1LS3 FINAL EXAM ***
INFORMATION - READ CAREFULLY
and location check the Registrar's website. Location for your exams is determined
according to your last name. Make sure that you know in
which building and in which room you write the exam. If your last name is split between two locations then you can write your exam at either location.
ON TIME to the RIGHT LOCATION. Bring your Mac ID, or if you lost
it, any picture ID ... If you do not have your ID with you, a new ID card will be issued
to you at the exam location, and you will have to pay for it.
On top of that, you night be late for your exam.
allowed: any Casio whose name starts with fx991 (such as fx991MS, fx991MS+,
fx991ES+, fx991ES+, fx991W, etc.).
Exam is 3 hours long.
you think YOU WILL MISS THE EXAM FOR ANY REASON, you must contact
the office of Associate Dean of YOUR faculty (if you are in Science,
go to BSB-133). Please do not go to your instructor, as she/he cannot
help you with this.
you FEEL SICK DURING THE EXAM,
you will have to make a decision: either to (a) stop writing,
identify yourself to the invigilator, get proper documentation
and contact the office of Associate Dean of YOUR faculty, or (b)
continue writing. In case of (a), you might be granted a deferral
(i.e. chance to write the exam at a later date); however, if you
decide to stay and complete the exam (no matter how sick you feel),
you will not be granted a deferral, and your exam will be used
to calculate your final mark.
DEFERRED exam is usually written several months later: during reading week
in February for a course that ends in December, and some time
in June for a course that ends in April. Ask student adviser in
your faculty office or the Registrar about exact dates of deferred
exams. Deferred exam is similar to the actual exam, same level of difficulty, and all announcements
below apply to deferred exam as well. Final course grades for
deferred exams are calculated in exactly the same way as for everyone
else in the course.
COVERED ON THE EXAM ... Sections
* 4.1-4.7 [optional: proofs of differentiation formulas (such as the binomial theorem, page 234; product and quotient rules in section 4.2; proof of the chain rule in 4.4; proofs for derivatives of sin x and cos x and proofs for derivatives of inverse trig in section 4.5); as well, "Derivation of key limits" subsection in Section 4.5 is optional. In Section 4.6, the subsection "Acceleration" is optional]
* 5.1, 5.3, 5.5, 5.6 [Section 5.1: material from (including) example 5.1.14 to end of section is optional; Section 5.6: the part from Ricker model on page 387 to end of section) is optional]
* 6.1-6.7 [Section 6.1: material from subsection 'Euler's Method' (page 410) to end of the section is optional; Section 6.2: Examples 6.2.14 and 6.2.15 are optional; Section 6.3: Example 6.3.3 is optional; Section 6.4: skip the subsection 'The Integral Function and the Proof of the Fundamental Theorem of Calculus' (bottom of page 461 to end of section); Section 6.6: material from subsection "Integrals and Averages" (page 493) to end of section is optional; Section 6.7: material from "Applying the Method ..." (bottom of page 504) to end of section is optional ]
(material labeled optional: it helps you understand things better, but will *not* be on the exam)
all theory, and the most relevant examples are done in lectures.
make sure you can do all exercises that that were done in lectures.
suggestion: study in backward order: start with integration
in chapter 6, then cover chapter 5, etc.
do not read solutions; instead, do questions yourself, and only
when you get stuck, look at solutions.
at tests 1-4 that you wrote this term,
make sure you can do all test questions. also, look at your tests
critically, understand things that you did not correctly, so
that you do not repeat the same mistakes.
from your coursepack: study all questions on sample tests 1-4; study sample final exam (starts on page 263), all questions except question #7.
this you feel you need extra practice in some areas, look at
the list of suggested practice problems in your
coursepack. you will not have time to do all suggested questions
in all sections, so you need to decide where you need most work;
for extra routine questions about exponential, logarithm and
trig functions, consult chapter 0 in your textbook.
to be prepared in all three areas: routine questions, applications,
has 15 pages with questions; so, it is about twice the size of
a term test - but you have three hours to do it.
covers all material that we did in the course; however, more
emphasis is placed on newer material: of total of 80 points on
the exam, questions from chapter 6 (integration) are worth 35
questions include ten multiple choice questions, 2 points each (that's 20 of 80 points) and three true/false
questions, 2 points each (6 of 80 points).
on multiple choice and true/false questions, you have to show work to get full
credit; so, do not just give an answer ... look at sample tests/sample
exams solutions in the coursepack to see how to write solutions;
even if a solution looks short (and maybe obvious) you must give
some support for your answer.
in mind that what you wrote is what is marked, and not what you
thought; make sure your answers are correct and complete.
common mistakes: simplifying, common denominator,solving equations, algebra (you
have to know rules for e's and ln's, canceling fractions, etc.),
i.e. all those things that are directly related to lack of practice;
do lots of routine questions; among other benefits, this will help you memorize
facts/formulas that you need
for disturbances and stress during the exam; because of circumstances (stress,
large room, lots of people, disturbances, etc.), when you first
look at the exam, it might appear difficult; spend 1-2 minutes
reading the questions first, identify what you can do right away,
and start working on these questions
or pen? - does not matter
key is practice - most questions that you will see are technical; there will be an integration by substitution question, integration by parts, computing critical points and absolute extreme values, area between curves, calculating taylor polynomial, finding equilibrium points and stability (none of these should take you more than 5 minutes to do)
find a domain of a function? can you recognize the range
of a function from its graph? do you know domains and graphs of 1/x, 1/x^2, sin (x), cos(x), tan(x), arcsin(x), arctan(x), ln(x), e^x,
a^x, |x| ? can you draw graphs related to those graphs by shifting
compute inverse function? composition of two functions? work with proportional and inversely proportional quantities?
articulate the difference between a linear and a non-linear function?
is an updating function?
do you know how to cobweb to find solutions for a given dynamical
system and to check for stability? what
is an equilibrium point? how do we find equilibrium points? do you know the derivative test for stability?
graphs [i.e., graphs that involve sin(x) and cos(x)], can you
identify minimum, maximum, average, amplitude and shift?
know how to solve equations that involve exponential and logarithm
functions? do you know laws of logarithms and exponents?
know and understand what half-life and doubling time are?
is average rate of change? what is instantaneous
rate of change?
functions are continuous? do you know definition of
practice chain, quotient, product rules? go through your class
notes and make sure that you know all derivative formulas?
can you calculate
the derivative from its definition? if the graph of f(x) is given, can you sketch f'(x)? the other way around - if you know f'(x), can you sketch f(x)?
know how to calculate linear and quadratic approximations? taylor polynomial?
know how to find critical points
of a function and test for local
? what does Extreme Value Theorem
say, can you state it? How do we find
absolute extreme values
know how to compare functions that go to infinity as x goes to
infinity? which is slowest, which is fastest? Do you know how
to compare functions that go to zero as x goes to infinity?
how do we define leading behaviour? do you know how to identify the leading behaviour as x approaches zero and as x approaches infinity?
practice L'Hopital's rule? how do we calculate horizontal and vertical asymptotes?
is a differential equation? Initial value problem? do you
know all antiderivative formulas that are mentioned in section 6.2? can you
do antiderivatives by substitution? integration by parts? did you check the table on page 483?
how do we approximate integrals using Taylor polynomials? how do we calculate improper integrals? which improper integrals of the form 1/x^p are convergent?
do you know what signed area means? what is the relation between the definite integral and area? can you
set up integration formulas for the area between curves? calculate left and