Module A 100 marks - 3 hours
Q.1 (a) Find the value of x such that:
)2(724 1xx
(05 marks)
(b) The y-intercept of a line has the same value as its gradient. If this line cuts the curve
2
38 at x = 3, find the equation of the line. (04 marks)
(c) Mr. Khan deposited an amount into a bank which will be doubled in eight years.
(i) Find the rate of interest considering that the amount is compounded annually.
(ii) How many years will it take for an amount to triple at the above calculated rate of
interest? (05 marks)
Q.2 (a) Asif purchased a car for Rs. 360,000. The amount is payable in forty monthly installments
which are in arithmetic progression. After paying thirty installments one third of the
amount would remain unpaid. Calculate the amount which Asif would be required to pay
as the 35th installment. (05 marks)
(b) Meena has invested Rs. 700,000 in an investment scheme. In return, she would receive
Rs. 74,587 semi-annually in arrears, for six years. She would not receive any amount
afterwards. Find the nominal and effective rate of return of the scheme. (05 marks)
Q.3 (a)
If
2
2
1x
ey , show that:
886
2
2
y
dx
dy
dx
yd (04 marks)
(b) Sketch the feasible region and identify the point of optimal solution for the
function 25 subject to the following constraints.
30
3 150
50
, 0 (07 marks)
Q.4 (a) Solve the following set of equations using Crammer’s rule or matrix inversion method.
210
3 2 2 8 0
2 1 0 (08 marks)
(b) Find the co-ordinates of the relative minima and/or maxima of the following function:
2
4 (07 marks)
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