Jacaranda Maths Quest 11 General Mathematics Units 1 and 2 for Queensland, 2e learnON & Print

Learning with learnON vii
Teaching with learnON xiii
Acknowledgements xiv

UNIT 1 MONEY, MEASUREMENT, ALGEBRA AND LINEAR EQUATIONS 1

TOPIC 1 CONSUMER ARITHMETIC

1 Consumer arithmetic -- earning and budgeting 3

1.1 Overview 4
1.2 Rates and percentages 5
1.3 Wages 12
1.4 Earning wages 16
1.5 Working overtime 20
1.6 Earnings -- commission and piecework 24
1.7 Payments -- government allowances and pensions 31
1.8 Personal budgets 35
1.9 Review 41
Answers 46

2 Consumer arithmetic -- managing finances 51

2.1 Overview 52
2.2 Unit cost 53
2.3 Mark-ups and discounts 57
2.4 Goods and services tax (GST) 62
2.5 Profit and loss 65
2.6 Simple interest 69
2.7 Compound interest (optional) 74
2.8 Exchange rates 79
2.9 Dividends 82
2.10 Review 87
Answers 90

TOPIC 2 SHAPE AND MEASUREMENT

3 Pythagoras' theorem and mensuration 93

3.1 Overview 94
3.2 Pythagoras' theorem in two dimensions 96
3.3 Pythagoras' theorem in three dimensions 102
3.4 Perimeter and area of polygons and circles 108
3.5 Perimeter and area of sectors and composite shapes 115
3.6 Volume and capacity 125
3.7 Surface area of three-dimensional objects 137
3.8 Review 147

TOPIC 3 SIMILARITY AND SCALE

4 Similar figures and scale factors 155

4.1 Overview 156
4.2 Similarity of two-dimensional figures 157
4.3 Linear scale factors 166
4.4 Scale drawings -- maps and plans 175
4.5 Area and volume scale factors 188
4.6 Review 194
Answers 199

TOPIC 4 ALGEBRA

5 Linear and non-linear relationships 201

5.1 Overview 202
5.2 Substitution 203
5.3 Formulas 208
5.4 Transposition 214
5.5 Review 219
Answers 222

TOPIC 5 LINEAR EQUATIONS AND THEIR GRAPHS

6 Linear equations 225

6.1 Overview 226
6.2 Solving linear equations 227
6.3 Developing linear equations and solving practical problems 232
6.4 Review 236
Answers 239

7 Straight-line graphs 241

7.1 Overview 242
7.2 Constructing straight-line graphs 243
7.3 Determine and interpret the slope and intercepts 254
7.4 Modelling with straight-line graphs 263

UNIT 2 APPLICATIONS OF LINEAR EQUATIONS AND TRIGONOMETRY, MATRICES AND UNIVARIATE DATA ANALYSIS 281

TOPIC 1 APPLICATIONS OF LINEAR EQUATIONS AND THEIR GRAPHS

8 Simultaneous equations and their applications 283

8.1 Overview 284
8.2 Solving simultaneous linear equations graphically 285
8.3 Solving simultaneous equations algebraically 293
8.4 Solving practical problems using simultaneous equations 300
8.5 Piecewise linear graphs and step graphs 307
8.6 Review 321
Answers 325

TOPIC 2 APPLICATIONS OF TRIGONOMETRY

9 Applications of trigonometry 331

9.1 Overview 332
9.2 Trigonometric ratios 334
9.3 Area of triangles 351
9.4 Angles of elevation and depression 357
9.5 The sine rule 362
9.6 The cosine rule 369
9.7 True bearings 375
9.8 Review 382
Answers 388

TOPIC 3 MATRICES

10 Matrices and matrix arithmetic 391

10.1 Overview 392
10.2 Types of matrices 393
10.3 Operations with matrices 403
10.4 Matrix multiplication 409
10.5 Applications of matrices 420
10.6 Review 428
Answers 433

TOPIC 4 UNIVARIATE DATA ANALYSIS 1

11 Univariate data analysis 437

11.1 Overview 438
11.2 Classifying data and displaying categorical data 440
11.3 Dot plots, stem-and-leaf plots, column charts and histograms 453
11.4 Measures of centre 460
11.5 Measures of spread 474
11.6 Review 483

TOPIC 5 UNIVARIATE DATA ANALYSIS 2

12 Univariate data comparisons 495

12.1 Overview 496
12.2 Constructing boxplots 497
12.3 Outliers and fences 503
12.4 Parallel boxplots 508
12.5 Review 516
Answers 522

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PRACTICE ASSESSMENT 3
Unit 2 Examination

PRACTICE ASSESSMENT 4
Units 1 & 2 Examination

Glossary 525