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1 Cmridge University Press E s s E n t i l MtheMtis for the ustrlin CurriCulum yer9 dditionl resoures online DviD GreenwooD JennY GooDMn Jennifer vughn sr woolley BeTh GoDwin

2 Cmridge University Press mridge university press Cmridge, New York, Melourne, Mdrid, Cpe Town, Singpore, São Pulo, Delhi, Meio City Cmridge University Press 477 Willimstown Rod, Port Melourne, VIC 07, Austrli Informtion on this title: / Dvid Greenwood, Jenny Goodmn, Jennifer Vughn, Sr Woolley, GT Instlltions, Georgi Sotiriou, Voul Sotiriou 0 This pulition is in opyright. Sujet to sttutory eeption nd to the provisions of relevnt olletive liensing greements, no reprodution of ny prt my tke ple without the written permission of Cmridge University Press. First pulished 0 Edited y Kelly Roinson Cover design y Denise Lne Typeset y Aptr Corp Printed in Chin y C & C Offset Printing Co. Ltd. A Ctloguing-in-Pulition entry is ville from the tlogue of the Ntionl Lirry of Austrli t ISBN Pperk Additionl resoures for this pulition t Reprodution nd Communition for edutionl purposes The Austrlin Copyright At 968 (the At) llows mimum of one hpter or 0% of the pges of this pulition, whihever is the greter, to e reprodued nd/or ommunited y ny edutionl institution for its edutionl purposes provided tht the edutionl institution (or the ody tht dministers it) hs given remunertion notie to Copyright Ageny Limited (CAL) under the At. For detils of the CAL liene for edutionl institutions ontt: Copyright Ageny Limited Level 5, Cstleregh Street Sydney NSW 000 Telephone: (0) Fsimile: (0) Emil: info@opyright.om.u Reprodution nd Communition for other purposes Eept s permitted under the At (for emple fir deling for the purposes of study, reserh, ritiism or review) no prt of this pulition my e reprodued, stored in retrievl system, ommunited or trnsmitted in ny form or y ny mens without prior written permission. All inquiries should e mde to the pulisher t the ddress ove. Cmridge University Press hs no responsiility for the persistene or ury of URLs for eternl or third-prty Internet wesites referred to in this pulition nd does not gurntee tht ny ontent on suh wesites is, or will remin, urte or pproprite. Informtion regrding pries, trvel timetles nd other ftul informtion given in this work re orret t the time of first printing ut Cmridge University Press does not gurntee the ury of suh informtion therefter.

3 Cmridge University Press Tle Contents of Contents Strnd nd ontent desription Aout the uthors Introdution nd how to use this ook viii i Reviewing numer Pre-test. Adding nd sutrting integers. Multiplying nd dividing integers 7. Deimls nd rounding.4 Rtionl numers 6.5 Adding nd sutrting frtions.6 Multiplying nd dividing frtions 5.7 Rtios 0.8 Rtes nd diret proportion 5 Puzzles nd gmes 40 Review: Chpter summry 4 Multiple-hoie questions 4 Short-nswer questions 4 Etended-response questions 44 Finnil mthemtis 45 Pre-test 46. Perentges 47. Applying perentges 5. Perentge inrese nd derese 55.4 Profi ts nd disounts 60.5 Inome 66.6 Ttion 7.7 Simple interest 75.8 Applitions of simple interest 80 Puzzles nd gmes 84 Review: Chpter summry 85 Multiple-hoie questions 86 Short-nswer questions 87 Etended-response questions 88 Numer nd Alger Rel numers Numer nd Alger Money nd finnil mthemtis iii

4 Cmridge University Press iv Contents 4 Liner equtions 89 Pre-test 90. Algeri epressions 9. Adding nd sutrting lgeri epressions 97. Multiplying nd dividing lgeri epressions 0.4 Epnding lgeri epressions 05.5 Solving liner equtions 0.6 Solving liner equtions involving frtions.7 Equtions with rkets 7.8 Equtions with vriles on oth sides 0.9 Solving word prolems 4.0 Using formuls 9 Puzzles nd gmes 4 Review: Chpter summry 5 Multiple-hoie questions 6 Short-nswer questions 6 Etended-response questions 8 Pythgors theorem nd trigonometry 9 Pre-test Eploring Pythgors theorem 4 4. Finding the length of the hypotenuse Finding the lengths of the shorter sides Applying Pythgors theorem Trigonometri rtios Finding side lengths Solving for the denomintor Finding n ngle Applying trigonometry 80 Puzzles nd gmes 84 Review: Chpter summry 85 Multiple-hoie questions 86 Short-nswer questions 87 Etended-response questions 88 Numer nd Alger Ptterns nd lger Mesurement nd Geometry Pythgors nd trigonometry

5 Cmridge University Press Contents v 5 Liner reltions 89 Pre-test Introdution to liner reltions nd y-interepts Grphing stright lines with interepts Lines with one interept Grdient Grdient nd diret proportion 5.7 Grdient interept form Finding the eqution of line 5.9 Midpoint nd length of line segment Liner modelling 4 5. Non-liner grphs 48 Puzzles nd gmes 55 Review: Chpter summry 56 Multiple-hoie questions 57 Short-nswer questions 59 Etended-response questions 60 Numer nd Alger Rel numers Liner nd non-liner reltionships Semester review 6 6 Mesurement 67 Pre-test Length nd perimeter Cirumferene of irle Are Are of irle Composite shpes Surfe re of prisms Surfe re of ylinder Volume Volume of ylinder 07 Puzzles nd gmes Review: Chpter summry Multiple-hoie questions Short-nswer questions 4 Etended-response questions 6 Mesurement nd Geometry Using units of mesurement

6 Cmridge University Press vi Contents 7 8 Indies 7 Pre-test 8 7. Inde nottion 9 7. Inde lws nd 5 7. Inde lw nd the zero power 7.4 Inde lws 4 nd Negtive indies Sientifi nottion Sientifi nottion using signifi nt fi gures 5 Puzzles nd gmes 56 Review: Chpter summry 57 Multiple-hoie questions 58 Short-nswer questions 59 Etended-response questions 60 Geometry 6 Pre-test 6 8. Angles nd tringles 6 8. Prllel lines Qudrilterls Polygons Congruent tringles Enlrgement nd similr fi gures Similr tringles Applying similr tringles 40 Puzzles nd gmes 406 Review: Chpter summry 407 Multiple-hoie questions 408 Short-nswer questions 409 Etended-response questions 4 Numer nd Alger Rel numers Ptterns nd lger Mesurement nd Geometry Geometri resoning

7 Cmridge University Press Contents vii 9 0 Algeri tehniques 4 Pre-test Reviewing lger Epnding inomil produts Epnding perfet squres Differene of perfet squres Ftorising lgeri epressions Simplifying lgeri frtions: multiplition nd division Simplifying lgeri frtions: ddition nd sutrtion 440 Puzzles nd gmes 444 Review: Chpter summry 445 Multiple-hoie questions 446 Short-nswer questions 447 Etended-response questions 448 Sttistis nd proility 449 Pre-test Proility review Venn digrms nd two-wy tles Multiple events using tles Tree digrms Eperimentl proility Summrising dt: rnge nd mesures of entre Interpreting dt from tles nd grphs Stem-nd-lef plots Grouped dt 505 Puzzles nd gmes 5 Review: Chpter summry 5 Multiple-hoie questions 54 Short-nswer questions 55 Etended-response questions 57 Numer nd Alger Ptterns nd lger Sttistis nd Proility Chne Dt representtion nd interprettion Semester review 59 Glossry 57 Answers 5

8 Cmridge University Press viii Aout the uthors Dvid Greenwood is the hed of Mthemtis t Trinity Grmmr Shool in Melourne nd hs 9 yers eperiene tehing mthemtis from Yers 7 to. He hs run numerous workshops within Austrli nd overses regrding the implementtion of the Austrlin Curriulum nd the use of tehnology for the tehing of mthemtis. He hs written more thn 0 mthemtis titles nd hs prtiulr interest in the sequening of urriulum ontent nd working with the Austrlin Curriulum profiieny strnds. Jenny Goodmn hs worked for 0 yers in omprehensive stte nd seletive high shools in NSW nd hs keen interest in tehing students of differing ility levels. She ws wrded the Jones medl for edution t Sydney University nd the Bourke prize for Mthemtis. She hs written for Cmridge NSW nd ws involved in the Spetrum nd Spetrum Gold series. Jennifer Vughn hs tught seondry mthemtis for more thn 0 yers in NSW, WA, QLD nd New Zelnd, nd hs tutored nd letured in mthemtis t Queenslnd University of Tehnology. She is pssionte out providing students of ll ility levels with opportunities to understnd nd to hve suess in using mthemtis. She hs tught speil needs students nd hs hd etensive eperiene in developing resoures tht mke mthemtil onepts more essile. Sr Woolley ws orn nd eduted in Tsmni. She ompleted n Honours degree in Mthemtis t the University of Tsmni efore ompleting her edution trining t the University of Melourne. She hs tught mthemtis in Vitori from yers 7 to sine 006 nd hs keen interest in the retion of resoures tht ter for wide rnge of ility levels. Consultnt Beth Godwin is the uthor of severl Cmridge titles, inluding Spetrum Mths Gold Yer 7 nd Yer 8. She hs presented seminrs nd workshops to edutors on topis inluding differentiting the urriulum, ehviour mngement nd developing litery skills. Currently the prinipl of Crmtt High Shool in NSW, Beth hs eperiene in ensuring tht the urriulum is essile to ll students. viii

9 Cmridge University Press Contents i Introdution nd how to use this ook The Essentil Mthemtis Gold for the Austrlin Curriulum series hs een developed espeilly to ter for students who require dditionl support in mthemtis. Using the Essentil Mthemtis for the Austrlin Curriulum series s strting point, the Gold series hevily revises tht mteril nd dds welth of new ontent to help students meet the Ahievement Stndrds of the Austrlin Curriulum. In ddition to n uthor tem of skilled tehers with eperiene tehing students t ll levels, the Gold series hs een refully reviewed y Speil Edution dvisors to mke sure tht the lnguge nd onepts re effetive for struggling students. The Gold series tkes prtil interprettion of the Austrlin Curriulum tht fouses on the Understnding nd Flueny profiieny strnds in order to help students lern ore mthemtil skills. These foundtion ilities re developed through ler eplntions of onepts tht re repeted nd losely linked to refully grded eerises, whih inlude linked emples nd hints throughout. Questions for the Prolem-solving nd Resoning profiieny strnds, long with Gold Str enrihment prolems, re provided to hllenge students tht wnt to improve their skills further. Litery nd numery skills re the other mjor fous of the Gold series. Key words re defined multiple times within the ooks to help students eome fluent with mthemtil terms nd onepts. Rel-world ontets nd pplitions of mthemtis help students onnet these onepts to everydy life. Eh hpter hs Puzzles nd gmes setion for stimulus nd motivtion. The Essentil Mthemtis Gold for the Austrlin Curriulum series omplements the full Essentil Mthemtis series nd Cmridge HOTmths to provide hoie of mthemtis resoures tht work well ross ll rnges of ility. i

10 Numers re used in mrketples ll round the world to desrie pries, quntity nd sometimes even qulity. Understnding Cmridge University Press Introdution nd how to use this ook How to use this ook Fetures: Austrlin Curriulum: strnds nd ontent desriptions for hpter Wht you will lern: n overview of hpter ontents Chpter introdution: use to set ontet for students Wht you will lern Adding nd sutrting integers Multiplying nd dividing integers Deimls nd rounding Rtionl numers Adding nd sutrting frtions Multiplying nd dividing frtions Rtios Rtes nd diret proportion Numer nd Alger Rel numers ACMNA08 hpter Reviewing numer Austrlin urriulum Negtive numers in the nient world The nient Bylonins, Hindus, Egyptins nd Chinese were ll known for their work with numers, ut there is no mention of negtive numers in their writings. The first mention of negtive numers is dted k to only 00 BCE in Chin. The Chinese used uses with lk rods for negtive numers nd red rods for positive numers. Pre-test: estlishes prior knowledge (lso ville s printle worksheet) Pre-test Chpter Reviewing numer Arrnge the following mthemtil terms under four hedings: Addition, Sutrtion, Multiplition nd Division. Sum Totl Less thn d Lots of e Produt f Into g Tke wy h Differene i Add j Times k Minus l More thn m Quotient Without using lultor, find n nswer to eh of the following. 6 less 4 more thn 8 the differene etween nd 8 d inrese 45 y 7 e the totl of 40, 4 nd 0 f 9 into 45 g the quotient of 7 nd 6 h 480 shred etween Evlute the following d e 9 7 f 0 4 g 7 60 h Use numer line to find: d - + e 6-7 f -4 + g h Copy nd omplete eh of the following sttements = = = 9 0 d - - = 6 The popultion of Austrli in 050 is projeted to e Round this numer to the nerest: ten hundred thousnd d million 7 Write down the ple vlue of the 5 in eh of the following numers d 0.56 e 0.5 f Arrnge the numers in eh of the following sets in desending order..645,.654,.465 nd , 0.564, nd Evlute eh of the following Evlute: d 4..9 e f Evlute eh of the following d Complete these equivlent frtions. 5 6 = 5 d Find the lowest ommon denomintor for these pirs of frtions. 4 Find: 4 d 9 = 8 = 4 = 6 nd 5 6 nd 4 5 nd Topi introdution: use to relte the topi to mthemtis in the wider world HOTmths ions: links to intertive online ontent vi the topi numer,. in this se Let s strt: n tivity (whih n often e done in groups) to strt the lesson Key ides: summrises the knowledge nd skills for the lesson (digitl version lso ville for use with IWB) Numer nd Alger. Adding nd sutrting integers Integers re the set of positive nd negtive whole numers, s well s zero. As we sw lst yer, eing le to work with whole numers is very importnt, s numers mke up our everydy lives. Let s strt: Nming groups Here re some groups of numers. In groups of two or three, n you use the orret mthemtil terms to desrie eh group? (Suggestions inlude: multiples of, ftors of, integers, squres nd ues.), 4, 6, 8,, 4, 9, 6,,, 5, 7, 9,,,, 4, 5, 6, -, -, -, -4, -5,, 8, 7, 64,,,, 4, 6, nd Integers re the positive nd negtive numers, inluding zero., -, -, -, 0,,,, You n dd nd sutrt integers. To dd negtive numer, you sutrt tht numer: + (-) = - e.g. 5 + (-7) = (-) = -6 - To sutrt negtive numer, you dd tht numer: - (-) = + e.g. 5 - (-7) = (-) = -6 + Adding or sutrting zero leves numer unhnged. + 0 = e.g = 5-0 = e.g. 5-0 = 5 Eerise A Mth eh of the following sentenes to the orret setting out on the right. The sum of 5 nd 7 i 5 + (-7) The totl of negtive 5 nd 7 ii 5 - (-7) The differene etween negtive 5 nd 7 iii d The sum of 5 nd negtive 7 iv -5-7 e The differene etween 5 nd negtive 7 v Key ides

11 Multiple-hoie questions is equl to: A B -47 C 47 D - E , when rounded to one signifint figure, gives: A 4.9 B 5.5 C 5.4 D 5 E 4.95 $450 is divided in the rtio 4 : 5. The vlue of the smller portion is: A $0 B $50 C $90 D $00 E $0 4 Con runs 4.5 km in 0 minutes. His speed is: A.5 km/h B.5 km/min C.5 km/h D 90 km/h E.5 km/h is equl to: A 0.7 B 0.07 C 0.07 D 0.8 E 7. Short-nswer questions Evlute the following Evlute: Find: d Divide $800 into the following rtios. : 4 : 7 : 5 Write these rtes nd rtios in simplest form. Prize money is shred etween people in the rtio 60 : 6. Jodie trvels 65 km in hours. 0 ml of rin flls in 4 hours. 6 A r verges 68 km/h on journey. How fr will it trvel t this speed for hours 40 minutes? 7 The height of tree is diretly proportionl to its width. A tree tht is metres tll hs width of 0.6 metres. How tll is tree with width. metres? Etended-response question Thoms wlks on verge, 6 km n hour. Phillip wlks t n verge speed of 8 km/h. How fr n Thoms wlk in 4 hours? If Phillips strts t 8 m nd stops t 9.45 m, how fr hs he wlked? Wht time does Phillip need to finish his wlk if he wnts to wlk twie s fr s Thoms? Semester review 69 Glossry 545 Answers 549 Adjent (side) In right-ngled tringle, the side djent to (net to) the unknown ngle Angle of depression The ngle of your line of sight from the horizontl when looking down t n ojet Angle of elevtion The ngle of your line of sight from the horizontl when looking up t n ojet Angle sum The totl mesure of the ngles in plne figure Angle The differene in diretion etween two lines Bk-to-k stem-nd-lef plot A visul representtion of two sets of dt tht groups the sores nd lists them in order horizontlly on either side of the stem Bse A numer or pronumerl tht is eing rised to power Binomil produt The produt of two inomil epressions Cpity The mount of liquid ontiner n hold Crtesin plne A plne on whih every point is relted to pir of numers lled oordintes Cirumferene The urved oundry of irle Clss intervl The nme for rnge of vlues tht elong in group of dt Coeffiient A numerl pled efore pronumerl Cointerior ngles A pir of ngles lying etween two lines on the sme side of trnsversl Complement A set of outomes ontining the elements tht re not in nother given set Congruent figures Figures tht re etly the sme size nd shpe Constnt term The prt of n eqution or epression without ny pronumerls Corresponding sides Sides tht re in the sme position in two or more shpes Cosine The rtio of the length of the djent side to the length of the hypotenuse Critil digit The digit tht determines whether you round the previous digit up or down Cross-setion The plne figure formed when you slie solid figure prllel to one of its surfes Cylinder A solid with two prllel, ongruent irulr fes onneted y urved surfe Denomintor The ottom prt of frtion Dependent vrile The vlue tht hnges in response to hnges mde in the independent vrile Dimeter A line pssing through the entre of irle with its end points on the irumferene Differene of perfet squres When one squre term is sutrted from nother Diret proportion The reltionship etween two quntities tht inrese or derese t the sme rte Disount An mount sutrted from prie Distriutive lw Adding numers in rkets, then multiplying the totl, gives the sme nswer s multiplying eh numer in the rkets seprtely first, then dding the produts Enlrgement A trnsformtion tht inreses the size of figure without hnging its shpe Eqution A sttement tht two epressions hve the sme vlue Equivlent equtions Two equtions tht produe the sme vlues for ll pronumerls Epeted outome The outome epeted from n eperiment Eperiment A sitution involving hne or proility trils Eperimentl proility Proility sed on mesuring the outomes of trils Epression A group of mthemtil terms ontining no equls sign Eterior ngle The ngle formed etween the etended side nd the djent side of polygon i Chpter Pre-test d e f g - h - i + j k - l + m 4 4 d 5 e 74 f 5 g 9 h d 0 e 6 f 80 g 00 h d 0 e - f - g 0 h d d d 5 0 e ,.645,.564, , 0.564, 0.456, f d 6.8 e.7 f d d Eerise A 4 8 iii v iv d ii e i iv ii v d i e iii F T T d T e T d 4 e -4 f -5 g - h 0 i -6 5 d 0 e - f -9 g - h -7 i -0 j 9 k - l m -7 n -8 o d 0 e -7 f 6 g -4 h 5 i d -9 e - f -89 g -4 h -8 i 0 j -805 k -57 l -67 m 4 n d 9 e 4 f 0 g -8 h -8 i 80 j k - l 40 m 755 n 94 o d 6 e 0 f -4 g -9 h 5 i d - e -7 f d d 4 e -9 f 0 g h 98 i Eerise B negtive positive negtive d positive e positive f positive Choose either O, A or O, H or A, H. Understnding Flueny positive negtive positive d negtive e negtive d 7 e 45 f -90 g -600 h 8 i -44 j -4 k -4 l -4 m 7 n 90 o d 9 e 00 f 69 g -8 h - i d -0 e f 5 g h - i -8 j 5 k -04 l 5 m -7 n -4 o d -4 e -0 f -8 g -7 h -8 i -90 j 0 k -4 l -8 m 9 n -6 o d -4 e - f 6 g -9 h -5 i -5 Cmridge University Press Introdution nd how to use this ook i How to use this ook Eerise questions tegorised y the four profiieny strnds nd Gold str Questions re linked to Emples: solutions with eplntions nd desriptive titles to id serhes 8 If television hs sreen size of 6 m, it mens tht the digonl length of the sreen is 6 m. If the vertil height of 6 m sreen is 9 m, find how wide the sreen is to the nerest entimetre. 9 A. m vertil fene post is supported y.7 m r, s shown in the digrm on the right. Find the distne (d metres) from the se of the post to where the support enters the ground. Give your nswer orret to two deiml ples. Emple 8 Find the vlue of, giving your nswer s surd. Solution + = = 9 = 9 = 9 Using et vlues 0 Find the vlue of s n et nswer. First find missing length Find the vlue of. Give n et nswer eh time. 8 4 Eplntion Mesurement nd Geometry 6 40 Fene.7 m d m Two sides re of length. Add like terms. Divide oth sides y. Tke the squre root of oth sides. To epress s n et nswer, do not round..9. m 74 Chpter 4 Pythgors theorem nd trigonometry Eerise 4F For the mrked ngle θ, θ deide if hypotenuse (H) side. θ Whih two sides (hoose pir from O, A nd θ θ m m 6 m 5 m Deide if you would use sin θ = O H, os θ = A H or tn θ = O tringles. A represents the length of the opposite (O), djent (A) or θ H) re given in these tringles? Do not find the vlue of, just stte whih rtio would e used Emple θ θ 7 m 4 m to help find the vlue of in these 0. 8 Use lultor to evlute the following, orret to two deiml ples. sin 50 os 6 tn 77 Solution sin 50 = 0.77 os 6 = 0.96 tn 77 = 4. Using lultor Eplntion sin 50 = the rd deiml ple is greter thn 4, so round up. os 6 = the rd deiml ple is less thn 5, so round down. tn 77 = the rd deiml ple is less thn 5, so round down Use lultor to evlute the following orret to two deiml ples. sin 0 os 7 tn 64 d sin 47 e os 84 f tn 4. g sin 7.4 h os 76. Puzzles nd gmes Mesurement nd Geometry 9 Mesurement nd Geometry 9 Chpter summry: mind mp of key onepts nd interonnetions How mny different right ngled tringles re there in this digrm? Find the vlue of in this digrm. m m A right-ngled isoseles tringle hs re of 4 squre units. Determine the et perimeter of the tringle. 4 Look t this right-ngled tringle nd the squres drwn on eh side. Eh squre is divided into smller setions. Cn you see how the prts of the two smller squres would fit into the lrger squre? Wht is the re of eh squre if the side lengths of the right-ngled tringle re, nd s mrked? Wht do the nswers to the ove two questions suggest out the reltionship etween, nd? 5 Imgine trying to ut the lrgest squre from irle of ertin size nd lulting the side length of the squre. If the irle hs dimeter of m, n you find good position to drw the dimeter tht lso helps to form right-ngled tringle? Cn you determine the side length of the lrgest squre? Wht perentge of the re of irle does the lrgest squre oupy? Puzzles nd gmes Sustitution The proess of repling pronumerl with given vlue e.g. if =, + 4 = () + 4 = = 0 e.g. if =, y = -4, then y = (-4) = -8 Addition/sutrtion Only like terms n e omined under ddition or sutrtion. Like terms hve the sme pronumerl ftors e.g = = 8 + e.g.. + y + 4y = + y + 4y = + 6y Multiplition/ Division In simplified from the multiplition sign ( ) nd division sign ( ) re not shown. Tht is = nd = Multiplying = = 6 Dividing 4 = 4 = 6 = = Epnding rkets e.g. ( + ) = + = + 6 -(4 ) = (-) (- ) = Formuls Some ommon formuls e.g. A = LW, C = πr An unknown vlue n e found y sustituting vlues for the other vriles. A formul n e trnsposed to mke different vrile the sujet. e.g. mke r the sujet in A = π r A = π r A = r Liner equtions Solving liner equtions The solution of line or eqution is the vlue tht mkes the eqution true. e.g. + 5 = 9 = 4 (sutrt 5) = (divide y ) e.g. 5( ) = = + 7 (epnd) 5 = 7 (sutrt ) = (dd 5) = 4 (divide y ) Equtions involving frtions e.g. + = 5 = 4 (sutrt ) e.g. Epressions e.g. y y + 5 term onstnt oeffiient e.g. more thn lots of m is m m + less thn is Solving word prolems Define vrile for the unknown Set up n eqution Solve the eqution 4 Chek the nswer nd write in words = (multiply y ) = = 4 (multiply y 4) = 6 (dd ) Chpter summry π π A = r r = π A where r > 0 Chpter reviews with multiple-hoie, short-nswer nd etended-response questions Mesurement nd Geometry Multiple-hoie questions If the re of squre field is 5 km, the length of one of its sides is: A 0 km B 5 km C 4 km D 50 km E 5 km If m = 00 m,.7 m is the sme s: A 70 m B km C m D 700 mm E 7 m The perimeter of this shpe is: A m B 4 m C 4 m m D 0 m E m 5 m 4 A prllelogrm hs re 0 m nd se 5 m. Using A = h, its perpendiulr height is: A 50 m B m C 50 m D m E 0.5 m 5 This omposite shpe ould e onsidered s retngle with n re in the shpe of squre removed. The shpe s re is: A 6 km 4 km B km C 0 km 5 km D 4 km E 6 km km 6 A semiirulr gol re hs dimeter 0 m. Its perimeter, orret to the nerest metre, is: A 4 m B 6 m C 8 m D 5 m E 5 m 0 m 7 The surfe re of the retngulr prism shown is: A 0 m B 6 m C m m 5 m D 60 m m E 00 m mm 5 mm 8 The re of the urved surfe only of ylinder with rdius 5 mm nd height mm is losest to: A 54 mm B 94 mm C 88 mm D 754 mm E 77 mm 9 A prism s ross-setionl re is 00 m. If its volume is 6500 m, the prism s totl height would e: A 0.65 m B m C 65 m D 6.5 m E 650 m 0 The volume of ylinder with rdius m nd height 0 m is losest to: A 88 m B 5 m C 4 m D 94 m E 8 m Mesurement nd Geometry 5 7 Find the totl surfe re of eh of the following solid ojets. 5 m 5 m m m m 8.5 m 4 m 8 Find the totl surfe re of eh of these ylinders orret to two deiml ples. 6 m 8 m 6 mm 5 mm 9 Find the volume of eh of these solid ojets, rounding to two deiml ples where neessry. Are = 5 m 0 mm 6 m m 6 m mm m Etended-response questions A kindergrten teher ollets some loks of wood for pinting tivity. Eh lok is retngulr prism, s shown. Find the volume of eh lok. Find the totl outside re to e pinted of eh lok. If the pint osts $.50 per 00 m, find the ost of pinting 0 loks. m 9 m d Another wood lok is ylinder with rdius m nd 5 m height 9 m ompred to the retngulr lok: does it hve greter volume? Eh tetook lso ontins: Two semester reviews Glossry Answers Reviewing numer 4 + d Semester review A B C D E Glossry Answers

12 Cmridge University Press This tetook is supported y online resoures... Digitl resoures nd support mteril for shools. Aout the free online resoures... Free dditionl student support resoures re ville online t Cmridge GO nd inlude: the PDF Tetook downlodle version of the student tet, with note-tking nd ookmrking enled etr mteril nd tivities links to other resoures. Aville free for users of this tetook. Use the unique ess ode found in the front of this tetook to tivte these resoures.

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14 Cmridge University Press Aknowledgements Authors knowledgements The uthors would like to thnk the following people: Beth Godwin for her thorough review of the mnusript nd for onsulting on hnges nd improvements to mke this tetook more pproprite for its intended udiene. Srh Wills for her ontriution to the teher resoure pkge for this tetook. Our fmilies nd friends for their support during the retion nd development of the series. The uthors nd pulisher wish to thnk the following soures for permission to reprodue mteril: Imges: ATO/to.gov.u, p. 7; 0 istokphoto LP/ DogTrumpet, p. 9; 0 istokphoto LP/ rftvision, p. 49; 0 istokphoto LP/Pgedesign, p. 0; 0 istokphoto LP/Rihrd Clrk, p. 08; 0 istokphoto LP/Uyen Le, p. 45; 0 istokphoto LP/TommL, p. 50; Almy/Cro, p. 78; Ns Imges, p. 50. All other Imges 0 Used under liense from Shutterstok.om Every effort hs een mde to tre nd knowledge opyright. The pulisher pologises for ny identl infringement nd welomes informtion tht would redress this sitution. iv