Higher 99 Answers

Paper 1

1 (a) Proof (b) 1/2 , -3

2 (a) 4y-3x = 5 (b) 3y+4x = 10

3 (a) 3x8 (rectangle) + 1/2x3x6 (triangle) = 33 unit2 (b) (c) 33

4 (x+3)2 + (y-4)2 = 25

5 24

6

7 1/3

8 (i) b2-4ac = 0 (ii) proof

9 y+10x = -3

10 (a) graph moves 1 unit to the left O'(-1,0), A'(0,-2), B'(2,0), C'(5,4), D'(6,0)
(b) graph is "flipped" in x-axis and scaled in the y direction by a factor of 2
O"(0,0), A"(1,4), B"(3,0), C"(6,-8), D"(7,0)

11 y = x4/4 - 1/x - x/4 + 3

12 -3/11

13 (a) 2(x-1)2 + 3 (b) Min stat point is (1,3)

14 13.9, 46.1 (to 3sf)

15 a = -2 , b = 5

16 proof ( Discriminant of 6x2 + 6x + 4 is negative )

17 (a) (i) 9 (ii) 8 (iii) 6 (b) 180 , 180

18 p = 2q

19 -2sin 2x

20

21 (a) 1 + 2x + 2x2 + 4x3/3 + 2x4/3 + 4x5/15 (b) f'(2x) = 2f(2x)

Paper 2

1 (a) y + 3x = 14 (b) 2y + x = -2 (c) (6,-4)

2 (a) y + 2x = -3 (b) B(0,-3) (c) C(-2,1) (d) (x+1)2 + (y+1)2 = 5

3 (a) (b) (c) 34.0° (to 3sf)

4 (a) (4,0) (b) 2y + x = 4 (c) Q(1/2,7/4)

5 (a) (i) 8x + 9y (ii) proof ( y = 40 - 8/9x etc) (b) x = 45/2 , y = 20; 2700 m2

6 (a) (i) x2 -1 (ii) x2-2x+1 (b) proof ; concave upwards parabola thro' (0,0) & (1,0) (c) 1/3 unit2

7 (a) k = 0.0719 (to 3sf) (b) 51.3% (to 3sf)

8 (a) proof (b) Q(cos(a-45)°,sin(a-45)°) (c) R(cos(a+45)°,sin(a+45)°) (d) -cosa/sina (or -1/tana) (e) proof

9 100.2° , 192.4° (to 1 dec place)

10 (a) p =1 , q = 2 (b) 5/2

11 (a) y - 3x = -12 , y - 3x = 20 (b) proof

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