WORKED SOLUTIONS

Worked solutions: Chapter 8

© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser’s institute

WORKED SOLUTIONS

11

Review exercise

Paper 1 style questions

1 a i

6

5

10

24

b G T

S

U

G′ ∩ S

2 a, b

A B

C 7 8

7 9

2 1 3

U

c

3

3 a

F

T

c

T

T

e

T

T

4 a _{A B C U}

b

4 + 6 + 5 = 15

c i

5, 10, 15, 20

ii

10, 20, 30

5

For example:

a

–3, 4

b ³ 4

, π

c ² 3

,

10 d ¹

2

,

6 e

π,

f

π,

6 a ^{4 1} 60 15 b ^{1 14}

15 15

1 

c ^{16 4} 20 5 7 a ^{3 1} 15 15 b ³

14

c ^{4 3 2} 15

u

A ∪ (B ∩ C ′ )

8 a

12

b ^{1 1 1} 2

u

6 3

9 a

3400 ≤ w < 3700

b ^{5 1} 50 10 c ^{45 9} 50 10 d ^{20 4}

45 9

Paper 2 style questions

1 a

U = {8, 9, 10, 11, 12}

b, e

P Q

R 11 9

10 8 12

U

c i

none

ii

none

d

numbers that are either multiples of 4 or factors of 24.

2 a i

D S

O

48 – x x 44 – x U

ii

48 − x + x + 44 − x = 70 92 − x = 70

x = 22

iii

Members who did not attend both Drama and Sport

iv

P(D or S) =

70 70 70 35

 

ª º

« »

¬



b i ³⁰₇₀ ³₇

ii ^{12 6}

70 35

3 a P Q

R 4

2 12

4 3

5 15

U

b

50 − 45 = 5

Worked solutions: Chapter 8

© Oxford University Press 2012: this may be reproduced for class use solely for the purchaser’s institute

WORKED SOLUTIONS

12 c i ^{35 7}

50 10 ii ²⁹

50 iii ^{6 1}

24 4 d ^{3 2 3}

50

u

4 a i

P = {2, 3, 5, 7, 11}

ii

Q = {1, 2, 3, 6, 9}

iii

R = {3, 6, 9, 12}

iv

P ∩ Q ∩ R = {3}

b _U

P Q

R 8

10 5

7

11 1

12 3 6 9 2

4

c i

{2, 3, 5, 6, 7, 9, 11}

ii

{1, 4, 8, 10}

iii

{4, 8, 10}

d i ⁵

12 ii ³

12

iii ⁴

12 iv ²

5

5 a

C

P

C

P C

P 6

10 4 10

6 10

4 10

6 10

4 10

b i ^{4 4 16} 10

u

ii ^{4 6 6 4 48} 10

u



u

a = 8 b = 9

ii

0

iii

1

d ^{1 4 1 1 5 1} 2

u

 u

60 ii ¹⁶ 60 iii ⁴² 60

b i ^{4 7 16 27} 60





13

c i ^{36 35 21} 60

u

u