year 8 maths

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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 gameslibrary5 Ratiosand ratesWhat you will learn5A Introducing ratios5B Simplifying ratios5C Dividing a quantity in a given ratio5D Scale drawings5E Introducing rates5F Ratios and rates and the unitary method5G Solving rate problems5H Speed5I Distance–time graphsCambridge 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 ALGEBRASUBSTRANDS: RATIOS AND RATESFINANCIAL MATHEMATICSOutcomesA student operates with ratios andrates, and explores their graphicalrepresentation.(MA4–7NA)A student solves financial problemsinvolving purchasing goods.(MA4–6NA)© NESA, 2012Bicycle gear ratiosThe bicycle is renowned as the most energy-efficient means of human transport. A bicyclewith a range of gears is an extremely versatile and enjoyable machine. The ‘gear ratio’ ofa bicycle is the ratio of pedal rotations compared to the rate at which the wheels rotate.Manufacturers apply the mathematics of gear ratios to provide cyclists with the range ofgears that is most useful for the style of bike.Have you ever tried to ride up a steep hill in too high a gear or reached the bottom of a hillwhile still in a very low gear? A bicycle rider has a comfortable range of pressures and rotationrates that they can apply to the pedals. Gears make it easier to stay in this comfortable rangeover a wide variety of riding conditions, such as BMX, downhill racing, a fast time trial forracing bikes on flat ground, or climbing steep, rough trails on a mountain bike.Unicycles have only one wheel and so have a ratio of 1 : 1 for pedal turns to wheel turns.Unicycles can’t reach high speeds because it is very difficult to rotate pedals more thanabout 100 rpm; however, riding a unicycle is fun and it requires strength and agility to remainstable, especially when playing unicycle hockey!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.
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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
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Chapter review11510 a The sum of th
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NSW syllabusSTRAND: MEASUREMENT AND
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3ALength and perimeter1193A Length
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3ALength and perimeter121Exercise 3
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3ALength and perimeter12311 Gillian
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3BCircumference of circles1253B Cir
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3BCircumference of circles127Exerci
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3BCircumference of circles12917 We
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3CArea131• Triangle A = 1 2 × b
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3CArea133c i How many m 2 in 1 km 2
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3CArea13513 Write down expressions
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3DArea of special quadrilaterals137
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3DArea of special quadrilaterals139
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3EArea of circles141■ The ratio o
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1 d3EArea of circles143Example 115
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3FArea of sectors and composite fig
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3GSurface area of prisms151Example
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3GSurface area of prisms1538 Find t
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3HVolume and capacity155■ Some co
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3HVolume and capacity157PROBLEM-SOL
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3IVolume of prisms and cylinders159
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3JTime165■ The Earth is divided i
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3JTime1671 2 3 4 5 6 7 8 9 10 11 12
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3JTime1692 Find the number of:a sec
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3JTime17117 A doctor earns $180 000
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3KIntroducing Pythagoras’ theorem
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3KIntroducing Pythagoras’ theorem
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3LUsing Pythagoras’ theorem1773L
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3LUsing Pythagoras’ theorem179Exe
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3MCalculating the length of a short
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Investigation187Pythagorean triads
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Chapter summary189PerimeterTriangle
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Chapter review191Short-answer quest
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Chapter review193Extended-response
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4AEquivalent fractions1974A Equival
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4AEquivalent fractions199Example 1G
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4AEquivalent fractions201Example 29
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4BComputation with fractions2034B C
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4BComputation with fractions205■
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4BComputation with fractions207Exam
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4BComputation with fractions209Exam
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4CDecimal place value and fraction/
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4DComputation with decimals2174D Co
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4DComputation with decimals219Examp
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Page 239 and 240: 4ETerminating decimals, recurring d
Page 245 and 246: 4FConverting fractions, decimals an
Page 253 and 254: 4GFinding a percentage and expressi
Page 259 and 260: 4HDecreasing and increasing by a pe
Page 265 and 266: 4IThe Goods and Services Tax (GST)2
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Page 269 and 270: 4JCalculating percentage change, pr
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: Chapter review271Extended-response
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 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
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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
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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 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 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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