Math 131, Final Exam Review-copyright Angela Allen 1 Math 131 Final Exam Review Sheet *** Important Reminders *** Remaining office hours: Mon.(4/28) 2-3:30pm, Thurs.(5/1) 1:30-3pm, and Fri.(5/2) 10:30am- 12pm. Remember, I cannot respond to emails after Sun.(5/4), so be sure you get your questions answered before then. Bring a blank, green scantron to the exam (and a pencil!) When you are told to do so, you will fill in your name, section #, exam version, and regular class seat # on your scantron. Bring your picture i.d. Bring your calculator. (You will clear your calculator before the exam starts as usual, and remove your lid from the calculator. Also, make sure your batteries are charged.) Make sure you are in the correct seat (the exams will be labeled with your name so it is important that you are in the correct seat so we can start on time); the seating chart will be posted at the back of the room. You may NOT have scratch paper; there is plenty of room on the exam itself to work the problems. When you come into the room, place your bags against the wall and make sure your cell phones are turned OFF. You may NOT leave the classroom under any circumstances during the exam. When you turn in your exam, place your scantron INSIDE your exam. Your final exam grade and course letter grade will be posted on WebCT (elearning) by Friday evening, May 9. **********The last day you can get your grades (including your final exam grade) from WebCT is Wednesday, May 14. If you do not get your final exam grade from WebCT by this date, you will have to wait until next semester to stop by my office hours to get your final exam grade.***************** I cannot give extra credit under ANY circumstances. I cannot discuss grades via email or phone. If you have a question about your final exam grade or course grade, you will have to email me at the beginning of next semester to set up an appointment to meet. Chapter 1 (1.1-1.5) Rules for combining functions (inputs same?, etc.) Combine functions Use intersect on your calculator to solve equations Know the elements of a model Linear Model: 1. f(x) = ax+b 2. Calculate and interpret slope 3. Know the shape, characteristics 4. Use LinReg for regression Know rounding rules Exponential Model: 1. f(x) = a(b x ) 2. Calculate and interpret percentage change = (b 1)100%.
Math 131, Final Exam Review-copyright Angela Allen 2 3. Know the shape, characteristics 4. Use LogisticReg for regression 5. Determine correct limit notation for end behavior 4. Use ExpReg for regression 5. Doubling Time/Half Life Quadratic Model: Logarithmic Model: 1. f(x) = a+blnx 1. f(x) = ax 2 + bx+c 2. Know the shape, characteristics 2. Know the shape, characteristics 3. Understand inverse functions 3. Use QuadReg for regression 4. Use LnReg for regression Logistic Model: 1. f(x) = L 1+Ae Bx Cubic Model: 1. f(x) = ax 3 + bx 2 + cx+d 2. Find inflection point and intervals of concavity 2. Know the shape, characteristics 3. Know the shape, characteristics 3. Use CubicReg for regression
Math 131, Final Exam Review-copyright Angela Allen 3 Find and use appropriate model Calculate and interpret slope of tangent line Rules for drawing tangent lines Non-existence of the instantaneous rate of change Derivative notation Chapter 2 (2.1-2.4) Calculate and interpret change, percentage change, average rate of change Calculate and interpret rate of change and percentage rate of change Numerically estimate the slope of the tangent line by calculating slopes of secant lines Find/calculate limits Compound interest Understand continuity Slope of the secant line between points x and x+h: Calculate APR and APY Slope of the tangent line at a point x: Calculate and interpret slope of secant line Limit definition of the derivative
Math 131, Final Exam Review-copyright Angela Allen 4 Chapter 3 (3.1-3.5) Analyze f (x) based on f(x), or vice versa Calculate and/or interpret marginal revenue, cost, and profit Find relative extrema (max/min) and increasing/decreasing intervals Calculate and interpret derivatives Find absolute extrema (max/min) compare endpoints of the given interval with x values of relative extrema in original function, f(x). Find inflection points and determine concavity Use and/or interpret the chain rule Interpret inflection points Chapter 4 (4.1-4.3) Approximate change or the result of change Find points of most (least) rapid increase (decrease) compare endpoints of the given interval with x values of inflection points in the first derivative of the function, f (x).
Math 131, Final Exam Review-copyright Angela Allen 5 Chapter 5 (5.1-5.6) Sum of signed areas gives the change Area does not always equal the change Understand/calculate area using left, right, and midpoint rectangles Calculate and interpret a definite integral Calculate indefinite integrals (simplify, then use u substitution if needed) Chapter 6 (6.1) Calculate improper integrals (diverge?) Chapter 7 (7.1-7.5) Determine amplitude, vertical shift, horizontal shift, and period from a given graph or sine function Construct a sine model without your calculator Understand/compute an accumulation function Know the shapes for an accumulation function based on information about its derivative Compute general antiderivatives (8 antiderivative formulas) Compute specific antiderivatives (use info.) and use your new function Calculate and interpret derivatives of sine and cosine functions Use derivatives to find relative extrema and inflection points of sine/cosine functions Compute a definite integral by hand Calculate/set up integral(s) representing the area of a region Interpret the area of a region Calculate/interpret the change Calculate/interpret the area between 2 curves Calculate/interpret the difference in accumulated change of 2 rate of change functions Average value of a function Calculate and interpret integrals of sine and cosine functions Chapter 8 (8.1) Types of differential equations Set up a differential equation from a word problem
Math 131, Final Exam Review-copyright Angela Allen 6 Solve a differential equation (general solution and particular solution) algebraically If we can t solve directly, we can use slope fields to get an idea of what the solution looks like Recognize the slope field for a given differential equation Recognize/use a particular solution for a given differential equation