16.7 Choices and outcomes Worked exemplars Ready to progress? Review questions
459 465 466 466
17 Quadratic equations
468
17.1 Plotting quadratic graphs 469 17.2 Solving quadratic equations by factorisation 472 17.3 Solving a quadratic equation by using the quadratic formula 478 17.4 Solving quadratic equations by completing the square 481 17.5 The significant points of a quadratic curve 485 17.6 Solving one linear and one non-linear equation using graphs 490 17.7 Solving quadratic equations by the method of intersection 492 Solving linear and non-linear 17.8 simultaneous equations algebraically 496 499 17.9 Quadratic inequalities Worked exemplars 502 Ready to progress? 504 Review questions 504
18 Sampling and more complex diagrams
506
18.1 18.2 18.3 18.4 18.5
Collecting data Frequency polygons Cumulative frequency graphs Box plots Histograms Worked exemplars Ready to progress? Review questions
507 510 514 520 524 531 533 533
19
Combined events
536
19.1 Addition rules for outcomes of events 537 19.2 Combined events 539 19.3 Tree diagrams 542 19.4 Independent events 547 19.5 Conditional probability 550 Worked exemplars 553 Ready to progress? 554 Review questions 554
20
Properties of circles
556
20.1 20.2 20.3 20.4
Circle theorems Cyclic quadrilaterals Tangents and chords Alternate segment theorem Worked exemplars Ready to progress? Review questions
557 564 567 571 574 576 576
206745 GCSE Maths Higher SB_Contents_AQA.indd 5
21 Variation 21.1 21.2
578
Direct proportion 579 Inverse proportion 585 Worked exemplars 590 Ready to progress? 592 Review questions 592
22 Triangles
594
22.1 Further 2D problems 22.2 Further 3D problems 22.3 Trigonometric ratios of angles between 0° and 360° 22.4 Solving any triangle 22.5 Using sine to calculate the area of a triangle Worked exemplars Ready to progress? Review questions
595 598
23 Graphs
626
23.1 23.2 23.3 23.4 23.5 23.6 23.7
602 609 619 622 624 624
Distance–time graphs 627 Velocity–time graphs 633 Estimating the area under a curve 638 Rates of change 641 Equation of a circle 644 Other graphs 647 Transformations of the graph y = f (x) 653 Worked exemplars 659 Ready to progress? 661 Review questions 661
24 Algebraic fractions and functions
664
24.1 24.2 24.3 24.4 24.5
Algebraic fractions 665 Changing the subject of a formula 670 Functions 672 Composite functions 675 Iteration 676 Worked exemplars 680 Ready to progress? 682 Review questions 682
25
Vector geometry
25.1 25.2
Properties of vectors 685 Vectors in geometry 690 Worked exemplars 696 Ready to progress? 698 Review questions 698
684
Glossary
700
Index
708
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