DEPARTMENT OF MATHEMATICS AND STATISTICS
Math 1030, F15
Midterm
1. This is a 50 minute test. Do NOT start until instructed.
2. Please fill out your personal details on the cover of the Examination Booklet(s). If you
use more than one booklet, please indicate how many you use, e.g. “1 of 3”, “2 of 3”,
“3 of 3” on each booklet.
3. You may quote results from lecture notes without proof, unless asked to do otherwise.
But notes or books are not permitted during the exam.
4. Give sufficient working as solutions with no justification will receive little or no credit.
5. You may use a scientific calculator and/or a ‘graphing calculator’. Note however that
graphical answers require justification. No other electronic equipment is permitted. Turn
off or ‘mute’ your cell phone!
6. If you copy the work of your neighbour this is considered Academic Misconduct and
will be reported to the appropriate university authority.
7. There are a total of 34 points to be awarded on this test.
1. (9 points)
(a) Sketch the region in the plane corresponding to the set:
{(x, y) | |y| ≥ 2}.
Use the convention that if the boundary of a region is included in the region it is
indicated using a solid line, otherwise use a dashed/dotted line.
(b) Calculate the midpoint of the line segment joining A = (−3, 1) and B = (3, 3).
(c) Use the method of substitution to solve the system of equations below:
(
x2 + y 2 = 25
3y − x = 9.
2. (8 points)
(a) Algebraically√determine the range and domain of the functions:
x−1
(i) f (x) = 2 − x, (ii) f (x) = 3x+2
.
(b) If a function is periodic with period 3, and on [0, 3) it has the form y = 6x, then sketch
the graph of the periodic function on [0, 9).
Please Turn Over
3. (8 points)
(a) Let f (x) =
domain.
√
√
5 − x. Find the function (f + g)(x) and its
x − 2 and g(x) =
(b) Given the function f (x) =
2−x3
,
5
find the inverse function f −1 .
(c) Consider the graphs of the sin and cosine functions below:
Using the rules of transformations describe in words how we obtain the graph of sin(x)
from the graph of cos(x)? Fill in the box below (copied into your answer booklet):
cos(
) = sin(x).
4. (9 marks)
(a) Producing x units of tacos costs C(x) = 5x + 20 dollars. The revenue earned is given
by R(x) = 15x dollars.
(i) What is the break-even quantity?
(ii) What is the profit from 100 units?
(iii) How many units will produce a profit of $500?
(b) Solve the equation
x
1
9
− 3 = 24
for x without the use of logarithms.
(c) Solve
2 log5 (3x) = 4
for x.
END OF TEST