ECON1003 Practice Mid-term exam Page 1 of 7
SID: ________________________


The University of Sydney

Quantitative methods in economics ECON1003


Practice Mid-semester exam (Note that the objective of this exam is to get you used to
the format of the exam. Note the questions on the midterm can and will be more
difficult than the practice exam)



Instructions:

Your exam consists of 20 selective questions including Multiple choice, True/False, Fill in the
blanks and Numerical. Each question is worth 1 mark.
Permitted materials: Non-programmable calculators


1. Find t to solve 1750753 03.0 =te
a. t = 28.11
b. t = 30.25
c. t = 6.883
d. t = 6.2133
e. t = -3.4510

2. ln(22)+ln(2) is equal to
a. ln(24)
ECON1003 Practice Mid-term exam Page 2 of 7
b. ln(44)
c. ln(20)
d. 0
e. ln(11)

3. The spread of a carrot fly through an untreated crop is modelled by the equation
)1(500 5.0 teY −−= , where Y is the weight of infected carrots in tons, t is time in days.
Calculate the time taken to infect 200 tons of carrots.
a. 1.0217 days
b. 2.4792 days
c. 1.8326 days
d. 2.3491 days
e. 3.4491 days

4. Find x to solve 0562 =++ xx
a. x=1
b. x = 8 or -10
c. x = 14
d. x= -1 or -5
e. x = 2 or 10

5. The supply equation is Ps = Q2 + 6Q + 9 and demand is given by Pd = Q2 – 10Q + 25.
What is the market equilibrium?
a. Q = 1; P = 16
b. Q = 16; P = 1
c. Q = 8; P = 106
d. Q = 1; P = 18
e. Q = 1; P = 25
ECON1003 Practice Mid-term exam Page 3 of 7

6. If demand is given by P = 100 – Q, what is TR and MR for a monopolist?
a. TR = 100Q – Q2; MR = 0
b. TR = 100 – Q2; MR = 2Q
c. TR = 100Q – Q; MR = - 1
d. TR = 100Q – 2Q2; MR = 100 – 4Q
e. TR = 100Q – Q2; MR = 100 – 2Q

7. A consumer can buy good 1 or good 2 at prices p1 and p2. The quantity of good 1
purchased is x1 and the quantity of good 2 that the consumer buys is x2. What is the
consumer’s budget line and budget set (the budget set is all the bundles that the consumer can
afford to buy) with income M?
a. x1.p1 = M; x2.p2 ≤ M
b. x1.p2 +x2.p1 = M; x1.p2 +x2.p1 ≤ M
c. x1.p1 +x2.p2 < M; x1.p1 +x2.p2 = M
d. x1.p1 +x2.p2 = M; x1.p1 +x2.p2 > M
e. x1.p1 +x2.p2 = M; x1.p1 +x2.p2 ≤ M

8. What is the price elasticity of demand at q = 20 when the demand equation is P = 50 – 2q?
a. e = -0.25
b. e = -1
c. e = -1.5
d. e = -2
e. e = -4

9. A consumer can buy two goods, good 1 and 2 for prices $5 and $10 respectively. The
consumer is currently buying 6 units of good 2 and is spending $100. What range of
quantities of good 1 (q1) can the consumer buy that ensures they are in their budget set (that
is, buying a set of goods that is affordable)?
ECON1003 Practice Mid-term exam Page 4 of 7
a. q1 ≤ 8
b. q1 ≤ 4
c. q1 ≤ 16
d. q1 ≤ 10
e. q1 ≤ 5

10. Solve ex+5 = 1.56
a. x = 1.34
b. x = -2.713
c. x = -4.5553
d. x = 22.22
e. x = - 1.728

11. Solve 38 + 12e-0.5t = 208
a. t = -6.4012
b. t = 4.5
c. t = 0
d. t = -5.3018
e. None of the above

12. Differentiate
2 ln( ) 1x x
y
x
+
=
a.
2
2 1
x x
−
b. ln( ) 2/ 1x x+ +
c. ln( ) 2 /x x+
d. 2ln( ) 2x +
ECON1003 Practice Mid-term exam Page 5 of 7
e. None of the above


13. Solve for x: x2 – 25 = 0
a. x = ±5
b. x = 5
c. x = 0
d. x = - 5
e. None of the above

14. Differentiate 5
3
20
xP xe −=
a. 5
3
20
xxe −
b. 5
3
(1 )
20
xe x− +
c.
3
1
20
xxe +
d.
3
( 5)
20
xxe x−
e. None of the above

15. Find Q to solve QQ 812 2 −=−
a. Q = 6
b. Q = 6 or 2
c. Q = 2.32
d. Q = -2 or 6
e. Q = 2 or 8
ECON1003 Practice Mid-term exam Page 6 of 7

16. Solve: 0.2( 5)x dx− :
a. 1.2
1
( 5)
1.2
x c− +
b. 22( 5)x c− +
c. 1.2( 5)x c−− +
d. 1.2( 5)x c− +
e. None of the above.

17. Consider a consumer with income M=100 who can consume two goods. The price of the
first good is 1 per unit and the price of the second good is 2 per unit. Suppose that the
consumer spends all of her income on good 1. Then she consumes …… units of good 1.

18. Consider a consumer with income M=100 who can consume two goods. The price of the
first good is 1 per unit and the price of the second good is 2 per unit. Suppose that the
consumer spends all of her income on good 2. Then she consumes …… units of good 2.

19. Answer True or False. The derivative of a linear function is a constant.

20. Answer True or False. Every maximization problem always has a solution.

21. Answer True or False. Consider the function () = −3 + 92 − 24 + 26 defined on
the constraint set = (−∞,∞). Then x=2 is a local minimizer.

22. Answer True or False. Consider the function () = −3 + 92 − 24 + 26 defined on
the constraint set = (−∞,∞). Then x=6 is a local maximizer.

23. Answer True or False. The indefinite integral of a linear function () = where > 0
is a constant.
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