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# Maths Quest 10+10a for the Australian Curriculum 2E & eBookPLUS

Author/s Boucher 9780730317890 November 2014 918 \$69.95

Maths Quest 10+10A for the Australian Curriculum Second Edition
has been updated based on in-depth research and feedback from practising teachers of Mathematics.

KEY FEATURES

Worked solutions available to students and teachers for every problem solving and reasoning question.
• An enhanced emphasis on both problem solving & reasoning, creating greater understanding of both mathematical concepts and skills.
• Assessment material incorporating the Australian Curriculum Achievement Standards.
• Improvements to student engagement, with enhanced Individual Pathway activities, new interactivities and new videos telling the Story of Mathematics.
• Teacher support: eGuidePLUS provides online access to the student textbook, teacher notes on each lesson, a range of activities to engage students and end of top assessment items.

Maths Quest 10+10A for Australian Curriculum 2E and eBookPLUS is a hard-copy student text accompanied by eBookPLUS.

> eBookPLUS resources include:

• Access from any digital device PC/MAC/iPad/Android Tablet.
• Worksheets - Word documents designed for easy customisation and editing.
Interactivities and games to reinforce and enhance student learning.
eLessons - engaging video clips and supporting material.
Weblinks to relevant support material on the internet.
ProjectsPLUS - unique ICT-based projects that provide opportunities for students to demonstrate creativity, thinking skills and teamwork.

Overview x
Acknowledgements xii

NUMBER AND ALGEBRA
Topic 1 Indices 2
1.1 Overview 2
1.2 Review of index laws 4
Exercise 1.2 6
1.3 Negative indices 9
Exercise 1.3 11
1.4 Fractional indices 14
Exercise 1.4 15
1.5 Combining index laws 18
Exercise 1.5 20
1.6 Review ONLINE ONLY 25
eBookPLUS activities 29
NUMBER AND ALGEBRA

Topic 2 Algebra and equations 34
2.1 Overview 34
2.2 Substitution 36
Exercise 2.2 38
2.3 Adding and subtracting algebraic fractions 41
Exercise 2.3 44
2.4 Multiplying and dividing algebraic fractions 45
Exercise 2.4 47
2.5 Solving simple equations 49
Exercise 2.5 52
2.6 Solving multi-step equations 55
Exercise 2.6 58
2.7 Literal equations 60
Exercise 2.7 61
2.8 Review ONLINE ONLY 63
eBookPLUS activities 67
NUMBER AND ALGEBRA

Topic 3 Coordinate geometry 72
3.1 Overview 72
3.2 Sketching linear graphs 74
Exercise 3.2 78
3.3 Determining linear equations 80
Exercise 3.3 84
3.4 The distance between two points 87
Exercise 3.4 89
3.5 The midpoint of a line segment 91
Exercise 3.5 93
3.6 Parallel and perpendicular lines 94
Exercise 3.6 99
3.7 Review ONLINE ONLY 105
eBookPLUS activities 109
NUMBER AND ALGEBRA

Topic 4 Simultaneous linear
equations and inequalities 116
4.1 Overview 116
4.2 Graphical solution of simultaneous
linear equations 118
Exercise 4.2 122
4.3 Solving simultaneous linear equations
using substitution 124
Exercise 4.3 126
4.4 Solving simultaneous linear equations
using elimination 128
Exercise 4.4 130
4.5 Applications of simultaneous linear equations 133
Exercise 4.5 135
4.6 Solving simultaneous linear and non-linear
equations 137
Exercise 4.6 142
4.7 Solving linear inequalities 144
Exercise 4.7 147
4.8 Inequalities on the Cartesian plane 149
Exercise 4.8 153
4.9 Solving simultaneous linear inequalities 155
Exercise 4.9 157
4.10 Review ONLINE ONLY 160
eBookPLUS activities 165
MEASUREMENT AND GEOMETRY

Topic 5 Trigonometry I 172
5.1 Overview 172
5.2 Pythagoras’ theorem 174
Exercise 5.2 178
5.3 Pythagoras’ theorem in three dimensions 181
Exercise 5.3 184
5.4 Trigonometric ratios 186
Exercise 5.4 189
5.5 Using trigonometry to calculate side
lengths 192
Exercise 5.5 194
5.6 Using trigonometry to calculate angle size 197
Exercise 5.6 199
5.7 Angles of elevation and depression 202
Exercise 5.7 203
5.8 Bearings 207
Exercise 5.8 211
5.9 Applications 213
Exercise 5.9 214
5.10 Review ONLINE ONLY 219
eBookPLUS activities 223
MEASUREMENT AND GEOMETRY

Topic 6 Surface area and
volume 228
6.1 Overview 228
6.2 Area 230
Exercise 6.2 234
6.3 Total surface area 239
Exercise 6.3 244
6.4 Volume 248
Exercise 6.4 254
6.5 Review ONLINE ONLY 261
eBookPLUS activities 265
NUMBER AND ALGEBRA

expressions 268
7.1 Overview 268
7.2 Expanding algebraic expressions 270
Exercise 7.2 273
7.3 Factorising expressions with three terms 276
Exercise 7.3 279
7.4 Factorising expressions with two or
four terms 281
Exercise 7.4 283
7.5 Factorising by completing the square 287
Exercise 7.5 290
7.6 Mixed factorisation 291
Exercise 7.6 292
7.7 Review ONLINE ONLY 295
eBookPLUS activities 299
NUMBER AND ALGEBRA

8.1 Overview 304
8.2 Solving quadratic equations algebraically 306
Exercise 8.2 310
Exercise 8.3 315
8.4 Solving quadratic equations graphically 318
Exercise 8.4 320
8.5 The discriminant 323
Exercise 8.5 326
8.6 Review ONLINE ONLY 329
eBookPLUS activities 333
NUMBER AND ALGEBRA

Topic 9 Non-linear
relationships 336
9.1 Overview 336
9.2 Plotting parabolas 338
Exercise 9.2 342
9.3 Sketching parabolas 345
Exercise 9.3 349
9.4 Sketching parabolas in turning point form 351
Exercise 9.4 355
9.5 Sketching parabolas of the form
y = ax2 + bx + c 358
Exercise 9.5 361
9.6 Exponential functions and graphs 362
Exercise 9.6 365
9.7 The hyperbola 368
Exercise 9.7 370
9.8 The circle 372
Exercise 9.8 374
9.9 Review ONLINE ONLY 377
eBookPLUS activities 381
MEASUREMENT AND GEOMETRY

Topic 10 Deductive geometry 394
10.1 Overview 394
10.2 Angles, triangles and congruence 396
Exercise 10.2 401
10.3 Similar triangles 406
Exercise 10.3 408
Exercise 10.4 418
10.5 Polygons 423
Exercise 10.5 424
10.6 Review ONLINE ONLY 429
eBookPLUS activities 433
ProjectsPLUS ICT ACTIVITY
Getting the budget in order pro-0087 436
STATISTICS AND PROBABILITY

Topic 11 Probability 438
11.1 Overview 438
11.2 Review of probability 440
Exercise 11.2 452
11.3 Tree diagrams 456
Exercise 11.3 459
11.4 Independent and dependent events 462
Exercise 11.4 465
11.5 Conditional probability 469
Exercise 11.5 471
11.6 Subjective probability 473
Exercise 11.6 474
11.7 Review ONLINE ONLY 477
eBookPLUS activities 481
STATISTICS AND PROBABILITY

Topic 12 Univariate data 488
12.1 Overview 488
12.2 Measures of central tendency 490
Exercise 12.2 495
Exercise 12.3 503
12.4 Box-and-whisker plots 506
Exercise 12.4 512
12.5 The standard deviation 516
Exercise 12.5 523
12.6 Comparing data sets 525
Exercise 12.6 527
12.7 Review ONLINE ONLY 533
eBookPLUS activities 537
STATISTICS AND PROBABILITY

Topic 13 Bivariate data 544
13.1 Overview 544
13.2 Bivariate data 546
Exercise 13.2 549
13.3 Lines of best fi t 554
Exercise 13.3 561
13.4 Time series 567
Exercise 13.4 572
13.5 Review ONLINE ONLY 577
eBookPLUS activities 581
STATISTICS AND PROBABILITY

Topic 14 Statistics in the media 586
14.1 Overview 586
14.2 Populations and samples 588
Exercise 14.2 591
14.3 Primary and secondary data 594
Exercise 14.3 599
14.4 Evaluating inquiry methods and
statistical reports 603
Exercise 14.4 611
14.5 Statistical investigations 616
Exercise 14.5 620
14.6 Review ONLINE ONLY 623
eBookPLUS activities 627
ProjectsPLUS ICT ACTIVITY
Climate change pro-0100 632
NUMBER AND ALGEBRA

Topic 15 Financial mathematics 634
15.1 Overview 634
Exercise 15.2 637
Exercise 15.3 641
15.4 Successive discounts 645
Exercise 15.4 647
15.5 Compound interest 649
Exercise 15.5 653
15.6 Depreciation 656
Exercise 15.6 657
15.7 Loan repayments 660
Exercise 15.7 661
15.8 Review ONLINE ONLY 663
eBookPLUS activities 667
NUMBER AND ALGEBRA

Topic 16 Real numbers 670
16.1 Overview 670
16.2 Number classification review 672
Exercise 16.2 675
FMPrelims.indd 7 9/22/14 3:08 PM
16.3 Surds 677
Exercise 16.3 679
16.4 Operations with surds 680
Exercise 16.4 688
16.5 Fractional indices 691
Exercise 16.5 693
16.6 Negative indices 696
Exercise 16.6 697
16.7 Logarithms 698
Exercise 16.7 700
16.8 Logarithm laws 701
Exercise 16.8 704
16.9 Solving equations 706
Exercise 16.9 709
16.10 Review ONLINE ONLY 713
eBookPLUS activities 717
NUMBER AND ALGEBRA

Topic 17 Polynomials 722
17.1 Overview 722
17.2 Polynomials 724
Exercise 17.2 725
polynomials 726
Exercise 17.3 727
17.4 Long division of polynomials 729
Exercise 17.4 732
17.5 Polynomial values 734
Exercise 17.5 735
17.6 The remainder and factor theorems 736
Exercise 17.6 738
17.7 Factorising polynomials 739
Exercise 17.7 742
17.8 Solving polynomial equations 744
Exercise 17.8 745
17.9 Review ONLINE ONLY 747
eBookPLUS activities 751
NUMBER AND ALGEBRA

Topic 18 Functions and
relations 756
18.1 Overview 756
18.2 Functions and relations 758
Exercise 18.2 766
18.3 Exponential functions 769
Exercise 18.3 773
18.4 Cubic functions 778
Exercise 18.4 781
18.5 Quartic functions 783
Exercise 18.5 785
18.6 Transformations 787
Exercise 18.6 793
18.7 Review ONLINE ONLY 795
eBookPLUS activities 799
MEASUREMENT AND GEOMETRY

Topic 19 Circle geometry 804
19.1 Overview 804
19.2 Angles in a circle 806
Exercise 19.2 811
19.3 Intersecting chords, secants and
tangents 814
Exercise 19.3 818
Exercise 19.4 822
19.5 Tangents, secants and chords 825
Exercise 19.5 827
19.6 Review ONLINE ONLY 831
eBookPLUS activities 835
MEASUREMENT AND GEOMETRY

Topic 20 Trigonometry II 838
20.1 Overview 838
20.2 The sine rule 840
Exercise 20.2 847
20.3 The cosine rule 849
Exercise 20.3 852
20.4 Area of triangles 854
Exercise 20.4 856
20.5 The unit circle 860
Exercise 20.5 863
20.6 Trigonometric functions 866
Exercise 20.6 868
20.7 Solving trigonometric equations 871
Exercise 20.7 872
20.8 Review ONLINE ONLY 875
eBookPLUS activities 879

Glossary 885
Index 893

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