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Mathematics

MAT223H1

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McMaster University Math 1A03/1ZA3 Fall 2013
Midterm 2 | PRACTICE
Duration: 90 minutes
Instructors: M. Bays, D. Haskell, E. Harper, C.McLean
Name:
Student ID Number:
This test paper is printed on both sides of the page. There are 20 question on 6 pages. You
are responsible for ensuring that your copy of this test is complete. Bring any discrepancies to
the attention of the invigilator.
Instructions
(1) Only the o▯cial university calculator Casio-fx-991 is allowed.
(2) All answers must be entered on the computer card with an HB pencil. Read the
marking instructions on the card. If you do not have a pencil, ask the invigilator.
(3) Write your name and ID number on the computer card.
(4) Fill in your ID number and the version number in the bubbles.
(5) Each question is worth one mark. No marks will be deducted for wrong answers or
blank answers.
(6) Any question left blank will receive 0 marks, even if the correct answer is circled on the
exam page. You must enter your answers on the computer card.
(7) Scratch paper is available for rough work; ask the invigilator.
This PRACTICE version of the midterm is intended to give you an idea of the format,
approximate length and approximate di▯culty of the actual midterm. There is no guarantee
as to the actual length and di▯culty of the actual exam. In particular, the actual midterm will
NOT be \just the same with the numbers changed".
Practice test answer key is on the last page.
page 1 of 6 Math 1A03/1ZA3 Fall 2013 Midterm 2 | PRACTICE
tan(3x)
1) Use l’Hopital’s rule to computex!0msin(4x):
4 3
A. 1 B. 3 C. 4 D. 0 E. Does not exist.
2) Given the Maple expression, h, which of the following Maple commands plots the graph of
the function on interval 2 ▯ x ▯ 6, and forces Maple to plot any discontinuities?
A. plot(h, x=2..6, discont=true); B. discontplot(h, x=2..6);
C. graph(h(x), x=2..6, discont=true); D. plot(h(x), 2..6, style=discont);
E. graph(h, x=2..6, discontinuous);
Z p
3) Find the inde▯nite integral 3x + 2dx.
2 2 2
A. (3x + 2)=2+ C B. (3x + 1)3=2+ C C. (3x + 2)▯1=2+ C
9 3 3
3 ▯1=2 3=2
D. 2(3x + 2) + C E. (3x + 2) + C
X00
4) Find the sum (▯1) .
i=0
A. 0 B. ▯100 C. 100 D. ▯1 E. 1
0 2 5 4
5) Suppose the derivative of a function f is f (x) = (x+4) (x▯3) (x▯5) : On which interval(s)
is f increasing?
A. (▯1;3) B. (3;1) C. (▯4;5) D. (▯1;▯4) [ (3;5) E. (▯1;▯4)
page 2 of 6 Math 1A03/1ZA3 Fall 2013 Midterm 2 | PRACTICE
6) The region bounded by the x-axis and the part of the graph of y = cosx between x = ▯
2
▯
and x = 2 is separated into two regions by the line x = k. If the area of the region for
▯ ▯
▯ ▯ x ▯ k is three times the area of the region for k ▯ , what is k?
2 ▯ ▯ ▯ ▯ 2
1 1 ▯ ▯ ▯
A. sin ▯1 B. sin1 C. D. E.
4 3 6 4 3
7) If f is a function such that f (x) > 0 for a < x < c, f (x) < 0 for a < x < b, and f (x) > 0
for b < x < c, which of the following could be the graph of f?
A. B.
C. D.
E.
2
8) Given that you have 108 m of materials to construct a box with a square bottom and open
top, ▯nd the largest possible volume of the box.
p 3 3 3 3 3
A. 54 2 m B. 36 m C. 64 m D. 144 m E. 108 m
page 3 of 6 Math 1A03/1ZA3 Fall 2013 Midterm 2 | PRACTICE
2
2x + 4
9) Which statement below is true about the graph o2 + 7x ▯ 4x
1
A. The line x = ▯ is a vertical asymptote.
4
B. The line x = 1 is a vertical asymptote.
1
C. The li

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