9709/May June/3/2002/Q8

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 equation x + 3y - 2z = 3

i) Given that l intersects p, find the position vector of the point of intersection.

ii) Find the equation of the plane which contains l and is perpendicular to p, giving your answer in the form ax + by + cz = 1.

Solution:

Reference: PYQ - May/Jun 2002 Paper 3 Q8

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9709/Oct Nov/13/2016/Q8

(i) Express 4x² + 12x + 10 in the form (ax + b)² + c, where a, b and c are constants.

(ii) Functions f and g are both defined for x > 0. It is given that f(x) = x² + 1 and fg(x) = 4x² + 12x + 10. Find g(x).

(iii) Find (fg)⁻¹ (x) and give the domain of (fg)⁻¹.

Solution:

Reference: PYQ - Oct/Nov 2016 Paper 13 Q8

9709/MayJune/1/2007/Q8

The function f is defined by f(x) = a + b cos 2x, for 0 ≤ x ≤ π. It is given that f(0) = −1 and f(1/2π) = 7.

i) Find the values of a and b.

ii) Find the x-coordinates of the points where the curve y = f(x) intersects the x-axis.

iii) Sketch the graph of y = f(x).

Solution:

i)

ii)

iii)

Reference: PYQ - May/June 2007 Paper 1 Q8