Camrig Essntials Mathmatis Cor 8 N. Homwork Answrs N. Homwork Answrs a i 6 ii i 0 ii 3 2 Any pairs of numrs whih satisfy th alulation. For xampl a 4 = 3 3 6 3 = 3 4 6 2 2 8 2 3 3 2 8 5 5 20 30 4 a 5 a 8 an +3 0 an 2 6 a 2 + = 5 3 8 = 5 8 2 = 6 20 4 = 5 Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N.2 Homwork Answrs N.2 Homwork Answrs a 49 52 96 256 2 a 8 3 26 54 3 a 96 = 4 49 = 2 = 4 484 = 4 2 = 2 = 22 800 = 8 00 = 9 0 = 90 4 a 9 m 8 m 2 5 a 3 u quals 2 8 is th u of 2 is th u root of 64 is th u of 4 Th u root of 25 is 5 f 000 is th u of 0 6 64 a 99 85 8 8 a 5 3 6 9 36 = 6 an 49 = 42 lis twn 36 an 49 so 42 must li twn 6 an. 0 a 36 024.29 33 9.5 f 3.6 g 9.22 h 2.3 i 3.6 Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N.3 Homwork Answrs N.3 Homwork Answrs a 3, 6, 9, 2, 5, 8, 2, 24, 2, 30 4, 8, 2, 6, 20, 24, 28, 32, 36, 40 2, 24 2 2 a 28 36 60 3 a 2 All multipls of 6 ar vn numrs an numrs ning in 5 ar o. 4 a, 2, 3, 4, 6, 8, 2, 24, 2, 4, 5, 8, 0, 20, 40, 2, 4, 8 8 5 a 6 42 2 6 a is a prim numr. Numr Numr Fators of fators 2, 2 2 3, 3 2 4, 2, 4 3 5, 5 2 6, 2, 3, 6 4, 2 8, 2, 4, 8 4 9, 3, 9 3 0, 2, 5, 0 4 is th only numr with just on fator. Numr Fators Numr of fators, 2 2, 2, 3, 4, 6, 2 6 3, 3 2 4, 2,, 4 4 5, 3, 5, 5 4 6, 2, 4, 8, 6 5, 2 8, 2, 3, 6, 9, 8 6 9, 9 2 20, 2, 4, 5, 0, 20 6 Numrs with just two fators ar prim numrs. Squar numrs hav an o numrs of fators. Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N.3 Homwork Answrs a 9, 2 3, 6 9, 25 8, 25 3, 43 8 a 90 = 2 3 3 5 = 2 3 2 5 9 26 = 2 3 3 = 2 3 2 0 a 264 = 2 2 2 3 = 2 3 3 008 = 2 2 2 2 3 3 = 2 4 3 2 Original matrial Camrig Univrsity Prss 2009 2
Camrig Essntials Mathmatis Cor 8 N2. Homwork Answrs N2. Homwork Answrs a 3 5 4 20 6 25 23 25 f 3 8 g 43 200 h 58 25 2 a 4 5 9 9 20 3 4 53 99 500 63 9 25 3 a 0.8 0.25 0. 0.35.25 f 2.2 g 4.5 h 2.5 i 5.8 j 5.35 4 a 0.0325 0.685 2.4 4.45 2.85 5 a 60 oys 4 0.25 6 0.66666 6 a i 0.4285 ii 0.2854 iii 0.4285 Rurring imals Th rurring imals ontain th sam rpating squn of six igits, ut start at iffrnt points in th squn. 8 =.4285 9 =.2854 0 =.4285 a i 0.25 ii 0.555555 iii 0.8542 iv 0.666666 v 0.5 vi 0.222 4 an 9 2 ar trminating imals. 5 9, 6, 0 5 an 8 ar rurring imals. Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N2. Homwork Answrs 8 a i 8 = 45 360 9 = 40 360 0 = 36 360 ii 8 = 8 4 9 = 8 8 3 = 6 8 iii 4 288 280 35 = = = 5 360 9 360 8 360 i 8, 9, 0 ii 4,, 9 8 3 iii 4,, 8 5 9 i 8 = 0.25 9 = 0. 0 = 0. 4 ii = 0.388888 = 0.444444 = 0.333333 8 9 3 iii 4 5 = 0.8 9 = 0. 8 = 0.85 9 a 5 8 5 6 is gratr than 0.6. is gratr than 0.3. 0.59 is gratr than 5 9. 0 a i 3 5 an 6 6 ii 5 6 an 4 5 iii 2 8 an 2 9 i 4 6 = 2 3 ii 0 5 = 2 3 iii 24 Original matrial Camrig Univrsity Prss 2009 2
Camrig Essntials Mathmatis Cor 8 N2.2 Homwork Answrs N2.2 Homwork Answrs a 9 8 2 = 4 = 2 3 6 8 5 = f 25 5 4 2 = g 2 3 2 2 = h 0 = 2 30 5 5 3 i 0 = j 20 2 24 4 = k 30 5 8 3 = l 24 4 3 = 5 5 2 3 5 4 5 + 4 9 + = + = = 4 5 20 20 20 20 3 a 3 4 0 2 9 20 5 6 f 9 g 5 6 h 5 8 i 3 4 4 a 5 2 24 9 22 29 35 f 6 90 g 33 50 h 53 5 5 a 2 0 3 6 9 22 3 0 f 3 24 g 9 h 3 20 6 a 0 9 40 36 20 29 42 f 60 g 6 33 h 2 35 a 6 9 40 30 36 5 2 f 2 3 g 40 5 4 h 28 5 30 8 a 8 2 40 20 8 5 5 6 f 40 g 3 20 h 3 36 Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N2.2 Homwork 2 Answrs N2.2 Homwork 2 Answrs a 5 8 20 g 40 m 2 mils f 20 g 2 h 3 g i 2 2 a 9 whit hoolats 5 plain hoolats 2 milk hoolats; 2 = 36 3 6 4 = 36 9 28 m 2 3 a 2 35 35 4 6 5 9 3 f 6 4 g 2 8 5 h 26 4 a 5 g 2 m 28 mm 56 25 kg f 38 m 5 a 5 fifths; 5 = 5 6 sixths; 6 = 6 24 sixths; 4 6 = 24 6 Diviing y 8 is th sam as multiplying y 8. a 45 48 2 64 50 f 20 8 a 40 8 = 5 thrfor 5 8 = 40 0 3 5 = 6 thrfor 6 3 5 = 0 2 3 4 = 9 thrfor 9 3 4 = 2 2 5 = 5 thrfor 5 5 = 2 Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N2.3 Homwork Answrs N2.3 Homwork Answrs a 20 = 00 5 32 8 = 00 25 55 = 00 20 84 2 = 00 25 00 f 2.5 5 = = 00 200 40 2 a 5% 3% 4% 23.5%.8% f 246% 3 Appl Par Strawrry Mlon Banana 2 0 5 6 a 3 3 0 40 4 8 20 30%.5% 25% 2.5% 5% 4 Dan shoul work out 2 00% = 28.5 %, so 2 = 29% to narst prnt. 5 a 9 9 4.3 8.4 32 f 5.04 6 a 28.50 6.3 m 6.5 km 2. kg 9.5 g f 5.46 m g 390.50 h 33 mm Ys, sh is orrt. 40% of 60 = 0.4 60 = 24 60% of 40 = 0.6 40 = 24 8 a 600 m 2 90 m 2 9 a 48% 20% 3.5% 0 a 3 50 26% a 5% 4.8%.5% 8% 32.5% Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N2.3 Homwork 2 Answrs N2.3 Homwork 2 Answrs a 54 62.2 6.28 5 8.2 f 53.09 2 028.3 = 6.64 3 a Th numr of arrls of oil prou aily in 2008 will 05% of th numr prou in 2000. As a fration, this prntag is quivalnt to 00 20 9602250 arrls 4 a 300.0 = 33 300 0.29 = 899 5 a 38 440 58 46 Option B is hapr y 02. 6 Original valu = 20 000 Aftr an inras of 5%, th valu is.05 20 000 = 220 500. Aftr a furthr ras of 5%, th valu is 0.95 220 500 = 209 45. Th hous is worth lss than whn h ought it, not th sam. Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N2.4 Homwork Answrs N2.4 Homwork Answrs a 0.6 0.25 0. 0.625 0.36 f 0.65 2 a 60% 25% 0% 62.5% 36% f 65% 3 a 0.23 0.6 0.35 0.48 0.05 4 a 23 00 6 4 = 00 25 35 = 00 20 48 2 = 00 25.5 5 3 = = 00 200 40 5 a 5.6.2 2.8 9.6.8 f 3.9 g 9.5 h 50. 6 a 6.60.48 kg 0.6 litrs 23.4 hours = 23 hours 24 minuts 5.95 m f 48.50 a Fin 0%. Thn halv it to fin 5%. Thn halv it it again to fin A all thr numrs togthr to fin 2 %. Or multiply y thn ivi y 4 thn ivi y 0 (or quivalnt). 3.50 493.50 8 Th trainrs ost 59.50 in th sal, so Charli os hav nough mony. 9 a 4.8 48 0.48 4800 4.8 f 0.48 g 0.48 h 4.8 0 a 0.5 0.05 0.005 2 2 %. Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N3. Homwork Answrs N3. Homwork Answrs a 300 000 8000 36 000 2 950 000 2 a 4 0 3 9 0 2 5 0 6 0 4 3 a.4 0.03.2 0.049 4 a 40 500 00 3000 5 a 0.8 0.004 0.3 60 2 f 40 6 a 0.0 0.2 = 0.002 0.2 0.0 = 20 a 0. 0.2 = 0.02 0 0.5 = 20 or 2 0. = 20 Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N3. Homwork 2 Answrs N3. Homwork 2 Answrs a 80 460 300 820 2 a 400 500 300 4600 3 a 000 2000 23 000 3 000 4 hunr pouns 5 a 35 608 36 000 6 250 km lngth < 255 km. Any lngth in this rang is orrt. a 4.8 6.4.5 8. 8 a.68 9.06 3.8 4.0 9 a.4.43.64 0 a 3.5 m 2 24.3 m 2 25.8 m 2 Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N3.2 Homwork Answrs N3.2 Homwork Answrs a 293 26 383 94 2.25 3 a 5.2 25.2 6.5 33 4 34.65 5 5.6 6 a 2 22.4 35 2.2 29.90 8 24.96 kg 9 a 308 893 62 644 0 44 a 23 68 89 4 2 3 3 a 5 600 600 000 4 25 Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N3.2 Homwork 2 Answrs N3.2 Homwork 2 Answrs To fin 50% of a numr ivi th numr y 5 To fin 4 of a numr ivi th numr y 3 To fin 0.333 of a numr ivi th numr y 2 To fin 20% of a numr ivi th numr y 0 To fin 0. of a numr ivi th numr y 4 2 a 63 30 48 68 f 6.9 g 28 h 52 3 0.36 kg 4 2.55 lss 5 245 6 Sam laim 2.25, Kat laim.50 an Sharon laim.25. 26 m 8 a 2.8 4. 6.5 8.4 9 Answrs may vary hk pupil s rouning. a 200 8 0 25 24 f 8000 Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N3.3 Homwork Answrs N3.3 Homwork Answrs a 26.08 283.6 23.02 34. 5.48 f 62.6 2 a 8.8 kg 23.48 kg Lss y.52 kg 3 a i 35 4 = 40 ii 5.2 i 50 5 = 50 ii 25.2 i 8 0. =.8 ii.424 4 US $ 553 5 3.98 6 20.6 a 4.2 6.4 2.8 Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N3.4 Homwork Answrs N3.4 Homwork Answrs a 4 4 34 5 f 2.3 2 a 440 2.5 3 a Qustion 3 Qustion 2 4 a 0 500 ran i 28 ran ii 220 5 0 gallons 6 a 65.2 p 25.80 8 3 of 2.56 is 4. 8 2 % of 6.5 is 4.86 So 2% of 6.5 is gratr 9 a 6 hours 9 hours 36 minuts 39 sons.2 hours f 42 minuts 0 a 360º 25 5 or 360 2 4 minuts 0 sons Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N4. Homwork Answrs N4. Homwork Answrs a 52 00 58 2 48 f 6 g 0 h 0 i 9 j 5 k 2.5 l 5.33 m n o 2 a 2 0 29 4 f 84 g 2 h 64 i 0 3 a (8 + 2) 4 + 2 = 8 + 2 4 + 2 = 3 (8 + 2) (4 + 2) = 3.33 8 + 2 (4 + 2) = 0 26 + 5 8 5 = 4 f (26 + 5) 8 5 = 323 g 26 + 5 (8 5) = h (26 + 5) (8 5) = 23 4 Sharmi work out 2 + 48 6 + 4 = 2 + 3 + 4 = 9 Sh shoul hav foun th answr to 2 + 48 first thn ivi y 6 + 4. Sh oul think of it as having rakts lik this (2 + 48). (6 + 4) 5 a P = 3 (4m + 2n) P = 8 m 6 a P = 4 m A = 2 m 2 ( + 3) m Ys aus th g lngths ar all qual. Q = 4 ( + 3) m f B = ( + 3) 2 m 2 g i W = 2 m 2 ii X = 3 m 2 iii Y = 3 m 2 iv Z = 9 m 2 v Ara = ( 2 + 3 + 3 + 9) m 2 = ( 2 + 6 + 9) m 2 h Primtr = 4 (5 + 3) = 32 m Ara = (5 + 3) 2 = 64 m 2 or 5 2 + 30 + 9 = 25 + 30 + 9 = 64 m 2 Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N4.2 Homwork Answrs N4.2 Homwork Answrs a 5 2 = 2 is inorrt. Multipliation must on for sutration so it is 0 =. (6 4) 2 8 2 = 68 is inorrt ivision must on for sutration so it is 44 4 = 40. 3 2.8 2 = 8 is inorrt 3 3 2 woul only 2 an it must lss than this. 2 4 3 = 8. is inorrt 4 3 2 = 4 9 whih is lss than 2. 2.5 So whn it is ivi y 2.5, th answr must lss than. 2 a 8 30 = 2340 80 30 = 2400 so 8 30 must a it smallr than 2400. 6.95 0.2 = 34.5 y 0.2 maks th answr iggr so it must iggr than 6.95. 48. = 380 48 = 48 so th answr must a it smallr than 48. 94 9 0.5 = 4.6 85 is aout 9. Multiplying y 0.5 is th sam as iviing y 2 so th answr must aout 4. 3 a x = 44 4 8 (i) x = 3 29 (iii) x = 20 5 + 6 (ii) 4 If you a th lngths togthr th total lngth ut is m whih an not orrt as thr was only 6 m of rion..9 + 2.4 +.4 +.3 =.0 5 Mo mans th most frquntly ourring valu. In this as it is 4. mo as it os not appar in th list of sho sizs. 4 2 is not a possil Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N4.3 Homwork Answrs N4.3 Homwork Answrs a 8 20 = 2 5 6 2 = 2 5 5 = 3 2 a 8 : 2 = 2 : 3 6 : 6 = : 5 : 0 = : 2 3 a 0 36 = 5 8 8 36 = 2 0 : 26 = 5 : 3 8 : 8 = : 4 a 2 : : 3 : 4 3 : 5 5 : 3 f 2 : g 3 : 2 h 2 : i : 5 j 2 : k : 2 l 3 : 4 5 a x = 2 p = 6 n = 3 y = 8 q = 5 f g = 9, h = 8 Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N4.3 Homwork 2 Answrs N4.3 Homwork 2 Answrs a 4 : 30 = 2 : 5 8 : 200 = : 25 0 : 000 = : 00 5 : 20 = : 8 300 : 2000 = 3 : 20 f 5 : 000 = : 200 g 25 : 600 = : 24 h 35 : 2000 = : 400 i 6 : 48 = : 8 2 a 9.6 m 5.25 m 3 a i 0 000 m ii 0 km 3.2 m 4 a Smallr part = 0 m, largr part = 50 m. Smallr part = 24 m, largr part = 36 m. Smallr part = 2 m, largr part = 48 m. Smallr part = 2 m, largr part = 33 m. Smallst part = 5 m, mil-siz part = 20 m, largst part = 25 m. 5 9 6 a i 800 ml ii litr 40 ml No it is not orrt, a ratio of : 4 mans thr ar 5 parts, so it is 5 not 4. a 6 : 0 = 8 : 5 2 : 5 = : 5 42 : 36 = : 6 No, it woul man thy wr th sam ag. Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N4.4 Homwork Answrs N4.4 Homwork Answrs a Pouns ( ) 0 5 0 5 20 Yn ( ) 0 000 2000 3000 4000 2 a Tim (hours) 0 2.5 5.5 0 Distan (km) 0 25 2250 335 4500 Sp of aroplan is 450 km/hour 2800 km (s graph) Original matrial Camrig Univrsity Prss 2009
Camrig Essntials Mathmatis Cor 8 N4.4 Homwork Answrs 3 a : 5.5 :.25 : 0. : 0.45 : 0.8 4 a Th two varials ar irtly proportional aus it is a linar graph (it is a straight lin whih passs through th origin). (approximatly) 220 pouns 0 pouns 2.2 pouns : 2.2 f (approximatly) 54 pouns g 0.45 kg h : 0.45 i 2200 pouns Original matrial Camrig Univrsity Prss 2009 2