Calculus for Phys./Life Sciences 1
Monday, Dec. 16, 2:30 - 5:30 pm (1:00 section)
Tuesday, Dec. 17th, 8:30 - 11:30 am (2:00 section)
The final exam is CUMULATIVE, that is, it covers all the material from the first
day of class onwards. Approximately 20-25% will cover material from Chapter 5. This is
sections 5.1 - 5.4. You should go over homework problems as well as your class notes.
Many of the problems and questions we discuss in class are excellent examples of
test questions. I have also listed some sample problems from the Chapter 5 Review below.
For questions from other chapters, see previous exam review sheets. (Ch. 1 -> Exam 1,
Ch. 2 -> Exam 2, Ch. 3 and 4 -> Exam 3.) It is also a good idea to go over your
Note: You will be given a scientific calculator for the exam which does NOT have graphing
capabilities so be prepared to answer questions WITHOUT your personal calculator.
The exam will be designed for 2 hours (twice the length of the
mid semester exams) so you should have plenty
of time to complete it in the allotted 3 hour time slot.
FINAL EXAM REVIEW: Friday, Dec. 13th, in HABERLIN 236 from 1:00 - 3:00 pm. Please come prepared
with specific questions from the chapter reviews, past exams, homework problems, conceptual questions, etc.
List of Topics By Chapter
Some types of questions you can expect to find on the final
- Chapter 1: Functions, various types of functions (linear, exponential, logarithmic, trigonometric,
polynomials, rational), increasing and decreasing functions, shifting and stretching functions,
inverse function, vertical and horizontal asymptotes
- Chapter 2: Rates of change, average velocity versus instantaneous velocity,
limits (left-hand, right-hand, involving infinity), the derivative, definition of the derivative,
the derivative as a function, the second derivative, continuity and differentiability
- Chapter 3: Rules of differentiation --- power rule, product rule, quotient rule, chain rule,
how to differentiate trig functions, implicit differentiation, related rates, parametric equations,
linear approximation (finding the tangent line), L'Hopital's Rule
- Chapter 4: Using the derivative to describe properties of a function (increasing, decreasing, relative
maxima, relative minima, concavity, inflection points), curve sketching,
global max's and min's, optimizing a function (word problems), hyperbolic functions,
First Derivative Theorem, Mean Value Theorem, Extreme Value Theorem
- Chapter 5: Approximating the area under a curve (left-hand and right-hand sums), using
the integral to calculate total change (eg. finding total distance traveled by integrating velocity),
the definite integral, average value, the Big Integral Theorem, the Fundamental Theorem of Calculus
One way to study concepts for the final is to do the problems in
the "Check Your Understanding" sections at the end of each Chapter.
The odd questions are in the back of the book for these conceptual
questions. These will help solidify concepts from over the course
of the semester. Part of what you'll be tested on is your ability
to see the "big picture."
- Finding the tangent line to a curve at a given point.
- Sketching a graph using the first and second derivative (perhaps some asymptotes as well).
- An optimization problem.
- Finding the area under a curve (either estimate or exact value using FTC).
- Conceptual questions regarding the derivative and/or integrals (eg. sketch the graph
of the derivative given the function).
The review problems below represent good questions to study from for Chapter 5, although
you should also review homework problems and class examples.
For example, there are no problems on average value in the chapter review even
though this is an important topic.
Chapter 5 review, pp. 252 - 255
Problems: 1, 3, 5, 6, 7, 9, 13, 14, 15, 17, 19, 22, 23, 25
The answers to the odd problems are in the back of the book.
The answers to the evens are:
6. Total area is 13. Integral is 1.
14. The integral is 4.
22. The integral is 1.