Page 33 - ACE YR IGCSE A TOP APPR' TO MATHS

Answers

1A
1A Numbers

Number fact = 1 − 1
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3145 0.03
1 (a) 26 [1] c = −0.030 [2]
(b) 23 and 29 [1] 1 a – b
(c) 27 [1] (b) c = ab
(d) 25 [1] ab
2 (a) 100 [1] c = a – b [2]
(b) –28 [1] 11 0.6 hours = 36 minutes
(c) 100 [1] Distance travelled = 50π × 100 × 36
(d) √7 [1] 100 × 1000
3
3 (a) π and √4 [1] = 5.655 km [2]
3
(b) 0, 64 and 3 2 [1] Standard form
(c) 0.5 [1]
(d) 64 [1] 1 (a) 70200.05 70200 [2]
∼
4 59 – 7 = 52 [2] (b) 2811.484 2811 [2]
∼
5 11, 13, 17, 19 [1] (c) 1232010000 [2]
∼
(d) 5343.5 5344 [2]
Inequalities (e) 16853932.58 16853933 [2]
∼
∼
(f) 11992578.95 11992579 [2]
1 cos 50° < 42 < tan 50° < 1.05 × 10 1 [2] 2 (8.97 × 10 ) – (6.2 × 10 )
10
12
50 = 10 (8.97 × 10 – 6.2)
10
2
1
12
3
2 0.3 < √0.3 < 10 < 0.3 [2] = 8.908 × 10 2 [2]
0.3
2
38
3 1 < 3.14 < π < 22 [2] 3 10 (4.05 + 4.05 × 10 ) [2]
= 4.0905 × 10

π
40
7
4 0.879 > 0.879 > 0.879 > 68 [2] 4 6.5 × 10 2 [2]
78 5 (a) 11809 × 85 + 8532 × 55
5 2.35 × 10 > 2.84 × 10 > 9.72 × 10 > 1.089 × 10 –3 = 1473025 [2]
0
–2
3
[2] (b) 1.473025 × 10 6 [2]
6 (4.5 × 60) × 24 × 365
Rounding off = 2365200
= 2.3652 ×10 6 [2]
–3
1 (a) 41.1484424 [1] 7 1.085 × 10 × 80000
(b) 41 [2] = 8.68 × 10 1 [2]
2 3.95 4.0 [2]
∼
√9 × 40 3 × 40 Recurring decimals
3 = =12 [2]
3
√1000 10 1 Let x = 0.26
4 211929381.5 212000000 [2] 10x = 2.6
∼
5 (a) 5.413 [1] 100x = 26.6
(b) 5.41 [1] 90x = 24
6 24 × 1 = 8 [2] x = 24 = 4
3 90 15
∼
7 1.047 1.0 [2] 2 Let x = 0.34 [2]
∼
8 12531.6 13000 [2] 100x = 34.34
9 0.006239 0.0062 [2] 99x = 34
∼
1 1 1
10 (a) = − a x = 34
c
b
99 [2]
Answers 153
Answers.indd 153 15/03/2022 11:08 AM