Additional Information
Book Details
Abstract
Exam Board: Edexcel
Level: GCSE
Subject: Maths
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 Higher Student Book | vi | ||
| Unit 1: Number | 1 | ||
| Prior knowledge check | 1 | ||
| 1.1: Number problems and reasoning | 2 | ||
| 1.2: Place value and estimating | 4 | ||
| 1.3: HCF and LCM | 6 | ||
| 1.4: Calculating with powers (indices) | 8 | ||
| 1.5: Zero, negative and fractional indices | 11 | ||
| 1.6: Powers of 10 and standard form | 14 | ||
| 1.7: Surds | 16 | ||
| Problem-solving | 19 | ||
| Check up | 20 | ||
| Strengthen | 22 | ||
| Extend | 25 | ||
| Knowledge check | 27 | ||
| Unit test | 28 | ||
| Unit 2: Algebra | 30 | ||
| Prior knowledge check | 30 | ||
| 2.1: Algebraic indices | 31 | ||
| 2.2: Expanding and factorising | 33 | ||
| 2.3: Equations | 35 | ||
| 2.4: Formulae | 37 | ||
| 2.5: Linear sequences | 40 | ||
| 2.6: Non-linear sequences | 42 | ||
| 2.7: More expanding and factorising | 46 | ||
| Problem-solving | 48 | ||
| Check up | 50 | ||
| Strengthen | 51 | ||
| Extend | 55 | ||
| Knowledge check | 58 | ||
| Unit test | 59 | ||
| Unit 3: Interpreting and representing data | 61 | ||
| Prior knowledge check | 61 | ||
| 3.1: Statistical diagrams 1 | 63 | ||
| 3.2: Time series | 67 | ||
| 3.3: Scatter graphs | 70 | ||
| 3.4: Line of best fit | 72 | ||
| 3.5: Averages and range | 75 | ||
| 3.6: Statistical diagrams 2 | 78 | ||
| Problem-solving: Pollution particulates | 81 | ||
| Check up | 82 | ||
| Strengthen | 84 | ||
| Extend | 89 | ||
| Knowledge check | 94 | ||
| Unit test | 94 | ||
| Unit 4: Fractions, ratio and percentages | 97 | ||
| Prior knowledge check | 97 | ||
| 4.1: Fractions | 98 | ||
| 4.2: Ratios | 101 | ||
| 4.3: Ratio and proportion | 103 | ||
| 4.4: Percentages | 105 | ||
| 4.5: Fractions, decimals and percentages | 108 | ||
| Problem-solving | 110 | ||
| Check up | 111 | ||
| Strengthen | 112 | ||
| Extend | 115 | ||
| Knowledge check | 118 | ||
| Unit test | 119 | ||
| Unit 5: Angles and trigonometry | 121 | ||
| Prior knowledge check | 121 | ||
| 5.1: Angle properties of triangles and quadrilaterals | 122 | ||
| 5.2: Interior angles of a polygon | 126 | ||
| 5.3: Exterior angles of a polygon | 128 | ||
| 5.4: Pythagoras’ theorem 1 | 131 | ||
| 5.5: Pythagoras’ theorem 2 | 134 | ||
| 5.6: Trigonometry 1 | 136 | ||
| 5.7: Trigonometry 2 | 139 | ||
| Problem-solving | 143 | ||
| Check up | 144 | ||
| Strengthen | 147 | ||
| Extend | 153 | ||
| Knowledge check | 155 | ||
| Unit test | 157 | ||
| Unit 6: Graphs | 159 | ||
| Prior knowledge check | 159 | ||
| 6.1: Linear graphs | 161 | ||
| 6.2: More linear graphs | 164 | ||
| 6.3: Graphing rates of change | 166 | ||
| 6.4: Real-life graphs | 170 | ||
| 6.5: Line segments | 174 | ||
| 6.6: Quadratic graphs | 176 | ||
| 6.7: Cubic and reciprocal graphs | 180 | ||
| 6.8: More graphs | 182 | ||
| Problem-solving: Profit parabolas | 186 | ||
| Check up | 187 | ||
| Strengthen | 190 | ||
| Extend | 195 | ||
| Knowledge check | 198 | ||
| Unit test | 200 | ||
| Unit 7: Area and volume | 203 | ||
| Prior knowledge check | 203 | ||
| 7.1: Perimeter and area | 204 | ||
| 7.2: Units and accuracy | 207 | ||
| 7.3: Prisms | 210 | ||
| 7.4: Circles | 213 | ||
| 7.5: Sectors of circles | 216 | ||
| 7.6: Cylinders and spheres | 220 | ||
| 7.7: Pyramids and cones | 222 | ||
| Problem-solving | 225 | ||
| Check up | 227 | ||
| Strengthen | 229 | ||
| Extend | 232 | ||
| Knowledge check | 235 | ||
| Unit test | 237 | ||
| Unit 8: Transformations and constructions | 239 | ||
| Prior knowledge check | 239 | ||
| 8.1: 3D solids | 240 | ||
| 8.2: Reflection and rotation | 242 | ||
| 8.3: Enlargement | 245 | ||
| 8.4: Transformations and combinations of transformations | 249 | ||
| 8.5: Bearings and scale drawings | 253 | ||
| 8.6: Constructions 1 | 256 | ||
| 8.7: Constructions 2 | 259 | ||
| 8.8: Loci | 262 | ||
| Problem-solving: Under construction | 265 | ||
| Check up | 266 | ||
| Strengthen | 268 | ||
| Extend | 273 | ||
| Knowledge check | 275 | ||
| Unit test | 277 | ||
| Unit 9: Equations and inequalities | 280 | ||
| Prior knowledge check | 280 | ||
| 9.1: Solving quadratic equations 1 | 281 | ||
| 9.2: Solving quadratic equations 2 | 282 | ||
| 9.3: Completing the square | 284 | ||
| 9.4: Solving simple simultaneous equations | 287 | ||
| 9.5: More simultaneous equations | 289 | ||
| 9.6: Solving linear and quadratic simultaneous equations | 291 | ||
| 9.7: Solving linear inequalities | 293 | ||
| Problem-solving: Overtaking | 296 | ||
| Check up | 297 | ||
| Strengthen | 298 | ||
| Extend | 300 | ||
| Knowledge check | 302 | ||
| Unit test | 303 | ||
| Unit 10: Probability | 305 | ||
| Prior knowledge check | 305 | ||
| 10.1: Combined events | 307 | ||
| 10.2: Mutually exclusive events | 310 | ||
| 10.3: Experimental probability | 312 | ||
| 10.4: Independent events and tree diagrams | 314 | ||
| 10.5: Conditional probability | 318 | ||
| 10.6: Venn diagrams and set notation | 321 | ||
| Problem-solving: Drug testing | 325 | ||
| Check up | 326 | ||
| Strengthen | 328 | ||
| Extend | 333 | ||
| Knowledge check | 335 | ||
| Unit test | 336 | ||
| Unit 11: Multiplicative reasoning | 339 | ||
| Prior knowledge check | 339 | ||
| 11.1: Growth and decay | 340 | ||
| 11.2: Compound measures | 343 | ||
| 11.3: More compound measures | 346 | ||
| 11.4: Ratio and proportion | 348 | ||
| Problem-solving | 351 | ||
| Check up | 352 | ||
| Strengthen | 354 | ||
| Extend | 357 | ||
| Knowledge check | 359 | ||
| Unit test | 360 | ||
| Unit 12: Similarity and congruence | 363 | ||
| Prior knowledge check | 363 | ||
| 12.1: Congruence | 364 | ||
| 12.2: Geometric proof and congruence | 367 | ||
| 12.3: Similarity | 370 | ||
| 12.4: More similarity | 374 | ||
| 12.5: Similarity in 3D solids | 378 | ||
| Problem-solving | 382 | ||
| Check up | 383 | ||
| Strengthen | 385 | ||
| Extend | 390 | ||
| Knowledge check | 394 | ||
| Unit test | 395 | ||
| Unit 13: More trigonometry | 399 | ||
| Prior knowledge check | 399 | ||
| 13.1: Accuracy | 400 | ||
| 13.2: Graph of the sine function | 402 | ||
| 13.3: Graph of the cosine function | 405 | ||
| 13.4: The tangent function | 408 | ||
| 13.5: Calculating areas and the sine rule | 411 | ||
| 13.6: The cosine rule and 2D trigonometric problems | 415 | ||
| 13.7: Solving problems in 3D | 418 | ||
| 13.8: Transforming trigonometric graphs 1 | 421 | ||
| 13.9: Transforming trigonometric graphs 2 | 423 | ||
| Problem-solving: Muddy tracks | 426 | ||
| Check up | 427 | ||
| Strengthen | 429 | ||
| Extend | 433 | ||
| Knowledge check | 435 | ||
| Unit test | 437 | ||
| Unit 14: Further statistics | 439 | ||
| Prior knowledge check | 439 | ||
| 14.1: Sampling | 440 | ||
| 14.2: Cumulative frequency | 443 | ||
| 14.3: Box plots | 446 | ||
| 14.4: Drawing histograms | 449 | ||
| 14.5: Interpreting histograms | 450 | ||
| 14.6: Comparing and describing populations | 453 | ||
| Problem-solving: Brain training | 456 | ||
| Check up | 457 | ||
| Strengthen | 458 | ||
| Extend | 463 | ||
| Knowledge check | 466 | ||
| Unit test | 468 | ||
| Unit 15: Equations and graphs | 471 | ||
| Prior knowledge check | 471 | ||
| 15.1: Solving simultaneous equations graphically | 472 | ||
| 15.2: Representing inequalities graphically | 475 | ||
| 15.3: Graphs of quadratic functions | 478 | ||
| 15.4: Solving quadratic equations graphically | 482 | ||
| 15.5: Graphs of cubic functions | 485 | ||
| Problem-solving | 490 | ||
| Check up | 491 | ||
| Strengthen | 492 | ||
| Extend | 496 | ||
| Knowledge check | 498 | ||
| Unit test | 499 | ||
| Unit 16: Circle theorems | 501 | ||
| Prior knowledge check | 501 | ||
| 16.1: Radii and chords | 502 | ||
| 16.2: Tangents | 504 | ||
| 16.3: Angles in circles 1 | 506 | ||
| 16.4: Angles in circles 2 | 509 | ||
| 16.5: Applying circle theorems | 512 | ||
| Problem-solving | 515 | ||
| Check up | 517 | ||
| Strengthen | 519 | ||
| Extend | 523 | ||
| Knowledge check | 526 | ||
| Unit test | 527 | ||
| Unit 17: More algebra | 531 | ||
| Prior knowledge check | 531 | ||
| 17.1: Rearranging formulae | 532 | ||
| 17.2: Algebraic fractions | 533 | ||
| 17.3: Simplifying algebraic fractions | 535 | ||
| 17.4: More algebraic fractions | 537 | ||
| 17.5: Surds | 539 | ||
| 17.6: Solving algebraic fraction equations | 541 | ||
| 17.7: Functions | 543 | ||
| 17.8: Proof | 545 | ||
| Problem-solving: Surface gravity | 548 | ||
| Check up | 549 | ||
| Strengthen | 550 | ||
| Extend | 553 | ||
| Knowledge check | 555 | ||
| Unit test | 556 | ||
| Unit 18: Vectors and geometric proof | 557 | ||
| Prior knowledge check | 557 | ||
| 18.1: Vectors and vector notation | 558 | ||
| 18.2: Vector arithmetic | 560 | ||
| 18.3: More vector arithmetic | 563 | ||
| 18.4: Parallel vectors and collinear points | 566 | ||
| 18.5: Solving geometric problems | 568 | ||
| Problem-solving | 572 | ||
| Check up | 574 | ||
| Strengthen | 576 | ||
| Extend | 579 | ||
| Knowledge check | 582 | ||
| Unit test | 584 | ||
| Unit 19: Proportion and graphs | 587 | ||
| Prior knowledge check | 587 | ||
| 19.1: Direct proportion | 588 | ||
| 19.2: More direct proportion | 590 | ||
| 19.3: Inverse proportion | 592 | ||
| 19.4: Exponential functions | 595 | ||
| 19.5: Non-linear graphs | 598 | ||
| 19.6: Translating graphs of functions | 602 | ||
| 19.7: Reflecting and stretching graphs of functions | 605 | ||
| Problem-solving: Modelling outbreaks | 610 | ||
| Check up | 611 | ||
| Strengthen | 613 | ||
| Extend | 615 | ||
| Knowledge check | 619 | ||
| Unit test | 621 | ||
| Answers | 624 | ||
| Index | 714 |