SPM QUESTIONS : ADDITIONAL MATHEMATICS

1. Given the functions g : x 2x + 1 and h : x 3x + 6 , find

(a) g-1 (x)

(b) hg-1 (9) [ 3 marks ]

2. It is given that the functions g(x) = 4x – 7 and h(x) = 2x.

Find the value of gh(2). [ 2 marks ]

3. Solve the simultaneous equations y-2x+1 = 0 and 4x2 + 3y2 – 2xy = 7 .

Give the answers correct to three decimal places. [ 5 marks ]

4. Given that 9(3n-1) = 27n , find the value of n. [ 3 marks ]

5. Solve the equation :

log2 (2x + 1) – 5 log4 x2 + 4 log2 x = 3 [ 2 marks ]

6. The normal to the curve y = x2 – 5x at a point P is parallel to the

straight line y = -x + 12 .

Find the equation to the normal to the curve at point P . [ 4 marks ]

7. The quadratic function f(x) = p(x + q)2 + r , where p, q and r are constants,

has a minimum value of - 4 . The equation of the axis of symmetry is x = 3 .

State

(a) the range of values of p

(b) the value of q

(c) the value of r [ 3 marks ]

8. Find the range of the values of x for (x – 3)2 < 5 – x . [ 3 marks ]

9. Diagram 21 shows part of a curve y =f(x) which passes through the points

( h , 0 ) and ( 4 , 7 ).

Given that the area of the coloured region is 22 unit2 , find the value of

dx . [ 2 marks ]

10. Given y = and = g(x), find the value of dx . [ 3 marks ]