FINAL EXAMS - IMPORTANT

Log into your MUGSI account, and access exam information. Read about the conduct in the examination room to learn what's allowed and what's not allowed during the exam.

Few more things about your exam

Note: dates for exams are set by the University, and cannot be changed. If for some reason you think you will not be able to write the final exam on the scheduled day/time, you must talk to a student adviser in your faculty office. Final exams are organized by the University, and not by your instructor - so your instructor cannot help you with this, you need to go to your faculty office.

 

*** MATH 1LS3 FINAL EXAM ***

IMPORTANT INFORMATION - READ CAREFULLY

Come ON TIME to the RIGHT LOCATION. Bring your Mac ID, or if you lost it, any government-issued 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 might be late for your exam.

Calculators allowed: McMaster standard calculator only, i.e., Casio fx991MS PLUS.

Exam is 3 hours long.

If 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.

If 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.

Please keep in mind that your final course grade is based on your best three tests and the exam only. We do not offer any kind of extra work with the purpose of improving marks.

MATERIAL COVERED ON THE EXAM ... Sections

* 0.1-0.3

* 1.1-1.3

* 2.1-2.3

* 3.1-3.5

* 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; subsection in Section 4.5 is optional. In Section 4.6, the subsection "Acceleration" is optional]

* 5.1, 5.3 [Section 5.1: material from (including) example 5.1.14 to end of section is optional; Section 5.3: L'Hopital's rule only (skip leading behaviour)]

* 6.1-6.5 [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). ]

(material labeled optional: it helps you understand things better, but will *not* be on the exam)

 

TO PREPARE

  • study class notes; 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.
  • re-do homework assignments; do not read solutions; instead, do questions yourself, and only when you get stuck, look at solutions (assignment 16: study #4 only, as we did not do leading behaviour).
  • look at tests 1-3 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 1-3; test 4: study all questions except #2b, #2c, and #7; study sample final exam (starts on page 289), all questions except questions #1a and #2b.
  • if after 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.
  • you have to be prepared in all three areas: routine questions, applications, and theory.

 

ADDITIONAL INFORMATION

  • exam has 15 pages with questions; so, it is about twice the size of a term test - but you have three hours to do it.
  • exam 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 32 points.
  • exam 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).
  • except 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.
  • keep in mind that what you wrote is what is marked, and not what you thought; make sure your answers are correct and complete.
  • most 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; as well, mixing up derivative and antiderivative formulas; do lots of routine questions; among other benefits, this will help you memorize facts/formulas that you need
  • be prepared 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
  • pencil 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)

 

CHECKLIST

  • can you 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 and scaling?
  • can you compute inverse function? composition of two functions? work with proportional and inversely proportional quantities?
  • can you articulate the difference between a linear and a non-linear function?
  • what 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?
  • for sinusoidal graphs [i.e., graphs that involve sin(x) and cos(x)], can you identify minimum, maximum, average, amplitude and shift?
  • do you know how to solve equations that involve exponential and logarithm functions? do you know laws of logarithms and exponents?
  • do you know and understand what half-life and doubling time are?
  • what is average rate of change? what is instantaneous rate of change?
  • which functions are continuous? do you know definition of continuity?
  • did you 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)?
  • do you know how to calculate linear and quadratic approximations? taylor polynomial?
  • do you know how to find critical points of a function and test for local minima/maxima? what does Extreme Value Theorem say, can you state it? How do we find absolute extreme values?
  • do you 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?
  • did you practice L'Hopital's rule? how do we calculate horizontal and vertical asymptotes?
  • what is a differential equation? Initial value problem? do you know all antiderivative formulas that are mentioned in section 6.2? can you compute steps in Euler's method? 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?
  • what is the relation between the definite integral and area? can you set up integration formulas for the area between curves? calculate left and right sums?