Follow:
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Here are some tips as you prepare for the Final Exam
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- Here are some definites that will be on the final this term according to one or two of the profs:
- There will be a Squeeze Theorem Limit question. Study my Lesson 2, pages 63-67 and learn my #17(a) and
(b).
- There will be a sinh/h limit question. Study my Lesson 2, pages 60-62 and learn my #16(a), (b) and (c).
- There will be a limit that requires you to factor a sum or difference of cubes. Study my Lesson 1, page 9 and learn my Lesson 2 Practise Problems #23 and 24.
- The max/min word problem will be
the cutting squares out of the four corners to make flaps to fold up to make a box question. Study my Lesson 10, #5 and Practise Problem #9 to prepare.
- Do the derivatives first! They usually are the first question on the exam, but, if not, go straight to them and get them down. Make sure you have thoroughly studied all the practice problems from Lesson 8 of my book (OMIT the part on inverse functions and
derivative of an inverse; that's gone from the course).
- Three things you should be reciting to yourself as you walk into the exam. Go straight to the derivatives and find the goofy constants, the a^u (taught in Lesson 8), and the var^var (also
taught in Lesson 8). Don't miss these things! Most students do!
- Then do the antiderivatives and integrals section of the exam. If you have practised Lesson 11 in my book, these should not be a problem. Be ready for an area word problem (like Lesson 11, #6-8) and be ready for the Fundamental Theorem of Calculus derivative problem (Lesson 11, #10).
- There will be NO proofs on the
final exam. Do not waste your time memorizing the "required proofs" summarized on pages 3 and 4. However, do read and learn the examples I write in the part (b) of some of those proofs. For example, last year's midterm exam did not make you do Proof number 1 on page 3, but it did quiz you on the concept I discuss in part (b) of that proof. In other words, be ready with an example showing that, although if f' is positive that means f is increasing, it is
not necessarily true that, if f is increasing, that f' is positive. The example is f(x)=x^3 where, f is always increasing but f' is not always positive (since f'=0 at x=0). Similarly, for decreasing and f' negative.
- I am prepared to bet that, since there is no proof this year, they will instead have a question where they will have you verify the Mean Value Theorem. See an example in distance assignment 3, #5 below. Here are some tips and
examples:
- You had better have practised Curve-Sketching! Be ready for a curve sketch (Lesson 9)
- There is
usually Implicit Differentiation on the final again, so practice Lesson 6. I also included more practice at that in Lesson 8.
- There is usually NO Continuity, NO Definition of Derivative, and NO Related Rates Word Problem on the final exam. There rarely are Limits either (other than as part of the curve-sketch). Don't waste your time there unless you have nothing else to do.
- The
Max/Min Word Problem is just a bonus. Almost nobody gets any marks there. There is a rumour going around that the question on the exam will be similar to my Lesson 10, #5 (the one where the cut squares out of all four corners of a rectangle to make flaps tofold up and make a box). That is a very possible exam question so I take that rumour seriously. If time allows, try to memorize how to solve my Lesson 10,
Lecture Problems 3-7 to give yourself about a 50/50 chance. Study every other topic first, and, only if time allows, try to learn how to setup as many of these questions as you can by just reading my solutions and learning what picture to draw, how to label it, and what you would have for a Q equation and a Constraint Equation. Don't waste time doing the derivative and solving the problem. Better to be able to start twenty questions, than only know how to do
five.
- Best wishes and STUDY HARD!
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