MATH 101 Practice Exam 1
Part 1 of 2
Duration: Complete Part 1 and Part 2 within 2.5 hours
Part 1 is the WeBWorK style portion of the exam.
You must scan and upload this part to Canvas.
If you are writing in-person, you’ll take this part home with you to
scan and upload to Canvas.
After exam submission is complete you’ll be given instructions to
self-grade this portion.
Rules governing UBC examinations:
1. Each candidate must be prepared to produce, upon request, a UBC card for identification.
2. No candidate shall be permitted to enter the examination room after the expiration of
one-half hour from the scheduled starting time, or to leave during the first half hour of
the examination.
3. Candidates suspected of any of the following, or similar, dishonest practices shall be
immediately dismissed from the examination and shall be liable to disciplinary action:
(a) Having at the place of writing any books, papers or memoranda, calculators, computers, sound or image players/recorders/transmitters (including telephones), or other
memory aid devices, other than those authorized by the examiners;
(b) Speaking or communicating with other candidates;
(c) Purposely exposing written papers to the view of other candidates or imaging devices.
The plea of accident or forgetfulness shall not be received.
4. Candidates must not destroy or mutilate any examination material; must hand in all
examination papers; and must not take any examination material from the examination
room without permission of the invigilator.
5. Candidates must follow any additional examination rules or directions communicated by
the instructor or invigilator.
Additional rules governing this examination:
1. This is a closed-book exam.
(a) Calculators and other calculating devices may not be used.
(b) Notes may not be used.
(c) Watches must be removed and taken off the table.
2. If an answer box is provided, you must write down your answer (but not its justification)
in the box.
√
√
3. Answers must be simplified and calculator-ready. For example, write log e 2 = 2,
√
but do not write 2 ≈ 1.414.
4. You must justify your answers unless an explicit exception is made.
5. You may use any result proven in class or on assignments.
Student number:
2
1. [5 marks] Evaluate
Z
7
|4x − 5| dx.
0
Answer:
Student number:
3
2. [5 marks] Evaluate the following definite integral using a right-endpoint Riemann sum:
Z 3
8 − 8x2 dx.
1
While you may use other methods to verify your answer, no credit will be awarded for
methods other than using a right-endpoint Riemann sum. You may use the facts below:
n
X
i=1
n(n + 1)
i=
,
2
n
X
i=1
i2 =
n(n + 1)(2n + 1)
.
6
Answer:
Student number:
4
3. [5 marks] A particle moves along a line. At t seconds the particle’s velocity is given by
v(t) = 3t2 − 2t − 8
in units of meters per second. Find the total distance traveled by the particle between
times t = 0 and t = 3. Simplify your answer.
Answer:
Student number:
5
4. [5 marks] Find the derivative of
Z
f (x) =
x2
sin3 t dt.
x
Answer:
Student number:
6
5. [5 marks] Evaluate A(x), where
Z
x2
A(x) =
t2 cos (t3 ) dt.
−x2
Answer:
Student number:
7
6. [5 marks] Evaluate
π/10
Z
cos7 (5x) sin3 (5x) dx.
0
Answer:
Student number:
8
7. [5 marks] Evaluate
Z
x2
Student number:
1
dx.
+ 7x + 6
9
8. [5 marks] Evaluate
Z
√
1
dx.
25 − x2
Answer:
Student number:
10
9. [5 marks] Using Simpson’s method, how many intervals are required to approximate
Z 3
1
dx
1 1+x
and ensure an error of at most
2
? You may use the error bound for Simpson’s below
3(55 )
where |f (4) (x)| ≤ L:
L (b − a)5
.
180 n4
Answer:
Student number:
11
10. [5 marks] √
Find the volume of the solid obtained by rotating the region bounded by the
curves y = x2 − 1, y = 0, x = 2, and x = 4 about the x-axis.
Student number:
12