| Introduction |
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vi | |
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Algebra, functions and equations (Topic 1: Algebra and Topic 2: Functions & equations) |
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1 | (33) |
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1A The quadratic form y = ax2 + bx + c |
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1 | (7) |
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1B The completed square form y = a(x - h)2 + k |
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8 | (5) |
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1C The factorised form y = a (x - p)(x - q) |
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13 | (2) |
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1D The quadratic formula and the discriminant |
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15 | (6) |
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1E Intersections of graphs and simultaneous equations |
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21 | (3) |
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1F Using quadratic functions to solve problems |
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24 | (10) |
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2 Exponents and logarithms |
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34 | (37) |
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34 | (9) |
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43 | (6) |
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49 | (2) |
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2D Introduction to logarithms |
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51 | (5) |
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56 | (5) |
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61 | (1) |
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2G Solving exponential equations |
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62 | (9) |
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71 | (15) |
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3A Solving equations by factorising |
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72 | (1) |
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3B Solving equations by substitution |
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73 | (3) |
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76 | (4) |
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3D Using a graphical calculator to solve equations |
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80 | (3) |
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3E Working with identities |
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83 | (3) |
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4 The theory of functions |
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86 | (27) |
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86 | (2) |
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88 | (4) |
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92 | (3) |
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95 | (6) |
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101 | (12) |
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5 Transformations of graphs |
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113 | (19) |
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113 | (3) |
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116 | (3) |
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119 | (2) |
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5D Consecutive transformations |
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121 | (11) |
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132 | (29) |
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132 | (4) |
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6B General series and sigma notation |
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136 | (2) |
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138 | (3) |
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141 | (3) |
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144 | (4) |
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148 | (2) |
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6G Infinite geometric series |
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150 | (5) |
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6H Mixed questions on sequences and series |
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155 | (6) |
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161 | (15) |
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7A Introduction to the binomial theorem |
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161 | (3) |
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164 | (2) |
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7C Applying the binomial theorem |
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166 | (10) |
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Geometry (Topic 3: Circular functions & trigonometry & Topic 4: Vectors) |
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8 Circular measure and trigonometric functions |
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176 | (40) |
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177 | (7) |
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8B Definitions and graphs of the sine and cosine functions |
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184 | (10) |
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8C Definition and graph of the tangent function |
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194 | (4) |
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8D Exact values of trigonometric functions |
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198 | (3) |
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8E Transformations of trigonometric graphs |
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201 | (7) |
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8F Modelling using trigonometric functions |
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208 | (8) |
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9 Trigonometric equations and identities |
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216 | (34) |
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9A Introducing trigonometric equations |
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216 | (8) |
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9B Harder trigonometric equations |
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224 | (9) |
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9C Trigonometric identities |
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233 | (3) |
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9D Using identities to solve equations |
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236 | (3) |
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9E Double angle identities |
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239 | (11) |
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10 Geometry of triangles and circles |
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250 | (45) |
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10A Right-angled triangles |
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251 | (3) |
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254 | (7) |
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261 | (6) |
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267 | (3) |
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10E Trigonometry in three dimensions |
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270 | (5) |
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275 | (4) |
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279 | (3) |
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10H Triangles and circles |
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282 | (13) |
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295 | (53) |
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11A Positions and displacements |
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295 | (9) |
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304 | (5) |
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309 | (4) |
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313 | (5) |
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11E Properties of the scalar product |
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318 | (4) |
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11F Vector equation of a line |
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322 | (8) |
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11G Solving problems involving lines |
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330 | (18) |
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Calculus (Topic 6: Calculus) |
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12 Basic differentiation and its applications |
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348 | (45) |
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12A Sketching derivatives |
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348 | (8) |
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12B Differentiation from first principles |
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356 | (2) |
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12C Rules of differentiation |
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358 | (3) |
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12D Interpreting derivatives and second derivatives |
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361 | (7) |
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12E Differentiating trigonometric functions |
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368 | (2) |
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12F Differentiating exponential and natural logarithm functions |
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370 | (2) |
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372 | (4) |
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376 | (6) |
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12I General points of inflexion |
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382 | (2) |
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384 | (9) |
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13 Basic integration and its applications |
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393 | (27) |
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13A Reversing differentiation |
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393 | (2) |
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13B Constant of integration |
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395 | (1) |
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396 | (3) |
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13D Integrating x-1 and ex |
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399 | (1) |
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13E Integrating trigonometric functions |
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400 | (1) |
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13F Finding the equation of a curve |
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401 | (3) |
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404 | (2) |
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13H Geometrical significance of definite integration |
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406 | (6) |
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13I The area between two curves |
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412 | (8) |
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14 Further differentiation |
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420 | (22) |
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14A Differentiating composite functions using the chain rule |
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420 | (5) |
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14B Differentiating products using the product rule |
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425 | (4) |
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14C Differentiating quotients using the quotient rule |
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429 | (4) |
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14D Optimisation with constraints |
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433 | (9) |
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442 | (24) |
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15A Reversing standard derivatives |
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442 | (4) |
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15B Integration by substitution |
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446 | (7) |
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453 | (4) |
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15D Volumes of revolution |
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457 | (9) |
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Statistics and probability (Topic 5: Statistics & probability) |
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466 | (41) |
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16A Measures of the centre of data |
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466 | (4) |
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470 | (2) |
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16C Frequency tables and grouped data |
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472 | (6) |
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478 | (7) |
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485 | (4) |
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16F Constant changes to data |
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489 | (2) |
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491 | (6) |
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497 | (10) |
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507 | (39) |
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17A Empirical probability |
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507 | (3) |
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17B Theoretical probability |
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510 | (5) |
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17C Combined events and Venn diagrams |
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515 | (5) |
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17D Tree diagrams and finding intersections |
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520 | (5) |
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525 | (3) |
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17F Conditional probability |
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528 | (5) |
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17G Further Venn diagrams |
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533 | (5) |
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17H Selections with and without replacement |
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538 | (8) |
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18 Probability distributions |
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546 | (32) |
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546 | (4) |
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18B Expectation of a discrete random variable |
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550 | (3) |
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18C The binomial distribution |
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553 | (9) |
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18D The normal distribution |
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562 | (7) |
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18E Inverse Normal Distribution |
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569 | (9) |
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19 Questions crossing chapters |
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578 | (10) |
| Answers |
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588 | (61) |
| Glossary |
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649 | (14) |
| Index |
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663 | (6) |
| Acknowledgements |
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669 | (1) |
| Terms and conditions for use of the CD-ROM |
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670 | |
