Page 44 - ACE YR IGCSE A TOP APPR' TO ADD MATH

1
1 4 0 k 4
12. (a) Area = 14. log y = – log x + 1
2 8 0 3 8 4 1
1 (4 × 0) + (0 × 3) + (k × 8) –
–
4
38 = log y = log x + log 10
2 (8 × 0) – (0 × k) – (3 × 4) – 1
1 y = x (10)
4
38 = |8k – 12|
2 – 1
2
8k – 12 = 76 or 8k – 12 = –76 y = 100x 2
k = 11 (invalid) or k = –8 a = 100, b = – 1
[3] 2 [5]
(b) Equation of line AB:
m = 8 – 3 15. m = 18 – 6 = 3
7 – 3
= 1 4 – (–8)
2 = 5 6 = 3(3) + c
= √3 12 c = –3
y
8 = 5 (4) + c x = 3√x – 3
= √(7) – 12 3 2
2
c = 19 y = 3x – 3x
3
3
2
2
= 1 8 + 3 y = 5 x + 19 c = 3, d = , e = –3 [4]
2
2
1 12 3
= 2 2 Point C: 8 – 3
= 5 19 16. m = 6 – 1 = 1
y = (1) +
12 3 y = mx + c
= 27 ln y = m ln x + c
4 3 = (1)(1) + c
1
C 1, 27 2 c = 2
4
ln y = ln x + 2
2
ln y = ln x + ln e
27
2
1
2
BC = (–8 – 1) + 3 –
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2
ln y = ln (xe )
4
2
2
= 1521 ln y = x(e ) [5]
16
= 39 units 5.1 – 3.4 1
4 17. (a) m = 4 – 0.6 = 2
1
CA = (4 – 1) + 8 – 27 2 2 3.4 = 0.5(0.6) + c
2
c = 3.1
4
1
2
= 169 lg y = x + 3.1
2
16 1 2 + 3.1
x
2
= 13 units lg y = lg 10
4 1 2
x
y = 10 × 10
2
3.1
BC : CA
3.1
:
39 13 A = 10 = 1258.93
4 4 1 2
39 : 13 B = 10 = 3.16
3 : 1 1 [5]
n = 3 (b) y = [10 2 (2) 2 ] × 10
3.1
[6] = 125892.5
13. m = 6 – (–3) = –3 = 126000
–3 – 0 [2]
2
x
2
= –3 1 2 – 3 1.2 – 0.6 3
y 3x 18. (a) m = = –
x
2
= –6 – 9x 0.1 – 0.5 2
y 3x 1.2 = −1.5(0.1) + c
3x = y(–9 – 6x) c = 1.35 2
3
y = – x 3 ln y = −1.5x + 1.35
3 + 2x [3] [3]
Cambridge IGCSE
TM
184 Ace Your Additional Mathematics
Answers Add Math.indd 184 14/03/2022 12:29 PM