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

* 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 [Section 6.1: example 6.1.18 is optional; Section 6.4: L'Hopital's rule only (skip leading behaviour)]

* 7.1 - 7.5 [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)]

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

ADDITIONAL INFORMATION

(1) The exam covers all material that we did in the course. Mark breakdown (out of a total of 40 marks, 2 marks per question): approximately 14 marks on chapter 7 content (DEs, integration), 18 marks on topics in chapters 4, 5, and 6 (limits, derivatives, applications of derivatives), and 8 marks on content in chapters 1 and 2 (functions, models, etc.)

(2) We did not cover: area between two curves, volumes of solids of revolution, improper integrals, discrete-time dynamical systems... please disregard assignment, test, exam questions referencing these concepts.

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 integration, then cover applications of derivatives, etc.
• from your coursepack: study relevant questions on sample tests; study sample final exam
• 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. blank copies can be found here: test 1 | test 2 | test 3 |

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 shifting?
• 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?
• what is the relation between the definite integral and area? can you calculate left and right sums?