Study Guide for the Final Exam

• The exam is Monday, 9 Dec from 3:30-5:30pm in the classroom. Seating assignments will be posted at the back of the classroom 20 minutes beforehand.
• The exam will consist of three parts. Part I will have 12 questions (3 pts each) with multiple-choice answers. You are to circle the correct choice on your exam (NO SCANTRON REQUIRED). No work will be graded and no partial credit will be given. Part II will consist of 3 short answer questions with multiple parts (7 parts total; 3 pts each part). No work is required, but partial credit may be given for appropriate work shown. Part III will consist of 9 workout problems (5 pts each, some with multiple parts). All answers must be justified with appropriate work and/or explanation. Partial credit will be given for appropriate work shown on these problems.
• You will be allowed to enter the room 15 minutes before your exam starts. Have your calculator ready to show me when you enter the room (RIGHT SIDE DOOR ONLY) and before you take your seat.
• Bring: Writing Utensils, Picture ID, (4-function) Calculator. All other materials should be in a closed container under your seat during the exam. Electronic devices other than your calculator must be off or silent and out of sight during the exam.

Approximate Breakdown of Material
• Exam I Material = 24.5%
• Exam II Material = 24.5%
• Exam III Material = 24.5%
• New Material = 26.5%

• Core Objectives: All applicable Core Objectives on the syllabus will be tested on the Final Exam. Reprinted here for convenience. Objectives not covered on previous exams are in bold.
• Students will evaluate limits of functions graphically and algebraically
• Students will evaluate limits of functions analytically by applying the Sandwich Theorem or L'Hospital's Rule.
• Students will justify whether a function is continuous or not using the mathematical definition of continuity.
• Students will compute derivatives using the limit definition of the derivative.
• Students will compute derivatives of polynomials and rational, trigonometric, exponential, logarithmic, and inverse functions.
• Students will use inquiry to determine the best method for taking derivatives of complicated functions.
• Students will apply calculus to find innovative ways to graph complicated functions without the aid of a graphing calculator or computer.
• Students will think creatively about how to accomplish a given optimization objective and apply calculus to achieve this goal.
• Students will compute the linear approximation of a function and use it in applications of approximation and error estimation.
• Students will think creatively about the relationship between two given rates of change and how they affect each other.
• Students will compute limits of sequences and recursions and synthesize the results by explaining the relationship between these limits and the long-term behavior of population growth.
• Students will evaluate and synthesize single-species population data to determine the best mathematical model to represent the population.
• Students will compute definite integrals using Riemann sums.
• Students will find the antiderivatives of basic functions.
• Students will compute definite integrals using the Fundamental Theorem of Calculus.
• Students will apply the substitution method to compute integrals.
• Students will recognize and construct graphs of basic functions, including polynomials, exponentials, logarithms, and trigonometric functions.
• Students will construct and interpret semilog and double-log plots used to model biological data.
• Students will justify results that require the use of theorems such as the Sandwich Theorem and Intermediate Value Theorem or mathematical definitions such as the definition of continuity by writing mathematical proofs.
• Students will explain the solutions to related rates problems and optimizations problems in writing.
• Students will develop sketches of the graphs of complicated functions by analyzing the function itself and its first and second derivatives.
• Students will analyze the stability of fixed points by applying the cobwebbing graphical technique.
• Students will interpret definite integrals as sums of signed areas under a graph.
• Students will analyze semilog and double-log plots and derive functional relationships associated with such plots.
• Students will analyze population data and determine whether an exponential discrete time model can be used to model the data.
• Students will understand the Intermediate Value Theorem and apply it to locate the roots of functions.
• Students will compute derivatives of functions and use derivatives in applications such as finding equations of tangent lines, computing the linear approximation of a function, solving related rates problems, solving optimization problems, and finding the rate at which a population is growing.
• Students will find the relationship between two given rates of change and make conclusions about how one is affecting the other.
• Students will make conclusions about monotonicity, concavity, extrema, and inflection points of a given function by analyzing the given function and its derivatives.
• Students will manipulate given information to develop a one-variable function to be used in an optimization problem and then apply calculus to find and interpret the optimal solution.
• Students will use antiderivatives and the Fundamental Theorem of Calculus to compute and interpret areas under curves.

• Suggestions for Studying
• For old material, I recommend looking over your old exams as a starting point. If you were unable to work a particular topic the first time and/or now, I would go back to the Resources below and work a few examples along that topic. If you were able to work a particular topic then and still can do it now, don't worry about doing much on that topic.
• Read your textbook, including all Examples
• Read your notes from lecture, including all Examples
• Suggested Homework Problems
• Online Homework (Can try variations of problems once completed: Click on "Study Plan", then "All Chapters")
• MATH 151 Past Common Exams (NOTE: Not all problems on these exams apply to 147, and not all 147 topics are covered, but there is overlap between these courses)
• MATH 152 Past Common Exams (Questions on sequences may be found on these exams according to This Mapping
• SI Sessions from the semester (last one Tues, 3 Dec).
• Help Sessions end Wed, 4 Dec
• Office Hours the week before the exam: M 2-3:30pm; WF 1-3:30pm OBA