year 8 maths

Recommendations

Info

Onlineresources• Auto-marked chapter pre-test• Video demonstrations of all workedexamples• Interactive widgets• Interactive walkthroughs• Downloadable HOTsheets• Access to all HOTmaths AustralianCurriculum courses• Access to the HOTmaths gameslibrary2 Equations2What you will learn2A Reviewing equations REVISION2B Equivalent equations REVISION2C Equations with fractions2D Equations with pronumerals on both sides2E Equations with brackets2F Solving simple quadratic equations2G Formulas and relationships EXTENSION2H Applications EXTENSION2I Inequalities EXTENSION2J Solving inequalities EXTENSIONCambridge Maths NSWStage 4 Year 8 Second editionISBN 978-1-108-46627-1 © Palmer et al. 2018Cambridge University PressPhotocopying is restricted under law and this material must not be transferred to another party.
NSW syllabusSTRAND: NUMBER AND ALGEBRASUBSTRAND: EQUATIONSOutcomeA student uses algebraic techniquesto solve simple linear and quadraticequations.(MA4–10NA)© NESA, 2012Protecting sea turtlesLoggerhead sea turtles are magnificent marine predators that feed on shellfish, crabs, seaurchins and jellyfish. Sadly, Australian loggerhead turtles have lost more than 50% of theirnesting females in the past 10 years. These diminishing numbers mean that loggerhead turtlesare now an endangered species. They are under threat for a number of reasons, includinghuman activity on the beaches where the females lay eggs and accidental death in fishingnets. In order to work out how to best save the loggerhead sea turtle, scientists need to workout what effect various actions, such as closing beaches, will have on the loggerheadturtle population.To do this scientists use mathematics! With a combination of data and equations, they usecomputer models to predict population numbers of future generations of the loggerhead turtle.For example, this simple equation describes the number of turtles that there will be next year:F = C(1 + B − D)The pronumerals used in this equation are:• F = future population• C = current population• B = birth rate• D = death rateBy mathematically predicting the future of the loggerhead turtle population, environmentalscientists can advise governments of the best decisions to help save the loggerhead seaturtle from extinction.Cambridge Maths NSWStage 4 Year 8 Second editionISBN 978-1-108-46627-1 © Palmer et al. 2018Cambridge University PressPhotocopying is restricted under law and this material must not be transferred to another party.
Page 1 and 2:
8YEARCambridgeMATHSNSWSTAGE 4SECOND
Page 3 and 4:
iiiTable of ContentsAbout the autho
Page 5 and 6:
vPuzzles and challenges 264Review:
Page 7 and 8:
vii9Data collection, representation
Page 9 and 10:
ixIntroduction and guide to this bo
Page 11 and 12:
xiGuide to this bookFeatures:NSW Sy
Page 13 and 14:
xiiiOverview of the digital resourc
Page 15 and 16:
xvDownloadable PDF TextbookThe conv
Page 17 and 18:
xviiAcknowledgementsThe author and
Page 19 and 20:
NSW syllabusSTRAND: NUMBER AND ALGE
Page 21 and 22:
1AThe language of algebra51A The la
Page 23 and 24:
1AThe language of algebra7Exercise
Page 25 and 26: 1AThe language of algebra911 A plum
Page 27 and 28: 1BSubstitution and equivalence11Exa
Page 29 and 30: 1BSubstitution and equivalence13PRO
Page 31 and 32: 1C Adding and subtracting terms 15E
Page 33 and 34: 1C Adding and subtracting terms 171
Page 35 and 36: 1DMultiplying and dividing terms19b
Page 37 and 38: 1DMultiplying and dividing terms211
Page 39 and 40: 1EAdding and subtracting algebraic
Page 41 and 42: 1EAdding and subtracting algebraic
Page 43 and 44: 1FMultiplying and dividing algebrai
Page 45 and 46: 1FMultiplying and dividing algebrai
Page 47 and 48: 1GExpanding brackets311G Expanding
Page 49 and 50: 1GExpanding brackets333 Consider th
Page 51 and 52: 1GExpanding brackets3516 Prove that
Page 53 and 54: 1HFactorising expressions37Example
Page 55 and 56: 1HFactorising expressions3913 Consi
Page 57 and 58: 1IApplying algebra41Exercise 1IUNDE
Page 59 and 60: 1IApplying algebra4313 Roberto draw
Page 61 and 62: 1JIndex laws for multiplication and
Page 63 and 64: 1JIndex laws for multiplication and
Page 65 and 66: 1KThe zero index and power of a pow
Page 67 and 68: 1KThe zero index and power of a pow
Page 69 and 70: Investigation536 Draw a number pyra
Page 71 and 72: Chapter summary55Pronumeral: a lett
Page 73 and 74: Chapter review57Multiple-choice que
Page 75: Chapter review59Extended-response q
Page 79 and 80: 2AReviewing equations632A Reviewing
Page 81 and 82: 2AReviewing equations65Example 3Wri
Page 83 and 84: 2AReviewing equations6715 a Explain
Page 85 and 86: 2BEquivalent equations69Example 4 F
Page 87 and 88: 2BEquivalent equations71Example 5bE
Page 89 and 90: 2CEquations with fractions732C Equa
Page 91 and 92: 2CEquations with fractions75Example
Page 93 and 94: 2CEquations with fractions7710 To s
Page 95 and 96: 2DEquations with pronumerals on bot
Page 97 and 98: 2DEquations with pronumerals on bot
Page 99 and 100: 2EEquations with brackets832E Equat
Page 101 and 102: 2EEquations with brackets853 Rolf i
Page 103 and 104: 2FSolving simple quadratic equation
Page 105 and 106: 2FSolving simple quadratic equation
Page 107 and 108: 2GFormulas and relationships91Examp
Page 109 and 110: 2GFormulas and relationships9312 Th
Page 111 and 112: 2HApplications952H ApplicationsEXTE
Page 113 and 114: 2HApplications97Exercise 2HEXTENSIO
Page 115 and 116: 2HApplications9914 The average of t
Page 117 and 118: 2IInequalities101Example 15Represen
Page 119 and 120: 2IInequalities10310 At a certain sc
Page 121 and 122: 2JSolving inequalities105Example 17
Page 123 and 124: 2JSolving inequalities107PROBLEM-SO
Page 125 and 126: Investigation109Tiling a pool edgeT
Page 127 and 128:
Puzzles and challenges1111 Find the
Page 129 and 130:
Chapter review113Multiple-choice qu
Page 131 and 132:
Chapter review11510 a The sum of th
Page 133 and 134:
NSW syllabusSTRAND: MEASUREMENT AND
Page 135 and 136:
3ALength and perimeter1193A Length
Page 137 and 138:
3ALength and perimeter121Exercise 3
Page 139 and 140:
3ALength and perimeter12311 Gillian
Page 141 and 142:
3BCircumference of circles1253B Cir
Page 143 and 144:
3BCircumference of circles127Exerci
Page 145 and 146:
3BCircumference of circles12917 We
Page 147 and 148:
3CArea131• Triangle A = 1 2 × b
Page 149 and 150:
3CArea133c i How many m 2 in 1 km 2
Page 151 and 152:
3CArea13513 Write down expressions
Page 153 and 154:
3DArea of special quadrilaterals137
Page 155 and 156:
3DArea of special quadrilaterals139
Page 157 and 158:
3EArea of circles141■ The ratio o
Page 159 and 160:
1 d3EArea of circles143Example 115
Page 161 and 162:
3FArea of sectors and composite fig
Page 163 and 164:
Page 165 and 166:
Page 167 and 168:
3GSurface area of prisms151Example
Page 169 and 170:
3GSurface area of prisms1538 Find t
Page 171 and 172:
3HVolume and capacity155■ Some co
Page 173 and 174:
3HVolume and capacity157PROBLEM-SOL
Page 175 and 176:
3IVolume of prisms and cylinders159
Page 177 and 178:
Page 179 and 180:
Page 181 and 182:
3JTime165■ The Earth is divided i
Page 183 and 184:
3JTime1671 2 3 4 5 6 7 8 9 10 11 12
Page 185 and 186:
3JTime1692 Find the number of:a sec
Page 187 and 188:
3JTime17117 A doctor earns $180 000
Page 189 and 190:
3KIntroducing Pythagoras’ theorem
Page 191 and 192:
3KIntroducing Pythagoras’ theorem
Page 193 and 194:
3LUsing Pythagoras’ theorem1773L
Page 195 and 196:
3LUsing Pythagoras’ theorem179Exe
Page 197 and 198:
3MCalculating the length of a short
Page 199 and 200:
Page 201 and 202:
Page 203 and 204:
Investigation187Pythagorean triads
Page 205 and 206:
Chapter summary189PerimeterTriangle
Page 207 and 208:
Chapter review191Short-answer quest
Page 209 and 210:
Chapter review193Extended-response
Page 211 and 212:
Page 213 and 214:
4AEquivalent fractions1974A Equival
Page 215 and 216:
4AEquivalent fractions199Example 1G
Page 217 and 218:
4AEquivalent fractions201Example 29
Page 219 and 220:
4BComputation with fractions2034B C
Page 221 and 222:
4BComputation with fractions205■
Page 223 and 224:
4BComputation with fractions207Exam
Page 225 and 226:
4BComputation with fractions209Exam
Page 227 and 228:
4CDecimal place value and fraction/
Page 229 and 230:
Page 231 and 232:
Page 233 and 234:
4DComputation with decimals2174D Co
Page 235 and 236:
4DComputation with decimals219Examp
Page 237 and 238:
4DComputation with decimals221Examp
Page 239 and 240:
4ETerminating decimals, recurring d
Page 241 and 242:
Page 243 and 244:
Page 245 and 246:
4FConverting fractions, decimals an
Page 247 and 248:
Page 249 and 250:
Page 251 and 252:
Page 253 and 254:
4GFinding a percentage and expressi
Page 255 and 256:
Page 257 and 258:
Page 259 and 260:
4HDecreasing and increasing by a pe
Page 261 and 262:
Page 263 and 264:
Page 265 and 266:
4IThe Goods and Services Tax (GST)2
Page 267 and 268:
4IThe Goods and Services Tax (GST)2
Page 269 and 270:
4JCalculating percentage change, pr
Page 271 and 272:
Page 273 and 274:
Page 275 and 276:
4KSolving percentage problems with
Page 277 and 278:
4KSolving percentage problems with
Page 279 and 280:
Investigation263Calculating phiPhi
Page 281 and 282:
Chapter summary2652=3Numerator2 par
Page 283 and 284:
Chapter summary267Fraction to perce
Page 285 and 286:
Chapter review2693 Evaluate each of
Page 287 and 288:
Chapter review271Extended-response
Page 289 and 290:
Page 291 and 292:
5AIntroducing ratios2755A Introduci
Page 293 and 294:
5AIntroducing ratios277Exercise 5AU
Page 295 and 296:
5AIntroducing ratios279ENRICHMENT-
Page 297 and 298:
5BSimplifying ratios281■ The quan
Page 299 and 300:
5BSimplifying ratios283Example 4bEx
Page 301 and 302:
5CDividing a quantity in a given ra
Page 303 and 304:
Page 305 and 306:
Page 307 and 308:
5DScale drawings2915D Scale drawing
Page 309 and 310:
5DScale drawings293Example 9Convert
Page 311 and 312:
5DScale drawings295Example 10Exampl
Page 313 and 314:
5DScale drawings29717 A cartographe
Page 315 and 316:
5EIntroducing rates299Example 12Wri
Page 317 and 318:
5EIntroducing rates30111 The Tungam
Page 319 and 320:
5FRatios and rates and the unitary
Page 321 and 322:
5FRatios and rates and the unitary
Page 323 and 324:
5GSolving rate problems3075G Solvin
Page 325 and 326:
5GSolving rate problems309Exercise
Page 327 and 328:
5GSolving rate problems311ENRICHMEN
Page 329 and 330:
5HSpeed313Example 20Finding average
Page 331 and 332:
5HSpeed315Exercise 5HUNDERSTANDING
Page 333 and 334:
5HSpeed317ENRICHMENT- -20Speed rese
Page 335 and 336:
5IDistance-time graphs319■ To dra
Page 337 and 338:
5IDistance-time graphs321Exercise 5
Page 339 and 340:
5IDistance-time graphs323Example 25
Page 341 and 342:
5IDistance-time graphs32511 This di
Page 343 and 344:
5IDistance-time graphs327ENRICHMENT
Page 345 and 346:
Puzzles and challenges3291 This dia
Page 347 and 348:
Chapter summary331Average rates720
Page 349 and 350:
Chapter review33311 A toddler walke
Page 351 and 352:
Chapter review33516 This distance-t
Page 353 and 354:
Semester review 1 3378 For the rect
Page 355 and 356:
Semester review 1 339Chapter 3: Mea
Page 357 and 358:
Semester review 1 3418 Find the val
Page 359 and 360:
Semester review 1 3439 a Increase $
Page 361 and 362:
Semester review 1 3452 The training
Page 363 and 364:
NSW syllabusSTRAND: MEASUREMENT AND
Page 365 and 366:
6AThe language, notation and conven
Page 367 and 368:
Page 369 and 370:
Page 371 and 372:
Page 373 and 374:
6BTransversal lines and parallel li
Page 375 and 376:
Page 377 and 378:
Page 379 and 380:
Page 381 and 382:
6CTriangles365■ Triangles classif
Page 383 and 384:
6CTriangles367Example 3a4 Use the a
Page 385 and 386:
6CTriangles36911 A triangle is cons
Page 387 and 388:
6DQuadrilaterals3716D Quadrilateral
Page 389 and 390:
6DQuadrilaterals373Example 5Using t
Page 391 and 392:
6DQuadrilaterals375Example 5b4 Use
Page 393 and 394:
6EPolygons3776E PolygonsEXTENSIONTh
Page 395 and 396:
6EPolygons379Example 7Finding angle
Page 397 and 398:
6EPolygons381ef16°40°85°x°x°10
Page 399 and 400:
6FLine symmetry and rotational symm
Page 401 and 402:
6FLine symmetry and rotational symm
Page 403 and 404:
6GEuler’s formula for three-dimen
Page 405 and 406:
6GEuler’s formula for three-dimen
Page 407 and 408:
Investigation391ConstructionsGeomet
Page 409 and 410:
Puzzles and challenges3931 This sha
Page 411 and 412:
Page 413 and 414:
Chapter review3975 These triangles
Page 415 and 416:
Page 417 and 418:
7AThe Cartesian plane4017A The Cart
Page 419 and 420:
7AThe Cartesian plane4033 Write the
Page 421 and 422:
7BUsing rules, tables and graphs to
Page 423 and 424:
7BUsing rules, tables and graphs to
Page 425 and 426:
7CFinding the rule using a table of
Page 427 and 428:
Page 429 and 430:
Page 431 and 432:
7DGradient4157D GradientEXTENSIONTh
Page 433 and 434:
7DGradient417Exercise 7DEXTENSIONUN
Page 435 and 436:
7DGradient419PROBLEM-SOLVING AND RE
Page 437 and 438:
7EGradient-intercept form4217E Grad
Page 439 and 440:
7EGradient-intercept form423Example
Page 441 and 442:
7EGradient-intercept form425Example
Page 443 and 444:
7EGradient-intercept form42713 Writ
Page 445 and 446:
7FThe x-intercept429Example 11Findi
Page 447 and 448:
7FThe x-intercept431PROBLEM-SOLVING
Page 449 and 450:
7GSolving linear equations using gr
Page 451 and 452:
Page 453 and 454:
Page 455 and 456:
Page 457 and 458:
7HApplying linear graphs4417H Apply
Page 459 and 460:
7HApplying linear graphs443Example
Page 461 and 462:
7HApplying linear graphs445PROBLEM-
Page 463 and 464:
7INon-linear graphs447Example 17Plo
Page 465 and 466:
7INon-linear graphs449c y = 5 − x
Page 467 and 468:
7INon-linear graphs4516 What are th
Page 469 and 470:
Investigation453Exploring families
Page 471 and 472:
Chapter summary455yy = 2x − 1−4
Page 473 and 474:
Page 475 and 476:
Chapter review4599 a Use the approp
Page 477 and 478:
NSW syllabusSTRANDS: NUMBER AND ALG
Page 479 and 480:
8AReflection4638A Re flectionWhen a
Page 481 and 482:
8AReflection465Example 2Using coord
Page 483 and 484:
8AReflection467Example 25 State the
Page 485 and 486:
8AReflection469ENRICHMENT- -15Refle
Page 487 and 488:
8BTranslation471Example 3Finding th
Page 489 and 490:
8BTranslation473Example 46 Copy the
Page 491 and 492:
8CRotation4758C Ro t a t ionWhen th
Page 493 and 494:
8CRotation477Exercise 8CUNDERSTANDI
Page 495 and 496:
8CRotation4797 The triangle shown h
Page 497 and 498:
8DCongruent figures4818D Congruent
Page 499 and 500:
8DCongruent figures4833 In this dia
Page 501 and 502:
8DCongruent figures48510 An isoscel
Page 503 and 504:
8ECongruent triangles487■ There a
Page 505 and 506:
8ECongruent triangles489Example 83
Page 507 and 508:
8ECongruent triangles4918 Two adjoi
Page 509 and 510:
8FSimilar figures4938F Similar figu
Page 511 and 512:
8FSimilar figures495Example 10Decid
Page 513 and 514:
8FSimilar figures4973 Decide if the
Page 515 and 516:
8FSimilar figures49911 a If a regul
Page 517 and 518:
8GSimilar triangles501• The hypot
Page 519 and 520:
8GSimilar triangles503Example 113 D
Page 521 and 522:
8GSimilar triangles5058 Trees on a
Page 523 and 524:
8HUsing congruent triangles to esta
Page 525 and 526:
Page 527 and 528:
Page 529 and 530:
Investigation513Exploring SSAWith t
Page 531 and 532:
Chapter summary515TranslationVector
Page 533 and 534:
Chapter review51710 ABCD is a paral
Page 535 and 536:
Chapter review51911 This quadrilate
Page 537 and 538:
NSW syllabusSTRAND: STATISTICS ANDS
Page 539 and 540:
9ATypes of data5239A Types of dataP
Page 541 and 542:
9ATypes of data525Example 12 Classi
Page 543 and 544:
9ATypes of data52710 A Likert-type
Page 545 and 546:
9BDot plots and column graphs5299B
Page 547 and 548:
9BDot plots and column graphs531Exa
Page 549 and 550:
9BDot plots and column graphs533Exa
Page 551 and 552:
9BDot plots and column graphs5357 E
Page 553 and 554:
9BDot plots and column graphs53712
Page 555 and 556:
9CLine graphs5399C Line graphsA lin
Page 557 and 558:
9CLine graphs541Exercise 9CUNDERSTA
Page 559 and 560:
9CLine graphs5439 The temperature i
Page 561 and 562:
9DSector graphs and divided bar gra
Page 563 and 564:
Page 565 and 566:
Page 567 and 568:
9EFrequency distribution tables5519
Page 569 and 570:
Page 571 and 572:
Page 573 and 574:
9FFrequency histograms and frequenc
Page 575 and 576:
Page 577 and 578:
Page 579 and 580:
Page 581 and 582:
9GMean, median, mode and range565fo
Page 583 and 584:
9GMean, median, mode and range5677
Page 585 and 586:
]]9HInterquartile range5699H Interq
Page 587 and 588:
9HInterquartile range5715 Calculate
Page 589 and 590:
9IStem-and-leaf plots5739I Stem-and
Page 591 and 592:
9IStem-and-leaf plots575Exercise 9I
Page 593 and 594:
9IStem-and-leaf plots57711 A group
Page 595 and 596:
9JSurveying and sampling5799J Surve
Page 597 and 598:
9JSurveying and sampling581Example
Page 599 and 600:
9JSurveying and sampling58312 Whene
Page 601 and 602:
Puzzles and challenges5851 Six numb
Page 603 and 604:
Page 605 and 606:
Page 607 and 608:
Chapter review59110 120 people were
Page 609 and 610:
Semester review 2 5932 Find the val
Page 611 and 612:
Semester review 2 5952 a Complete t
Page 613 and 614:
Semester review 2 5973 Triangle ABC
Page 615 and 616:
Semester review 2 5997 A set of six
Page 617 and 618:
60118 a Multiplication is commutati
Page 619 and 620:
60315 a 1836 b 1836c i 154 ii 352 i
Page 621 and 622:
6052 a xy − x2b 33 m 2 c 2x + 2y
Page 623 and 624:
6075 a u = 6 b j = 3 c p = 6 d m =
Page 625 and 626:
g609Exercise 2J1 a true b true c fa
Page 627 and 628:
61112 a A = 4 triangle areasExercis
Page 629 and 630:
613Exercise 3K1 a 9 b 25 c 144 d 2.
Page 631 and 632:
6159 a 1 3e 1 45i310 a 1 4e 5 4b 1
Page 633 and 634:
61712 A13 aFraction Decimal %142434
Page 635 and 636:
61916Raw material $110 (includes th
Page 637 and 638:
6219 a 2 : 5 b 14 : 1 c 3 : 25 d 1
Page 639 and 640:
623Exercise 5H6 a segments B and D
Page 641 and 642:
625Puzzles and challenges1 a 2 b 3
Page 643 and 644:
6278 a 5.6 b 11.76 c 85.5 m d $1.98
Page 645 and 646:
62911 a Isosceles, the two radii ar
Page 647 and 648:
631Short-answer questions1 a 50 b 6
Page 649 and 650:
633iiyey321−3 −2 −1O−11 2 3
Page 651 and 652:
63510 a y = 2x + 3 b y = − 1 2 x
Page 653 and 654:
6374 a x = 2 b x = 0.5 c x = 3d x =
Page 655 and 656:
63910 a d = 15t b 3 hoursc 3 hours
Page 657 and 658:
641b8642−3 −2 −1O−2−4−6
Page 659 and 660:
643ef13 They are on the mirror line
Page 661 and 662:
6454 a i E ii Hb i EHc i ∠Gii GHi
Page 663 and 664:
64710 a ∠A = ∠D (corresponding
Page 665 and 666:
6494 a discrete numericalb continuo
Page 667 and 668:
651Exercise 9C1 a 3 kg b 4 kg c 5 k
Page 669 and 670:
653Exercise 9E1 a true b false c tr
Page 671 and 672:
65511 aSurvey locationHeightgraph (
Page 673 and 674:
6574 a Yes, it is required informat
Page 675 and 676:
659Linear relationships 1Multiple-c
Page 677 and 678:
661acute angles 350, 365adding frac
Page 679 and 680:
663surface area 150survey 579tally
show all

year 8 maths

Create successful ePaper yourself

Delete template?

Save as template?