Jacaranda Maths Quest General Mathematics 11 VCE Units 1&2

Half title page......Page 1
Title page......Page 3
Copyright page......Page 4
Contents......Page 5
About this resource......Page 9
eBookPLUS features......Page 10
studyON — an invaluable exam preparation tool......Page 11
About eBookPLUS and studyON......Page 12
Acknowledgements......Page 13
1.1.1 Introduction......Page 15
1.1.2 Kick off with CAS......Page 16
1.2.1 Identifying linear relations......Page 17
1.2.2 Rules for linear relations......Page 18
1.2.3 Transposing linear equations......Page 20
1.3.1 Solving linear equations with one variable......Page 23
1.3.2 Substituting into linear equations......Page 25
1.3.3 Literal linear equations......Page 26
1.4.2 Word problems with more than one unknown......Page 29
1.4.3 Tables of values......Page 30
1.4.4 Linear relations defined recursively......Page 32
1.5.1 Solving simultaneous equations graphically......Page 37
1.5.2 Solving simultaneous equations using substitution......Page 39
1.5.3 Solving simultaneous equations using elimination......Page 40
1.6.1 Setting up simultaneous equations......Page 45
1.6.2 Break-even points......Page 46
1.7 Review: exam practice......Page 53
Topic 1 Linear relations and equations......Page 58
TOPIC 1......Page 63
2.1.1 Introduction......Page 64
2.1.2 Kick off with CAS......Page 65
2.2.1 Order of operations......Page 66
2.2.2 Directed numbers......Page 67
2.2.3 Scientific notation......Page 69
2.2.4 Significant figures and rounding......Page 71
2.2.5 Exact and approximate answers......Page 73
2.3.3 Scientific notation and orders of magnitude......Page 77
2.3.4 Units of measure......Page 78
2.3.5 Logarithmic scales......Page 79
2.3.6 Why use a logarithmic scale instead of a linear scale?......Page 81
2.4.1 Percentages......Page 83
2.4.2 Ratios......Page 84
2.4.4 Rates......Page 85
2.4.6 The unitary method......Page 86
2.5 Review: exam practice......Page 92
Topic 2 Computation and practical arithmetic......Page 95
3.1.1 Introduction......Page 98
3.1.2 Kick off with CAS......Page 99
3.2.1 Calculating percentage change......Page 100
3.3.2 Percentage dividends......Page 106
3.3.4 Mark-ups and discounts......Page 107
3.3.5 Goods and services tax (GST)......Page 108
3.4.1 The simple interest formula......Page 113
3.4.2 Calculating the principal, rate or time......Page 114
3.4.3 Simple interest loans......Page 115
3.4.4 Cash flow......Page 116
3.4.5 Minimum balance calculations......Page 117
3.5.1 Step-by-step compounding......Page 123
3.5.2 The compound interest formula......Page 124
3.5.3 Calculating the interest rate or principal......Page 125
3.5.4 Non-annual compounding......Page 126
3.5.6 Spending power......Page 127
3.6.3 Debit cards......Page 132
3.6.4 Personal loans......Page 133
3.6.6 The effective rate of interest......Page 135
3.7 Review: exam practice......Page 140
Topic 3 Financial arithmetic......Page 143
TOPICS 2 and 3......Page 147
4.1.1 Introduction......Page 148
4.1.2 Kick off with CAS......Page 149
4.2.2 Describing matrices......Page 150
4.2.3 Networks......Page 151
4. 2.5 Elements of matrices......Page 153
4.2.7 The zero matrix......Page 154
4.3.1 Matrix addition and subtraction......Page 159
4.3.3 Subtracting matrices......Page 160
4.4.1 Scalar multiplication......Page 164
4.4.3 Multiplying matrices......Page 166
4.4.4 Multiplying by the identity matrix......Page 168
4.4.5 Powers of square matrices......Page 169
4.5.1 Inverse matrices......Page 174
4.5.2 Finding inverse matrices......Page 175
4.5.3 Using inverse matrices to solve problems......Page 177
4.5.4 Using inverse matrices to solve a system of simultaneous equations......Page 178
4.5.5 Using matrix equations to solve worded problems......Page 179
4.5.6 Adjacency matrices......Page 180
4. 5.7 Determining the number of connections between objects......Page 181
4.6 Review: exam practice......Page 189
Topic 4 Matrices......Page 194
5.1.1 Introduction......Page 199
5.1.2 Kick off with CAS......Page 200
5.2.1 Graphs......Page 201
5.2.2 The degree of a vertex......Page 204
5.2.3 Isomorphic graphs......Page 205
5.2.5 Characteristics of adjacency matrices......Page 207
5.3 Planar graphs......Page 217
5.3.1 Euler’s formula......Page 219
5.4.1 Traversing connected graphs......Page 225
5.4.3 Hamiltonian pathsand cycles......Page 227
5.5.1 Weighted graphs......Page 233
5.5.3 Prim’s algorithm......Page 234
5.6 Review: exam practice......Page 243
Topic 5 Graphs and networks......Page 252
6.1.1 Introduction......Page 264
6.1.2 Kick off with CAS......Page 265
6.2.3 Sequences expressed as functions......Page 266
6.2.5 The common difference......Page 267
6.2.6 Equations representing arithmetic sequences......Page 268
6.2.8 Determining other values of an arithmetic sequence......Page 270
6.2.9 Graphical displays of sequences......Page 271
6.2.10 Drawing graphs of sequences......Page 272
6.2.12 Simple interest......Page 276
6.2.13 Depreciating assets......Page 277
6.3.2 Common ratios......Page 281
6.3.3 Equations representing geometric sequences......Page 283
6.3.4 Determining future terms of a geometric sequence......Page 286
6.3.5 Determining other values of a geometric sequence......Page 287
6.3.6 Graphs of geometric sequences......Page 288
6.3.8 Compound interest......Page 291
6.3.9 Reducing balance depreciation......Page 293
6.4.1 Using first-order linear recurrence relations to generate number sequences......Page 297
6.4.2 Using a recurrence relation to generate arithmetic sequences......Page 298
6.4.6 Spotting geometric sequences......Page 299
6.4.7 The Fibonacci sequence......Page 301
6.4.10 Graphing the Fibonacci sequence......Page 302
6.5 Review: exam practice......Page 306
Topic 6 Sequences......Page 308
TOPICS 4 to 6......Page 311
7.1.1 Introduction......Page 312
7.1.2 Kick off with CAS......Page 313
7.2.1 Review of Pythagoras’ theorem......Page 314
7.2.2 Pythagorean triads......Page 315
7.2.3 Pythagoras’ theorem in three dimensions......Page 316
7.3.1 Units of length and area......Page 324
7.3.2 Perimeter and area of standard shapes......Page 325
7.3.3 Heron’s formula......Page 327
7.4.1 Composite shapes......Page 331
7.4.2 Annulus......Page 332
7.4.3 Sectors......Page 333
7.4.4 Applications......Page 334
7.5.2 Prisms......Page 339
7.5.3 Common prisms......Page 340
7.5.5 Cones......Page 341
7.5.6 Pyramids......Page 342
7.5.7 Spheres......Page 343
7.5.8 Volumes of composite solids......Page 344
7.6.2 Nets......Page 349
7.6.3 Surface area formulas......Page 350
7.6.4 Surface areas of composite solids......Page 353
7.7 Review: exam practice......Page 358
Topic 7 Shape and measurement......Page 363
8.1.1 Introduction......Page 366
8.1.2 Kick off with CAS......Page 367
8.2.2 Conditions for similarity......Page 368
8.2.3 Similar triangles......Page 369
8.3.1 Linear scale factors......Page 376
8.4.1 Area scale factor......Page 381
8.4.2 Volume scale factor......Page 382
8.5 Review: exam practice......Page 386
Topic 8 Similarity......Page 390
9.1.1 Introduction......Page 392
9.1.2 Kick off with CAS......Page 393
9.2.2 The sine ratio......Page 394
9.2.3 The cosine ratio......Page 396
9.2.4 The tangent ratio......Page 398
9.2.5 The unit circle......Page 399
9.2.6 Extending sine and cosine to 180°......Page 401
9.2.7 SOH–CAH–TOA......Page 403
9.3.1 Angles of elevation and depression......Page 408
9.3.2 Bearings......Page 409
9.3.3 Bearings from A to B......Page 411
9.3.4 Using trigonometry in bearings problems......Page 412
9.4.2 Formulating the sine rule......Page 417
9.4.3 The ambiguous case of the sine rule......Page 419
9.4.4 Determining when we can use the ambiguous case......Page 420
9.5.1 Formulating the cosine rule......Page 424
9.5.2 Sets of sufficient information to determine a triangle......Page 427
9.6.1 Area of triangles......Page 431
9.6.2 Heron’s formula......Page 432
9.7 Review: exam practice......Page 437
Topic 9 Applications of trigonometry......Page 442
TOPICS 7 to 9......Page 444
10.1.1 Introduction......Page 445
10.1.2 Kick off with CAS......Page 446
10.2.4 Gradient–intercept form......Page 447
10.2.5 Determining the gradient from a graph......Page 449
10.2.6 Finding the gradient given two points......Page 451
10.2.7 Plotting linear graphs......Page 452
10.2.8 Sketching graphs using the gradient and y-intercept method......Page 454
10.2.9 Sketching graphs using the x- and y-intercepts......Page 456
10.3.3 Solving practical problems......Page 463
10.3.4 The domain of a linear model......Page 465
10.4.3 Finding the equation of straight lines given two points......Page 470
10.4.5 Creating a line of best fit when given only two points......Page 472
10.4.8 Reliability of predictions......Page 475
10.5.1 Piecewise linear and step graphs......Page 483
10.5.2 Modelling with piecewise linear and step graphs......Page 487
10.6 Review: exam practice......Page 497
Topic 10 Linear graphs and models......Page 502
11.1.1 Introduction......Page 512
11.1.2 Kick off with CAS......Page 513
11.2.2 Graphing linear inequalities......Page 514
11.2.3 Linear inequalities in one variable......Page 515
11.2.4 Transposing linear inequalities......Page 516
11.2.5 Linear inequalities in two variables......Page 517
11.3.1 Simultaneous linear inequalities......Page 524
11.3.2 Linear programming......Page 528
11.3.3 Identifying the constraints in a linear programming problem......Page 534
11.3.4 The objective function......Page 536
11.4.1 The corner point principle......Page 542
11.4.2 The sliding-line method......Page 549
11.4.3 Solving linear programming problems......Page 554
11.5 Review: exam practice......Page 562
Topic 11 Inequalities and linear programming......Page 569
12.1.1 Introduction......Page 577
12.1.2 Kick off with CAS......Page 578
12.2.1 Direct variation......Page 579
12.2.3 Joint variation......Page 580
12.3.1 Linearising data......Page 584
12.3.2 Transforming data with x2......Page 585
12.3.3 Transforming data with 1/x......Page 587
12.3.4 Transforming data with technology......Page 589
12.4.1 Modelling non-linear data......Page 596
12.4.2 Modelling with y =k/x+ c......Page 598
12.4.4 Functions of the type y = a log10(x) + c......Page 601
12.5 Review: exam practice......Page 608
Topic 12 Variation......Page 614
TOPICS 10 to 12......Page 624
13.1.1 Introduction......Page 625
13.1.2 Kick off with CAS......Page 626
13.2.3 Numerical data......Page 627
13.2.5 Frequency tables......Page 628
13.2.6 Bar charts......Page 629
13 .2.7 The mode......Page 630
13.3.2 Displaying numerical distributions......Page 638
13.3.3 Histograms......Page 639
13.3.5 Back-to-back stem plots......Page 641
13.3.6 Dot plots......Page 642
13.3.9 Shape......Page 643
13.3.12 Outliers......Page 644
13.4.2 The mean (or arithmetic mean)......Page 651
13.4.3 Calculating the mean for grouped data......Page 652
13.4.4 The median......Page 654
13.4.6 Limitations of the median as a measure of centre......Page 656
13.4.7 Choosing between measures of centre......Page 657
13.5.4 The interquartile range......Page 663
13.5.7 Standard deviation......Page 665
13.5.8 Preferred measures of spread......Page 667
13.6.3 The shape of boxplots......Page 674
13.6.4 Identifying possible outliers......Page 676
13.6.5 Lower and upper fences......Page 677
13.6.8 Parallel boxplots......Page 679
13.7 Review: exam practice......Page 687
Topic 13 Investigating and comparing data distributions......Page 695
14.1.1 Introduction......Page 711
14.1.2 Kick off with CAS......Page 712
14.2.2 Scatterplots......Page 713
14.2.3 Correlation......Page 714
14.2.4 Pearson’s product-moment correlation coefficient......Page 716
14.2.5 Causation and coefficient of determination......Page 717
14.3.2 Line of best fit by eye......Page 722
14.3.3 Least squares regression......Page 723
14.3.4 Manually calculating the equation for the least squares regression line......Page 724
14.4.1 Interpreting the regression line equation......Page 728
14.4.3 Using the regression line equation to make predictions......Page 729
14.4.4 Limitations of regression line predictions......Page 730
14.5 Review: exam practice......Page 735
Topic 14 Relationships between two numerical variables......Page 741
TOPICS 13 and 14......Page 746
15.1 Overview......Page 747
15.2.1 Revisiting recurrence relations......Page 748
15.2.2 Modelling reducing balance loans with a recurrence relation......Page 752
15.2.3 Amortisation of a reducing balance loan using a table......Page 755
15.3 Reducing balance loan problems using the Finance Solver......Page 760
15.3.2 Finding the payments......Page 761
15.3.3 Finding the present value......Page 762
15.3.4 Finding time......Page 763
15.3.5 Finding the interest rate......Page 764
15.4.1 Modelling an annuity using a recurrence relation......Page 767
15.4.2 Annuity problems and the Finance Solver......Page 769
15.5.1 The perpetuity formula......Page 773
15.5.2 Perpetuity problems and the Finance Solver......Page 775
15.6 Review: exam practice......Page 779
Financial Extension......Page 782
Glossary......Page 785
Index......Page 792