## Edexcel GCSE (9-1) Mathematics: Foundation Student Book

(2016)

### Abstract

Exam Board: Edexcel

Level:  GCSE

Subject: Science

First teaching: September 2015

First exams: June 2017

• Help students reach a higher level in each topic before they move onto the next topic with content broken down into larger chunks.
• Check and consolidate understanding with formative assessment followed by an opportunity to strengthen learning at the end of each topic
• Challenge the higher abilities to broaden learning further with extend sections.
• Build confidence with fluency, reasoning and problem solving integrated in every unit to give students the tools to answer new question types.
• Support lower ability students with strategies proven to help them access concepts, such as concrete- pictorial-abstract.
• Encourage students to reflect on their learning, something that has been proven to nurture confidence and raise achievement in all abilities.

Section Title Page Action Price
Cover Cover
Contents iii
Welcome to Edexcel GCSE (9-1) Mathematics Foundation Student Book vi
Unit 1: Number 1
Prior knowledge check 1
1.1: Calculations 3
1.2: Decimal numbers 5
1.3: Place value 8
1.4: Factors and multiples 10
1.5: Squares, cubes and roots 12
1.6: Index notation 15
1.7: Prime factors 18
Problem-solving 20
Check up 21
Strengthen 23
Extend 26
Knowledge check 28
Unit test 30
Unit 2: Algebra 32
Prior knowledge check 32
2.1: Algebraic expressions 32
2.2: Simplifying expressions 35
2.3: Substitution 37
2.4: Formulae 39
2.5: Expanding brackets 41
2.6: Factorising 43
2.7: Using expressions and formulae 45
Problem-solving 47
Check up 49
Strengthen 50
Extend 53
Knowledge check 55
Unit test 56
Unit 3: Graphs, tables and charts 58
Prior knowledge check 58
3.1: Frequency tables 60
3.2: Two-way tables 62
3.3: Representing data 65
3.4: Time series 67
3.5: Stem and leaf diagrams 69
3.6: Pie charts 71
3.7: Scatter graphs 74
3.8: Line of best fit 76
Problem-solving: Worldwide data 79
Check up 80
Strengthen 82
Extend 85
Knowledge check 87
Unit test 88
Unit 4: Fractions and percentages 92
Prior knowledge check 92
4.1: Working with fractions 93
4.2: Operations with fractions 96
4.3: Multiplying fractions 98
4.4: Dividing fractions 100
4.5: Fractions and decimals 102
4.6: Fractions and percentages 104
4.7: Calculating percentages 1 106
4.8: Calculating percentages 2 108
Problem-solving 111
Check up 112
Strengthen 113
Extend 116
Knowledge check 118
Unit test 119
Unit 5: Equations, inequalities and sequences 121
Prior knowledge check 121
5.1: Solving equations 1 122
5.2: Solving equations 2 125
5.3: Solving equations with brackets 127
5.4: Introducing inequalities 129
5.5: More inequalities 131
5.6: Using formulae 133
5.7: Generating sequences 135
5.8: Using the nth term of a sequence 136
Problem-solving: Paediatric medicine 139
Check up 140
Strengthen 141
Extend 145
Knowledge check 147
Unit test 147
Unit 6: Angles 149
Prior knowledge check 149
6.1: Properties of shapes 151
6.2: Angles in parallel lines 154
6.3: Angles in triangles 157
6.4: Exterior and interior angles 160
6.5: More exterior and interior angles 163
6.6: Geometrical problems 166
Problem-solving 169
Check up 170
Strengthen 172
Extend 175
Knowledge check 178
Unit test 179
Unit 7: Averages and range 181
Prior knowledge check 181
7.1: Mean and range 182
7.2: Mode, median and range 185
7.3: Types of average 188
7.4: Estimating the mean 192
7.5: Sampling 194
Problem-solving: Watching statistics 197
Check up 198
Strengthen 199
Extend 203
Knowledge check 205
Unit test 206
Unit 8: Perimeter, area and volume 1 209
Prior knowledge check 209
8.1: Rectangles, parallelograms and triangles 211
8.2: Trapezia and changing units 214
8.3: Area of compound shapes 217
8.4: Surface area of 3D solids 220
8.5: Volume of prisms 222
8.6: More volume and surface area 225
Problem-solving 228
Check up 229
Strengthen 231
Extend 235
Knowledge check 239
Unit test 240
Unit 9: Graphs 243
Prior knowledge check 243
9.1: Coordinates 244
9.2: Linear graphs 247
9.4: y = mx+c 252
9.5: Real-life graphs 254
9.6: Distance–time graphs 258
9.7: More real-life graphs 262
Problem-solving: Dinosaur trackways 265
Check up 266
Strengthen 267
Extend 271
Knowledge check 274
Unit test 275
Unit 10: Transformations 277
Prior knowledge check 277
10.1: Translation 278
10.2: Reflection 282
10.3: Rotation 285
10.4: Enlargement 288
10.5: Describing enlargements 291
10.6: Combining transformations 293
Problem-solving: Exploding shapes 296
Check up 297
Strengthen 299
Extend 304
Knowledge check 308
Unit test 309
Unit 11: Ratio and proportion 313
Prior knowledge check 313
11.1: Writing ratios 314
11.2: Using ratios 1 316
11.3: Ratios and measures 318
11.4: Using ratios 2 321
11.5: Comparing using ratios 323
11.6: Using proportion 326
11.7: Proportion and graphs 328
11.8: Proportion problems 330
Problem-solving 332
Check up 333
Strengthen 335
Extend 338
Knowledge check 340
Unit test 341
Unit 12: Right-angled triangles 344
Prior knowledge check 344
12.1: Pythagoras’ theorem 1 345
12.2: Pythagoras’ theorem 2 348
12.3: Trigonometry: the sine ratio 1 351
12.4: Trigonometry: the sine ratio 2 354
12.5: Trigonometry: the cosine ratio 357
12.6: Trigonometry: the tangent ratio 360
12.7: Finding lengths and angles using trigonometry 364
Problem-solving 367
Check up 368
Strengthen 369
Extend 373
Knowledge check 376
Unit test 377
Unit 13: Probability 379
Prior knowledge check 379
13.1: Calculating probability 380
13.2: Two events 382
13.3: Experimental probability 385
13.4: Venn diagrams 388
13.5: Tree diagrams 391
13.6: More tree diagrams 394
Problem-solving: Ciphers, language and probability 398
Check up 399
Strengthen 401
Extend 405
Knowledge check 407
Unit test 408
Unit 14: Multiplicative reasoning 411
Prior knowledge check 411
14.1: Percentages 413
14.2: Growth and decay 415
14.3: Compound measures 418
14.4: Distance, speed and time 421
14.5: Direct and inverse proportion 424
Problem-solving: Second-hand cars 427
Check up 428
Strengthen 430
Extend 434
Knowledge check 436
Unit test 437
Unit 15: Constructions, loci and bearings 439
Prior knowledge check 439
15.1: 3D solids 440
15.2: Plans and elevations 442
15.3: Accurate drawings 1 446
15.4: Scale drawings and maps 449
15.5: Accurate drawings 2 452
15.6: Constructions 454
15.7: Loci and regions 458
15.8: Bearings 461
Problem-solving 465
Check up 466
Strengthen 468
Extend 472
Knowledge check 475
Unit test 476
Unit 16: Quadratic equations and graphs 479
Prior knowledge check 479
16.1: Expanding double brackets 480
16.5: Solving quadratic equations algebraically 491
Problem-solving 493
Check up 494
Strengthen 496
Extend 499
Knowledge check 501
Unit test 502
Unit 17: Perimeter, area and volume 2 504
Prior knowledge check 504
17.1: Circumference of a circle 1 505
17.2: Circumference of a circle 2 507
17.3: Area of a circle 509
17.4: Semicircles and sectors 512
17.5: Composite 2D shapes and cylinders 515
17.6: Pyramids and cones 519
17.7: Spheres and composite solids 522
Problem-solving: Designing a pencil case 526
Check up 527
Strengthen 528
Extend 532
Knowledge check 535
Unit test 536
Unit 18: Fractions, indices and standard form 539
Prior knowledge check 539
18.1: Multiplying and dividing fractions 540
18.2: The laws of indices 542
18.3: Writing large numbers in standard form 544
18.4: Writing small numbers in standard form 547
18.5: Calculating with standard form 549
Problem-solving: Space race 552
Check up 553
Strengthen 554
Extend 557
Knowledge check 559
Unit test 560
Unit 19: Congruence, similarity and vectors 562
Prior knowledge check 562
19.1: Similarity and enlargement 563
19.2: More similarity 566
19.3: Using similarity 569
19.4: Congruence 1 571
19.5: Congruence 2 574
19.6: Vectors 1 576
19.7: Vectors 2 579
Problem-solving 581
Check up 582
Strengthen 584
Extend 586
Knowledge check 590
Unit test 591
Unit 20: More algebra 594
Prior knowledge check 594
20.1: Graphs of cubic and reciprocal functions 595
20.2: Non-linear graphs 597
20.3: Solving simultaneous equations graphically 601
20.4: Solving simultaneous equations algebraically 604
20.5: Rearranging formulae 606
20.6: Proof 609
Problem-solving: Breaking even 612
Check up 613
Strengthen 615
Extend 619
Knowledge check 622
Unit test 623