Answers


Section 1 Chapter 1


Exercise 1


1. (a) 10 (b) 14 (c) 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15 (d) 48 (e) 32 (f) 5; 2 is a divisor (g) 24; 16 (h) 30; 30; They are equal (i) 2 + 2 + 2 + 2 + 2 = 10 (j) 2 × 2 × 2 × 2 × 2 = 32 2. (a) 27 (b) 6 (c) 26 (d) 24 (e) 18 (f) 2 (g) 3 (h) 7 (i) 5 (j) 2 3. (a) U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12}, A = {3, 5, 7, 9}, B = {1, 2, 3, 4, 5} (i) {1, 2, 3, 4, 5, 7, 9} (ii) {3, 5} (iii) {7, 9} (iv) {1, 2, 4} (v) {1, 2, 4, 6, 8, 10, 11, 12} (vi) {6, 7, 8, 9, 10, 11, 12} (vii) {6, 8, 9, 10, 11, 12} (viii) {1, 2, 3, 4, 5, 6, 8, 10, 11, 12} (b) U = {5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20}, C = {6, 8, 10, 12, 14}, D = {5, 10, 15, 20} (i) {5, 6, 8, 10, 12, 14, 15, 20} (ii) {10} (iii) {6, 8, 12, 14} (iv) {5, 15, 20} (v) {5, 7, 9, 11, 13, 15, 16, 17, 18, 19, 20} (vi) {6, 7, 8, 9, 11, 12, 13, 14, 16, 17, 18, 19} (vii) {7, 9, 11, 13, 16, 17, 18, 19} (viii) {6, 7, 8, 9, 10, 11, 12, 13, 14, 16, 17, 18, 19} 4. (a) (i) U = {6, 9, 12, 15, 18, 21, 24}, A = {9, 15, 18}, B = {6, 15, 18, 21} (ii) 12 ∉ A (iii) The set of natural numbers between 6 and 24 inclusive which are divisible by 3 (iv) {6, 9, 15, 18, 21} (v) {15, 18} (vi) {9} (vii) {6, 12, 21, 24} (b) (i) U = {1, 3, 4, 5, 6, 8, 9, 10, 11, 12}, C = {1, 3, 4, 8, 12}, D = {4, 8, 9, 10, 11} (ii) #(C) = 5, #(D) = 5 (iii) {1, 3, 4, 8, 9, 10, 11, 12} (iv) {4, 8} (v) {1, 3, 12} (vi) {5, 6} (vii) 3 ∉ D\C 5. (a) 18 composite; 2 × 3 × 3 (b) 45 composite; 3 × 3 × 5 (c) 11 prime (d) 28 composite; 2 × 2 × 7 (e) 90 composite; 2 × 3 × 3 × 5 (f ) 85 composite; 5 × 17 (g) 62 composite; 2 × 31 (h) 79 prime (i) 51 composite; 3 × 17 6. Prime numbers 47, 91 7. Not prime; Even number 8. Not prime; Divisible by 3 9. (a) 8, 16, 32, 64; Not prime; Even number (b) 25, 125, 625, 3125; Not prime; Divisible by 5 10. 17 girls, 19 boys 11. 3 = 2 + 1


Exercise 2


1. (a) A = {−3, −2, −1, 0, 1, 2, 3, 4} (b)


− −34 −2 −1 012 345


(c) (i) 0 < 4 (ii) −1 > −3 (iii) 0 > −2 (iv) 2 > −3 (v) −4 < −3 2. (a) −2 (b) −3 (c) −17 (d) −3 (e) −4 (f) 3 (g) −27 (h) −3 (i) 4 (j) 1


3. Z N −3 2 5 −10


4. (a) +20 m (b) −2 m 5. (a) −1200 m (b) −1700 m 6. (a) (i) 6168 m (ii) −86 m (b) 6254 m 7. 75 °C 8. 503 years 9. −1 °C 10. €26 000 11. 125 °C


12. 180 °F 13. €293 14. 37 °C 15. (a) 2 310 241 (b) +30 094 (c) 2 340 335 16. 100 17. −27, −26, −25 18. −9, −8, −7 19. (a) −1 (b) −1 (c) 1 (d) 1 (e) 0 (f) −1


Exercise 3 1. (a)


Q Z N 14 −


3 2


−3 1 27 0


1 2


1 −6 0


Power of Maths: Paper 1 – Answers


(b) (i) Yes; Z ⊂ Q (All integers are rational numbers) (ii) Yes; N ⊂ Q (All natural numbers are rational numbers) (c) {Rational numbers that are not integers} 2. Infi nite number; 0 < x < 1 3.


1 6


1


4. (a) 4 _


(i) 1 _


5 (b) 3 _


3 (j) 7 __


7 (c) − 1 _


25 5. (a) 3 _


(g) −2 (h) − 4 _


3 (d) 61 __


60 (e) 8 __


2 (b) 2 (c) 1 _


15 (f) 4 __


4 (d) − 2 _


25 (g) 49 __


9 (e) 35 __


2 9


1 3


5 6


0


4 (h) 4 _


7


18 (f ) 3 _


2 7 (i) 2 6. (a) 0·6 (b) 0·75 (c) 1·21


(d) 0·78 (e) −0·2875 (f ) −3·4 (g) 0·24 (h) −5·125 (i) 7·2 (j) 0·08 7. (a) 5


_ 8 (b) − 713


____ 1000 (c) − 107


__ 15 10. Son: 1


_ 6 , daughter: 1


_ 3


___ 50 (d) 141


___ 25


8. €4750 9. Treadmill: 36 minutes, Pool: 30 minutes, Weights: 24 minutes, 4


11. Mechanical: 315, Chemical: 140, Electrical: 385, 11 __


24


12. 287 875 13. 75 mph 14. 7 11 __


16. 13 5 _


8 km 17. 3 _


12 litres 15. 2 7 _


5 18. 2 19. 18 8 cm


339


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