### Additional Information

#### Book Details

### 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.

### Table of Contents

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 | ||

9.3: Gradient | 250 | ||

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 | ||

16.2: Plotting quadratic graphs | 483 | ||

16.3: Using quadratic graphs | 486 | ||

16.4: Factorising quadratic expressions | 489 | ||

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 | ||

Answers | 627 | ||

Index | 700 |