Tkss Prelim 2009 Am Answers

Paper 1 1.

x = 0.5, y = 2

3. 5.

1 ≤ f(x) ≤ 7 (a) Hint: Use Factor Theorem 2 1 1+ + , 6.52 x  1 x  12 (a) (i) 2 sin 2x  5 sin x (ii) 4 cos 2x  5 cos x 5 (i) 5  2 4 (c) Draw y = 2  x 5 (a) k =  5 n n  1 2 (b) (i) 1 + nx + x + ... 2 (b) 4 + 160 cos (  18.43) (b) (i) k = 0.0479, n = 1.14

6. 7. 8. 9. 10.

11. 12.

6 13 4. x = 4, y = 16 or x = 16, y = 4 (b) 0, 72, 90, 144, 180

2.

6 ≤ k ≤

(b) (, 6), minimum, point (ii) 24 

5 2 2

(ii) 1 + 10nx + 40x2 + . . .

(iii) n = 5, b = 100

(c)  = 56.2 (ii) 8.91 s

Paper 2 1. (i) 900.5 g (iii) 546 g 2. (i) α + β = 3 and αβ =  92

(ii) 0.05 (iv) 35.4 g/year (ii) 13x2  2x  2 = 0

3.

(a) (i) Hint: Use Double Angle

(ii) 68.0, 292.0

4.

(a)

5.

(c) Hint: Remove log (ii) Hint: Use discriminant

1 178

(b) Draw y =  4 x + 2

(b) 2.55 y

y = 2x3  x2  2x  8

(iii) x

2 8

6. 7.

8. 9. 10.

(a) Use Mid Point Theorem (c) Use Intersecting Chords Theorem 4x sin 3x  (2x 2  3)3 cos 3x (a) sin 2 3x  6  (b) (i)    3x  1  (a) 0.896

(b) Use Tangent-Secant Theorem (d) State Pythagoras Theorem

(i) (x + 4)2 + y2 = 16 (i) t = 0.5 s (iii) a = 2 + 4 2

(iii) x2 + y2 + 8y + 32 2  32 = 0 (ii) s = t2  2 ln (2t + 1) + 3 (iv) 3.28 m

(i) 5.5

(ii)

 2 t  1

11.

(iii)

 dA 1 55 2 = 110x  3025 16  4 x  dx 2

1 2

(c) x = 2.5 6 decibels/sec 11 (b) (i) (0, 3)

(ii) 



55 11 4 2

(iii) 49.1 (ii)

52 121 units2

55 2  x x  52  or 110x  3025 16  4 x

110  552 x  , A is maximum at x = 4