Paper 1

1 y = 2x - 5

2 (x - 1)(x + 2)(x - 5)

3 (a) (b) 1 (c) 5

4 4y + 3x = 26

5 (a) (b) C(5, 0, 0) and D(7, 1, -2)

6 (a) x ⁴ + 4x ² + 3 (b) (x ² + 1)(x ² + 3)

7 (a) 24 / 25 (b) 7 / 25 (c) 323 / 325

8 (a) multiplier (0.3) lies between -1 and 1 (b) 40 / 7

(c) (i) n = 7 (ii) required term is 1749.8

9 x = / 6 , / 2 , 7/ 6 , 3/ 2

10 y = 2x ³ - x ² + 5

11 k = 1

12 97 / 10 (or 9.7)

13 (a) flip graph in x -axis then shift 2 units up ( showing clearly points (0,2) , (a , 1) and (b ,2) ) (b) parabola ( concave upwards ) crossing x -axis at (a ,0) and (b ,0) (c) (0,)

14

15 (a) p = / 2 and q = 3/ 4 (b) 1 / 2

16 33 / 2

17 (a) 9.8 m/sec (b) after 2 seconds

18 (a) Discriminant = 0 so equal roots (b) cos= -2 but least value of cosis -1

19 x = 1.54

Paper 2

1 (a) (b) 51.9 (c) 27.4

2 (a) (0,-2) and (3,25)

(b) (0,-2) is a point of inflection and (3,25) is a maximum stationary point.

3 (a) y + 2x = -1 (b) 26.6

4 (a) b = 6 and a = 1 (b) 36 (c) (i) P(5,5) (ii) 125 / 6

5 (a) (i) A(-2,10) (ii) y - 3x = 16 (b) B(4,28)

6 (a) (x -)² + (y - 3)² = 13/4 (b) (i) B(8,8) (ii) F(14,12) C(13/2,7) (c) proof

7 (a) alpha = 56.3 ; k = 13

(b) Max 13 when x = 303.7 Min - 13 when x = 123.7

(c) 0

8 (a) after 4 weekly feeds (b) A_n+1 = 0.75 A_n + 1 (c) Limit = 4 ; Less than 5 so safe

9 (a) 31/ 5 (b) (i) 16/ 3 (ii) 32/ 3

10 (a) proof (b) 3.49 cm

11 (a) log_ey = b x + log_ea (b) b = 3.00 a = 2.00

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