*** MATH 1LS3 FINAL EXAM ***

IMPORTANT INFORMATION - PLEASE READ CAREFULLY

* Come ON TIME to the RIGHT LOCATION (campus map). Bring your Mac ID, or if you lost it, any government-issued picture ID.

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

* Exam is 2.5 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-129). Please do not go to your instructor, as your instructor 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.

* The DEFERRED exam is usually written several months later. Ask a student adviser in your faculty office or the Registrar about exact dates of deferred exams. The deferred exam is similar to the actual exam, same level of difficulty, and all announcements below apply to a deferred exam as well. Final course grades for deferred exams are calculated in exactly the same way as for everyone else in the course.

Exam Date:

Thursday, June 20th, 2019

Time:

7:00pm - 9:30pm

Location:

MATERIAL COVERED ON THE EXAM ... Sections
[if you have the first (elephants) edition of the textbook, go here]

* 1.2 - 1.4

* 2.1 - 2.3

* 3.1 - 3.3

* 4.1 - 4.5

* 5.1 - 5.7 [optional: proofs of differentiation formulas (such as the binomial theorem, page 262; product and quotient rules in section 5.2; proof of the chain rule in 5.3; proofs for derivatives of sin x and cos x and proofs for derivatives of inverse trig in section 5.4); as well, "Derivation of key limits" subsection in Section 5.4 is optional. In Section 5.6, the subsection "Acceleration" is optional]

* 6.1, 6.4, 6.7, 6.8 [Section 6.1: example 6.1.18 is optional; Section 6.4: L'Hopital's rule only (skip leading behaviour); Section 6.8: the part from Ricker model on page 446 to end of section) is optional]

* 7.1 - 7.7 [Section 7.2: Examples 7.2.13 and 7.2.14 are optional; Section 7.3: Example 7.3.3 is optional; Section 7.4: skip the subsection 'The Integral Function and the Proof of the Fundamental Theorem of Calculus' (bottom of page 519 to end of section); Section 7.6: subsection "Integrals and Lengths" (page 560) is optional; Section 7.7: skip the subsections" Applying the Method of Leading Behaviour to Improper Integrals" (pages 577-578), "Comparison Test" (pages 578-579) and "Applying the Method of Leading Behaviour to Improper Integrals" (pages 581-583) ]

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

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TO PREPARE

• study class notes; all theory, and the most relevant examples are done in lectures. make sure you can do all exercises that were done in lectures independently, i.e., without referring to your notes.
• suggestion: study in backward order: start with dynamical systems and integration, then cover applications of derivatives, etc.
• from your coursepack: study all questions on sample tests 1-4 (2017); study sample final exam 2016 (starts on page 327).
• look at tests 1 and 2 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. blank copies can be found here: test 1 blank | test 2 blank |
• re-do homework assignments from your coursepack; do not read solutions; instead, do questions yourself, and only when you get stuck, look at solutions. make sure to study the multiple choice and true/false assignments. Assignment 17 (#2 and 3 only); Assignment 30 - skip.
• if after this you feel you need extra practice in some areas, look at the list of suggested practice problems (SCHEDULE AND HOMEWORK link). 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.
• Attend the Math 1LS3 Exam Review session. Details are posted below:

ADDITIONAL INFORMATION

• exam has 14 pages with questions, so it's twice the size of a test - but you have 2.5 hours to do it.
• exam covers all material that we did in the course; however, more emphasis is placed on newer material.
• exam questions: sixteen multiple choice questions at 2 points each (that's 32 of 65 points), three true/false questions at 2 points each (6 of 65 points) and five questions which require that you show work (and can earn part marks) worth 27/65.
• 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 exam solutions posted online 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/problems: 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 and formulas that you need
• be prepared for disturbances and stress during the exam; 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: among other things, you will have to evaluate limits, compute derivatives of complicated functions, find equilibria of a DTDS, evaluate integrals using substitution and by parts (as well as more basic techniques), evaluate improper integrals, etc.

CHECKLIST OF MATH CONCEPTS FOR THE EXAM

• can you find the 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 scaling, reflecting, and translating?
• can you: compute an inverse function? find the composition of two functions? work with proportional and inversely proportional quantities?
• 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? did you practice semilog and log-log graphs?
• do you know and understand what half-life and doubling time are?
• what is average rate of change? what is instantaneous rate of change?
• did you review computing limits? which functions are continuous? do you know the definition of continuity?
• did you practice chain, quotient, product rules? did you 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)? and 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?What does Euler's method do, and how do we use it? What is (and how do we solve) and initial value problem? do you know all antiderivative formulas that are mentioned in section 6.2 (elephants) 7.2 (geese)?
• can you do antiderivatives by substitution? integration by parts? did you check the table on page 483 (elephants) 543 (geese)?
• how do we approximate integrals using Taylor polynomials?
• how do we calculate improper integrals? which improper integrals from 1 to infinity of the form 1/x^p are convergent? which improper integrals from 0 to 1 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?
• can you compute the average value of a function and the volume of a solid of revolution?
• what is an updating function? can you translate a word problem into a dynamical system? 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?