Page 37 - ACE YR IGCSE A TOP APPR' TO ADD MATH

(x − x − 14x + 24)÷ (x − 2) 15. –x – 2x + 5x – 10x + 7
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= x + x − 12 2x – 3 4x + 4x – 35x + 44x – 21
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= (x − 3)(x + 4) 4x – 6x
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4x 10x – 35x + 10
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+ + 4x 10x – 15x + 10
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a b c 4x 10x – 20x + 44x
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= (x + 4)(x − 2) + (x − 3)(x − 2) + (x − 3)(x + 4) 4x 10x – 20x + 30x
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(x − 3)(x + 4)(x − 2) 4x 10x – 35x + 14x – 21
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= 3x − 2x − 14 4x 10x – 35x + 14x – 21
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(x − 3)(x + 4)(x − 2) [6]
1 [3]
12. x = ± √2 16. –x – 3x – 3x + 3x + 5
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x – = 0 –x + 0x + 2 –x – 3x – 3x + 6x + 10
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2 –x + 0x + 2x
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2x – 1 = 0 –x – 3x – 5x + 6x + 10
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8x + 2x +4x + x + 3 –x – 3x – 0x + 6x + 10
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2x – 1 8x + 2x + 2x – x – 3 –x – 3x – 5x + 10
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8x + 2x – 4x – x – 3 –x – 3x – 3x + 10
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8x + 2x + 6x – x – 3 [3]
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8x + 2x + 2x – x – 3
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8x + 2x + 6x – x – 3 17. When x = –2,
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8x + 2x + 6x – x – 3 f(−2) =(−2) − 4(−2) − 7(−2) + 10
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= 0
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(8x + 2x + 2x − x − 3) ÷ (2x − 1) = 4x + x + 3 x – 4x – 6x + 5
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a = 2, b = −1, c = 4, d = 1, e = 3 x + 2 x – 4x – 7x + 10
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[5] x + 2x
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13. Using long division x – 6x – 7x
8x + 2x + x – 3x + 2 x – 6x – 12x
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x + 0x – 2 x – 3x + 0x + 6x – 4 x – 4x – 5x + 10
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x + 0x – 2x x – 4x – 5x + 10
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x – 3x + 2x + 6x
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x – 3x + 0x + 6x f(x) = (x + 2)(x − 6x + 5)
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x – 3x + 2x + 6x – 4 = (x + 2)(x − 1)(x − 5)
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x – 3x + 2x + 6x – 4 x = −2 or x = 1 or x = 5
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(x − 3x + 6x − 4) ÷ (x − 2) a = 5, b = 1
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= x − 3x + 2 [6]
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=(x − 2)(x − 1) 18. (a) f(0) = –6
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Factors of x − 3x + 6x − 4 p(0) + q(0) + r(0) + s = –6
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= (x − 2)(x − 1)(x − 2) s = –6 (shown)
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[4] [1]
(b) p + q + r − 6 = 0
14. −8p + 4q − 2r − 6 = 60
x – 5x + 12x – 7x + (26 – a)
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x + 2x + a x – 5x + 12x + 8x – 9 −27p + 9q − 3r − 6 = 240
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x + 2x + ax Solve the simultaneous equations to get:
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x – 7x + (12 – a)x + 8x p = −9, q = 4, r = 11
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x – 7x – 14x – 7ax [6]
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x – 5x (26 – a)x + (8 + 7a)x – 9 (c) f(x) = −9x + 4x + 11x − 6
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x – 5x (26 – a)x + (52 – 2a)x + a(26 – a) = (x − 1)(−9x − 5x + 6)
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Remainder: (9a – 44)x – 9 – a(26 – a) = −(x − 1)(9x + 5x − 6)
(9a − 44)x = −71x a = 9, b = 5, c = −6
9a − 44 = −71 [3]
a = −3 19. (a) (−3) + a(−3) − 17(−3) + b = 0
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b = −9 − a(26 − a) 9a + b = −24
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= −9 − 26a + a (−1) + a(−1) − 17(−1) + b = 0
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= −9 − 26(−3) + (−3) a + b = −16
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= 78 [2]
[6]
Answers 177
Answers Add Math.indd 177 14/03/2022 12:29 PM