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 gameslibraryFractions, decimals,percentagesand financial4mathematicsWhat you will learn4A Equivalent fractions REVISION4B Computation with fractions REVISION4C Decimal place value and fraction /decimal conversions REVISION4D Computation with decimals REVISION4E Terminating decimals, recurring decimals and rounding REVISION4F Converting fractions, decimals and percentages REVISION4G Finding a percentage and expressing as a percentage4H Decreasing and increasing by a percentage4I The Goods and Services Tax (GST)4J Calculating percentage change, profit and loss4K Solving percentage problems with the unitary method and equationsCambridge 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: FRACTIONS,DECIMALS ANDPERCENTAGESFINANCIALMATHEMATICSOutcomesA student operates with fractions,decimals and percentages.(MA4–5NA)A student solves financial problemsinvolving purchasing goods.(MA4–6NA)© NESA, 2012Phi and golden rectanglesPhi is a unique and mysterious decimal number approximately equal to 1.618 . As of 2015,the value of phi has now been calculated to two trillion (2 000 000 000 000) decimal places.Phi’s decimal places continue forever; no pattern has been found and it cannot be writtenas a fraction.Golden rectangles are rectangles that have the proportion of length to width equal to phi : 1 .This ratio is thought to be the most visually appealing proportion to the human eye.Proportions using the decimal phi are found in an astounding variety of places includingancient Egyptian pyramids, Greek architecture and sculptures, art, the nautilus shell, anant, a dolphin, a beautiful human face, an ear, a tooth, the body, the graphic design of creditcards, websites and company logos, DNA and even the shape of the Milky Way galaxy.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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Page 161 and 162: 3FArea of sectors and composite fig
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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 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 203 and 204: Investigation187Pythagorean triads
Page 205 and 206: Chapter summary189PerimeterTriangle
Page 207 and 208: Chapter review191Short-answer quest
Page 209: Chapter review193Extended-response
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 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 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
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4HDecreasing and increasing by a pe
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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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