Cmrig Essntils Mthmtis Cor 8 N1.1 Homwork N1.1 Homwork 1 A thr shows hr lss 2 six-si i. On h of thm r th numrs +6, 5, +4, 3, +2, 1. Th two i r roll. Th sor is otin y ing th numrs on th uppr fs. Clult th sor in h of th following ss: i 5 1 ii +4 3 Whn Alx roll th i h sor +8. Whn Sni roll th i sh sor 3. By how mny is Alx s sor grtr thn tht of Sni? Th ruls of th gm r now hng. Th sor is otin y multiplying th numrs on th uppr fs. Clult th sor in h of th following ss: i 5 +2 ii 3 1 2 Complt ths sttmnts y filling in th oxs using only ngtiv numrs. = 3 = 3 3 Complt this multiplition gri. 1 2 12 3 5 20 Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N1.1 Homwork 4 Mk two opis of th igrm. In th first, h pir of numrs to gt th numr in th irl ov. Us th rul to fin ll th missing numrs. In th son, multiply h pir of numrs to gt th numr in th irl ov. Us th rul to fin ll th missing numrs. 5 Two numrs multiply togthr to mk 24. Thy togthr to mk 5. Wht r th two numrs? Anothr two numrs multiply togthr to mk 20. Thy togthr to mk 12. Wht r th two numrs? 6 Complt h of ths. + 7 = 5 3 = 5 8 2 = 20 = 5 7 Complt th numrs in h sgmnt of th snk, working from h to til, using th ruls givn. Originl mtril Cmrig Univrsity Prss 2009 2
Cmrig Essntils Mthmtis Cor 8 N1.2 Homwork N1.2 Homwork 1 Work ths out. 7 2 4 2 + 6 2 11 2 5 2 20 2 12 2 2 Work ths out. 64 169 900 16 81 36 3 Complt ths sttmnts. 196 = 4 49 = = 484 = 4 121 = = 8100 = 100 = 10 = 4 Hr r thr squr tils fitt togthr. On til hs n r of 25m 2. On til hs n r of 16m 2. Wht is th si lngth of th lrgst squr til? Work out th r of th lrgst squr til. Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N1.2 Homwork 5 Complt th following sttmnts y filling in th gps. 3 u quls 8 is th u of 1 is th u roof of is th u of 4 f Th u root of 125 is 1000 is th u of 6 Thr is just on two-igit numr tht is oth squr numrs n u numr. Wht is it? 7 Work ths out. 2 3 + 3 3 + 4 3 10 3 5 3 20 3 10 3 8 Work ths out. 3 125 3 3 64 1 3 3 27 8 9 42 lis twn 6 n 7. Explin how you know this without oing th lultion. 10 Us your lultor to work ths out. Roun your nswr to 2 iml pls whr nssry. 19 2 32 2 2.7 2 11 3 4.3 3 f 10 g 85 h 162 i 187 Originl mtril Cmrig Univrsity Prss 2009 2
Cmrig Essntils Mthmtis Cor 8 N1.3 Homwork N1.3 Homwork 1 Writ th first tn multipls of 3. Writ th first tn multipls of 4. Writ th numrs tht r ommon multipls of 3 n 4. Wht is th lowst ommon multipl of 3 n 4? 2 Fin th lowst ommon multipl of h st of numrs. 4, 7 9, 12 3, 4, 5 3 Writ on numr whih fits ll thr of ths sttmnts. It is multipl of 6. It is multipl of 8. It ns in 2. Explin why numr whih ns in 5 nnot multipl of 6. 4 Writ own ll th ftors of 24. Writ own ll th ftors of 40. Writ own th ftors tht r ommon to 24 n 40. Wht is th highst ommon ftor of 24 n 40? 5 Fin th highst ommon ftor of h st of numrs. 30, 48 84, 210 48, 84, 132 6 11 hs two ftors: 1 n 11. Wht typ of numr is 11? Invstigt th numr of ftors tht h numr from 1 to 20 hs. It my hlp you to us tl lik th on shown. Commnt on your rsults. Numr Ftors Numr of ftors 1 1 1 2 1, 2 2 Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N1.3 Homwork 7 3, 6, 8, 9, 15, 24, 25, 32, 43, 72, 125 Writ own two numrs from th list ov whih hv ths proprtis. You n us numr mor thn on. multipls of 9 ftors of 12 squr numrs u numrs prim numrs 8 Copy n omplt this ftor tr Writ 90 s prout of its prim ftors. 9 Us ftor tr to writ 126 s prout of its prim ftors. 10 Copy n omplt this tl to fin th prim ftors of 264. Copy n omplt: 264 = = 11 Us th iviing mtho shown in qustion 10 to writ 1008 s prout of prim ftors. Originl mtril Cmrig Univrsity Prss 2009 2
Cmrig Essntils Mthmtis Cor 8 N2.1 Homwork N2.1 Homwork 1 Writ h iml s frtion in its lowst trms. 0.6 0.25 0.55 0.64 0.92 f 0.375 g 0.215 h 0.464 2 Chng ths imls to mix numrs. Giv your nswrs in thir lowst trms. 1.8 9.45 13.25 99.306 791.504 3 Chng ths frtions to imls. Do not us lultor. 4 5 1 4 7 10 3 8 9 8 f 11 5 g 19 4 h 5 2 i 29 5 j 43 8 4 Us lultor to writ h frtion s iml. 1 32 11 16 60 25 89 20 70 32 5 Gin sk som oys in Yr 8 whih is thir fvourit sport to wth on tlvision. Th tl shows th rsults. Golf Footll Tnnis Crikt Motor Ring 15 24 6 10 5 How mny oys i Gin sk? Wht frtion of th totl hos golf? Giv your nswr in its lowst trms. Chng your nswr to prt into iml. Wht frtion of th totl hos rikt? Giv your nswr in its lowst trms. Chng your nswr to prt into iml. Us lultor. Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N2.1 Homwork 6 Us lultor to nswr this prt. i Writ 1 7 s iml. ii Writ 2 7 s iml. iii Writ 3 7 s iml. Wht sort of imls r th nswrs to prt? Wht o you noti out your nswrs to prt? Prit th iml forms of 8 9, 7 7 n 10 7. Chk tht your pritions in prt r orrt. 7 Convrt h frtion into iml. i 1 4 ii 5 9 iii 6 7 iv 10 15 v 9 12 vi 8 11 Stt whthr h frtion in prt orrspons to trminting iml or rurring iml. 8 Writ th frtions in h group with ommon nomintor. i ii iii 1 1 1,, 8 9 10 7 4 1,, 18 9 3 4 7 7,, 5 9 8 A ommon nomintor of 8 1, 9 1 n 10 1 is 360. Writ th originl frtions in orr of siz, lrgst first. Convrt th frtions in h group to imls. You my us lultor. 9 Whih numr in h pir is grtr? Us lultor to onvrt frtions to imls. 0.6 or 5 8 0.3 or 5 16 0.59 or 5 9 10 Writ h pir of frtions with ommon nomintor. i 1 2 n 5 6 ii 2 5 n 14 15 iii 2 3 n 3 4 Fin th frtion tht is xtly hlfwy twn h pir of frtions. Originl mtril Cmrig Univrsity Prss 2009 2
Cmrig Essntils Mthmtis Cor 8 N2.2 Homwork 1 N2.2 Homwork 1 1 Work ths out, giving h nswr in its lowst trms. 2 5 + 9 9 4 3 7 7 7 1 + 12 12 9 5 +16 16 11 6 f 25 25 19 5 21 21 g 23 11 h 30 30 14 4 i 15 15 7 3 + 20 20 j 17 7 + k 30 30 11 7 + l 24 24 1 2 + 15 15 2 Complt this lultion. + = 3 4 + 1 5 = + 20 20 = + 20 = 20 3 Work ths out y hnging to ommon nomimtors. 1 1 + 2 4 2 3 + 5 10 7 1 + 12 3 9 1 + 10 20 11 1 + f 16 4 1 4 + 3 9 g 1 2 + h 6 3 2 2 +15 5 i 6 1 +14 7 Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N2.2 Homwork 1 4 Work ths out. Giv your nswrs in thir simplst form. 1 2 + 3 5 3 1 + 4 6 3 1 + 8 3 4 1 + 11 2 2 3 + f 5 7 4 3 + g 9 10 9 3 + h 25 10 7 6 + 15 25 5 Work ths out. 11 1 12 3 2 1 5 10 5 2 6 3 21 1 11 22 9 3 10 5 f 17 1 g 24 6 7 2 h 9 3 17 7 20 10 6 Work ths out. Giv your nswrs in thir simplst form. 1 2 2 5 7 2 8 5 5 1 9 4 3 2 4 5 5 1 f 6 7 7 2 g 12 5 9 1 h 11 3 6 4 7 5 7 Work ths out. Giv your nswrs in thir simplst form. 1 2 + 2 3 3 5 + 5 8 7 2 + 10 3 1 7 + 4 9 3 2 1 + f 4 3 2 7 2 + g 5 8 3 3 3 + h 7 4 5 2 4 + 6 5 8 Work ths out. Giv your nswrs in thir simplst form. 3 1 11 2 7 1 5 8 3 9 1 4 10 1 4 1 3 5 1 2 1 f 2 3 3 7 1 g 10 8 2 3 1 h 5 4 1 8 1 4 9 Originl mtril Cmrig Univrsity Prss 2009 2
Cmrig Essntils Mthmtis Cor 8 N2.2 Homwork 2 N2.2 Homwork 2 1 Work ths out. 3 4 of 20 2 9 of 36 4 5 2 3 of 60 m 3 7 g nin tnths of 30 2 Thr r 36 hoolts in ox. h of 150 g of 28 mils f four fifths of 25 7 12 of 54 g i 3 8 of 76 m 1 4 5 12 of th hoolts r whit hoolt. How mny whit hoolts r thr? of th hoolts r plin hoolt. How mny plin hoolts r thr? All th othr hoolts r r milk hoolt. How mny milk hoolts r thr? Wht frtion of th hoolts r milk hoolt? Writ th frtion s simply s possil. 20 of th hoolts r wrpp in foil. Writ th frtion tht r not wrpp in foil s simply s possil. 3 Work ths out. 3 4 28 5 6 of 42 7 9 45 2 5 17 2 3 of 14 f 1 1 5 g 4 2 1 5 6 h 5 1 8 16 4 Fin ths mounts. 3 8 40 g 9 11 33 m 3 1 16 mm 4 5 1 9 36 2 1 3 15 kg f 7 1 12 24 m Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N2.2 Homwork 2 5 How mny fifths r thr in this irl? Complt th lultion. 1 5 1 = How mny sixths r thr in this hxgon? Complt th lultion. 1 6 1 = How mny sixths r thr in ths hxgons? Complt th lultion. 4 6 1 = 6 Complt this sntn. Diviing y 1 8 is th sm s multiplying y. 7 Work ths out. 15 1 3 12 1 4 7 1 3 8 1 8 5 1 10 f 1 1 20 8 Complt ths sntns. 40 1 8 = thrfor 1 8 = 40. 10 3 5 = thrfor 3 5 = 10. 3 4 = 9 thrfor 9 3 4 =. 5 7 = 15 thrfor 15 5 7 =. Originl mtril Cmrig Univrsity Prss 2009 2
Cmrig Essntils Mthmtis Cor 8 N2.3 Homwork 1 N2.3 Homwork 1 1 Writ h prntg s frtion in its simplst form. 20% 32% 55% 84% 7% f 2.5% 2 Writ h iml s prntg. 0.75 0.13 0.04 0.235 0.018 f 2.46 3 Gr sk 40 pupils in hr yr to nm thir fvourit fruit. Hr rsults r shown in th tl. Appl Pr Strwrry Mlon Bnn 12 7 10 5 6 Work out wht frtion of th group hos h typ of fruit. Writ h frtion in its simplst form. Wht prntg of th group hos h typ of fruit? 4 Hrry us his lultor to hng 1 7 to prntg. H si To th nrst prnt, 1 7 is 14%. His frin Dn si So to th nrst prnt, 2 7 is 28%. Show tht Dn is wrong. 5 Work out h mount y hnging th prntg to frtion. 15% of 60 36% of 25 22% of 65 7% of 120 40% of 80 f 9% of 56 It my hlp to simplify som of th frtions. 6 Fin ths mounts without using th % ky on your lultor 38% of 75 42% of 15 m 54% of 125 km 3.5% of 620 kg 125% of 78 g f 17% of 338 m g 7.1% of 5500 h 37.5% of 88 mm Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N2.3 Homwork 1 7 Sophi si tht 40% of 60 is th sm s 60% of 40. Is sh orrt? Explin how you i. 8 Jim is to ig up 15% of his grn to mk vgtl plot. 30 m vgtl plot 20 m Wht is th r of th grn? Wht is th r of th vgtl plot? 9 Work out ths prntgs. You my us lultor. 36 s prntg of 75 16 s prntg of 80 45 s prntg of 120 10 Th flg of th Unit Stts of Amri hs 13 strips n 50 strs. Th strips rprsnt th 13 originl stts. Th strs rprsnt ll th stts of Amri (inluing th 13 originl ons). Writ th numr of originl stts s frtion of ll th stts. Writ your nswr to prt s prntg. 11 Work out ths prntgs. 30p s prntg of 6 12 m s prntg of 2.5 m Rmmr to onvrt oth mounts to th sm unit. 30p out of 6 is th sm s 30 out of 600. 300 ml s prntg of 4 litrs 24 minuts s prntg of 5 hours 650 kg s prntg of 2 tonns Originl mtril Cmrig Univrsity Prss 2009 2
Cmrig Essntils Mthmtis Cor 8 N2.3 Homwork 2 N2.3 Homwork 2 You my us lultor to nswr ths qustions. 1 Clult th nw vlus. 45 is inrs y 20% 56 is inrs y 12% 123 is inrs y 36% 75 is ru y 80% 156 is ru y 88% f 189 is ru y 19% 2 Gs pris ros y 13% in yr. Fin th nw ost of gs tht originlly ost 1028. 3 In 2000, th numr of rrls of oil prou ily in Sui Ari ws 9 145 000. By 2008 it h inrs its proution y 5%. Complt ths sttmnts. Th numr of rrls of oil prou ily in 2008 will % of th numr prou in 2000. As frtion, this prntg is quivlnt to. Work out th numr of rrls of oil prou ily in 2008. 4 Lst yr 3100 ws ris y shool in sponsor spll. This yr th mount ris ws 7% mor thn lst yr. How muh mony ws ris this yr? 29% of th mony ris lst yr ws ris y yr 8 pupils. How muh mony i yr 8 pupils ris lst yr? 5 Mrty wnts to uy plsm-srn TV tht osts 1380. H n py ithr A posit of 10% n 24 qul monthly pymnts of 60 or B posit of 20% n 12 qul monthly pymnts of 100 How muh is th posit of 10%? Wht is th totl of th 24 pymnts of 60? How muh os h py ltogthr if h hooss option A? Work out how muh h pys ltogthr if h hooss option B. Whih option is hpr, n y how muh? 6 Lroy ought hous for 210 000. Six months ltr, th vlu inrs y 5%. Six months ftr tht, th vlu rs y 5%. Is th vlu of th hous th sm s whn h ought it? Explin how you i. Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N2.4 Homwork N2.4 Homwork No lultor llow. 1 Writ ths frtions s imls. 3 5 1 4 7 10 5 8 9 25 f 13 20 2 Writ h frtion in qustion 1 s prntg. 3 Chng ths prntgs to imls. 23% 16% 35% 48% 7.5% 4 Writ h prntg in qustion 3 s frtion. Giv h nswr in its simplst form. 5 Clult ths prntgs. 10% of 56 20% of 56 5% of 56 35% of 56 10% of 78 f 5% of 78 g 25% of 78 h 65% of 78 6 Work out th following prntgs. 15% of 44 23% of 76 kg 2% of 38 litrs 39% of 60 hours 85% of 7 m f 99% of 150 7 Explin how to work out VAT t rt of 17.5% mntlly. Work out th VAT on n itm osting 420. Wht is th totl ost of th itm? 8 Chrli hs sv 60 of his pokt mony. Th trinrs h wnts ost 70 ut r ru in sl y 15%. Dos Chrli hv nough mony to uy th trinrs? Explin your nswr. 9 Us th ft tht 6 8 = 48 to nswr ths qustions. 0.6 8 60 0.8 0.6 0.8 6 800 6 0.8 f 0.06 8 g 6 0.08 h 60 0.08 10 Us th ft tht 30 6 = 5 to nswr ths qustions. 3 6 0.3 6 0.03 6 Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N3.1 Homwork 1 N3.1 Homwork 1 Do not us lultor to nswr th qustions on this sht. 1 Writ ths s numrs without using powrs. 3 10 5 8 10 3 3.6 10 4 2.95 10 6 2 Writ ths using powrs of 10. four thousn nin hunr fiv million svnty thousn 3 Work out ths multiplitions. 14 0.1 3 0.01 720 0.01 49 0.1 0.01 4 Work out ths ivisions. 4 0.1 50 0.1 17 0.01 3 0.1 0.01 5 Fin th missing numr in h lultion. 0.3 0.6 = 0.04 0.1 = 0.7 = 0.21 0.01 = 0.6 2.4 0.2 = f 3.2 0.08 = 6 Look t th numrs in th ox. Whih two of ths numrs multiply togthr to giv th smllst possil nswr? Wht is tht nswr? Us thr of th numrs to fill in th gps to mk tru sttmnt. = 7 Look t ths numr rs. Choos two of th rs to omplt h of ths. = 0.02 = 20 Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N3.1 Homwork 2 N3.1 Homwork 2 1 Roun h numr to th nrst 10. 77 464 296 815 2 Roun h numr to th nrst 100. 360 490 250 4640 3 Roun h numr to th nrst 1000. 6725 2498 23 499 136 521 4 A shool ris 2738 for hrity. A nwsppr wrot: Shool riss ovr 2700 for hrity Complt this sntn. Th nwsppr roun 2738 to th nrst. 5 Writ th numr thirty fiv thousn, six hunr n ight in figurs. Writ your nswr to prt to th nrst 1000. 6 A rivr hs lngth of 300 km to th nrst 100 km n lngth of 250 km to th nrst 10 km. Writ own possil lngth of th rivr. 7 Roun h numr to 1 iml pl. 14.82 6.445 11.49 18.72 8 Roun h numr to 2 iml pls. 1.682 9.055 37.806 4.0138 9 Us lultor to work ths out. Giv your nswr to th numr of iml pls givn. 11 8 (1.p.) 10 7 (2.p.) 18 11 (2.p.) 10 Clult th r of h shp. Giv your nswr to 1 iml pl. Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N3.2 Homwork 1 N3.2 Homwork 1 Us mntl strtgis to work out th nswrs to ths qustions. Show ny jottings you us to fin your nswr. Do not us lultor. 1 Work out ths sums. 236 + 57 354 138 149 + 234 187 93 2 Clin ought DVD for 8.75. Wht hng i h gt from 20 not? 3 Work out ths multiplitions. 13 0.4 84 0.3 130 0.05 165 0.2 4 Huw uys 7 tins of pint t 4.95 h. Fin th totl ost. 5 A n of ol osts 0.32. How muh o 18 ns ost? 6 Work out ths multiplitions. 15 1.8 24 5.1 130 2.7 66 3.2 7 Fin th totl ost of 23 xris ooks t 1.30 h. 8 A txtook hs mss of 0.78 kg. Wht is th totl mss of 32 similr txt ooks? 9 Work out ths multiplitions. 28 11 47 19 76 22 84 91 10 Anni is plnting gs. Sh plnts 18 rows with 23 gs in h row. How mny gs os sh plnt ltogthr? 11 Work out ths ivisions. 345 15 1632 24 2268 12 846 18 12 208 solirs r lin up in rows of 16. How mny rows of solirs r thr? 13 Work out ths ivisions. 2.5 0.5 42 0.07 180 0.3 350 0.05 Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N3.2 Homwork 1 14 Louis wnts to uy s mny golf lls s h n for 15. Th golf lls ost 60p h. How mny golf lls n h uy? Originl mtril Cmrig Univrsity Prss 2009 2
Cmrig Essntils Mthmtis Cor 8 N3.2 Homwork 2 N3.2 Homwork 2 Do not us lultor to nswr th qustions on this sht. 1 Drw lins to mth ths oxs. Th first on is on for you. To fin 50% of numr ivi th numr y 5 To fin 4 1 of numr ivi th numr y 3 To fin 0.333 of numr ivi th numr y 2 To fin 20% of numr ivi th numr y 10 To fin 0.1 of numr ivi th numr y 4 2 Work ths out. 3 of 84 25% of 120 0.2 of 35 80% of 60 4 0.1 of 680 f 3% of 230 g 7 of 32 h 130% of 40 8 3 Nw-orn is usully los wight in th first wk ftr irth. Nish wigh 3.6 kg whn sh ws orn. Sh lost 1 10 of hr wight in th first wk ftr irth. How muh wight i sh los? 4 A lultor normlly osts 12.75. It is in th sl t 20% off. How muh lss will th lultor ost in th sl? Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N3.2 Homwork 2 5 Mri s holiy osts 350. Sh hs sv up 10 7 of th ost. How muh mony hs sh sv? 6 Thr girls foun purs whil out for wlk. Thy hn it k to th ownr who gv thm 5 rwr. Sm si I ll hv 45% of th 5 rwr us I sw th purs first. Kt si I pik up th purs, So I ll hv 10 3 of th rwr. Shron si I ll hv th rst. Work out how muh h girl lim. 7 Tim is 160 m tll. Mik s hight is 8 7 of Tim s hight. Srh s hight is 90% of Mik s hight. How tll is Srh? 8 Estimt th vlus of ths squr roots to 1 iml pl. Choos from th nswrs in th ox. 8 17 8.4 4.1 42 70 2.8 6.5 9 Estimt th nswr to h lultion y rouning. Show your working lrly. 29 72 407 49 21 48 97 26 42 8 2 39 10 200 f 41 19 99 Originl mtril Cmrig Univrsity Prss 2009 2
Cmrig Essntils Mthmtis Cor 8 N3.3 Homwork N3.3 Homwork Do not us lultor to nswr th qustions on this sht. 1 Work ths out. 16.7 + 9.38 235.9 + 47.26 14 + 75.08 + 147.94 73.2 38.5 24.8 9.32 f 99.2 1.8 34.73 2 Tin flis from Mnhstr to Pris. At Mnhstr irport hr s is wigh n th sls show 15.3 kg. In Pris sh uys prsnts for hr fmily, thy wigh 3 kg, 1.45 kg, 2.9 kg n 0.83 kg. Wht is th totl wight of th prsnts in kilogrms? Tin puts th prsnts in hr s whn sh flis hom. Wht os it wigh now? Tin my tk s on or wighing up to 25 kg without pying xss ggg hrgs. Dos hr s wigh lss or mor thn 25 kg? How muh lss or mor? 3 i Estimt th nswr to h lultion y rouning. Show your working lrly. ii Work out h nswr. 36 4.2 148 4.9 17.8 0.08 4 Th urrny xhng rt twn British pouns n Amrin ollrs is 1 = US $ 1.58. How mny ollrs woul you gt for 350? 5 Hnry ought th itms on th list. H pi with 20 not. Work out his hng. Show ll your working. 6 Wht is th ost of 2.4 mtrs of fri t 8.65 mtr? 3 pnils t 28p h 4 ps of ppr t 2.35 h 2 mgzins t 2.89 h 7 Work ths out. 96.6 23 243.2 38 742.4 58 Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N3.4 Homwork N3.4 Homwork 1 Us your lultor to work ths out. 14 2 6 14 6 2 2.8 + 6.4 2.3 11 2 6 2.5 2 49.5 1.8 + 1.5 f 4.6 + 11.27 3 2 Us your lultor to work ths out. (38 + 67) (71 29) 38 + 67 71 29 3 Som stunts r using lultors to work out four qustions. Qustion 1 1.34 + 2.76 4.28+ 3.52 Qustion 2 1.34 + 2.76 4.28 + 3.52 Qustion 3 1.34 + 2.76 4.28 + 3.52 Qustion 4 1.34 + 2.76 4.28+ 3.52 Asif prsss kys s follows 1. 3 4 + 2. 7 6 4. 2 8 + 3. 5 2 =] For whih of th four qustions is this th orrt mtho? My prsss kys s follows ( 1. 3 4 + 2. 7 6 ) 4. 2 8 + 3. 5 2 =] For whih of th four qustions is this th orrt mtho? Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N3.4 Homwork 4 Susn hng 1000 into South Afrin rn whn th rt of xhng ws 1 = 10.5 rn. How mny rn i sh gt? During hr holiy, sh spnt 8322 rn. i How mny rn i sh hv lft? ii Sh hng hr rmining rn into pouns whn th xhng rt ws 1 = 9.9 rn. How mny pouns i sh gt? 5 A ptrol sttion shows this informtion. How mny gllons r thr in 500 litrs? 10 litrs = 2.2 gllons 6 A group of 23 ftory workrs wins lottry priz of 1500. Clult how muh h ftory workr wins. Thy put th lft ovr mony into th hrity jr in th ntn. How muh i thy put in? 7 Wht is th totl ost in pouns of 148 mgzins t 85p h? 8 Us your lultor to work out whih is grtr. Show your rsults. 3 of 12.56 or 72% of 6.75 8 9 Fin th nswrs to th following. 0.25 of y in hours 0.375 of y in hours 0.6 of n hour in minuts 0.65 of minut in sons 0.3 of y in hours f 0.7 of n hour in minuts 10 Jk runs r in th tim it tks th minut hn of lok to turn through n ngl of 25º. How mny grs woul th minut hn turn through in omplt hour? Wht frtion of n hour i Jk's r tk? Work out th tim Jk took to run his r in minuts n sons. Originl mtril Cmrig Univrsity Prss 2009 2
Cmrig Essntils Mthmtis Cor 8 N4.1 Homwork N4.1 Homwork 1 Work ths out without using lultor. 3 + 7 2 (3 + 7) 2 3 2 + 7 2 14 2 5 2 (14 2) 3 2 f 2 14 2 3 g 10 5 2 h (10 5) 2 i 30 2 + 4 j 30 (2 + 4) k (48 8 + 4) 4 l 48 (8 + 4 4) m 48 8 + 4 4 n 48 (8 + 4) 4 o (48 8) + (4 4) 2 Work ths out without using lultor. 8 3 2 (8 3) 2 6 2 14 2 (6 2 14) 2 5 2 2 2 3 + 1 f (5 2 2 2 ) (3 + 1) g 5 2 (2 2 3 + 1) h (5 2 2 2 ) 3 + 1 i 10 5 2 + 15 3 Whr nssry, insrt rkts in th following lultions in orr to mk thm orrt. 8 + 12 4 + 2 = 7 8 + 12 4 + 2 = 13 8 + 12 4 + 2 = 3.33 8 + 12 4 + 2 = 10 26 + 15 8 5 = 141 f 26 + 15 8 5 = 323 g 26 + 15 8 5 = 71 h 26 + 15 8 5 = 123 4 Shrmi uss hr lultor to work out th nswr to 12 + 48. 16 + 4 Sh sys th nswr is 19. Any isgrs n sys th nswr is 3. Explin why Any is orrt. Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N4.1 Homwork 5 Th primtr of th rtngl shown is givn y th formul P = 4m + 2n. Writ formul for th primtr of rtngl whos sis r thr tims th lngth of thos in th igrm. Us rkts in th formul. If m = 4 m n n = 5 m, lult th primtr of th rtngl sri in prt. 6 This squr hs n g lngth of m. m m Writ formul for th primtr, P, of th squr. Writ formul for th r, A, of th squr. Th lngth of h si of th squr is now inrs y 3 m. m 3 m Wht is th lngth of th nw shp? m Is th shp squr? Explin your nswr. 3 m f Writ formul, using rkts, for th primtr, Q, of th nw shp. Writ formul, using rkts, for th r, B, of th nw shp. Th nw shp is ivi into four smllr shps. g i Wht is th r of shp W? ii Wht is th r of shp X? m m W 3 m X iii Wht is th r of shp Y? 3 m Y Z iv Wht is th r of shp Z? v Writ n xprssion for th r of th shp using your nswrs to prts i to iv. h Whn = 5 m, lult th primtr n r of th shp in prt g. Originl mtril Cmrig Univrsity Prss 2009 2
Cmrig Essntils Mthmtis Cor 8 N4.2 Homwork N4.2 Homwork Do not us lultor for ths qustions. 1 Intify, giving rsons, whih lultion in h pir must inorrt. i 11 5 2 = 12 ii 11 5 2 = 1 i (16 4) 2 8 2 = 68 ii (16 4) 2 8 2 = 140 i 3 2.8 2 = 81 ii 3 2.8 2 = 23.52 i 14 3 2.5 2 = 0.622 ii 14 3 2.5 2 = 8.71 2 Choos, giving rsons, possil nswr to h lultion from th nswrs givn. 78 30 i 2440 ii 234 iii 2340 6.95 0.2 i 3.475 ii 34.75 iii 1.39 418 1.1 i 38 ii 380 iii 418.11 94 9 0.5 i 46.6 ii 6.4 iii 4.61 3 (x + 8) 4 = 44. Whih mtho is orrt for fining x? i x = 44 4 8 ii x = (44 8) 4 iii x = 44 32 x 3 = 729. Whih mtho is orrt for fining x? i x = 729 3 ii x = 729 3 iii x = 3 729 (x 6) 5 = 20. Whih mtho is orrt for fining x? i x = 20 5 + 6 ii x = 20 5 + 6 iii x = 20 5 6 4 Ali hs 6 m lngth of rion whih sh uts into four iffrnt pis. Sh givs Jo 1.9 m, Fion 2.4 m, My 1.4 m n sh kps 1.3 m hrslf. Explin why ths msurmnts r inorrt. 5 Th sho sizs of 10 pupils r 5, 3, 4, 4, 4, 3, 6, 5, 2, 6 Explin why th mo nnot siz 1 4 2. Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N4.3 Homwork 1 N4.3 Homwork 1 1 Writ th proportion of h shp tht is sh s frtion in its simplst form. 2 Us th shps in qustion 1. Writ th rtio of sh r to unsh r. 3 Th r hrt shows th numr of ooks r y group of 36 pupils in thr months. Wht proportion of pupils r 5 ooks? Giv your nswr s frtion in its simplst form. Wht proportion of pupils r 5 or mor ooks? Giv your nswr s frtion in its simplst form. Wht is th rtio of pupils who r 5 ooks to ll th othr pupils? Wht is th rtio of pupils who r 5 or mor ooks to pupils who r lss thn 5 ooks? 4 Simplify ths rtios. 6 : 3 4 : 12 5 : 20 15 : 25 40 : 24 f 60 : 35 g 42 : 28 h 16 : 8 i 9 : 45 j 10 : 55 k 49 : 14 l 36 : 48 5 Th following pirs of rtios r quivlnt. Work out th unknown vlus. 1 : 3 = 4 : x 11 : p = 33 : 18 n : 7 = 18 : 42 2 : 9 = y : 36 5 : 25 = 1 : q f 1 : 3 : 6 = 3 : g : h Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N4.3 Homwork 2 N4.3 Homwork 2 1 Writ oth quntitis in th sm units thn simplify to giv th rtio in its simplst form. 4 mm : 3 m 8 m : 2 m 10 g : 1 kg 15 min : 2 hours 300 kg : 2 tonn f 5 mm : 1 m g 25 sons : 10 min h 35 ml : 2 litrs i 6 hours : 2 ys 2 A mol ot is m to sl of 1 : 80. Th mol hs lngth of 12 m. Clult th lngth of th rl ot in mtrs. Th rl ot hs with of 4.2 m. Clult th with of th mol ot in ntimtrs. 3 A mp is rwn to sl of 1 : 250 000. Clult th rl istn if th istn on th mp is 4 m. i ii Giv your nswr in mtrs. Giv your nswr in kilomtrs. Clult th istn on th mp if th istn on th groun is 8 km. Giv your nswr in ntimtrs. 4 A pi of rion 60 m long is ut into smllr pis in ths rtios. Clult th lngth of h of th pis. 1 : 5 2 : 3 4 : 1 9 : 11 3 : 4 : 5 5 Luk hs m 24 firy ks. H wnts to put vnill iing on som n hoolt iing on th othrs. Aftr sking his frins whih thy prfr, h is to i thm in th rtio of 3 : 5, vnill to hoolt. How mny ks will h hv to put vnill iing on? Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N4.3 Homwork 2 6 Winsrn wsh is us to ln r winows. Winsrn wsh is mix with wtr in ths rtios. Wintr mixtur Summr mixtur Winsrn wsh : Wtr Winsrn wsh : Wtr 1 : 4 1 : 9 i In wintr, how muh wtr shoul mix with 200 ml of winsrn wsh? ii Whn mix, th mixtur is pss into th srnwsh ontinr in th r. Wht volum of liqui is pss into th ontinr? In summr, how muh winsrn wsh shoul mix with 360 ml of wtr? Ptr sys 1 4 of th wintr mixtur is winsrn wsh. Is this sttmnt orrt? Explin your nswr. 7 Morgn is 16 yrs ol. His sistr is 6 yrs youngr, so this yr sh is 10 yrs ol. Wht is th rtio of Morgn s g to his sistr s g? Writ your nswr s simply s possil. Whn Morgn is 21 yrs ol, wht will th rtio of his g to his sistr s g? Writ th rtio s simply s possil. Whn his sistr is 36, wht will th rtio of Morgn s g to his sistr s g? Giv your nswr in its simplst form. Coul th rtio of thir gs vr 7 : 7? Explin your nswr. Originl mtril Cmrig Univrsity Prss 2009 2
Cmrig Essntils Mthmtis Cor 8 N4.4 Homwork N4.4 Homwork 1 In July 2008, th xhng rt from pouns ( ) to Jpns yn ( ) ws pproximtly 1 : 200. Thrfor 1 oul xhng for 200. Complt this xhng rt tl. Pouns ( ) Yn ( ) 0 0 5 10 15 20 4000 Plot grph showing th rltionship twn pouns n yn. 2 An ropln is trvlling t onstnt sp. Th tl shows th totl numr of kilomtrs th ropln hs trvll ftr iffrnt lngths of tim. Tim (hours) 0 2.5 5 7.5 10 Distn (km) 1125 3375 Complt th tl. Clult th sp of th ropln in kilomtrs pr hour. Plot grph with tim on th x xis showing th rltionship twn tim n istn trvll. Us your grph to stimt th istn trvll ftr 6 hours 15 minuts. 3 Writ h rtio in th form 1 : n. 2 : 11 4 : 5 10 : 7 20 : 9 2.5 : 2 Originl mtril Cmrig Univrsity Prss 2009 1
Cmrig Essntils Mthmtis Cor 8 N4.4 Homwork 4 This grph is us to onvrt twn kilogrms n pouns. Explin how you know from th grph tht th rltionship twn th two vrils is irtly proportionl. From th grph fin th numr of pouns quivlnt to 100 kg. f g h Clult th numr of pouns quivlnt to 50 kg. Clult th numr of pouns quivlnt to 1 kg. Us your nswrs to to writ th rtio numr of kilogrms : numr of pouns in th form 1: n. Clult th numr of pouns quivlnt to 70 kilogrms. Clult th numr of kilogrms quivlnt to 1 poun. Writ th rtio numr of pouns : numr of kilogrms in th form 1 : n using your nswrs to g. i Clult th numr of pouns quivlnt to 1 tonn using your nswr to prt. Originl mtril Cmrig Univrsity Prss 2009 2