ACADEMIC CENTRE OF EXCELLENCE (ACE) - MATHEMATICS 9709

The variables x and y satisfy the relation 3^y = 4^(2−x). (i) By taking logarithms, show that the graph of y against x is a straight line...

The plane with equation 2x + 2y − z = 5 is denoted by m. Relative to the origin O, the points A and B  have coordinates (3, 4, 0) and (−1, ...

A curve has equation y = 2/3 ln ( 1 + 3 cos 2 x ) for 0 ≤ x ≤ ½ (i) Express d y/ d x in terms of tan x . (ii) Hence find the x-coordi...

Find the area of the shaded region for each of the following graphs. Solution:

In this question the origin is taken to be at a harbour and the unit vectors i and j to have lengths of 1 km in the directions E and N. A c...

The straight line l passes through the points A and B whose position vectors are i + k and 4i - j + 3k respectively. The plane p has equat...

The polynomial p(z) is defined by p(z) = z^3 + mz^2 + 24z + 32, where m is a constant. It is given that (z + 2) is a factor of p(z). (i) ...