IGCSE Mathematics for Edexcel
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Entries: 283
Alan Smith
igcse
Hodder
edexcel
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IGCSE Mathematics for Edexcel
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Entries
283
1. Working with whole numbers
Theory
Page 8
Starter: Four fours
Problem
Page 8
1.1 Addition and subtraction without a calculator
Theory
Page 9
1.2 Multiplication without a calculator
Theory
Page 11
1.3 Division without a calculator
Theory
Page 14
1.4 Positive and negative integers
Theory
Page 16
1.5 Factors, multiples and primes
Theory
Page 18
1.6 Highest common factor, HCF
Theory
Page 19
1.7 Lowest common multiple (LCM)
Theory
Page 21
Key points
Theory
Page 25
Internet Challenge 1
Problem
Page 26
2. Fractions and decimals
Theory
Page 27
Starter: Half and half
Problem
Page 27
2.1 Equivalent fractions
Theory
Page 28
2.2 Multiplying and dividing with fractions
Theory
Page 32
2.3 Arithmetic with decimals
Theory
Page 35
2.4 Decimals and fractions
Theory
Page 37
2.5 Rounding and approximation
Theory
Page 41
Key points
Theory
Page 45
Internet Challenge 2
Problem
Page 46
3. Ratios and percentages
Theory
Page 47
Starter: How many per cent?
Problem
Page 47
3.1 Working with ratios
Theory
Page 48
3.2 Simple percentages
Theory
Page 50
3.3 Percentage increase and decrease
Theory
Page 52
3.4 Reverse percentage problems
Theory
Page 55
3.5 Simple and compound interest
Theory
Page 57
Key points
Theory
Page 61
Internet Challenge 3
Problem
Page 62
4. Powers, roots and reciprocals
Theory
Page 63
Starter: Roman numerals
Problem
Page 63
4.1 Basic powers and roots
Theory
Page 64
4.2 Higher powers and roots
Theory
Page 66
4.3 Fractional (rational) indices
Theory
Page 67
4.4 Negative powers and reciprocals
Theory
Page 68
4.5 The laws of indices
Theory
Page 70
4.6 Standard index form
Theory
Page 73
4.7 Calculating with numbers in standard form
Theory
Page 74
Key points
Theory
Page 78
Internet Challenge 4
Problem
Page 79
5. Working with algebra
Theory
Page 80
Starter: Right or wrong?
Problem
Page 80
5.1 Substituting numbers into formulae and expressions
Theory
Page 80
5.2 Working with indices
Theory
Page 83
5.3 Expanding brackets
Theory
Page 85
5.4 Multiplying two brackets together
Theory
Page 87
5.5 Factorising – common factors
Theory
Page 89
5.6 Factorising – quadratic expressions
Theory
Page 90
5.7 Factorising – harder quadratic expressions
Theory
Page 92
5.8 Factorising – difference of two squares
Theory
Page 92
5.9 Generating formulae
Theory
Page 94
5.10 Changing the subject of a formula
Theory
Page 96
Key points
Theory
Page 101
Internet Challenge 5
Problem
Page 102
6. Algebraic equations
Theory
Page 103
Starter: Triangular arithmagons
Problem
Page 103
6.1 Expressions, equations and identities
Theory
Page 104
6.2 Simple equations
Theory
Page 105
6.3 Harder linear equations
Theory
Page 106
6.4 Equations and brackets
Theory
Page 108
6.5 Equations with fractional coefficients
Theory
Page 109
Key points
Theory
Page 113
Internet Challenge 6
Problem
Page 114
7. Graphs of straight lines
Theory
Page 115
Starter: Matchstick puzzles
Problem
Page 115
7.1 Coordinates in all four quadrants
Theory
Page 116
7.2 Graphs of linear functions
Theory
Page 119
7.3 Gradient and intercept of linear functions
Theory
Page 121
7.4 Equations and graphs
Theory
Page 125
7.5 Parallel lines
Theory
Page 127
Key points
Theory
Page 131
Internet Challenge 7
Problem
Page 132
8. Simultaneous equations
Theory
Page 133
Starter: Fruity numbers
Problem
Page 133
8.1 Solving simultaneous equations by inspection
Theory
Page 134
8.2 Solving simultaneous equations by algebraic elimination
Theory
Page 135
8.3 Solving simultaneous equations by a graphical method
Theory
Page 139
8.4 Setting up and solving problems using simultaneous equations
Theory
Page 140
Key points
Theory
Page 144
Internet Challenge 8
Problem
Page 145
9. Inequalities
Theory
Page 146
Starter: Treasure hunt
Problem
Page 146
9.1 Whole-number solutions to inequalities
Theory
Page 147
9.2 Using algebra to solve linear inequalities
Theory
Page 148
9.3 Illustrating inequalities on a number line
Theory
Page 149
9.4 Graphs of linear inequalities in two variables
Theory
Page 151
9.5 Quadratic inequalities
Theory
Page 154
Key points
Theory
Page 158
Internet Challenge 9
Problem
Page 159
10. Number sequences
Theory
Page 160
Starter: Circles, lines and regions
Problem
Page 160
10.1 Number sequences
Theory
Page 161
10.2 Describing number sequences with rules
Theory
Page 163
10.3 Arithmetic sequences
Theory
Page 165
Key points
Theory
Page 171
Internet Challenge 10
Problem
Page 172
11. Travel and other graphs
Theory
Page 173
Starter: Animal races
Problem
Page 173
11.1 Modelling with straight-line graphs
Theory
Page 174
11.2 Distance–time graphs
Theory
Page 179
11.3 Velocity–time graphs
Theory
Page 183
Key points
Theory
Page 191
Internet Challenge 11
Problem
Page 192
12. Working with shape and space
Theory
Page 193
Starter: Alphabet soup
Problem
Page 193
12.1 Corresponding and alternate angles
Theory
Page 194
12.2 Angles in triangles and quadrilaterals
Theory
Page 197
12.3 Angles in polygons
Theory
Page 203
12.4 Areas and perimeters of simple shapes
Theory
Page 207
12.5 Surface area and volume
Theory
Page 214
Key points
Theory
Page 226
Internet Challenge 12
Problem
Page 227
13. Circles and cylinders
Theory
Page 228
Starter: Three and a bit …
Problem
Page 228
13.1 Circumference and area of a circle
Theory
Page 229
13.2 Sectors of a circle
Theory
Page 234
13.3 Circumference and area in reverse
Theory
Page 236
13.4 Surface area and volume of a cylinder
Theory
Page 238
13.5 Exact calculations using pi
Theory
Page 241
Key points
Theory
Page 247
Internet Challenge 13
Problem
Page 248
14. Geometric constructions
Theory
Page 249
Starter: Round and round in circles
Problem
Page 249
14.1 Constructing triangles from given information
Theory
Page 250
14.2 Constructions with line segments
Theory
Page 257
14.3 Bearings
Theory
Page 261
Key points
Theory
Page 264
Internet Challenge 14
Problem
Page 265
15. Transformation and similarity
Theory
Page 266
Starter: Monkey business
Problem
Page 266
15.1 Reflections
Theory
Page 267
15.2 Rotations
Theory
Page 273
15.3 Combining transformations
Theory
Page 278
15.4 Enlargements
Theory
Page 282
15.5 Similar shapes and solids
Theory
Page 286
Key points
Theory
Page 295
Internet Challenge 15
Problem
Page 296
16. Pythagoras’ theorem
Theory
Page 297
Starter: Finding squares and square roots on your calculator
Problem
Page 297
16.1 Introducing Pythagoras’ theorem
Theory
Page 298
16.2 Using Pythagoras’ theorem to find a hypotenuse
Theory
Page 300
16.3 Using Pythagoras’ theorem to find one of the shorter sides
Theory
Page 301
16.4 Pythagoras’ theorem in three dimensions
Theory
Page 304
16.5 Pythagoras’ theorem on a coordinate grid
Theory
Page 306
Key points
Theory
Page 311
Internet Challenge 16
Problem
Page 312
17. Introducing trigonometry
Theory
Page 313
Starter: A triangular spiral
Problem
Page 313
17.1 The sine ratio
Theory
Page 314
17.2 The cosine ratio
Theory
Page 317
17.3 The tangent ratio
Theory
Page 321
17.4 Choosing the right trigonometrical function
Theory
Page 323
17.5 Finding an unknown angle
Theory
Page 325
17.6 Multi-stage problems
Theory
Page 327
17.7 Angles of elevation and depression
Theory
Page 330
Key points
Theory
Page 338
Internet Challenge 17
Problem
Page 339
18. 2-D and 3-D objects
Theory
Page 340
Starter: Making cubes
Problem
Page 340
18.1 Drawing and constructing 3-D objects
Theory
Page 341
18.2 Coordinates in 3-D
Theory
Page 347
18.3 Volume and surface area of pyramids, cones and spheres
Theory
Page 349
18.4 Converting between units
Theory
Page 353
Key points
Theory
Page 357
Internet Challenge 18
Problem
Page 358
19. Circle theorems
Theory
Page 359
Starter: Circle vocabulary
Problem
Page 359
19.1 Tangents, chords and circles
Theory
Page 360
19.2 Angle properties inside a circle
Theory
Page 366
19.3 Further circle theorems
Theory
Page 372
19.4 Intersecting chords
Theory
Page 376
Key points
Theory
Page 384
Internet Challenge 19
Problem
Page 386
20. Sets
Theory
Page 387
Starter: Does it all add up?
Problem
Page 387
20.1 Introducing set notation
Theory
Page 387
20.2 Venn diagrams
Theory
Page 391
20.3 Further Venn diagrams
Theory
Page 395
Key points
Theory
Page 402
Internet Challenge 20
Problem
Page 403
21. Working with data
Theory
Page 404
Starter: Lies, damned lies and statistics
Problem
Page 404
21.1 Calculations with frequency tables
Theory
Page 405
21.2 Frequency polygons and histograms
Theory
Page 412
21.3 Cumulative frequency
Theory
Page 420
21.4 Median and quartiles for a discrete data set
Theory
Page 426
Key points
Theory
Page 432
Internet Challenge 21
Problem
Page 433
22. Probability
Theory
Page 434
Starter: Dice throws
Problem
Page 434
22.1 Theoretical and experimental probability
Theory
Page 435
22.2 Mutually exclusive outcomes
Theory
Page 438
22.3 Independent events
Theory
Page 441
22.4 Tree diagrams
Theory
Page 444
Key points
Theory
Page 449
Internet Challenge 22
Problem
Page 450
23. Using a calculator efficiently
Theory
Page 451
Starter: Big numbers
Problem
Page 451
23.1 Powers, roots and reciprocals
Theory
Page 452
23.2 Using brackets
Theory
Page 454
23.3 Using the fraction key
Theory
Page 456
23.4 Using the ANS key
Theory
Page 457
23.5 Upper and lower bounds
Theory
Page 459
Key points
Theory
Page 463
Internet Challenge 23
Problem
Page 464
24. Direct and inverse proportion
Theory
Page 465
Starter: A sense of proportion
Problem
Page 465
24.1 Direct proportion
Theory
Page 466
24.2 Inverse proportion
Theory
Page 469
24.3 Graphical representation of direct and inverse proportion
Theory
Page 472
Key points
Theory
Page 477
Internet Challenge 24
Problem
Page 478
25. Quadratic equations
Theory
Page 479
Starter: Solutions of equations
Problem
Page 479
25.1 Solving quadratic equations – factorising
Theory
Page 480
25.2 Solving quadratic equations – formula
Theory
Page 482
25.3 Problems leading to quadratic equations
Theory
Page 483
Key points
Theory
Page 486
Internet Challenge 25
Problem
Page 487
26. Advanced algebra
Theory
Page 488
Starter: How many shapes?
Problem
Page 488
26.1 Working with surds
Theory
Page 489
26.2 Algebraic fractions
Theory
Page 492
26.3 Cancelling common factors in rational expressions
Theory
Page 494
26.4 Simultaneous equations, one linear and one quadratic
Theory
Page 497
26.5 Changing the subject of an equation where the symbol occurs twice
Theory
Page 499
Key points
Theory
Page 502
Internet Challenge 26
Problem
Page 503
27. Functions and function notation
Theory
Page 504
Starter: Number crunchers
Problem
Page 504
27.1 Introducing functions and function notation
Theory
Page 505
27.2 Domain and range
Theory
Page 506
27.3 Inverse functions
Theory
Page 508
27.4 Composite functions
Theory
Page 510
Key points
Theory
Page 513
Internet Challenge 27
Problem
Page 514
28. Further trigonometry
Theory
Page 515
Starter: How tall is the church?
Problem
Page 515
28.1 The sine rule
Theory
Page 516
28.2 The ambiguous case of the sine rule
Theory
Page 520
28.3 The cosine rule
Theory
Page 523
28.4 Area of a triangle using 1/2 ab sin C, and segments of circles
Theory
Page 527
28.5 Trigonometry in 3-D
Theory
Page 530
Key points
Theory
Page 535
Internet Challenge 28
Problem
Page 536
29. Graphs of curves
Theory
Page 537
Starter: Making waves
Problem
Page 537
29.1 Tables of functions
Theory
Page 538
29.2 Plotting and using graphs of curves
Theory
Page 540
29.3 Graphs of sine, cosine and tangent functions
Theory
Page 545
Key points
Theory
Page 551
Internet Challenge 29
Problem
Page 552
30. Vectors
Theory
Page 553
Starter: Knight’s tours
Problem
Page 553
30.1 Introducing vectors
Theory
Page 554
30.2 Adding and subtracting vectors
Theory
Page 556
30.3 Multiplying a vector by a number (scalar multiplication)
Theory
Page 558
30.4 Using vectors
Theory
Page 559
Key points
Theory
Page 567
Internet Challenge 30
Problem
Page 568
31. Mathematical proofs
Theory
Page 569
Starter: 1 = 2
Problem
Page 569
31.1 Algebraic proofs
Theory
Page 570
31.2 Use of counter-examples
Theory
Page 571
Key points
Theory
Page 574
Internet Challenge 31
Problem
Page 575
32. Calculus
Theory
Page 576
Starter: Steeper and steeper
Problem
Page 576
32.1 Gradient of a curve
Theory
Page 577
32.2 Gradient of a curve – differentiation
Theory
Page 580
32.3 Harder differentiation
Theory
Page 581
32.4 Maximum and minimum points on curves
Theory
Page 583
32.5 Further problems on maximum and minimum
Theory
Page 586
32.6 Distance, velocity and acceleration
Theory
Page 589
Key points
Theory
Page 593
Internet Challenge 32
Problem
Page 594
33. Further probability and statistics
Theory
Page 595
Starter: Christmas shopping
Problem
Page 595
33.1 The combined mean of two groups
Theory
Page 595
33.2 Conditional probability
Theory
Page 597
Key points
Theory
Page 601
Internet Challenge 33
Problem
Page 602
Index
Other
Page 603
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