Final examination
The MATH 101 final examination will take place on Monday, April
23, from 3:30–6:00 PM. Make sure
that any travel plans you might make don't conflict with sitting the
exam at this time. The final exam will cover the
entire
syllabus for the course. However, in order to ensure an equal
course weighting to all the topics since the beginning of the course
(and the topics covered by the midterm), 62% of the marks on the final
exam relate to material covered since our midterm (starting with
improper integrals). The exam will have a similar format to the
final exams in the past three years, in that there is a mix of
multiple-choice, short-answer, and then long-answer questions, for a
total of 75 points.
The location of your final exam depends on your section:
UBC has
very
detailed policies about what constitutes a conflict with a final
examination and what constitutes an exam hardship that requires
rescheduling. If you have difficulties, disabilities, religious
conflict, or three exams in a 24-hour period, check that web page to
find out how to request an accommodation.
Preparing for the final exam
You should bring your UBC student ID to the final, as well as
something to write with. (Pens are preferred, but pencils are allowed
as long as they write darkly enough to be easily read. Ren pens are
not allowed.) The final is completely closed book: you cannot
bring any books or notes of any kind with you. Also, you cannot use
calculators on the final. You will not be allowed to have
phones, pencil cases, digital watches, or other electronic devices out
while taking the final, nor will you be allowed to use headphones or
earbuds; you will not be allowed to wear a baseball cap or any other
hat with a brim.
The
Math
Exam/Education Resources wiki has final exams from the past
several years. The makers of this resource (graduate students in
mathematics) have tagged the problems according to topic, and they
have included hints and solutions as well. Please make use of this
website as it is a really good resource. You can find old final exams
on the Mathematics department web page as well. It will also help you
to review the list of MATH 101 learning outcomes. We also strongly
suggest that you go through many of the CLP Problem Book Stage II type
problems, and review the webwork problems. You can find old final
exams on the
Mathematics
department web page as well. It will also help you to review the
list of
MATH
101 learning outcomes (this is the version from 2013 which has not
changed much at all, except that you no longer need to be familiar
with applications of differential equations such as mixing of salt
solutions, population dynamics, etc.). In addition, please go through
some of the midterm versions A--F with detailed solutions that are on the
midterm page.
Here is a brief summary of some key topics .
- Since there is no formula sheet allowed; You should remember basic
trig identities: cos^2(x)+sin^2(x)=1;
1+tan^2(x) = sec^2(x); cos^2(x)=(1/2)[1+cos(2x)] and a similar
one for sin^2(x), as well as sin(2x)=2sin(x)cos(x).
- converting riemann sums to integrals....
- FTC I combined with the chain or product rule....
- calculating areas between two curves through integration
in x or y as appropriate depending on the shape of the region
- calculating volumes of revolution about the x-axis,
y-axis or some other vertical or horizontal axis. (need to remember
the formula for volumes of revolution).
- calculating volumes by integrating over the cross-sectional area, i.e
V=int_{a}^{b} A(x) dx
- Being able to EASILY recognize how to integrate standard integrals
using either the subsitution rule, integration by parts,
sin^a cos^b integrals, simple tan^a sec^b integrals, inverse
trig substitutions, and partial fraction decompositions.
- Numerical quadrature: the midpoint rule, simpson's rule and the
trapezoid rule. Use of the error estimate for determining the accuracy
of the approximation ( we will provide the formula for the error
estimate if you need it).
- Improper integrals; determining whether improper integrals converge
or diverge using a comparison test with a p-type integral;
calculating the value of convergent improper
integrals using a proper limiting process.
- Calculating the average of a function over an interval. Calculate the
moments and centroid of a region (you need to remember the key formulas
such as finding the centroid of a region bounded by two curves).
- The calculation of work for various applications like in the webwork
(lifting a heavy chain over a building, work required to pump water out
of a container, etc). You need to remember how to set up the required
integrals to compute the work needed to oppose gravity.
- Solving separable first order differential equations.
- Basic properties of sequences, including taking limits of sequences.
- Using and evaluating the two special types of series: geometric series
and telescoping series.
- Being able to apply our 6 key tests for convergence or divergence of
various series and being able to competently recognize which method is
appropriate for a given series. Recall that the
key tests are: basic divergence test (if a_n does not tend to zero as
n to infinity, then the series diverges), the integral test, the
comparison test, the limit comparison test, the alternating series
test, and the ratio test. You should know the statements of all of these
results, and in working out specific problems you need to carefully
CHECK THE HYPOTHESES in the statements of the theorems.
- Need to know the distinction between absolute versus conditional
convergence.
- Calculation of the radius of convergence (by ratio test) and the
interval of convergence (checking the endpoints) of a given power
series.
- Differentiating and integrating power series within their domains
of convergence to get new power series, and for geometric series being
able to sum the series; i.e. calculate $\sum_{n=1}^{\infty} n x^n $.
- Estimating the error in taking N terms in an alternating series.
- The definition of Taylor and Maclaurin series.
- We suggest remembering 4 key Maclaurin series (for sin(x), cos(x),
e^x, and 1/(1-x)), and the leading-order approximation
(1+x)^p approx 1+ px + .... for small x. You can derive all sorts of
other series by integrating, differentiating, substituting, etc... from
these basic ones within their domains of convergence.
- Use of Taylor series to calculate complicated limits (without L'Hopital),
to calculate high derivatives (i.e. f^{(12)(0) of f(x)=cos(x^2)), and to
estimate integrands to see if improper integrals converge or not.
Pre-Exam Office Hours
Your instructors may not hold their regular office hours during the
exam period. We recommend you go to the website for your specific
section and check there for exam-period office hours. Also see the
MLC website for their
exam-period times and two pre-exam problem solving sessions.
Special circumstances
From the Faculty of Science web site: "Students who miss a final exam due to illness or extreme personal distress and would like to apply for a deferred exam (a.k.a. SD) must report to the Science Information Centre within 48 hours of the missed exam...." Your performance in a course up to the exam is taken into consideration in granting a deferred exam status (for example, failing badly generally means you won't be granted a deferred exam). In Mathematics, generally students sit the next available exam for the course they are taking, which could be several months after the original exam was scheduled.
A student who wishes to view their final exam for pedagogic
purposes may initiate this process by filling out the appropriate
Mathematics department form. Note that this viewing of a final
exam cannot change the grade of a final exam (except in the case
of an obvious addition or recording error). Requesting a regrade of a
final exam would be done at the university level by initiating a
review
of assigned standing procedure.