Jacaranda Maths Quest 10+10A (for Victorian Curriculum v2.0)
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Table of Contents:
About this resource ix
Acknowledgements xvi
1 Exponents, surds and logarithms 1
1.1 Overview 2
1.2 Number classification review 4
1.3 Surds (10A) 10
1.4 Operations with surds (10A) 14
1.5 Review of exponent laws 28
1.6 Negative exponents 36
1.7 Fractional exponents (10A) 42
1.8 Combining exponent laws 48
1.9 Application of exponentials: Compound interest 54
1.10 Logarithms 61
1.11 Logarithm laws (10A) 69
1.12 Solving equations (10A) 76
1.13 Review 84
Answers 96
2 Algebra and equations 105
2.1 Overview 106
2.2 Substitution 108
2.3 Adding and subtracting algebraic fractions 115
2.4 Multiplying and dividing algebraic fractions 121
2.5 Solving simple equations 126
2.6 Solving multi-step equations 133
2.7 Literal equations 140
2.8 Review 146
Answers 151
3 Networks 157
3.1 Overview 158
3.2 Properties of networks 163
3.3 Planar graphs 176
3.4 Connected graphs 184
3.5 Trees and their applications (Extending) 195
3.6 Review 204
Answers 212
4 Linear relationships 219
4.1 Overview 220
4.2 Sketching linear graphs 224
4.3 Determining linear equations 235
4.4 Parallel and perpendicular lines 250
4.5 Graphical solution of simultaneous linear equations 255
4.6 Solving simultaneous linear equations using substitution 264
4.7 Solving simultaneous linear equations using elimination 269
4.8 Applications of simultaneous linear equations 275
4.9 Solving simultaneous linear and non-linear equations (10A) 283
4.10 Solving linear inequalities 293
4.11 Inequalities on the Cartesian plane 302
4.12 Review 312
Answers 321
5 Trigonometry I 337
5.1 Overview 338
5.2 Pythagoras’ theorem 341
5.3 Pythagoras’ theorem in three dimensions (10a) 350
5.4 Trigonometric ratios 356
5.5 Using trigonometry to calculate side lengths 363
5.6 Using trigonometry to calculate angle size 369
5.7 Angles of elevation and depression 376
5.8 Bearings 381
5.9 Applications 388
5.10 Review 396
Answers 404
6 Surface area and volume 409
6.1 Overview 410
6.2 Area 414
6.3 Total surface area 424
6.4 Volume 435
6.5 Review 449
Answers 457
7 Quadratic expressions 461
7.1 Overview 462
7.2 Expanding algebraic expressions 464
7.3 Factorising expressions with three terms 472
7.4 Factorising expressions with two or four terms 478
7.5 Factorising by completing the square 483
7.6 Mixed factorisation 489
7.7 Review 493
Answers 499
8 Quadratic equations 505
8.1 Overview 506
8.2 Solving quadratic equations algebraically 508
8.3 The quadratic formula 517
8.4 Solving quadratic equations graphically 522
8.5 The discriminant 531
8.6 Review 538
Answers 546
Semester review 1 552
9 Non-linear relationships 555
9.1 Overview 556
9.2 Plotting parabolas from a table of values 560
9.3 Sketching parabolas using transformations 569
9.4 Sketching parabolas using turning point form 580
9.5 Sketching parabolas in expanded form 589
9.6 Exponential graphs 596
9.7 Inverse proportion 604
9.8 Sketching the graph of a reciprocal 609
9.9 Sketching the circle 615
9.10 Review 621
Answers 629
10 Deductive geometry 653
10.1 Overview 654
10.2 Angles, triangles and congruence 657
10.3 Scale factor and similar triangles 670
10.4 Calculating measurements from scale drawings 679
10.5 Creating scale drawings 690
10.6 Quadrilaterals 699
10.7 Polygons 712
10.8 Review 719
Answers 728
11 Probability 733
11.1 Overview 734
11.2 Review of probability 737
11.3 Tree diagrams 754
11.4 Independent and dependent events 762
11.5 Conditional probability 768
11.6 Counting principles and factorial notation (10A) 774
11.7 Review 790
Answers 797
12 Univariate data 807
12.1 Overview 808
12.2 Measures of central tendency 813
12.3 Measures of spread 827
12.4 Box plots 834
12.5 The standard deviation (10A) 845
12.6 Comparing data sets 858
12.7 Populations and samples 866
12.8 Evaluating inquiry methods and statistical reports 874
12.9 Review 888
Answers 900
13 Bivariate data 911
13.1 Overview 912
13.2 Bivariate data 916
13.3 Two-way frequency tables and Likert scales 928
13.4 Lines of best fit by eye 939
13.5 Linear regression and technology (10A) 951
13.6 Time series 959
13.7 Review 967
Answers 976
14 Circle geometry (10A) 987
14.1 Overview 988
14.2 Angles in a circle 992
14.3 Intersecting chords, secants and tangents 1000
14.4 Cyclic quadrilaterals 1008
14.5 Tangents, secants and chords 1013
14.6 Review 1020
Answers 1027
15 Trigonometry II (10A) 1031
15.1 Overview 1032
15.2 The sine rule 1035
15.3 The cosine rule 1045
15.4 Area of triangles 1051
15.5 The unit circle 1057
15.6 Trigonometric functions 1064
15.7 Solving trigonometric equations 1072
15.8 Review 1078
Answers 1086
16 Polynomials (10A) 1093
16.1 Overview 1094
16.2 Polynomials 1096
16.3 Adding, subtracting and multiplying polynomials 1100
16.4 Long division of polynomials 1104
16.5 Polynomial values 1109
16.6 The remainder and factor theorems 1113
16.7 Factorising polynomials 1116
16.8 Solving polynomial equations 1122
16.9 Review 1125
Answers 1130
17 Functions and relations (10A) 1135
17.1 Overview 1136
17.2 Functions and relations 1142
17.3 Exponential functions 1155
17.4 Cubic functions 1165
17.5 Quartic functions 1173
17.6 Transformations 1178
17.7 Review 1187
Answers 1193
18 Algorithms and pseudocode 1201
18.1 Overview 1202
18.2 Algorithms 1204
18.3 Pseudocode 1210
18.4 Review 1228
Answers 1230
Semester review 2 1232
19 Algorithmic thinking
19.1 Overview
19.2 Programs
19.3 Data structures
19.4 Algorithms
19.5 Matrices
19.6 Graphics
19.7 Simulations
19.8 Review
Answers
Glossary 1234
Index 1245
