# Maths for Economists: Multiple Choice Test 2

Reproduced with permission of Hilary Lamaison, Brunel University, ecsthjl@brunel.ac.uk. Hosted by the Economics Network.

EC1011 Mathematics for Economics
Multiple Choice Test 2 for self-assessment

In answering each of the following questions, click the boxes next to each correct answer. More than one may be correct in some cases. Do not guess. There are 15 correct choices in total. The feedback box at the foot of the page will tell you how many of your answers are correct.

Time allowed = 15 minutes. CALCULATORS MAY BE USED FOR THIS TEST.

1: Which of the following is/are true?

x / x = x0
xb−1 / xb = x
xb / xb+1 = x-1
xb . x = xb+1

2: log ab may be expressed as:

log a + log b
log a . log b
log ( a + b )
b log a

3: £100 invested for 5 years at 6% per annum interest compounded annually will grow to:

1065
100[1 + (.06)(5)]
100(1 + .06)5
[100(1.06)]5

4: d(√x) =
d(x)

1
√x
1
2√x
√x
2
x-1/2
2

5: Which of the following are true?

f(x) = ax3 − bx + c implies f'(x) = 3ax2 − b + c
f(x) = 4x + 3 / x2 implies f'(x) = 4 − 6/x3
f(x) = 3x2/3 implies f'(x) = 6x-1/3
f(x) = 6x3 − 3x-2 + 5x + 7 implies f'(x) = 18x2 + 6x-3 + 5

6: For the following total cost function, find marginal cost (MC), average total cost (ATC) and average variable cost (AVC) and then decide which of the following are true. TC = 0.1Q3 − 4Q2 + 80Q + 150 implies

MC = 0.3Q2 − 8Q + 80
ATC = 0.1Q2 − 4Q + 80
AVC = 0.1Q2 − 4Q + 80
MC = AVC at Q = 20

7: The function y = f(x) reaches a (relative) minimum where:-

f(x) = 0 and f'(x) < 0
f(x) = 0 and f'(x) > 0
f'(x) = 0 and f''(x) < 0
f'(x) = 0 and f''(x) > 0

8: A demand function is given by: Qd = 52 − P2
At the point (P,Q) = (2,48) the price elasticity of demand
PED = P . dQ
Q   dP
is equal to:

2 − 104/Q
-1/6
-1/8
-4

Attempts: