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AP Calculus BC Midterm Review ProblemsTopics covered: (Bold are the “newer” material not from Math Analysis or Calc AB)Unit 1 – Limits and continuityDefinition of continuityLimit definition of derivativesSimplifying and solving limits (also graphically)Infinite limits (DNE)Limits as x approaches infinity (horizontal asymptotes)Intermediate Value TheoremUnit 2 – Derivatives Basic rules of derivativesImplicit differentiationRate of change (average and instantaneous)Inverse trig functionsDerivatives of log/ln and exponential functionsMean Value TheoremEquation of tangent lineParametric, polar, vector derivativesUnit 3 – Applications of Differentiation (Ch. 3)L’HopitalsExtrema and 1st and 2nd Derivative Tests (critical points)Extreme Value TheoremCurve Sketching (increasing/decreasing, concavity)Relationship between graphs of f, f ‘, and f “Tangent Line ApproximationOptimizationRelated RatesRectilinear motion – position, velocity, accelerationUnit 4 – Integration (Ch. 4)AntiderivativesPropertiesFundamental Theorem of Calculus (two parts)U-substitutionAverage value (versus average rate of change from Unit 2)Given graph of f ‘, characteristics of f and f “ graphNumerical integration – Riemann sums, Trapezoidal sums, Simpson’s ruleParametric, polar, vector integrationPosition, velocity, acceleration integrationUnit 5 – Techniques of Advanced Integration (Ch. 8)Different methods (completing the square, add/subt. same number, etc.)By parts (tabular method; LIPET)Trig identitiesTrig substitutionPartial fractionsL’HopitalsImproper IntegralsFormat of Midterm (AP style)Section IPart A – 20 minutes, 10 multiple choice questions, no calculatorPart B – 30 minutes, 10 multiple choice questions, calculator okaySection IIPart A – 30 minutes, 2 free response, calculator okayPart B – 30 minutes, 2 free response, no calculatorFree Response Practice Problems: Use previous reviews and tests and all the previous AP practice problems you’ve been given. Multiple Choice Practice Problems (Disclaimer: These are just some practice problems. They do not cover everything on the midterm. You should try these but also study more. Use your unit tests and reviews for those unit tests as a study guide. Also, some of these problems might be repeats from previous tests/reviews that you’ve been given…sorry)NO CALCCALCULATOR OKAYNO CALC_____ 1) If , then the graph of is decreasing if and only ifa) b) c) d) e) _____ 2) For , the slope of the tangent to equals zero whenever a) b) c) d) e) _____ 3) The function F is defined by where the graph of the function 348234013335 G is shown below. Find the approximate value of .a) b) c) d) e) _____ 4) a) b) c) d) e) _____ 5) Find an equation of the line tangent to the graph of at its point of inflection.a) b) c) d) e) _____ 6) a) b) c) d) e) _____ 7) What is ?a) b) c) d) 1e) The limit does not exist._____ 8) Suppose for all real x. Find F ’(-1). a) 2b) 1c) -2d) e) _____ 9) What is the average value of over the interval ?0346_____ 10) Find .a) 0b) c) 1d) e) The limit does not exist._____ 11) If , find .a) b) 0c) d) e) _____ 12) Find the area under the graph of on the interval .a) b) c) d) e) _____ 13) Evaluate .a) b) c) d) e) _____ 14) Find an equation for a tangent to the graph of at the origin.(There is one like this on the midterm!)a) b) c) d) e) _____ 15) Find .a) 1b) 3c) d) e) _____ 16) The acceleration at time of a particle moving along the x-axis is . If at seconds the velocity is and the position is ft, find the position at seconds.a) 8 ftb) 11 ftc) 12 ftd) 13 fte) 15 ft_____ 25) Find the approximate value of at , obtained from the tangent to the graph at .a) 2.01b) 2.02c) 2.03d) 2.04e) 2.05398716562865_____ 26) The function f is defined on the interval and its graph is shown to the right. Which of the following statements are true?a) I onlyb) II onlyc) I and II onlyd) II and III onlye) I, II, and IIIMore practice1.Find a. 1b. 0c. d. Does not existe. None of these2.Find a. b.0c. d. Does not existe. None of these3.Find the limit: a. 0b. c. d. e. None of these48006001168404.Determine the sign of the second derivative at the indicated point:a. Zerob. Undefinedc. Positived. Negativee. None of these5.Find if a. b. c. d. e. None of these 6.Find for a. b. c. d. e. None of these7.Find the derivative of y = arctan a. b. c. d. e. None of these8.Evaluate a.b. c. d.e.None of these9.Which integral represents the trig substitution form of the integral a.b. c. d.e.None of these10.Evaluate a.0b.c.d.e.None of these11. Evaluate a. b. c. d. e. None of these12. Find the arc length , on interval [1, 4]a. 30b. 75c. 15d. 5e. None of these13. Find the slope of the tangent for the curve at the point where .a. 6b. c. d. 1e. None of these14. Calculate the area inside the cardioid .a. b. c. d. e. None of these15. Calculate the distance around the graph of the polar curve .a. b. c. 16d. e. None of these ................
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