代做Mathematics C Mid‐Term Term 1 Examination SAMPLE  B代做Python编程

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.