Worked exemplars Ready to progress? Review questions
244 246 246
9 Length, area and volume
248
9.1 Circumference and area of a circle 9.2 Area of a parallelogram 9.3 Area of a trapezium 9.4 Sectors 9.5 Volume of a prism 9.6 Cylinders 9.7 Volume of a pyramid 9.8 Cones 9.9 Spheres Worked exemplars Ready to progress? Review questions
249 252 253 256 259 262 264 266 268 270 272 272
10
274
Linear graphs
12 Similarity
344
12.1 12.2
345 351 358 361 361
Similar triangles Areas and volumes of similar shapes Worked exemplars Ready to progress? Review questions
13 Exploring and applying probability 13.1 Experimental probability 13.2 Mutually exclusive and exhaustive outcomes 13.3 Expectation 13.4 Probability and two-way tables 13.5 Probability and Venn diagrams Worked exemplars Ready to progress? Review questions
362 363 368 372 374 377 382 384 384
14 Powers and standard form 386
10.1 Drawing linear graphs from points 10.2 Gradient of a line 10.3 Drawing graphs by gradientintercept and cover-up methods 10.4 Finding the equation of a line from its graph 10.5 Real-life uses of graphs 10.6 Solving simultaneous equations using graphs 10.7 Parallel and perpendicular lines Worked exemplars Ready to progress? Review questions
275 278
295 297 300 302 302
15 Equations and inequalities 402
11
304
410
Right-angled triangles
282 286 290
11.1 Pythagoras’ theorem 305 11.2 Finding the length of a shorter side 307 11.3 Applying Pythagoras’ theorem in real-life situations 309 11.4 Pythagoras’ theorem and isosceles triangles 311 11.5 Pythagoras’ theorem in three dimensions 314 11.6 Trigonometric ratios 316 11.7 Calculating angles 319 11.8 Using the sine and cosine functions 321 11.9 Using the tangent function 326 11.10 Which ratio to use 328 11.11 Solving problems using trigonometry 332 11.12 Trigonometry and bearings 336 11.13 Trigonometry and isosceles triangles 338 Worked exemplars 340 Ready to progress? 342 Review questions 342
206745 GCSE Maths Higher SB_Contents_AQA.indd 4
14.1 Powers (indices) 387 14.2 Rules for multiplying and dividing powers 389 14.3 Standard form 391 Worked exemplars 399 Ready to progress? 400 Review questions 400
15.1 Linear equations 15.2 Elimination method for simultaneous equations 15.3 Substitution method for simultaneous equations 15.4 Balancing coefficients to solve simultaneous equations 15.5 Using simultaneous equations to solve problems 15.6 Linear inequalities 15.7 Graphical inequalities 15.8 Trial and improvement Worked exemplars Ready to progress? Review questions
16 Counting, accuracy, powers and surds
403 408
411 413 416 421 426 430 432 432
436
16.1 Rational numbers, reciprocals, terminating and recurring decimals 437 16.2 Estimating powers and roots 440 16.3 Negative and fractional powers 442 16.4 Surds 447 16.5 Limits of accuracy 452 16.6 Problems involving limits of accuracy 455
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