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English
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Entries: 253
Mal Coad
Glen Whiffen
core math
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Entries
253
Graphics Calculator Instructions
Other
Page 15
GCA. Casio fx-9860G
Other
Page 16
GCB. Texas Instruments TI-84 Plus
Other
Page 25
GCC. Texas Instruments TI-nspire
Other
Page 34
1. Number Properties
Theory
Page 45
1A. Words used in mathematics
Theory
Page 46
1B. Index notation
Theory
Page 48
1C. Factors of positive integers
Theory
Page 51
1D. Multiples of positive integers
Theory
Page 56
1E. Order of operations
Theory
Page 57
Review set 1A
Test
Page 60
Review set 1B
Test
Page 61
2. Measurement
Theory
Page 63
2A. Time
Theory
Page 64
2B. Temperature
Theory
Page 68
2C. Scientific notation (standard form)
Theory
Page 70
2D. International system (SI) units
Theory
Page 72
2E. Rounding numbers
Theory
Page 74
2F. Rates
Theory
Page 80
2G. Accuracy of measurements
Theory
Page 86
2H. Error and percentage error
Theory
Page 88
Review set 2A
Test
Page 92
Review set 2B
Test
Page 93
Review set 2C
Test
Page 94
3. Sets and Venn Diagrams
Theory
Page 95
3A. Set notation
Theory
Page 96
3B. Special number sets
Theory
Page 98
3C. Set builder notation
Theory
Page 101
3D. Complements of sets
Theory
Page 102
3E. Venn diagrams
Theory
Page 105
3F. Venn diagram regions
Theory
Page 108
3G. Numbers in regions
Theory
Page 109
3H. Problem solving with Venn diagrams
Theory
Page 112
Review set 3A
Test
Page 115
Review set 3B
Test
Page 117
4. Laws of Algebra
Theory
Page 119
4A. Index laws
Theory
Page 120
4B. The distributive law
Theory
Page 128
4C. The product (a + b)(c + d)
Theory
Page 129
4D. Difference of two squares
Theory
Page 131
4E. Perfect squares expansions
Theory
Page 132
4F. Further expansion
Theory
Page 134
Review set 4A
Test
Page 137
Review set 4B
Test
Page 137
5. Equations and Formulae
Theory
Page 139
5A. Algebraic substitution
Theory
Page 140
5B. Linear equations
Theory
Page 142
5C. Fractional equations
Theory
Page 146
5D. Solving linear equations using technology
Theory
Page 148
5E. Problem solving with linear equations
Theory
Page 149
5F. Formula substitution
Theory
Page 151
5G. Formula rearrangement
Theory
Page 154
5H. Linear simultaneous equations
Theory
Page 156
5I. Problem solving with simultaneous equations
Theory
Page 161
5J. Exponential equations
Theory
Page 164
Review set 5A
Test
Page 166
Review set 5B
Test
Page 167
6. Pythagoras' Theorem
Theory
Page 169
6A. Pythagoras' theorem
Theory
Page 170
6B. Right angles in geometry
Theory
Page 175
6C. The converse of Pythagoras' theorem
Theory
Page 180
6D. Problem solving
Theory
Page 182
6E. True bearings
Theory
Page 186
6F. Three-dimensional problems
Theory
Page 189
Review set 6A
Test
Page 192
Review set 6B
Test
Page 193
Review set 6C
Test
Page 194
Review set 6D
Test
Page 195
7. Descriptive Statistics
Theory
Page 197
7A. Types of data
Theory
Page 199
7B. Simple quantitative discrete data
Theory
Page 200
7C. Grouped quantitative discrete data
Theory
Page 205
7D. Quantitative continuous data
Theory
Page 210
7E. Measuring the centre of data
Theory
Page 213
7F. Measuring the spread of data
Theory
Page 223
7G. Box and whisker plots
Theory
Page 226
7H. Cumulative frequency graphs
Theory
Page 231
7I. Statistics using technology
Theory
Page 235
7J. Standard deviation
Theory
Page 237
Review set 7A
Test
Page 245
Review set 7B
Test
Page 246
Review set 7C
Test
Page 248
8. Coordinate Geometry
Theory
Page 251
8A. Distance between two points
Theory
Page 253
8B. Midpoints
Theory
Page 257
8C. Gradient
Theory
Page 260
8D. Rates
Theory
Page 267
8E. Vertical and horizontal lines
Theory
Page 269
8F. Equations of lines
Theory
Page 270
8G. Graphing lines
Theory
Page 276
8H. Perpendicular bisectors
Theory
Page 281
Review set 8A
Test
Page 282
Review set 8B
Test
Page 283
Review set 8C
Test
Page 284
Review set 8D
Test
Page 285
9. Quadratic Algebra
Theory
Page 287
9A. Factorisation with common factors
Theory
Page 289
9B. The difference of two squares factorisation
Theory
Page 290
9C. Perfect square factorisation
Theory
Page 292
9D. Sum and product factorisation
Theory
Page 293
9E. Factorisation of ax² + bx + c
Theory
Page 294
9F. Quadratic equations
Theory
Page 297
9G. The Null Factor law
Theory
Page 298
9H. The quadratic formula (extension)
Theory
Page 301
9I. Solving quadratic equations using technology
Theory
Page 303
9J. Problem solving with quadratics
Theory
Page 304
Review set 9A
Test
Page 307
Review set 9B
Test
Page 307
Review set 9C
Test
Page 308
Review set 9D
Test
Page 308
10. Functions
Theory
Page 309
10A. Relations and functions
Theory
Page 310
10B. Function notation
Theory
Page 313
10C. Domain and range
Theory
Page 315
10D. Mappings
Theory
Page 317
10E. Linear functions
Theory
Page 321
Review set 10A
Test
Page 326
Review set 10B
Test
Page 327
Review set 10C
Test
Page 328
11. Perimeter, Area and Volume
Theory
Page 329
11A. Conversion of units
Theory
Page 331
11B. Perimeter
Theory
Page 333
11C. Area
Theory
Page 337
11D. Volume
Theory
Page 347
11E. Capacity
Theory
Page 353
11F. Density (extension)
Theory
Page 357
11G. Harder applications
Theory
Page 359
Review set 11A
Test
Page 360
Review set 11B
Test
Page 361
Review set 11C
Test
Page 363
12. Quadratic Functions
Theory
Page 365
12A. Quadratic functions
Theory
Page 366
12B. Graphs of quadratic functions
Theory
Page 369
12C. Axes intercepts
Theory
Page 371
12D. Axis of symmetry
Theory
Page 376
12E. Vertex
Theory
Page 378
12F. Finding a quadratic from its graph
Theory
Page 380
12G. Where functions meet
Theory
Page 382
12H. Quadratic modelling
Theory
Page 383
Review set 12A
Test
Page 388
Review set 12B
Test
Page 389
Review set 12C
Test
Page 390
13. Trigonometry
Theory
Page 391
13A. Labelling right angled triangles
Theory
Page 392
13B. The trigonometric ratios
Theory
Page 393
13C. Using trigonometry in geometric figures
Theory
Page 399
13D. Problem solving using trigonometry
Theory
Page 403
13E. 3-dimensional problem solving
Theory
Page 406
13F. Areas of triangles
Theory
Page 411
13G. The cosine rule
Theory
Page 414
13H. The sine rule
Theory
Page 416
13I. Using the sine and cosine rules
Theory
Page 418
13J. The ambiguous case (extension)
Theory
Page 421
13K. Bearings (extension)
Theory
Page 423
Review set 13A
Test
Page 426
Review set 13B
Test
Page 427
Review set 13C
Test
Page 429
14. Sequences and Series
Theory
Page 431
14A. Number patterns
Theory
Page 432
14B. Sequences of numbers
Theory
Page 433
14C. Arithmetic sequences
Theory
Page 434
14D. Geometric sequences
Theory
Page 438
14E. Applications of sequences
Theory
Page 441
14F. Series
Theory
Page 446
Review set 14A
Test
Page 452
Review set 14B
Test
Page 452
Review set 14C
Test
Page 453
15. Financial Mathematics
Theory
Page 455
15A. Foreign exchange
Theory
Page 456
15B. Simple interest
Theory
Page 463
15C. Compound interest
Theory
Page 467
15D. Depreciation
Theory
Page 478
15E. Personal loans
Theory
Page 481
15F. Inflation
Theory
Page 484
Review set 15A
Test
Page 486
Review set 15B
Test
Page 487
16. Probability
Theory
Page 489
16A. Experimental probability
Theory
Page 491
16B. Sample space
Theory
Page 497
16C. Theoretical probability
Theory
Page 499
16D. Two-dimensional grids
Theory
Page 501
16E. Compound events
Theory
Page 504
16F. Using tree diagrams
Theory
Page 508
16G. Sampling
Theory
Page 511
16H. Probabilities from Venn diagrams
Theory
Page 515
16I. Laws of probability
Theory
Page 518
16J. Independent events
Theory
Page 524
Review set 16A
Test
Page 525
Review set 16B
Test
Page 526
Review set 16C
Test
Page 527
17. Logic
Theory
Page 529
17A. Propositions
Theory
Page 530
17B. Compound propositions
Theory
Page 534
17C. Truth tables and logical equivalence
Theory
Page 539
17D. Implication and equivalence
Theory
Page 543
17E. Converse, inverse and contrapositive
Theory
Page 545
17F. Valid arguments (extension)
Theory
Page 548
Review set 17A
Test
Page 553
Review set 17B
Test
Page 554
Review set 17C
Test
Page 555
18. Trigonometric Functions
Theory
Page 557
18A. Observing periodic behaviour
Theory
Page 559
18B. The sine function
Theory
Page 562
18C. The cosine function
Theory
Page 568
18D. Modelling using sine and cosine functions
Theory
Page 570
18E. Trigonometric equations
Theory
Page 572
18F. Using trigonometric models
Theory
Page 575
Review set 18A
Test
Page 577
Review set 18B
Test
Page 578
Review set 18C
Test
Page 579
19. Exponential Functions
Theory
Page 581
19A. Evaluating exponential functions
Theory
Page 583
19B. Graphs of exponential functions
Theory
Page 583
19C. Growth and decay
Theory
Page 586
Review set 19A
Test
Page 592
Review set 19B
Test
Page 592
20. Two Variable Statistics
Theory
Page 593
20A. Correlation
Theory
Page 594
20B. Measuring correlation
Theory
Page 597
20C. Line of best fit by eye
Theory
Page 604
20D. Linear regression
Theory
Page 608
20E. The χ² test of independence
Theory
Page 614
Review set 20A
Test
Page 621
Review set 20B
Test
Page 623
21. Differential Calculus
Theory
Page 625
21A. Rates of change
Theory
Page 626
21B. Limits
Theory
Page 632
21C. The derivative function
Theory
Page 634
21D. Simple rules of differentiation
Theory
Page 638
21E. Tangents to curves
Theory
Page 641
21F. The second derivative
Theory
Page 642
Review set 21A
Test
Page 645
Review set 21B
Test
Page 645
Review set 21C
Test
Page 646
22. Applications of Differential Calculus
Theory
Page 647
22A. Properties of curves
Theory
Page 648
22B. Rates of change
Theory
Page 655
22C. Optimisation
Theory
Page 660
Review set 22A
Test
Page 666
Review set 22B
Test
Page 666
Review set 22C
Test
Page 667
23. Unfamiliar Functions
Theory
Page 669
23A. Properties of functions
Theory
Page 670
23B. Asymptotes
Theory
Page 673
23C. Optimisation
Theory
Page 676
23D. Where functions meet
Theory
Page 678
Review set 23A
Test
Page 680
Review set 23B
Test
Page 681
24. Miscellaneous Problems
Problem
Page 683
24A. Short questions
Problem
Page 684
24B. Long questions
Problem
Page 712
Answers
Answer
Page 735
Index
Other
Page 806
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