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Mathematics

MATA32H3

Raymond Grinnell

Fall

Description

*** Sorry...No solutions will be posted***
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
FINAL EXAMINATION
MATA32 - Calculus for Management I
Examiners: R. Grinnell Date: April 27, 2011
Time: 2:00 pm
Duration: 3 hours
Provide the following information:
Lastname (PRINT):
Given Name(s) (PRINT):
Student Number :
Signature:
Read these instructions:
1. This examination has 13 numbered pages. It is your responsibility to ensure that at the
beginning of the exam, all of these pages are included.
2. If you need extra answer space, use the back of a page or page 13. Clearly indicate the location
of your continuing work. You may write in pencil, pen, or other ink.
3. You may use one standard hand-held calculator (graphing capability is permitted). All other
electronic devices (e.g. cell phone, smart phone, i-pod), extra paper, notes, textbooks, and
backpacks are forbidden at your workspace.
4. If you have brought a cell/smart phone into the GYM, it must be turned o▯ and left at the
front of the GYM.
Print letters for the Multiple Choice Questions in these boxes:
1 2 3 4 5 6 7 8 9 10
Do not write anything in the boxes below.
A 1 2 3 4 5 6 7 8 TOTAL
40 16 16 13 12 15 12 18 8 150
1 The following may be helpful:
▯ n ▯ ▯ ▯n▯
S = P(1 + r) n S = Pe rt S = R (1 + r) ▯ 1 A = R 1 ▯ (1 + r)
r r
▯ n+1 ▯ ▯ ▯n+1 ▯
S = R (1 + r) ▯ 1 ▯ R A = R + R 1 ▯ (1 + r)
r r
▯ p/q
Proﬁt = Revenue - Cost NPV =( PV )▯Initial ▯ =
dp/dq
Part A - Multiple Choice Questions For each of the following, clearly print the
letter of the answer you think is most correct in the boxes on page 1. Each right answer
earns 4 points and no answer/wrong answers earn 0 points. No justiﬁcation is required.
3 2
1. The function g(x)= ▯2x ▯ x has
(A) a relative maximum at 0 (B) a relative minimum at 0
(C) an absolute maximum at 0 (D) an absolute minimum at 0
(E) both A and C (F) both (B) and D (G) no extrema at 0
2. The area of the region lying between the curve y = x +4 x and the lines x =0 ,y = ▯1,
and x = 2 equals
(A) 6 (B) 26/3 (C)3 )2/3( /3 (E) 14 (F) a number not in (A) - (E)
2 2 2
3. Assume y is deﬁned implicitly as a function of x by the equation xy +4x y =4 x+8. Then
y evaluated at x =1and y =2is
(A) ▯2 (B) 2 (C) 0 (D) ▯8/5 (E) a number not in (A) - (D)
x +5 x +2
4. Assume the average revenue obtained by selling x units is a(x)= . Then the
x +3
marginal revenue from selling 7 units is
(A) 1.04 (B) 2.19 (C) 35.48 (D) 15.88 (E) a number not in (A) - (D)
▯ ▯
5. If y =3 x and y(1) = 5, then y(4) equals
(A) 13 (B) 16 (C) 18 (D) 19 (E) 20 (F) a number not in (A) - (E)
6. The maximum amount of compound interest (expressed as a percentage to one decimal) that
can be earned on a deposit of $D over 25 years at 3% APR is
(A) 104.3 (B) 108.6 (C) 109 (D) 111.7 (E) a number not in (A) - (D)
(F) uncertain because we are not given enough information.
3 7. If p = ▯4q + 96 is a demand function (p is price, q is quantity) where 0

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