| Preface |
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ix | |
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1 | (8) |
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1 | (1) |
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2 | (3) |
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5 | (2) |
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7 | (2) |
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9 | (24) |
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Simplification of Algebraic Expressions |
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10 | (5) |
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Highest Common Factor (HCF) and Lowest Common Multiple (LCM) |
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15 | (2) |
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17 | (3) |
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20 | (1) |
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21 | (3) |
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24 | (3) |
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27 | (3) |
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30 | (3) |
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33 | (42) |
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Further Examples on Simple Equations |
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39 | (2) |
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Summary of the Important Points |
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41 | (2) |
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Practical Problems Involving Simple Equations |
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43 | (2) |
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45 | (3) |
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Problems Involving Simple Equations |
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48 | (3) |
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Transposition of Formulae |
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51 | (15) |
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66 | (5) |
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Logarithmic or Indicial Equations |
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71 | (2) |
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73 | (2) |
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75 | (21) |
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Two Unknowns Where the Coefficients Are Whole Numbers |
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75 | (4) |
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Two Unknowns Where the Coefficients Are Fractions |
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79 | (1) |
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Two Unknowns Where the Coefficients Are Decimals |
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80 | (1) |
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Two Unknowns Involving Reciprocals |
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81 | (3) |
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Practical Problems: Simultaneous Equations in Two Unknowns |
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84 | (4) |
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A More Complicated Situation |
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88 | (5) |
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93 | (3) |
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96 | (23) |
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Solution by Factorisation |
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96 | (3) |
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Solution by `Completing the Square' |
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99 | (3) |
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Solution of Quadratic Equations by Formula |
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102 | (6) |
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Simultaneous Equations -- One Linear and One Quadratic |
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108 | (2) |
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Recap: Polynomial Division |
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110 | (1) |
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111 | (1) |
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112 | (1) |
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113 | (4) |
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117 | (2) |
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119 | (22) |
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Plotting of Straight-Line Graphs |
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120 | (2) |
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Determining the Equation to a Straight-Line Graph |
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122 | (5) |
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Graphical Solution of Simultaneous Linear Equations |
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127 | (1) |
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Graphical Solution of Quadratic Equations |
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128 | (5) |
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Graphical Solution of Simultaneous Quadratic and Linear Equations |
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133 | (2) |
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135 | (3) |
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138 | (1) |
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139 | (2) |
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7 Trigonometry and Geometry |
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141 | (54) |
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141 | (5) |
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146 | (3) |
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Alternative Notation for the Right-Angled Triangle, ABC |
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149 | (1) |
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Properties of Angles and Straight Lines |
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150 | (1) |
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151 | (6) |
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Examples Where Trigonometry can be Used |
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157 | (1) |
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158 | (3) |
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161 | (3) |
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The Equation of a Sine Wave |
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164 | (1) |
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165 | (8) |
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Addition of Sine Waves of Equal Frequency |
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173 | (1) |
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174 | (1) |
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Relationships Between Sine, Cosine and Tangents of Angles |
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175 | (2) |
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177 | (2) |
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Introduction to Hyperbolic Functions |
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179 | (1) |
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180 | (1) |
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Solving Equations Using Hyperbolic Functions |
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180 | (2) |
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Addition of sinh(ax) and cosh(ax) |
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182 | (1) |
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Basic Hyperbolic Trigonometric Identities |
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183 | (1) |
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183 | (3) |
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186 | (2) |
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188 | (2) |
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190 | (2) |
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192 | (3) |
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195 | (18) |
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Inverse Trigonometric Functions |
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196 | (2) |
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Cosine Rule and the Sine Rule for Non-Right-Angled Triangles |
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198 | (1) |
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Plane Trigonometry -- Sine and Cosine Rules |
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199 | (3) |
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Application of Trigonometry |
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202 | (4) |
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206 | (4) |
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210 | (1) |
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211 | (2) |
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213 | (21) |
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213 | (8) |
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221 | (1) |
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222 | (1) |
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223 | (1) |
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223 | (1) |
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224 | (8) |
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232 | (2) |
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10 Volume-Mass, Centre of Gravity, Moment |
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234 | (33) |
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235 | (2) |
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237 | (1) |
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Oblique Prisms and Pyramids |
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238 | (1) |
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239 | (25) |
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264 | (3) |
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11 Differential Calculus (Differentiation) |
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267 | (24) |
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Gradient of a Straight Line |
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268 | (1) |
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Infinitesimally Small Changes `d' |
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268 | (2) |
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270 | (1) |
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271 | (1) |
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Differentiation from First Principles |
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271 | (4) |
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General Rule for Differentiating a Power |
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275 | (1) |
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Differential Coefficient of a Constant |
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276 | (1) |
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Differential Coefficient of a Sum of Terms |
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276 | (1) |
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Second Differential Coefficient |
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277 | (1) |
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Distance, Velocity and Acceleration |
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278 | (1) |
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279 | (6) |
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Differentiation of sin(x) and cos(x) |
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285 | (1) |
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Differentiation of ln(x) and ex |
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286 | (1) |
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287 | (1) |
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288 | (3) |
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12 Integral Calculus (Integration) |
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291 | (23) |
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291 | (1) |
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General Rule for Integration of Powers of x |
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292 | (1) |
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Integration of a Sum of Terms |
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293 | (2) |
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Evaluating the Constant of Integration |
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295 | (2) |
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Definite Integration: Area Under a Curve |
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297 | (8) |
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Integration as a Summation |
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305 | (5) |
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310 | (4) |
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13 Advanced Calculus: Methods of Differentiation |
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314 | (34) |
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Differentiation -- The Product Rule |
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314 | (1) |
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314 | (2) |
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316 | (5) |
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321 | (11) |
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Applications of Integration |
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332 | (10) |
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Application of Differentiation |
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342 | (3) |
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345 | (3) |
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348 | (51) |
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348 | (1) |
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Tabular Presentation of Data |
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348 | (2) |
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350 | (1) |
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Pictorial Representation of Data |
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351 | (1) |
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352 | (1) |
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353 | (1) |
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Cumulative Frequency Curves (Ogives) |
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353 | (1) |
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354 | (1) |
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355 | (1) |
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356 | (2) |
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358 | (2) |
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360 | (1) |
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Calculation of the Mean of a Grouped Frequency Distribution |
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361 | (5) |
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366 | (6) |
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Correlation and Regression |
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372 | (10) |
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382 | (2) |
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The Addition Law of Probability |
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384 | (1) |
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The Multiplication Law of Probability |
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385 | (1) |
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385 | (13) |
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398 | (1) |
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15 Selection of Examination Standard Questions |
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399 | (66) |
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Suggested Solutions to Examination Questions |
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413 | (52) |
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465 | (22) |
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465 | (4) |
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Approximating and Estimating |
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469 | (1) |
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470 | (6) |
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476 | (2) |
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478 | (3) |
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481 | (6) |
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APPENDIX 2 COMPLEX NUMBERS |
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487 | (14) |
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487 | (1) |
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487 | (1) |
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487 | (1) |
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Diagrammatic Representation |
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488 | (6) |
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Alternating Current in a Resistor |
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494 | (1) |
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Alternating Current in an Inductor |
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495 | (1) |
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Alternating Current in a Capacitor |
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495 | (1) |
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Inductive and Capacitive Reactance |
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496 | (1) |
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496 | (1) |
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Complex Number Applications |
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497 | (2) |
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499 | (1) |
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Solutions to Test Example -- Complex |
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499 | (2) |
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APPENDIX 3 LAPLACE TRANSFORMS |
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501 | (31) |
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501 | (1) |
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Standard Laplace Transforms |
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502 | (2) |
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Standard Inverse Laplace Transforms |
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504 | (1) |
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Inverse Laplace Transforms Using Partial Fractions |
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505 | (1) |
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Inverse Laplace Transforms Using `Completing the Square' |
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506 | (2) |
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508 | (1) |
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Solving Differential Equations Using Laplace Transforms |
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509 | (16) |
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525 | (1) |
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Solutions to Test Examples -- LAPLACE |
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526 | (6) |
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APPENDIX 4 FOURIER ANALYSIS |
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532 | (29) |
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532 | (1) |
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533 | (5) |
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538 | (4) |
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Functions with Periods Other than 2π |
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542 | (1) |
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543 | (6) |
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Rectified Sinusoidal Waveforms |
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549 | (7) |
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556 | (1) |
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Solution to Test Examples -- Fourier |
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557 | (4) |
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APPENDIX 5 SOLUTIONS TO TEXT EXAMPLES |
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561 | (66) |
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Solutions to Test Examples 1 |
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561 | (2) |
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Solutions to Test Examples 2 |
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563 | (3) |
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Solutions to Test Examples 3 |
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566 | (4) |
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Solutions to Test Examples 4 |
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570 | (8) |
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Solutions to Test Examples 5 |
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578 | (4) |
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Solutions to Test Examples 6 |
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582 | (7) |
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Solutions to Test Examples 7 |
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589 | (3) |
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Solutions to Test Examples 8 |
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592 | (7) |
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Solutions to Test Examples 9 |
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599 | (7) |
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Solutions to Test Examples 10 |
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606 | (7) |
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Solutions to Test Examples 11 |
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613 | (3) |
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Solutions to Test Examples 12 |
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616 | (5) |
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Solutions to Test Examples 13 |
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621 | (3) |
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Solutions to Test Examples 14 |
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624 | (3) |
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APPENDIX 6 MATHEMATICAL FORMULAE |
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627 | (17) |
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629 | (2) |
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Applications of Integration |
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631 | (2) |
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633 | (2) |
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635 | (1) |
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636 | (6) |
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Normal Probabilities for Positive Values of z |
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642 | (2) |
| Index |
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644 | |
