IGCSE (0607) Cambridge International Mathematics (Extended)
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Entries: 302
Keith Black
Alison Ryan
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IGCSE (0607) Cambridge International Mathematics (Extended)
Preparing book pages
1
Entries
302
Symbols and Notation Used in This Book
Theory
Page 6
Graphics Calculator Instructions
Theory
Page 11
GCA. Basic calculations
Theory
Page 12
GCB. Basic functions
Theory
Page 13
GCC. Secondary function and alpha keys
Theory
Page 17
GCD. Memory
Theory
Page 17
GCE. Lists
Theory
Page 19
GCF. Statistical graphs
Theory
Page 21
GCG. Working with functions
Theory
Page 22
GCH. Two variable analysis
Theory
Page 26
Assumed Knowledge (Number)
Theory
Page 29
Assumed Knowledge (Geometry and Graphs)
Theory
Page 30
1. Algebra (Expansion and Factorisation)
Theory
Page 31
1A. The distributive law
Theory
Page 32
1B. The product (a+b)(c+d)
Theory
Page 33
1C. Difference of two squares
Theory
Page 35
1D. Perfect squares expansion
Theory
Page 37
1E. Further expansion
Theory
Page 39
1F. Algebraic common factors
Theory
Page 40
1G. Factorising with common factors
Theory
Page 42
1H. Difference of two squares factorisation
Theory
Page 45
1I. Perfect squares factorisation
Theory
Page 47
1J. Expressions with four terms
Theory
Page 48
1K. Factorising ax² + bx + c
Theory
Page 49
1L. Splitting the middle term
Theory
Page 51
1M. Miscellaneous factorisation
Theory
Page 54
Review set 1A
Test
Page 55
Review set 1B
Test
Page 56
2. Sets
Theory
Page 57
2A. Set notation
Theory
Page 57
2B. Special number sets
Theory
Page 60
2C. Interval notation
Theory
Page 61
2D. Venn diagrams
Theory
Page 63
2E. Union and intersection
Theory
Page 65
2F. Problem solving
Theory
Page 69
Review set 2A
Test
Page 72
Review set 2B
Test
Page 73
3. Algebra (Equations and Inequalities)
Theory
Page 75
3A. Solving linear equations
Theory
Page 75
3B. Solving equations with fractions
Theory
Page 80
3C. Forming equations
Theory
Page 83
3D. Problem solving using equations
Theory
Page 85
3E. Power equations
Theory
Page 87
3F. Interpreting linear inequalities
Theory
Page 88
3G. Solving linear inequalities
Theory
Page 89
Review set 3A
Test
Page 91
Review set 3B
Test
Page 92
4. Lines, Angles and Polygons
Theory
Page 93
4A. Angle properties
Theory
Page 93
4B. Triangles
Theory
Page 98
4C. Isosceles triangles
Theory
Page 100
4D. The interior angles of a polygon
Theory
Page 103
4E. The exterior angles of a polygon
Theory
Page 106
Review set 4A
Test
Page 107
Review set 4B
Test
Page 109
5. Graphs, Charts and Tables
Theory
Page 111
5A. Statistical graphs
Theory
Page 112
5B. Graphs which compare data
Theory
Page 116
5C. Using technology to graph data
Theory
Page 119
Review set 5A
Test
Page 120
Review set 5B
Test
Page 122
6. Exponents and Surds
Theory
Page 123
6A. Exponent or index notation
Theory
Page 123
6B. Exponent or index laws
Theory
Page 126
6C. Zero and negative indices
Theory
Page 129
6D. Standard form
Theory
Page 131
6E. Surds
Theory
Page 134
6F. Properties of surds
Theory
Page 137
6G. Multiplication of surds
Theory
Page 139
6H. Division by surds
Theory
Page 142
Review set 6A
Test
Page 143
Review set 6B
Test
Page 145
7. Formulae and Simultaneous Equations
Theory
Page 147
7A. Formula substitution
Theory
Page 148
7B. Formula rearrangement
Theory
Page 150
7C. Formula derivation
Theory
Page 153
7D. More difficult rearrangements
Theory
Page 155
7E. Simultaneous equations
Theory
Page 158
7F. Problem solving
Theory
Page 164
Review set 7A
Test
Page 166
Review set 7B
Test
Page 167
8. The Theorem of Pythagoras
Theory
Page 169
8A. Pythagoras' theorem
Theory
Page 170
8B. The converse of Pythagoras' theorem
Theory
Page 176
8C. Problem solving
Theory
Page 177
8D. Circle problems
Theory
Page 181
8E. Three-dimensional problems
Theory
Page 185
Review set 8A
Test
Page 187
Review set 8B
Test
Page 188
9. Mensuration (Length and Area)
Theory
Page 191
9A. Length
Theory
Page 192
9B. Perimeter
Theory
Page 194
9C. Area
Theory
Page 196
9D. Circles and sectors
Theory
Page 201
Review set 9A
Test
Page 206
Review set 9B
Test
Page 207
10. Topics in Arithmetic
Theory
Page 209
10A. Percentage
Theory
Page 209
10B. Profit and loss
Theory
Page 211
10C. Simple interest
Theory
Page 214
10D. Reverse percentage problems
Theory
Page 217
10E. Multipliers and chain percentage
Theory
Page 218
10F. Compound growth
Theory
Page 222
10G. Speed, distance and time
Theory
Page 224
10H. Travel graphs
Theory
Page 226
Review set 10A
Test
Page 228
Review set 10B
Test
Page 229
11. Mensuration (Solids and Containers)
Theory
Page 231
11A. Surface area
Theory
Page 231
11B. Volume
Theory
Page 239
11C. Capacity
Theory
Page 245
11D. Mass
Theory
Page 248
11E. Compound solids
Theory
Page 249
Review set 11A
Test
Page 253
Review set 11B
Test
Page 254
12. Coordinate Geometry
Theory
Page 255
12A. Plotting points
Theory
Page 256
12B. Distance between two points
Theory
Page 258
12C. Midpoint of a line segment
Theory
Page 261
12D. Gradient of a line segment
Theory
Page 263
12E. Gradient of parallel and perpendicular lines
Theory
Page 267
12F. Using coordinate geometry
Theory
Page 270
Review set 12A
Test
Page 272
Review set 12B
Test
Page 273
13. Analysis of Discrete Data
Theory
Page 275
13A. Variables used in statistics
Theory
Page 277
13B. Organising and describing discrete data
Theory
Page 278
13C. The centre of a discrete data set
Theory
Page 282
13D. Measuring the spread of discrete data
Theory
Page 285
13E. Data in frequency tables
Theory
Page 288
13F. Grouped discrete data
Theory
Page 290
13G. Statistics from technology
Theory
Page 292
Review set 13A
Test
Page 293
Review set 13B
Test
Page 295
14. Straight Lines
Theory
Page 297
14A. Vertical and horizontal lines
Theory
Page 297
14B. Graphing from a table of values
Theory
Page 299
14C. Equations of lines (gradient-intercept form)
Theory
Page 301
14D. Equations of lines (general form)
Theory
Page 304
14E. Graphing lines from equations
Theory
Page 307
14F. Lines of symmetry
Theory
Page 308
Review set 14A
Test
Page 310
Review set 14B
Test
Page 311
15. Trigonometry
Theory
Page 313
15A. Labelling sides of a right angled triangle
Theory
Page 314
15B. The trigonometric ratios
Theory
Page 316
15C. Problem solving
Theory
Page 322
15D. The first quadrant of the unit circle
Theory
Page 327
15E. True bearings
Theory
Page 330
15F. 3-dimensional problem solving
Theory
Page 331
Review set 15A
Test
Page 336
Review set 15B
Test
Page 337
16. Algebraic Fractions
Theory
Page 339
16A. Simplifying algebraic fractions
Theory
Page 339
16B. Multiplying and dividing algebraic fractions
Theory
Page 344
16C. Adding and subtracting algebraic fractions
Theory
Page 346
16D. More complicated fractions
Theory
Page 348
Review set 16A
Test
Page 351
Review set 16B
Test
Page 352
17. Continuous Data
Theory
Page 353
17A. The mean of continuous data
Theory
Page 354
17B. Histograms
Theory
Page 355
17C. Cumulative frequency
Theory
Page 359
Review set 17A
Test
Page 364
Review set 17B
Test
Page 365
18. Similarity
Theory
Page 367
18A. Similarity
Theory
Page 367
18B. Similar triangles
Theory
Page 370
18C. Problem solving
Theory
Page 373
18D. Area and volume of similar shapes
Theory
Page 376
Review set 18A
Test
Page 380
Review set 18B
Test
Page 381
19. Introduction to Functions
Theory
Page 383
19A. Mapping diagrams
Theory
Page 383
19B. Functions
Theory
Page 385
19C. Function notation
Theory
Page 389
19D. Composite functions
Theory
Page 391
19E. Reciprocal functions
Theory
Page 393
19F. The absolute value function
Theory
Page 395
Review set 19A
Test
Page 398
Review set 19B
Test
Page 399
20. Transformation Geometry
Theory
Page 401
20A. Translations
Theory
Page 402
20B. Rotations
Theory
Page 404
20C. Reflections
Theory
Page 406
20D. Enlargements and reductions
Theory
Page 408
20E. Stretches
Theory
Page 410
20F. Transforming functions
Theory
Page 413
20G. The inverse of a transformation
Theory
Page 416
20H. Combinations of transformations
Theory
Page 417
Review set 20A
Test
Page 419
Review set 20B
Test
Page 420
21. Quadratic Equations and Functions
Theory
Page 421
21A. Quadratic equations
Theory
Page 422
21B. The Null Factor law
Theory
Page 423
21C. The quadratic formula
Theory
Page 427
21D. Quadratic functions
Theory
Page 429
21E. Graphs of quadratic functions
Theory
Page 431
21F. Axes intercepts
Theory
Page 438
21G. Line of symmetry and vertex
Theory
Page 441
21H. Finding a quadratic function
Theory
Page 445
21I. Using technology
Theory
Page 446
21J. Problem solving
Theory
Page 447
Review set 21A
Test
Page 451
Review set 21B
Test
Page 453
22. Two Variable Analysis
Theory
Page 455
22A. Correlation
Theory
Page 456
22B. Line of best fit by eye
Theory
Page 459
22C. Linear regression
Theory
Page 461
Review set 22A
Test
Page 466
Review set 22B
Test
Page 467
23. Further Functions
Theory
Page 469
23A. Cubic functions
Theory
Page 469
23B. Inverse functions
Theory
Page 473
23C. Using technology
Theory
Page 475
23D. Tangents to curves
Theory
Page 480
Review set 23A
Test
Page 481
Review set 23B
Test
Page 481
24. Vectors
Theory
Page 483
24A. Directed line segment representation
Theory
Page 484
24B. Vector equality
Theory
Page 485
24C. Vector addition
Theory
Page 486
24D. Vector subtraction
Theory
Page 489
24E. Vectors in component form
Theory
Page 491
24F. Scalar multiplication
Theory
Page 496
24G. Parallel vectors
Theory
Page 497
24H. Vectors in geometry
Theory
Page 499
Review set 24A
Test
Page 501
Review set 24B
Test
Page 503
25. Probability
Theory
Page 505
25A. Introduction to probability
Theory
Page 506
25B. Estimating probability
Theory
Page 507
25C. Probabilities from two-way tables
Theory
Page 510
25D. Expectation
Theory
Page 512
25E. Representing combined events
Theory
Page 513
25F. Theoretical probability
Theory
Page 515
25G. Compound events
Theory
Page 519
25H. Using tree diagrams
Theory
Page 522
25I. Sampling with and without replacement
Theory
Page 524
25J. Mutually exclusive and non-mutually exclusive events
Theory
Page 527
25K. Miscellaneous probability questions
Theory
Page 528
Review set 25A
Test
Page 530
Review set 25B
Test
Page 531
26. Sequences
Theory
Page 533
26A. Number sequences
Theory
Page 534
26B. Algebraic rules for sequences
Theory
Page 535
26C. Geometric sequences
Theory
Page 537
26D. The difference method for sequences
Theory
Page 539
Review set 26A
Test
Page 544
Review set 26B
Test
Page 545
27. Circle Geometry
Theory
Page 547
27A. Circle theorems
Theory
Page 547
27B. Cyclic quadrilaterals
Theory
Page 556
Review set 27A
Test
Page 561
Review set 27B
Test
Page 562
28. Exponential Functions and Equations
Theory
Page 565
28A. Rational exponents
Theory
Page 566
28B. Exponential functions
Theory
Page 568
28C. Exponential equations
Theory
Page 570
28D. Problem solving with exponential functions
Theory
Page 573
28E. Exponential modelling
Theory
Page 576
Review set 28A
Test
Page 577
Review set 28B
Test
Page 578
29. Further Trigonometry
Theory
Page 579
29A. The unit circle
Theory
Page 579
29B. Area of a triangle using sine
Theory
Page 583
29C. The sine rule
Theory
Page 585
29D. The cosine rule
Theory
Page 588
29E. Problem solving with the sine and cosine rules
Theory
Page 591
29F. Trigonometry with compound shapes
Theory
Page 593
29G. Trigonometric graphs
Theory
Page 595
29H. Graphs of y = a sin(bx) and y = a cos(bx)
Theory
Page 599
Review set 29A
Test
Page 601
Review set 29B
Test
Page 602
30. Variation and Power Modelling
Theory
Page 605
30A. Direct variation
Theory
Page 606
30B. Inverse variation
Theory
Page 612
30C. Variation modelling
Theory
Page 615
30D. Power modelling
Theory
Page 619
Review set 30A
Test
Page 622
Review set 30B
Test
Page 623
31. Logarithms
Theory
Page 625
31A. Logarithms in base a
Theory
Page 625
31B. The logarithmic function
Theory
Page 627
31C. Rules for logarithms
Theory
Page 629
31D. Logarithms in base 10
Theory
Page 630
31E. Exponential and logarithmic equations
Theory
Page 634
Review set 31A
Test
Page 636
Review set 31B
Test
Page 637
32. Inequalities
Theory
Page 639
32A. Solving one variable inequalities with technology
Theory
Page 639
32B. Linear inequality regions
Theory
Page 641
32C. Integer points in regions
Theory
Page 644
32D. Problem solving (Extension)
Theory
Page 645
Review set 32A
Test
Page 647
Review set 32B
Test
Page 648
33. Multi-topic Questions
Problem
Page 649
34. Investigation and Modelling Questions
Problem
Page 661
34A. Investigation questions
Problem
Page 661
34B. Modelling questions
Problem
Page 669
Answers
Answer
Page 673
Index
Other
Page 752
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