Foundation Program
SAMPLE B
Mathematics C
Mid-Term Term 1 Examination
Question 1 Use a SEPARATE book clearly marked Question 1
(i) Simply |x - 3||x + 1| for -1 < x < 3 .
(ii) Find the equation of the function formed by reflecting the graph of y = 3 x over the x axis and shifting it 2 units vertically upwards.
(iii) Find the equation of the axis of symmetry of the parabola y = x2 + 4x + 3 .
(iv) Solve |9 - x| > 5 .
(v) U = {positive integers less than 10} , S = {1,3,5,7} and T = {1,2,4,8} .
(a) List the elements in T ' .
(b) Find n(S T ' ) .
(vi) Find the value of the constant k if x +1 is a factor of P(x) = x 4 + kx3 + 2 .
(vii) Write down the domain of the function y = x(x+1)/1 .
(viii) Find the equation of the circle with centre C(0, - 4) which passes through the point P(- 8, 2) .
Question 2 Use a SEPARATE book clearly marked Question 2
(i) Sketch each of the following functions showing their essentials features:
(a) y = 1 - x/1 .
(b) y = 4 -x .
(ii) Solve (3x + 1)2 ≤ (x + 1)(x + 7).
(iii) The number of black bears in a forest after t years is given by N = 110 × 100.03t .
(a) How many black bears are initially in the forest?
(b) After how many years there are 1000 black bears in the forest?
(iv) Prove the result loga x = logx a/1 .
(b) Use this result to solve for x if log x 5 + log5 x = 2 .
Question 3 Use a SEPARATE book clearly marked Question 3
(i) (a) On the same set of axes, sketch the graphs of y = x , y = —x and y = |x — 2|.
(b) By using part (a) or otherwise, determine the values of c for which the equation |x — 2| = cx has exactly one solution.
(ii) A company manufactures radios with a production level of x thousand radios per month where 1 ≤ x ≤ 20 . The cost of producing x thousand radios, C(x) thousand dollars, and the revenue on the sale of these radios, R(x) thousand dollars, are given by the functions:
C(x) = 160 + 10x and R(x) = 50x —1. 25x2 .
(a) Show that the monthly profit, P(x) thousand dollars, when x thousand
radios are produced and sold is given by P(x) = 160 —1. 25(x —16)2 .
(b) Find the maximum monthly profit.
(c) Find the break-even point.
(d) Sketch the graph of P(x) for 1 ≤ x ≤ 20 clearly indicating the break- even point and the point of maximum profit.