Given that f(x) = (3x-5)2, find the value of f of f -1 (2).

3

Given the functions functi ons f:x

2x-1 and g:x

(3 marks)

3 x 2 5 x

, x

{

2 5

Form the quadratic equation which has the roots 2

(4 marks)

, find

(a) fg(1)

4

(3 marks)

(b) gf(-1)

3 2

and -5. Give the answer in the form

(3 marks)

of ax +bx+c = 0, where the a,b and c are constants.

5

6

Find the range of values of x which satisfies the inequality x(x-3) 10

Find the range of values of k so that the equation 2x 2+

1 5

kx +

1 !

2

0 has two distinct

(3 marks)

(3 marks)

roots.

7

Simplify the log3 5 +2 log3 4 ± log3 40.

(3 marks)

8

Solve the equation log 2 x + log2 (2x-3) = 3. Give the answer correct to four significant figures.

(4 marks)

9

Given that log 2 5 = p and log2 7 = q, express log 2

(4 marks)

10

A straight line joining points A (0, k) and B (3, 5) is parallel to straight line y = 2x-3. Find the value of k.

(3 marks)

11

Given A (2, 3), B (-4, 1) and C (-1, 5) are the vertices of ¨ ABC .

(3 marks)

12

The coordinates of points A and B are (-1, 2) and (3, -6) respectively. Find the equation of a straight line that passes through point P (3, 4) and is perpendicular to AB.

(4 marks)

1.4 in terms of p and q.

Paper 2 1

Solve the simultaneous equations 2x-y = 7 and x 2 + 3xy ± y2 = -1

[6 marks]

2

Given that one of the roots of the quadratic equation x 2 ± (p+5) x +4(p+1) = 0 is twice the other; find the possible values of p.

[6 marks]

3

Given that 2 log10 y + 1 = log10 (3x-2), express y in terms of x.

[2 marks]

4

5

Given log a

3 !

2

p , log a

10 !

3

q and log a

375 !

2

r , show that 4p + 3q ±r =0.

Given that log3 2 = 0.631 and log 3 5 = 1.465, find the value of log 3 1.2