Page 29 - ACE YR IGCSE A TOP APPR' TO ADD MATH

5. y = 2x − k [3(–13) + 3]x – 12x – 1 = 0
2
x + (2x − k) = 1 + x(2x − k) –36x – 12x – 1 = 0
2
2
2
x + 4x – 4xk + k – 1 – 2x + kx = 0 (6x + 1) = 0
2
2
2
2
2
3x – 3kx + k – 1 = 0 x = – 1
2
2
6
b – 4ac . 0 [7]
2
(–3k) – 4(3)(k – 1) . 0 9. (3a + 1)x + 2ax + a − 4 = 0
2
2
2
9k – 12k + 12 . 0 b – 4ac . 0
2
2
2
3k , 12 (2a) – 4(3a + 1)(a – 4) . 0
2
2
k , 4 2a – 11a – 4 , 0
2
2
–2 , k , 2 11 – 3√7 11 + 3√7
[5] 4 , a , 4
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6. x(2x − 1) + (2x − 1) = x + 11 [5]
2
2
2
x – x – 2 = 0 10. 2x – 5x – 2x – 1 = 0
2
2
(x – 2)(x + 1) = 0 2x – 7x – 1 = 0
x = 2 or x = –1 x = 3.637 or x = −0.137
y = 3 or y = –3 [3]
3
Midpoint of PQ 11. 3( x – 2) + 4x = 3
,
= 1 2 – 1 3 – 3 2 4 9x + 4x = 9
2
2
4
2
= 1 1 2 , 0 x = 36
25
m m = –1 Intersection point: x = 36 , y = – 23
25
25
2
1
m = –1 ÷ 1 –3 – 3 2 3y = 3 – 4x
2
–1 – 2
4
= – 1 y = – x + 1
3
2
3
m = , m = – 4
2
1 2
1
0 = – 1 1 + c 4 3
2 2 m × m = × – 4
3
c = 1 1 2 4 3
4 = –1
1
y = – x + 1 Both lines are perpendicular to each other.
2 4 [8] [5]
7. x = 8 – 5y 12. y = 2ax + 6
3 m = 2a
1
3 1 8 – 5y 2 y = 1 – x
2y – 3 = 6 3 6b
8 – 5y y x
3 y = – 2b + 3
6y – 8 – 5y = 6 1
8 – 5y y m = – 2b
2
–19y + 80y – 64 = 6
2
y(8 – 5y) m × m = –1
2
1
1
11y + 32y – 64 = 0 2a × – 1 2 = –1
2
–16 + 8√15 –16 – 8√15 2b
y = or y = a = b
11 11 [4]
x = 168 – 40√15 or y = 168 + 40√15 2
33 33 [6] 13. (a) −2 = −(0 + h) + k

−2 = −h + k
2
2
8. sx – 4 = 1 – x k = h – 2
3x 2
3sx – 12x = 1 – 3x –2 = –(3 + h) + k
2
2
2
2
(3s + 3)x – 12x – 1 = 0 −2 = −(3 + h) + h − 2
2
b – 4ac = 0 6h = −9 3
2
(–12) – 4(3s + 3)(–1) = 0 h = – 2
2
144 + 12s + 12 = 0
s = –13
Answers 169
Answers Add Math.indd 169 14/03/2022 12:29 PM