Calculus for Phys./Life Sciences 1

Final Exam

Saturday, Dec. 10th, 2:30 - 5:30 pm (Section 02)
Swords 328

Friday, Dec. 16th, 8:30 - 11:30 am (Section 04)
O'Neil 101

Note: You MUST take the final with your 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 Section 4.8 and Chapter 5. It is recommended that you 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 and Check Your Understanding Sections below. Answers to the even numbered problems are provided. For questions from other chapters, see previous exam review sheets. It is also a good idea to go over your previous exams.

Click here for a Practice Exam (PDF file). Solutions (PDF file) are available here. It is recommended you try the exam first before looking at the solutions.

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.


Please come prepared with specific questions from the chapter reviews, practice exam, past exams, homework problems, conceptual questions, etc.

List of Topics By Chapter

  • Chapter 1: Functions, various types of functions (linear, exponential, logarithmic, trigonometric, power, polynomials, rational), increasing and decreasing functions, shifting and stretching functions, inverse function, vertical and horizontal asymptotes, limits (left-hand, right-hand, involving infinity), the Big Limit Theorem
  • Chapter 2: Rates of change, average velocity versus instantaneous velocity, 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 and hyperbolic functions, implicit differentiation, logarithmic differentiation, derivatives of inverse functions, linear approximation (finding the tangent line), Mean Value Theorem
  • 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), related rates, L'Hopital's Rule, parametric equations
  • Chapter 5: Approximating the area under a curve (left-hand and right-hand sums), using the integral to calculate total change (eg. if the velocity is positive, then the total distance traveled is the integral of the velocity), the definite integral, average value, the Big Integral Theorem, the Fundamental Theorem of Calculus
Some types of questions you can expect on the final
  • 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).

Chapter 5 Review Problems: The answers to the odd problems are in the back of the book. The answers to the evens are provided.

Chapter 5 review, pp. 272 - 277
Problems:   3, 5, 7, 9, 11, 15, 18, 19, 20, 21, 22, 23, 27, 35, 37, 43, 47

The answers to the evens are:
18.   The integral is 4.
20.   The integral is 10.
22.   The integral is 1 (draw a picture).

Chapter 5 Check Your Understanding, pp. 278 - 279
Problems:   3, 7, 9, 11, 17, 19, 21, 27