year 8 maths

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166 Chapter 3 Measurement and Pythagoras’ theorem11 10 9 8 7 6 54 3 2 1 0 164GREENLAND03 1ALASKA96ICELANDNORWAYSWQCANADA43½IRELANDK UNITEDKINGDOMNGERMANYLPFRANCE8UNITED STATES765RP1PORTUGALSPAINITALYMOROCCOALGERIALIBYMEXICOCUBAVENEZUELAMAURITANIAoMALINIGERNIGERIACH1World cities keyJ AucklandK EdinburghL GreenwichM JohannesburgN LondonP New YorkQ VancouverR Washington, DCCOLUMBIA54PERUBOLIVIA3ARGENTINACHILEBRAZILDOFANGONAMIBIASun1:00Sun2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:0011 10 9 8 7 6 54 3 2 1 0 1Australian cities keyA AdelaideB Alice SpringsC BrisbaneD CairnsE Canberra, ACTF DarwinG HobartH MelbourneI PerthIWesternStandardTimeWesternAustraliaFCentralStandardTimeNorthernTerritoryBAUSTRALIA9½SouthAustraliaQueenslandEasternStandardTimeNew South Wales20:00 21:00 Tasmania 22:00G89 10ADVictoriaHECCambridge 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.
3JTime1671 2 3 4 5 6 7 8 9 10 11 12 12 113AYSWEDENFINLAND3457RUSSIA891011129ERMANYPOLANDUKRAINEROMANIA4KAZAKHSTAN6MONGOLIA10ITALYIGERERIALIBYAGREECEEGYPTCHADSUDAN1 2TURKEYSYRIAIRAQSAUDIARABIAETHIOPIAIRAN3½4AFGHANISTAN4½ 5PAKISTANNEPAL5¾INDIA5½SRI LANKACHINA8BURMA6½THAILAND5½MALAYSIAPHILIPPINESJAPAN9DEM. REP.OF THE CONGOTANZANIAINDONESIAANGOLAZAMBIANAMIBIAMSOUTHAFRICAZIMBABWEMADAGASCAR3AUSTRALIA9½11½JNEW ZEALAND513:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:001 2 3 4 5 6 7 8 9 10 11 12 12 1112¾Sun24:00Sun20:00Sun1:00WANTSAQLDNSWDaylight savingNo daylight savingVICTASACTCambridge 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.
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8YEARCambridgeMATHSNSWSTAGE 4SECOND
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iiiTable of ContentsAbout the autho
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vPuzzles and challenges 264Review:
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vii9Data collection, representation
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ixIntroduction and guide to this bo
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xiGuide to this bookFeatures:NSW Sy
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xiiiOverview of the digital resourc
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xvDownloadable PDF TextbookThe conv
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xviiAcknowledgementsThe author and
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NSW syllabusSTRAND: NUMBER AND ALGE
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1AThe language of algebra51A The la
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1AThe language of algebra7Exercise
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1AThe language of algebra911 A plum
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1BSubstitution and equivalence11Exa
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1BSubstitution and equivalence13PRO
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1C Adding and subtracting terms 15E
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1C Adding and subtracting terms 171
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1DMultiplying and dividing terms19b
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1DMultiplying and dividing terms211
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1EAdding and subtracting algebraic
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1EAdding and subtracting algebraic
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1FMultiplying and dividing algebrai
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1FMultiplying and dividing algebrai
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1GExpanding brackets311G Expanding
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1GExpanding brackets333 Consider th
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1GExpanding brackets3516 Prove that
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1HFactorising expressions37Example
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1HFactorising expressions3913 Consi
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1IApplying algebra41Exercise 1IUNDE
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1IApplying algebra4313 Roberto draw
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1JIndex laws for multiplication and
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1JIndex laws for multiplication and
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1KThe zero index and power of a pow
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1KThe zero index and power of a pow
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Investigation536 Draw a number pyra
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Chapter summary55Pronumeral: a lett
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Chapter review57Multiple-choice que
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Chapter review59Extended-response q
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2AReviewing equations632A Reviewing
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2AReviewing equations65Example 3Wri
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2AReviewing equations6715 a Explain
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2BEquivalent equations69Example 4 F
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2BEquivalent equations71Example 5bE
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2CEquations with fractions732C Equa
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2CEquations with fractions75Example
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2CEquations with fractions7710 To s
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2DEquations with pronumerals on bot
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2DEquations with pronumerals on bot
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2EEquations with brackets832E Equat
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2EEquations with brackets853 Rolf i
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2FSolving simple quadratic equation
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2FSolving simple quadratic equation
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2GFormulas and relationships91Examp
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2GFormulas and relationships9312 Th
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2HApplications952H ApplicationsEXTE
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2HApplications97Exercise 2HEXTENSIO
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2HApplications9914 The average of t
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2IInequalities101Example 15Represen
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2IInequalities10310 At a certain sc
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2JSolving inequalities105Example 17
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2JSolving inequalities107PROBLEM-SO
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Investigation109Tiling a pool edgeT
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Puzzles and challenges1111 Find the
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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 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 181: 3JTime165■ The Earth is divided i
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 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: NSW syllabusSTRAND: NUMBER AND ALGE
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/
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4DComputation with decimals2174D Co
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4DComputation with decimals219Examp
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4DComputation with decimals221Examp
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4ETerminating decimals, recurring d
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4FConverting fractions, decimals an
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4GFinding a percentage and expressi
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4HDecreasing and increasing by a pe
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4IThe Goods and Services Tax (GST)2
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4IThe Goods and Services Tax (GST)2
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4JCalculating percentage change, pr
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4KSolving percentage problems with
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4KSolving percentage problems with
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Investigation263Calculating phiPhi
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Chapter summary2652=3Numerator2 par
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Chapter summary267Fraction to perce
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Chapter review2693 Evaluate each of
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Chapter review271Extended-response
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5AIntroducing ratios2755A Introduci
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5AIntroducing ratios277Exercise 5AU
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5AIntroducing ratios279ENRICHMENT-
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5BSimplifying ratios281■ The quan
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5BSimplifying ratios283Example 4bEx
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5CDividing a quantity in a given ra
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5DScale drawings2915D Scale drawing
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5DScale drawings293Example 9Convert
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5DScale drawings295Example 10Exampl
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5DScale drawings29717 A cartographe
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5EIntroducing rates299Example 12Wri
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5EIntroducing rates30111 The Tungam
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5FRatios and rates and the unitary
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5FRatios and rates and the unitary
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5GSolving rate problems3075G Solvin
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5GSolving rate problems309Exercise
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5GSolving rate problems311ENRICHMEN
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5HSpeed313Example 20Finding average
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5HSpeed315Exercise 5HUNDERSTANDING
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5HSpeed317ENRICHMENT- -20Speed rese
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5IDistance-time graphs319■ To dra
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5IDistance-time graphs321Exercise 5
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5IDistance-time graphs323Example 25
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5IDistance-time graphs32511 This di
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5IDistance-time graphs327ENRICHMENT
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Puzzles and challenges3291 This dia
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Chapter summary331Average rates720
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Chapter review33311 A toddler walke
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Chapter review33516 This distance-t
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Semester review 1 3378 For the rect
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Semester review 1 339Chapter 3: Mea
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Semester review 1 3418 Find the val
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Semester review 1 3439 a Increase $
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Semester review 1 3452 The training
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NSW syllabusSTRAND: MEASUREMENT AND
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6AThe language, notation and conven
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6BTransversal lines and parallel li
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6CTriangles365■ Triangles classif
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6CTriangles367Example 3a4 Use the a
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6CTriangles36911 A triangle is cons
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6DQuadrilaterals3716D Quadrilateral
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6DQuadrilaterals373Example 5Using t
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6DQuadrilaterals375Example 5b4 Use
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6EPolygons3776E PolygonsEXTENSIONTh
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6EPolygons379Example 7Finding angle
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6EPolygons381ef16°40°85°x°x°10
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6FLine symmetry and rotational symm
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6FLine symmetry and rotational symm
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6GEuler’s formula for three-dimen
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6GEuler’s formula for three-dimen
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Investigation391ConstructionsGeomet
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Puzzles and challenges3931 This sha
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Chapter review3975 These triangles
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7AThe Cartesian plane4017A The Cart
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7AThe Cartesian plane4033 Write the
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7BUsing rules, tables and graphs to
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7BUsing rules, tables and graphs to
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7CFinding the rule using a table of
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7DGradient4157D GradientEXTENSIONTh
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7DGradient417Exercise 7DEXTENSIONUN
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7DGradient419PROBLEM-SOLVING AND RE
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7EGradient-intercept form4217E Grad
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7EGradient-intercept form423Example
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7EGradient-intercept form425Example
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7EGradient-intercept form42713 Writ
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7FThe x-intercept429Example 11Findi
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7FThe x-intercept431PROBLEM-SOLVING
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7GSolving linear equations using gr
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7HApplying linear graphs4417H Apply
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7HApplying linear graphs443Example
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7HApplying linear graphs445PROBLEM-
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7INon-linear graphs447Example 17Plo
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7INon-linear graphs449c y = 5 − x
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7INon-linear graphs4516 What are th
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Investigation453Exploring families
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Chapter summary455yy = 2x − 1−4
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Chapter review457Short-answer quest
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Chapter review4599 a Use the approp
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NSW syllabusSTRANDS: NUMBER AND ALG
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8AReflection4638A Re flectionWhen a
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8AReflection465Example 2Using coord
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8AReflection467Example 25 State the
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8AReflection469ENRICHMENT- -15Refle
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8BTranslation471Example 3Finding th
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8BTranslation473Example 46 Copy the
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8CRotation4758C Ro t a t ionWhen th
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8CRotation477Exercise 8CUNDERSTANDI
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8CRotation4797 The triangle shown h
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8DCongruent figures4818D Congruent
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8DCongruent figures4833 In this dia
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8DCongruent figures48510 An isoscel
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8ECongruent triangles487■ There a
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8ECongruent triangles489Example 83
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8ECongruent triangles4918 Two adjoi
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8FSimilar figures4938F Similar figu
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8FSimilar figures495Example 10Decid
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8FSimilar figures4973 Decide if the
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8FSimilar figures49911 a If a regul
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8GSimilar triangles501• The hypot
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8GSimilar triangles503Example 113 D
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8GSimilar triangles5058 Trees on a
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8HUsing congruent triangles to esta
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Investigation513Exploring SSAWith t
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Chapter summary515TranslationVector
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Chapter review51710 ABCD is a paral
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Chapter review51911 This quadrilate
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NSW syllabusSTRAND: STATISTICS ANDS
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9ATypes of data5239A Types of dataP
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9ATypes of data525Example 12 Classi
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9ATypes of data52710 A Likert-type
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9BDot plots and column graphs5299B
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9BDot plots and column graphs531Exa
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9BDot plots and column graphs533Exa
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9BDot plots and column graphs5357 E
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9BDot plots and column graphs53712
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9CLine graphs5399C Line graphsA lin
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9CLine graphs541Exercise 9CUNDERSTA
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9CLine graphs5439 The temperature i
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9DSector graphs and divided bar gra
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9EFrequency distribution tables5519
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9FFrequency histograms and frequenc
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9GMean, median, mode and range565fo
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9GMean, median, mode and range5677
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]]9HInterquartile range5699H Interq
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9HInterquartile range5715 Calculate
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9IStem-and-leaf plots5739I Stem-and
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9IStem-and-leaf plots575Exercise 9I
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9IStem-and-leaf plots57711 A group
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9JSurveying and sampling5799J Surve
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9JSurveying and sampling581Example
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9JSurveying and sampling58312 Whene
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Puzzles and challenges5851 Six numb
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Chapter review589Short-answer quest
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Chapter review59110 120 people were
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Semester review 2 5932 Find the val
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Semester review 2 5952 a Complete t
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Semester review 2 5973 Triangle ABC
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Semester review 2 5997 A set of six
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60118 a Multiplication is commutati
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60315 a 1836 b 1836c i 154 ii 352 i
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6052 a xy − x2b 33 m 2 c 2x + 2y
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6075 a u = 6 b j = 3 c p = 6 d m =
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g609Exercise 2J1 a true b true c fa
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61112 a A = 4 triangle areasExercis
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613Exercise 3K1 a 9 b 25 c 144 d 2.
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6159 a 1 3e 1 45i310 a 1 4e 5 4b 1
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61712 A13 aFraction Decimal %142434
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61916Raw material $110 (includes th
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6219 a 2 : 5 b 14 : 1 c 3 : 25 d 1
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623Exercise 5H6 a segments B and D
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625Puzzles and challenges1 a 2 b 3
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6278 a 5.6 b 11.76 c 85.5 m d $1.98
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62911 a Isosceles, the two radii ar
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631Short-answer questions1 a 50 b 6
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633iiyey321−3 −2 −1O−11 2 3
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63510 a y = 2x + 3 b y = − 1 2 x
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6374 a x = 2 b x = 0.5 c x = 3d x =
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63910 a d = 15t b 3 hoursc 3 hours
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641b8642−3 −2 −1O−2−4−6
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643ef13 They are on the mirror line
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6454 a i E ii Hb i EHc i ∠Gii GHi
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64710 a ∠A = ∠D (corresponding
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6494 a discrete numericalb continuo
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651Exercise 9C1 a 3 kg b 4 kg c 5 k
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653Exercise 9E1 a true b false c tr
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65511 aSurvey locationHeightgraph (
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6574 a Yes, it is required informat
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659Linear relationships 1Multiple-c
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661acute angles 350, 365adding frac
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663surface area 150survey 579tally
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