Jacaranda Maths Quest 10 Stage 5 NSW AC Second Edition

Half Title page......Page 1
Title page......Page 3
Copyright page......Page 4
Contents......Page 5
Overview......Page 10
Learnon......Page 11
Acknowledgements......Page 12
1.1 Overview......Page 15
1.2 Simple interest [Stage 5.1]......Page 16
1.3 Buying on terms [Stage 5.1]......Page 20
1.4 Compound interest [Stage 5.2]......Page 25
1.5 Depreciation [Stage 5.2]......Page 32
1.6 Review [Stage 5.2]......Page 36
Answers......Page 40
2.1 Overview......Page 43
2.2 Review of index laws [Stage 5.1]......Page 44
2.3 Negative indices [Stage 5.2]......Page 49
2.4 Fractional indices [Stage 5.3]......Page 53
2.5 Combining index laws [Stage 5.3]......Page 58
2.6 Review......Page 63
Answers......Page 68
3.1 Overview......Page 73
3.2 Pythagoras’ theorem [Stage 4]......Page 74
3.3 Pythagoras’ theorem in three dimensions [Stage 5.3]......Page 81
3.4 Trigonometric ratios [Stage 5.2]......Page 86
3.5 Using trigonometry to calculate side lengths [Stage 5.2]......Page 91
3.6 Using trigonometry to calculate angle size [Stage 5.2]......Page 95
3.7 Angles of elevation and depression [Stage 5.2]......Page 100
3.8 Bearings [Stage 5.2]......Page 105
3.9 Applications [Stages 5.2 and 5.3]......Page 111
3.10 Review......Page 116
Answers......Page 122
4.1 Overview......Page 127
4.2 Calculating relative frequencies [Stage 5.1]......Page 128
4.3 Two- and three-step chance experiments [Stage 5.2]......Page 141
4.4 Independent and dependent events [Stage 5.2]......Page 147
4.5 Conditional probability [Stage 5.2]......Page 153
4.6 Review......Page 157
Answers......Page 162
5.1 Overview......Page 173
5.2 Comparing data displays using mean, median and range [Stage 5.1]......Page 174
5.3 Quartiles and interquartile range [Stage 5.2]......Page 183
5.4 Constructing, interpreting and comparing boxplots [Stage 5.2]......Page 187
5.5 The standard deviation [Stage 5.3]......Page 197
5.6 Comparing data sets [Stage 5.3]......Page 206
5.7 Review......Page 211
Answers......Page 217
6.1 Overview......Page 225
6.2 How is data collected? [Stage 5.1]......Page 226
6.3 Evaluating statistical reports [Stages 5.1 and 5.2]......Page 236
6.4 Statistical investigations [Stages 5.2 and 5.3]......Page 250
6.5 Estimating population means and medians [Stages 5.2 and 5.3]......Page 258
6.6 Review......Page 263
Answers......Page 270
7.1 Overview......Page 277
7.2 Substitution [Stage 5.2]......Page 278
7.3 Adding and subtracting algebraic fractions [Stages 5.2 and 5.3]......Page 283
7.4 Multiplying and dividing algebraic fractions [Stages 5.2 and 5.3]......Page 287
7.5 Solving simple equations [Stage 5.2]......Page 290
7.6 Solving complex linear equations [Stage 5.3]......Page 296
7.7 Rearranging literal equations [Stage 5.3]......Page 300
7.8 Review......Page 304
Answers......Page 308
8.1 Overview......Page 313
8.2 The distance between two points [Stages 5.2 and 5.3]......Page 314
8.3 Sketching linear graphs [Stages 5.2 and 5.3]......Page 318
8.4 Standard forms of the equation of a straight line [Stages 5.2 and 5.3]......Page 324
8.5 The midpoint of a line segment [Stages 5.2 and 5.3]......Page 330
8.6 Parallel and perpendicular lines [Stages 5.2 and 5.3]......Page 333
8.7 Review......Page 343
Answers......Page 348
9.1 Overview......Page 359
9.2 Graphical solution of simultaneous linear equations [Stage 5.2]......Page 360
9.3 Solving simultaneous linear equations using substitution [Stage 5.2]......Page 367
9.4 Solving simultaneous linear equations using elimination [Stage 5.2]......Page 370
9.5 Applications of simultaneous linear equations [Stage 5.2]......Page 375
9.6 Solving simultaneous linear and non-linear equations [Stage 5.3]......Page 379
9.7 Solving linear inequalities [Stage 5.2]......Page 386
9.8 Review......Page 391
Answers......Page 396
10.1 Overview......Page 403
10.2 Area [Stage 5.1]......Page 404
10.3 Total surface area [Stages 5.2 and 5.3]......Page 413
10.4 Volume [Stages 5.2 and 5.3]......Page 421
10.5 Review......Page 435
Answers......Page 441
11.1 Overview......Page 445
11.2 Expanding algebraic expressions [Stages 5.2 and 5.3]......Page 446
11.3 Factorising expressions with three terms [Stages 5.2 and 5.3]......Page 452
11.4 Factorising expressions with two or four terms [Stage 5.3]......Page 457
11.5 Factorising by completing the square [Stage 5.3]......Page 462
11.6 Mixed factorisation [Stage 5.3]......Page 466
11.7 Review......Page 468
Answers......Page 472
12.1 Overview......Page 479
12.2 Solving quadratic equations algebraically [Stage 5.3]......Page 480
12.3 The quadratic formula [Stage 5.3]......Page 487
12.4 Solving quadratic equations graphically [Stage 5.3]......Page 491
12.5 The discriminant [Stage 5.3]......Page 495
12.6 Review......Page 500
Answers......Page 505
13.1 Overview......Page 511
13.2 Plotting parabolas [Stage 5.3]......Page 512
13.3 Sketching parabolas [Stage 5.3]......Page 518
13.4 Sketching parabolas of the form y = a(x – h)2 + k [Stage 5.3]......Page 524
13.5 Sketching parabolas of the form y = ax2 + bx + c [Stage 5.3]......Page 531
13.6 Exponential functions and graphs [Stage 5.3]......Page 535
13.7 The hyperbola [Stage 5.3]......Page 541
13.8 The circle [Stage 5.3]......Page 544
13.9 Review......Page 548
Answers......Page 554
14.1 Overview......Page 577
14.2 Angles, triangles and congruence [Stages 5.2 and 5.3]......Page 578
14.3 Similar triangles [Stages 5.2 and 5.3]......Page 588
14.4 Quadrilaterals [Stages 5.2 and 5.3]......Page 595
14.5 Polygons [Stages 5.2 and 5.3]......Page 606
14.6 Review......Page 611
Answers......Page 617
15.1 Overview......Page 621
15.2 Bivariate data [Stage 5.2]......Page 622
15.3 Lines of best fit [Stage 5.3]......Page 630
15.4 Time as the independent variable [Stages 5.2 and 5.3]......Page 641
15.5 Review......Page 650
Answers......Page 655
16.1 Overview......Page 665
16.2 Rational and irrational numbers [Stage 5.3]......Page 666
16.3 Surds [Stage 5.3]......Page 671
16.4 Operations with surds [Stage 5.3]......Page 675
16.5 Fractional indices [Stage 5.3]......Page 685
16.6 Negative indices [Stage 5.3]......Page 690
16.7 Logarithms [Stage 5.3]......Page 692
16.8 Logarithm laws [Stage 5.3]......Page 696
16.9 Solving equations [Stage 5.3]......Page 701
16.10 Review......Page 707
Answers......Page 711
17.1 Overview......Page 719
17.2 Polynomials [Stage 5.3]......Page 720
17.3 Adding, subtracting and multiplying polynomials [Stage 5.3]......Page 723
17.4 Long division of polynomials [Stage 5.3]......Page 725
17.5 Polynomial values [Stage 5.3]......Page 730
17.6 The remainder and factor theorems [Stage 5.3]......Page 732
17.7 Factorising polynomials [Stage 5.3]......Page 736
17.8 Solving polynomial equations [Stage 5.3]......Page 740
17.9 Review......Page 742
Answers......Page 746
18.1 Overview......Page 751
18.2 Functions and relations [Stage 5.3]......Page 752
18.3 Exponential functions [Stage 5.3]......Page 762
18.4 Cubic functions [Stage 5.3]......Page 770
18.5 Quartic functions [Stage 5.3]......Page 776
18.6 Transformations [Stage 5.3]......Page 780
18.7 Review......Page 788
Answers......Page 792
19.1 Overview......Page 801
19.2 Angles in a circle [Stage 5.3]......Page 802
19.3 Intersecting chords, secants and tangents [Stage 5.3]......Page 809
19.4 Cyclic quadrilaterals [Stage 5.3]......Page 817
19.5 Tangents, secants and chords [Stage 5.3]......Page 821
19.6 Review......Page 828
Answers......Page 833
20.1 Overview......Page 837
20.2 The sine rule [Stage 5.3]......Page 838
20.3 The cosine rule [Stage 5.3]......Page 846
20.4 Area of triangles [Stage 5.3]......Page 850
20.5 The unit circle [Stage 5.3]......Page 855
20.6 Trigonometric functions [Stage 5.3]......Page 862
20.7 Solving trigonometric equations [Stage 5.3]......Page 867
20.8 Review......Page 870
Answers......Page 875
Glossary......Page 885
Index......Page 907