Econ300 First Midterm Exam Fall 2014 version A This exam consists of 25 multiple choice questions. The maximum duration of the exam is 50 minutes. 1. In the spaces provided on the scantron, write your last name, then your first name, and also be sure to include university identification number. 2. Also fill in the bubbles below your name and id number. 3. Write your name here: ______________________________________ 4. In the “special codes” section of the scantron under “K” write the letter A 5. DO NOT OPEN this exam booklet until you are told to do so and STOP writing when you are told that the exam is over. Failure to comply will result in a 10% loss in the grade. 6. You MUST return this exam booklet with the scantron; otherwise no credit will be awarded. 7. Only the answers you provide on the scantron will be counted towards your grade. But you may also want to record your answers on this booklet, since it will be returned to you next week. 8. Please make sure you use dark pencil marks to indicate your answer; the scantron reader may not give you credit for an answer if it can’t detect it. 10. Choose the single best possible answer for each question. You are responsible for upholding the University of Maryland Honor Code while taking this exam.

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1. Which one is NOT a function on the domain (1,∞)?

A. 𝑦 = −2𝑥

B. 𝑦 = 𝑥𝑒𝑥−1 + 2𝑥 C. 𝑦 = 𝑙𝑛 1

𝑥−5

D. 𝑦 = 1𝑥+2

E. None of the above

2. The function 𝑦 = −2𝑥 + 5 is A. Concave B. Convex C. Linear D. All of the above E. None of the above

3. The roots of the equation 𝑓(𝑥) = 𝑥2 − 3𝑥 are

A. {0, 3} B. {0, 1

3}

C. { −3,0} D. {−3, 0, 3} E. None of the above

4. Consider the function𝑦 = 𝐿0.4𝐾0.6 where y is output, K is capital and L is labor. A formula

for the isoquant is

A. 𝐿 = 𝑦5/2/𝐾3/2 B. 𝐿 = 2.5𝑦/𝐾 C. 𝐾 = 𝑦4/𝐿3 D. 𝐾 = 0.6𝑦5/𝐿 E. None of the above

5. The difference quotient of 𝑦 = 𝑥4 + 5 is

A. 4𝑥3 + 5 B. (2𝑥 + ∆𝑥)2 + 5 C. 4𝑥3 + 3𝑥2∆𝑥 + 3𝑥(∆𝑥)2 + 5 D. 4𝑥3 + 6𝑥2∆𝑥 + 4𝑥(∆𝑥)2 + (∆𝑥)3 + 5 E. None of the above

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6. Which function is continuous on the domain [1,∞)?

A. 𝑦 = 𝑥−5 + 2𝑥 B. 𝑦 = 𝑒2𝑥ln (3 + 𝑥) C. If 𝑥 > 3, 𝑦 = 2𝑥2; if 𝑥 ≤ 3, 𝑦 = 3𝑥 + 9 D. All of the above E. None of the above

7. The function f is convex if and only if

A. f is at or above all secant lines B. the average rate of change is decreasing C. for all a, b in domain and α in [0,1], ( (1 ) ) ( ) (1 ) ( )f a b f a f bα α α α+ − ≤ + − D. All of the above E. None of the above

8. You invest $15 at 20% interest with continuous compounding. What is it worth after 4 years?

A. $30.64 B. $31.10 C. $31.79 D. $33.38 E. None of the above

9. What is the present value of $200 in 5 years with 15% annual interest compounded yearly?

A. $94.47 B. $96.72 C. $99.44 D. $103.28 E. None of the above

10. For 0 < 𝑎 < 𝑏 < 1 and 0 < 𝑥 < 1, what can you say about log ( )a x and log ( )b x ?

A. Both functions are convex B. log ( ) log ( )a bx x> C. The slope of log ( )a x is steeper than the slope of log ( )b x at point 𝑥 D. All of the above E. None of the above

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11. Your mutual fund increased in value from $10 to $40 over the last 7 years. What was the average annual return with continuous compounding for the mutual fund over the 7-year period?

A. 12.39% B. 15.92% C. 19.80% D. 23.17% E. None of the above

12. Simplify ln � 𝑒2

1+2𝑥2�

A. 1 − 4 ln 𝑥 B. 2 − 2𝑥ln (1 + 2𝑥2) C. 2 − 4𝑥

1+2𝑥2

D. 1 + 𝑥2 E. None of the above

13. How many years does it take for $20 to grow to $50 with 3% interest and annually

compounding?

A. 34.12 B. 32.65 C. 31.00 D. 30.54 E. None of the above

14. Consider the following system. Supply: 𝑄 = 2𝑃 – 1; Demand: 𝑄 = 4 – 3𝑃. The

equilibrium quantity and price are

A. (1, $1) B. (2, $3) C. (3, $1) D. (1, $2) E. None of the above

15. Suppose the function 𝑓 has an inverse function 𝑓−1. Then

A. 𝑓 must be strictly increasing B. 𝑓−1must be strictly decreasing C. (𝑓−1) −1 must be strictly monotonic D. All of the above E. None of the above

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16. Suppose 𝑓(𝑥) = 3𝑥 − 2𝑥2. Then A. f is decreasing B. f is decreasing on the domain [0,1] C. f is increasing when 𝑥 < 0 D. f is increasing when 𝑥 > 1 E. None of the above

17. The difference quotient of 𝑦 = 𝑥2 − 𝑥 is

A. 2𝑥 − 1 B. 2𝑥 + ∆𝑥 − 1 C. 𝑥2 − ∆𝑥 D. 4𝑥 − 2 − 2∆𝑥 E. None of the above

18. If the difference quotient of 𝑦 is 2 − 3𝑥4 + 3𝑥∆𝑥 + (∆𝑥)2, then 𝑑𝑦

𝑑𝑥 is

A. −12𝑥3 B. 2−3𝑥

4+3𝑥∆𝑥+(∆𝑥)2

∆𝑥

C. 2 − 3𝑥4 D. 6𝑥 E. None of the above

19. Total revenue = 𝑃⋅𝑄, where 𝑃 = 5 – 𝑄2. The average rate of change of total revenue is

A. 5 2Q Q− −∆ B. 5 2Q P− − C. 5 − 2𝑄 − 2∆𝑄 D. 5 2Q− E. None of the above

20. The derivative of 𝑓(𝑥) is

A. The average rate of change as x∆ approaches to 0

B. 0

( ) ( )limx

f x x f xx∆ →

+ ∆ −∆

C. The slope of the tangent line at 𝑥 D. All of the above E. None of the above

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21. Revenue is 𝑅(𝑥) = 4𝑥 − 2𝑥2. Marginal revenue is

A. −2𝑥 B. 4∆𝑥 − 2(∆𝑥)2 C. −2 D. 4 − 4𝑥 E. None of the above

22. Let 𝑦 = 𝑥(2𝑥2 + 1). The derivative of y is

A. 2𝑥 B. 1 + 3𝑥 C. 6𝑥2 + 1 D. 𝑥2 + 𝑥 E. None of the above

23. Let 𝑦 = 𝑒2𝑥. The differential of y is

A. (2𝑥)𝑒2𝑥𝑑𝑥 B. 2𝑒2𝑥𝑑𝑥 C. 𝑒2𝑥 + ∆𝑥 D. 2𝑒2𝑥 + ∆𝑥 E. None of the above

24. Suppose a financial index grows at a continuously compounding rate of 5% for one year.

What is the effective rate?

A. Exactly 5% B. Less than 5% C. More than 5% D. All of the above E. None of the above

25. Let 𝑦 = 2𝑥2 − 3𝑥, 𝑥0 = 2 and ∆𝑥 = 3, then the approximated change in 𝑦 using differential is

A. 35 B. 2 C. 33 D. 15 E. None of the above

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