of formulae |
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46 | (2) |
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Revision Test 2 Indices, units, calculator and evaluation of formulae |
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48 | (2) |
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50 | (8) |
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51 | (1) |
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51 | (2) |
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53 | (1) |
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54 | (1) |
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55 | (1) |
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56 | (2) |
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6 Solving simple equations |
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58 | (8) |
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58 | (1) |
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59 | (3) |
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6.3 Practical problems involving simple equations |
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62 | (3) |
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Revision Test 3 Algebra and simple equations |
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65 | (1) |
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66 | (6) |
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66 | (1) |
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66 | (2) |
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7.3 Further transposing of formulae |
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68 | (2) |
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7.4 More difficult transposing of formulae |
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70 | (2) |
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8 Solving simultaneous equations |
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72 | (6) |
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72 | (1) |
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8.2 Solving simultaneous equations in two unknowns |
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73 | (2) |
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8.3 Further solving of simultaneous equations |
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75 | (1) |
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8.4 Practical problems involving simultaneous equations |
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76 | (2) |
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9 Logarithms and exponential functions |
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78 | (13) |
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9.1 Introduction to logarithms |
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79 | (1) |
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79 | (2) |
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81 | (1) |
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9.4 Graphs of logarithmic functions |
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82 | (1) |
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9.5 Exponential functions |
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82 | (1) |
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9.6 Graphs of exponential functions |
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83 | (1) |
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84 | (2) |
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9.8 Laws of growth and decay |
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86 | (4) |
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Revision Test 4 Transposition of formulae, simultaneous equations, logarithms and exponential functions |
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90 | (1) |
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91 | (14) |
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10.1 Introduction to graphs |
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91 | (1) |
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10.2 Axes, scales and co-ordinates |
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92 | (1) |
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10.3 Straight line graphs |
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93 | (3) |
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10.4 Gradients, intercepts and equation of a graph |
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96 | (4) |
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10.5 Practical problems involving straight line graphs |
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100 | (5) |
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11 Introduction to trigonometry |
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105 | (18) |
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105 | (1) |
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11.2 The theorem of Pythagoras |
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105 | (3) |
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11.3 Sines, cosines and tangents |
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108 | (2) |
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11.4 Evaluating trigonometric ratios of acute angles |
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110 | (2) |
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11.5 Solving right-angled triangles |
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112 | (3) |
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11.6 Graphs of trigonometric functions |
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115 | (1) |
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11.7 Sine and cosine rules |
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116 | (1) |
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11.8 Area of any triangle |
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116 | (1) |
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11.9 Worked problems on the solution of triangles and their areas |
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116 | (2) |
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11.10 Practical situations involving trigonometry |
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118 | (3) |
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Revision Test 5 Straight line graphs and trigonometry |
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121 | (2) |
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12 Areas of common shapes |
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123 | (13) |
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123 | (1) |
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124 | (2) |
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12.3 Calculating areas of common shapes |
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126 | (8) |
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12.4 Areas of similar shapes |
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134 | (2) |
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136 | (7) |
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136 | (1) |
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13.2 Properties of circles |
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136 | (2) |
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138 | (1) |
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13.3 Arc length and areas of circles and sectors |
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139 | (4) |
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14 Volumes of common solids |
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143 | (24) |
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143 | (1) |
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14.2 Calculating volumes and surface areas of common solids |
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143 | (7) |
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14.3 Summary of volumes and surface areas of common solids |
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150 | (1) |
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14.4 Calculating more complex volumes and surface areas |
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150 | (5) |
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14.5 Volumes of similar shapes |
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155 | (2) |
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Revision Test 6 Areas and volumes |
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157 | (3) |
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Multiple-choice questions on Applied Mathematics |
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160 | (7) |
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SECTION II MECHANICAL APPLICATIONS |
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167 | (194) |
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169 | (6) |
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169 | (2) |
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171 | (4) |
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16 Atomic structure of matter |
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175 | (6) |
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16.1 Elements, atoms, molecules and compounds |
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175 | (1) |
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16.2 Mixtures, solutions, suspensions and solubility |
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176 | (2) |
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178 | (1) |
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178 | (3) |
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181 | (8) |
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181 | (1) |
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182 | (3) |
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185 | (1) |
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186 | (3) |
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189 | (6) |
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18.1 Introduction to acceleration |
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190 | (1) |
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190 | (1) |
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18.3 Free-fall and equation of motion |
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191 | (4) |
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19 Force, mass and acceleration |
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195 | (8) |
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196 | (1) |
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19.2 Newton's laws of motion |
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196 | (3) |
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19.3 Centripetal acceleration |
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199 | (3) |
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Revision Test 7 SI units, density, speed and velocity, force, mass and acceleration |
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202 | (1) |
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20 Forces acting at a point |
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203 | (15) |
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203 | (1) |
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20.2 Scalar and vector quantities |
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204 | (1) |
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20.3 Centre of gravity and equilibrium |
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204 | (1) |
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205 | (1) |
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20.5 The resultant of two coplanar forces |
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205 | (1) |
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20.6 Triangle of forces method |
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206 | (1) |
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20.7 The parallelogram of forces method |
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207 | (1) |
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20.8 Resultant of coplanar forces by calculation |
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208 | (1) |
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20.9 Resultant of more than two coplanar forces |
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209 | (2) |
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20.10 Coplanar forces in equilibrium |
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211 | (1) |
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20.11 Resolution of forces |
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212 | (3) |
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215 | (3) |
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21 Work, energy and power |
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218 | (16) |
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219 | (1) |
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219 | (4) |
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223 | (2) |
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225 | (3) |
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21.5 Potential and kinetic energy |
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228 | (6) |
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22 Simply supported beams |
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234 | (10) |
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234 | (1) |
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22.2 The moment of a force |
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235 | (1) |
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22.3 Equilibrium and the principle of moments |
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236 | (2) |
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22.4 Simply supported beams having point loads |
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238 | (5) |
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Revision Test 8 Forces acting at a point, work, energy and power and simply supported beams |
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243 | (1) |
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23 Linear and angular motion |
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244 | (9) |
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244 | (1) |
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244 | (1) |
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23.3 Linear and angular velocity |
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245 | (1) |
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23.4 Linear and angular acceleration |
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246 | (1) |
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23.5 Further equations of motion |
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247 | (2) |
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249 | (4) |
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253 | (5) |
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24.1 Introduction to friction |
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253 | (1) |
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24.2 Coefficient of friction |
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254 | (1) |
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24.3 Applications of friction |
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255 | (3) |
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258 | (12) |
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258 | (1) |
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25.2 Force ratio, movement ratio and efficiency |
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258 | (3) |
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261 | (1) |
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262 | (1) |
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263 | (2) |
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265 | (4) |
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Revision Test 9 Linear and angular motion, friction and simple machines |
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269 | (1) |
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26 The effects of forces on materials |
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270 | (12) |
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271 | (1) |
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271 | (1) |
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271 | (1) |
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272 | (1) |
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272 | (1) |
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272 | (1) |
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273 | (2) |
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26.8 Elasticity, limit of proportionality and elastic limit |
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275 | (1) |
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276 | (3) |
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26.10 Ductility, brittleness and malleability |
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279 | (3) |
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27 Linear momentum and impulse |
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282 | (8) |
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283 | (1) |
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283 | (2) |
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27.3 Impulse and impulsive forces |
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285 | (4) |
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Revision Test 10 Forces on materials and linear momentum and impulse |
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289 | (1) |
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290 | (10) |
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290 | (1) |
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291 | (1) |
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28.3 Work done and power transmitted by a constant torque |
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291 | (2) |
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28.4 Kinetic energy and moment of inertia |
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293 | (3) |
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28.5 Power transmission and efficiency |
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296 | (4) |
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300 | (14) |
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300 | (1) |
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301 | (2) |
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29.3 Atmospheric pressure |
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303 | (1) |
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29.4 Archimedes' principle |
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304 | (2) |
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29.5 Measurement of pressure |
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306 | (1) |
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306 | (2) |
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29.7 Absolute and gauge pressure |
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308 | (1) |
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308 | (1) |
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29.9 The Bourdon pressure gauge |
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309 | (1) |
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310 | (4) |
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30 Heat energy and transfer |
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314 | (14) |
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315 | (1) |
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30.2 Heat and temperature |
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315 | (1) |
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30.3 The measurement of temperature |
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316 | (1) |
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30.4 Specific heat capacity |
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316 | (2) |
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318 | (1) |
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30.6 Latent heats of fusion and vaporisation |
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319 | (2) |
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30.7 A simple refrigerator |
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321 | (1) |
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30.8 Conduction, convection and radiation |
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321 | (1) |
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322 | (1) |
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30.10 Use of insulation in conserving fuel |
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322 | (1) |
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322 | (1) |
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30.12 Calorific value and combustion |
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323 | (1) |
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323 | (4) |
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Revision Test 11 Torque, pressure in fluids, heat energy and transfer |
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327 | (1) |
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328 | (9) |
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329 | (1) |
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31.2 Practical applications of thermal expansion |
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329 | (1) |
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31.3 Expansion and contraction of water |
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329 | (1) |
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31.4 Coefficient of linear expansion |
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330 | (2) |
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31.5 Coefficient of superficial expansion |
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332 | (1) |
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31.6 Coefficient of cubic expansion |
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332 | (5) |
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337 | (12) |
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338 | (1) |
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339 | (2) |
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32.3 The pressure or Gay-Lussac's law |
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341 | (1) |
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32.4 Dalton's law of partial pressure |
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342 | (1) |
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32.5 Characteristic gas equation |
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343 | (1) |
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32.6 Worked problems on the characteristic gas equation |
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343 | (2) |
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32.7 Further worked problems on the characteristic gas equation |
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345 | (4) |
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33 The measurement of temperature |
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349 | (12) |
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350 | (1) |
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33.2 Liquid-in-glass thermometers |
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350 | (1) |
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351 | (2) |
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33.4 Resistance thermometers |
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353 | (2) |
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355 | (1) |
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355 | (2) |
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33.7 Temperature-indicating paints and crayons |
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357 | (1) |
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33.8 Bimetallic thermometers |
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357 | (1) |
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33.9 Mercury-in-steel thermometer |
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357 | (1) |
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358 | (1) |
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33.11 Choice of measuring device |
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358 | (2) |
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Revision Test 12 Thermal expansion, ideal gas laws and temperature measurement |
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360 | (1) |
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SECTION III ELECTRICAL APPLICATIONS |
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361 | (152) |
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34 An introduction to electric circuits |
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363 | (12) |
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364 | (1) |
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34.2 Standard symbols for electrical components |
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364 | (1) |
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34.3 Electric current and quantity of electricity |
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364 | (2) |
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34.4 Potential difference and resistance |
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366 | (1) |
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34.5 Basic electrical measuring instruments |
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366 | (1) |
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367 | (1) |
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34.7 Multiples and sub-multiples |
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368 | (1) |
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34.8 Conductors and insulators |
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369 | (1) |
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34.9 Electrical power and energy |
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369 | (2) |
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34.10 Main effects of electric current |
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371 | (1) |
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372 | (3) |
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375 | (9) |
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35.1 Resistor construction |
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376 | (1) |
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35.2 Resistance and resistivity |
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376 | (2) |
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35.3 Temperature coefficient of resistance |
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378 | (2) |
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35.4 Resistor colour coding and ohmic values |
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380 | (4) |
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36 Batteries and alternative sources of energy |
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384 | (19) |
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36.1 Introduction to batteries |
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385 | (1) |
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36.2 Some chemical effects of electricity |
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385 | (1) |
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386 | (1) |
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387 | (1) |
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36.5 E.m.f. and internal resistance of a cell |
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387 | (2) |
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389 | (1) |
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390 | (2) |
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36.8 Lithium-ion batteries |
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392 | (3) |
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395 | (1) |
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36.10 Safe disposal of batteries |
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395 | (1) |
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395 | (1) |
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36.12 Alternative and renewable energy sources |
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396 | (1) |
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397 | (2) |
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399 | (4) |
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37 Series and parallel networks |
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403 | (15) |
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403 | (1) |
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404 | (1) |
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405 | (2) |
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407 | (3) |
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410 | (3) |
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37.6 Wiring lamps in series and in parallel |
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413 | (3) |
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Revision Test 13 Electric circuits, resistance variation, batteries and series and parallel networks |
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416 | (2) |
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418 | (6) |
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418 | (1) |
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38.2 Kirchhoff's current and voltage laws |
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418 | (1) |
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38.3 Worked problems on Kirchhoff's laws |
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419 | (5) |
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39 Magnetism and electromagnetism |
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424 | (14) |
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39.1 Introduction to magnetism and magnetic circuits |
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425 | (1) |
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425 | (3) |
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428 | (2) |
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39.4 Magnetic flux and flux density |
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430 | (1) |
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39.5 Force on a current-carrying conductor |
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431 | (3) |
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39.6 Principle of operation of a simple d.c. motor |
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434 | (1) |
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435 | (3) |
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40 Electromagnetic induction |
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438 | (12) |
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40.1 Introduction to electromagnetic induction |
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439 | (1) |
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40.2 Laws of electromagnetic induction |
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440 | (3) |
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443 | (1) |
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443 | (1) |
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444 | (5) |
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Revision Test 14 Kirchhoff's laws, magnetism, electromagnetism and electromagnetic induction |
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449 | (1) |
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41 Alternating voltages and currents |
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450 | (11) |
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451 | (1) |
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451 | (1) |
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451 | (2) |
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453 | (3) |
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41.5 Electrical safety - insulation and fuses |
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456 | (1) |
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41.6 Semiconductor diodes |
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457 | (1) |
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457 | (1) |
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41.8 Smoothing of the rectified output waveform |
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458 | (3) |
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42 Capacitors and inductors |
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461 | (17) |
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42.1 Capacitors and capacitance |
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462 | (3) |
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42.2 The parallel-plate capacitor |
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465 | (1) |
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42.3 Capacitors connected in parallel and series |
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466 | (2) |
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468 | (1) |
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42.5 Energy stored in capacitors |
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468 | (1) |
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42.6 Practical types of capacitor |
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469 | (2) |
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471 | (1) |
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42.8 Discharging capacitors |
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471 | (1) |
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471 | (2) |
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473 | (1) |
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42.11 Practical inductors |
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473 | (1) |
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42.12 Energy stored by inductors |
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473 | (1) |
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42.13 Inductance of a coil |
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474 | (4) |
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43 Electrical measuring instruments and measurements |
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478 | (16) |
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479 | (1) |
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43.2 Electronic instruments |
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479 | (1) |
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479 | (1) |
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479 | (1) |
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43.5 Instrument `loading' effect |
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479 | (2) |
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481 | (5) |
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43.7 Virtual test and measuring instruments |
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486 | (1) |
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43.8 Virtual digital storage oscilloscopes |
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487 | (3) |
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43.9 Null method of measurement |
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490 | (1) |
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491 | (1) |
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491 | (3) |
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44 Global climate change and the future of electricity production |
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494 | (19) |
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495 | (1) |
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44.2 Global climate change |
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495 | (1) |
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44.3 Evidence of rapid climate change |
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496 | (1) |
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44.4 Consequences of global climate change |
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497 | (1) |
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44.5 How does electric power production affect the global climate? |
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497 | (1) |
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44.6 Generating electrical power using coal |
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498 | (1) |
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44.7 Generating electrical power using oil |
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499 | (2) |
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44.8 Generating electrical power using natural gas |
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501 | (1) |
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44.9 Generating electrical power using nuclear energy |
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502 | (1) |
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44.10 Generating electrical power using hydro power |
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503 | (1) |
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44.11 Generating electrical power using pumped storage |
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504 | (1) |
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44.12 Generating electrical power using wind |
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505 | (1) |
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44.13 Generating electrical power using tidal power |
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505 | (2) |
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44.14 Generating electrical power using biomass |
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507 | (1) |
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44.15 Generating electrical power using solar energy |
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507 | (1) |
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44.16 Harnessing the power of wind, tide and sun on an `energy island' - a future possibility? |
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508 | (3) |
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Revision Test 15 Alternating voltages and currents, capacitors and inductors, measurements and electricity production |
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511 | (2) |
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SECTION IV ENGINEERING SYSTEMS |
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513 | (11) |
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45 Introduction to Engineering systems |
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515 | (9) |
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516 | (1) |
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516 | (1) |
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516 | (1) |
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516 | (1) |
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516 | (1) |
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517 | (1) |
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518 | (2) |
|
|
520 | (1) |
|
45.9 Negative and positive feedback |
|
|
521 | (1) |
|
45.10 Evaluation of system response |
|
|
522 | (2) |
List of main Formulae for Science and Mathematics for Engineering |
|
524 | (7) |
Answers to Practice Exercises |
|
531 | (19) |
Glossary of terms |
|
550 | (7) |
Index |
|
557 | |