9709/May June/33/2016/Q2

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. State the exact value of the gradient of this line. [3]

(ii) Calculate the exact x-coordinate of the point of intersection of this line with the line with equation y = 2x, simplifying your answer. [2]

Solutions:

Reference: PYQ - May/Jun 2016 Paper 33 Q2

9709/May June/31/2017/Q6

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, 0, 2) respectively.

(i) Show that the plane m bisects AB at right angles.

A second plane p is parallel to m and nearer to O. The perpendicular distance between the planes is 1.

(ii) Find the equation of p, giving your answer in the form ax + by + cz = d.

Solution:

Reference: PYQ - May/Jun 2017 Paper 31 Q6