# A32_exam_fall_2009.pdf

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University of Toronto Scarborough

Mathematics

MATA32H3

Raymond Grinnell

Fall

Description

*** Sorry...solutions will not be posted***
University of Toronto at Scarborough
Department of Computer and Mathematical Sciences
FINAL EXAMINATION
MATA32 - Calculus for Management I
Examiners: R. Grinnell Date: December 9, 2009
G. Pete Time: 9:00 am
B. Szegedy Duration: 3 hours
Provide the following information:
Surname (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 space for any question, use the back of a page or the blank page at the end
of the exam. 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. All other electronic devices, extra paper,
notes, and textbooks are forbidden at your workspace.
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 15 15 12 12 13 17 10 150
1 The following may be helpful:
" n # " ¡n#
n rt (1 + r) ¡ 1 1 ¡ (1 + r)
S = P(1 + r) S = Pe S = R r A = R r
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 the ﬂrst page. Each right
answer earns 4 points and no answer/wrong answers earn 0 points. No justiﬂcation is required.
1. If y is deﬂned implicitly as a function of x by the equation xe + y = 2 then y evaluated at
x = 2 and y = 0 is equal to
(a) 0 (b) ¡1 (c) ¡1=3 (d) 1=3 (e) none of (a) - (d)
0 5
2. If y = p and y(9) = 32 then y(4) is equal to
x
(a) ¡94=3 (b) 59=2 (c) 27 (d) 22 (e) none of (a) - (d)
3. The area of the region bounded by the curve y = 3x ¡ 3 , the y¡axis, x¡axis, and the line
x = 2 is equal to
(a) 9 (b) 13=3 (c) 2 (d) 6 (e) none of (a) - (d)
2 4. To what approximate amount will $1;200 accumulate in 20 years if it is invested at an
eﬁective rate of 2:4% per year ?
(a) We cannot ﬂnd the amount because the number of interest periods per year is not given.
(b) $1;938:36 (c) $1;928:33 (d) $1;517:35 (e) none of (a) - (d)
x + 5
5. The equation of the tangent line to the curve y = x2 at the point where x = 1 is
(a) y = ¡9x + 15 (b) y = 13x ¡ 7 (c) y = ¡12x + 18 (d) y = ¡11x + 17
Z 3
e ln(x)
6. The exact value of dx is
e x
(a) 4 (b) 8 (c) ¡4=9 (d) 1 (e) none of (a) - (d)
7. If p = ¡3q + 60 is a demand function where 0 < q < 20 then we have unit elasticity at
(a) no value of q (b) q = 20 (c) q = 15 (d) q = 10
(e) a value of q not given in (a) - (d)
3 8. If g(x) = xe kx where k < 0 is a constant, then we may conclude that g has
(a) a relative maximum at x = ¡1=k (b) a relative minimum at x = ¡1=k
(c) a relative maximum at x = 1=k (d) a relative minimum at x = 1=k
(e) none of (a) - (d)
Z p
9. If h(x) dx = 4x + 1 + 32 then h (x) equals
(a) 2(4x + 1)¡1=2 (b) 4(4x + 1) ¡3=2 (c) ¡2(4x + 1) ¡3=2 (d) ¡4(4x + 1) ¡3=2
10. Exactly how many of the following four mathematical statements are always true:
(i) If a function is diﬁerentiable at a then it is also continuous at a.
00
(ii) If f (c) = 0 then f has a point of in°ection at x = c.
(iii) The deﬂnite integral of a function gives the area under the graph of the function.
Z b Z
(iv) g(x) dx = G(b) ¡ G(a) whenever g is continuous and g(x) dx = G(x).
a
(a) 4 (b) 3 (c) 2 (d) 1 (e) 0
(Be sure you have printed the letters for your answers in the boxes on the ﬂrst page)
4 Part B: Full-Solution Questions Write clear, full solutions in the spaces provided.
Full points will be awarded only if your solutions are correct, complete, and su–ciently display
appropriate concepts from MATA32.
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