CAMBRIDGE O LEVEL® 1 Number Answers Exercise 1.1 1 a) Integers: –7, 27, 1534, 0, –12 b) Natural numbers: 27, 1534 17 2 a) is a fraction, so it is rational 20 b) 0.46 is a terminating decimal, so it is rational 2 2 2 c)  and 2 is irrational, so is irrational 25 5 25 d) π is irrational, so 5is irrational e) 3.14159 is a terminating decimal, so it is rational . . f) 0.234 is a recurring decimal, so it is rational 4 2 g)  which is a fraction, so it is rational 25 5 h) 225 15 which is a integer, so it is rational i) 2 3 3 3 3 and 3 3is irrational, so 2 3 3is irrational 3 a) 169 13 which is a integer, so it is rational b) 0.49 is a terminating decimal, so it is rational c) 3is irrational, so 5 3is irrational d) 2.718 is a terminating decimal, so it is rational e) π is irrational, so 52is irrational 4 4 f)  which is a fraction, so it is rational 3 3 g) 27 3 3 and 3 3is irrational, so 27is irrational 7 16 4 h) 1   which is a fraction, so it is rational 9 9 3 i) 2 is irrational, so 6 2is irrational Cambridge O Level Mathematics © Hodder & Stoughton Limited 2016 1 CAMBRIDGE O LEVEL® 1 Number 4 a) π is an example of an irrational number between 3 and 4 b) 110 is an example of an irrational number between 10 and 11 c) 390 is an example of an irrational number between 19 and 20 Exercise 1.2 1 a) 1, 2, 4, 8 b) 1, 3, 5, 15 c) 1, 3, 9, 27 d) 1, 2, 3, 6, 9, 18, 27, 54 2 2, 3, 5, 7, 11, 13, 17, 19, 23, 29 3 a) 2, 3 b) 2, 5 c) 5, 11 d) 2, 3, 7 4 a) 24 × 3 b) 23 × 32 c) 2 × 3 × 5 × 7 d) 2 × 52 × 7 e) 3 × 52 f) 52 × 11 g) 23 × 3 × 5 h) 2 × 32 × 11 5 a) 32 × 5 × 11 b) 22 × 5 × 13 c) 22 × 33 × 52 d) 2 × 72 × 11 e) 22 × 3 × 5 × 7 Cambridge O Level Mathematics © Hodder & Stoughton Limited 2016 2 CAMBRIDGE O LEVEL® 1 Number f) 32 × 53 g) 24 × 7 h) 23 × 5 × 72 6 a) i) 52 ii) 22 × 32 iii) 22 × 52 iv) 24 × 32 b) Prime factors are all in pairs 7 a) 25 × 3 b) k = 6 8 a) 23 × 72 b) k = 7 Exercise 1.3 1 a) i) 18 = 2 × 32, 24 = 23 × 3 ii) HCF = 6 iii) LCM = 72 b) i) 64 = 26, 100 = 22 × 52 ii) HCF = 4 iii) LCM = 1600 c) i) 50 = 2 × 52, 350 = 2 × 52 × 7 ii) HCF = 50 iii) LCM = 350 d) i) 72 = 23 × 32, 126 = 2 × 32 × 7 ii) HCF = 18 iii) LCM = 504 2 a) HCF = 9, LCM = 189 Cambridge O Level Mathematics © Hodder & Stoughton Limited 2016 3 CAMBRIDGE O LEVEL® 1 Number b) HCF = 10, LCM = 100 c) HCF = 12, LCM = 336 d) HCF = 2, LCM = 1600 e) HCF = 7, LCM = 294 3 a) i) 260 = 22 × 5 × 13, 300 = 22 × 3 × 52 ii) HCF = 20 iii) LCM = 3900 b) i) 340 = 22 × 5 × 17, 425 = 52 × 17 ii) HCF = 85 iii) LCM = 1700 c) i) 756 = 22 × 33 × 7, 2100 = 22 × 3 × 52 × 7 ii) HCF = 84 iii) LCM = 18 900 d) i) 1980 = 22 × 32 × 5 × 11, 2376 = 23 × 33 × 11 ii) HCF = 396 iii) LCM = 11 880 4 a) HCF = 252, LCM = 49 896 b) HCF = 504, LCM = 42 336 5 a) 15 b) 900 6 12 mm by 12 mm 7 10:02:56 p.m. 8 10:15 a.m. Cambridge O Level Mathematics © Hodder & Stoughton Limited 2016 4 CAMBRIDGE O LEVEL® 2 Set Language and Notation Exercise 2.1 1 11, 12, 13, 14, 15, 16, 17, 18 2 2, 3, 5, 7, 11 3 1, 2, 3, 4, 6, 12 4 8, 16, 24, 32, 40, 48 5 a, e, i, o, u Exercise 2.2 1 2 Cambridge O Level Mathematics © Hodder & Stoughton Limited 2016 5 CAMBRIDGE O LEVEL® 2 Set Language and Notation 3 4 5 6 Cambridge O Level Mathematics © Hodder & Stoughton Limited 2016 6 CAMBRIDGE O LEVEL® 2 Set Language and Notation Exercise 2.3 1 a) {1, 3, 9} b) {1, 2, 3, 5, 6, 7, 9, 11, 13, 15, 17, 18, 19} 2 a) Ø b) {2, 3, 4, 5, 7, 8, 11, 12, 13, 16, 17, 19, 20, 23, 24} 3 a) Ø b) {a, b, e, f, g, l, m, o} 4 a) {4, 8, 12, 16, 20} b) {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} 5 a) {Sunday} b) {Sunday, Monday, Friday, Saturday} 6 a) {3, 9} b) {3, 6, 9, 12, 15, 18, 21, 27, 33, 36, 39, 45} Exercise 2.4 1 a) 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 b) 4, 8, 10, 12, 14, 16, 20 2 a) 1, 4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24 b) 1, 6, 9, 10, 14, 15, 18, 21, 22 3 a) c, d, f, g, h, i, j, k, l, n, o b) c, d, h, i, j, k, n 4 a) 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 14, 15, 17, 18, 19 b) 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 5 a) Monday, Tuesday, Wednesday, Thursday, Friday b) Tuesday, Wednesday, Thursday 6 a) 6, 12, 18, 24, 30, 36, 42, 48 b) 24, 30, 42, 48 Cambridge O Level Mathematics © Hodder & Stoughton Limited 2016 7 CAMBRIDGE O LEVEL® 2 Set Language and Notation Exercise 2.5 1 a) b) c) Cambridge O Level Mathematics © Hodder & Stoughton Limited 2016 8 CAMBRIDGE O LEVEL® 2 Set Language and Notation 2 a) b) c) 3 a) b) {squares} Cambridge O Level Mathematics © Hodder & Stoughton Limited 2016 9 CAMBRIDGE O LEVEL® 2 Set Language and Notation 4 a) i) and ii) b) They are the same 5 a) i) and ii) b) They are the same Exercise 2.6 1 Ø, {p}, {q}, {r}, {p, q}, {p, r}, {q, r}, {p, q, r} 2 64 3 a) b) 13 c) 10 4 a) 17 Cambridge O Level Mathematics © Hodder & Stoughton Limited 2016 10