O Level Answers

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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
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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

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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

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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.

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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

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2 Set Language and Notation

3

4

5

6

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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
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2 Set Language and Notation

Exercise 2.5

1 a)

b)

c)

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2 Set Language and Notation

2 a)

b)

c)

3 a)

b) {squares}
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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

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