Answers to all pages - Hodder Plus Home

Model answers
Calculator methods (page 17)
1 (a) 3 ÷ 5 × 200 = 120 g
19
(b) 2 ab/c 3 ab/c 4 – 1 ab/c 4 ab/c 5 = ––
20 or 0·95
(c) 4 ÷ 7 × 2 6 · 6 = $15·20
1
2 1 ÷ ( 3 x 2 ) = –
9
3 (a) ( 1 8 · 6 – 2 · 7 5 ) ÷ ( 3 · 5 + 1 · 0 4 3 ) = 3·49
(b) 1 ÷ ( 4 · 5 + 6 · 8 ) = 0·088
(c) 3 · 2 × ( 5 · 2 – ( 1 ÷ 1 · 6 ) ) = 14·64
4 (a) ( 4 · 2 x y 5 – 1 · 7 x y 4 ) ÷ 1 · 2 5 x 2 = 831·08
(b) √ ( 3 x 2 + 2 · 7 x y 3 ) = 5·36
5 (a) 6 · 3 EXP 9 + 5 · 8 EXP 1 0 = 6·43 × 10 10
(b) ( 9 · 5 2 EXP 1 4 ) x 2 ÷ 8 EXP +/– 3 = 1·13 × 10 32
6 (a) 6 × ( cos 2 7 + sin 2 7 ) = 8·07
(b) 3 – ( 4 × sin 2 8 · 7 ) = 1·08
7 6 4 x y ( 4 ab/c 3 ) = 256
Solving problems (page 18)
1 (a) $58·80 ÷ 12 × 5 = $24·50 (b) $5·49 ÷ 3 × 4 = $7·32
2 (a) $4000 × 1·07 3 = $4900·17
(b) 8 years. Found from repeated multiplication by 1·07.
90
3 –– = 1·5 h = 1 h 30 min
60
Total time = 1 h 30 min + 50 min + 1 h 40 min = 4 h
180
––– = 45 km/h
4
4 (a) Total = 4·47 × 10 7 or 4·5 × 10 7 (b) 5·14 × 10 6 ÷43000 = 120
5 $900 = 120% of 1998 bonus = 1·2 × 1998 bonus
1998 bonus = $900 ÷ 1·2 = $750
165 × 40
6 –––––––– = 44·9 cm to 1 d.p.
147
Symbols, indices, factors and expansions (page 21)
1 3pq(4p – 5q)
2 (a) 2(3x + 1) – 4(x – 3) = 6x + 2 – 4x + 12 = 2x + 14 (b) (3 – x) 2 =(3–x)(3 – x) =9–3x –3x + x 2 =9–6x + x 2
3 (a) 4s 2 – 2s – 5 (b) 2e 2 + 6ef – ef – 3f 2 = 2e 2 + 5ef – 3f 2 (c) 8pq 3
4 Let a small radiator cost $x. A large radiator will cost $(x + 45)
Therefore 3x + 2(x + 45) = 415
3x + 2x + 90 = 415
5x = 415 – 90 = 325
x = 65
Small radiators cost $65 each
5 (a) 6a (b) 2a(2a – 1)
6 ( a + b)( a – b) = a + a b – a b – b = a – b
7 (a) 12a 3 b 4 (b)
7a
–––
2
b
8 (a) (3x – 2)(x + 4) = 3x 2 + 12x – 2x – 8 = 3x 2 + 10x – 8 (b) (2y – 1)(y – 3) = 2y 2 – 6y – y + 3 = 2y 2 – 7y + 3
9 (a) 15a – 9 – 10ab + 6b (b) 3a – 6 + 10b – 5ab
= (15a – 10ab) – (9 – 6b) = (3a – 6) + (10b – 5ab)
= 5a(3 – 2b) – 3(3 – 2b) = 3(a – 2) + 5b(2 – a)
= (5a – 3)(3 – 2b) = 3(a – 2) – 5b(a – 2)
= (a – 2)(3 – 5b)
IGCSE Revision Guide for Mathematics Model Answers © 2004, Hodder & Stoughton Educational
3