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
