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**Extra info for AP Calculus AB**

**Sample text**

Click Here for Terms of Use. 0267-02/Part II 12/18/2001 17:23 Page 12 This page intentionally left blank. 0267-02/Part II 12/18/2001 17:23 Page 13 What You Need to Know About the AP Calculus AB Exam • 13 BACKGROUND ON THE AP EXAM What Is Covered in the AP Calculus AB Exam? The AP Calculus AB exam covers the following topics: • Functions, Limits and Graphs of Functions, Continuity • Definition and Computation of Derivatives, Second Derivatives, Relationship between the Graphs of Functions and their Derivatives, Applications of Derivatives • Finding Antiderivatives, Definite Integrals, Applications of Integrals, Fundamental Theorem of Calculus, Numerical Approximations of Definite Integrals, and Separable Differential Equations.

Volume = π ∫0 (5x) dx = 225π. Simply indicating the answer without writing the integral would only get you one point for the answer but no other credit for the work. • You may not use calculator syntax to substitute for calculus notations. For example, you may not write “ Volume = ∫ ( π)(5 ∗ x)ˆ 2, x, 0, 3 = 225π ” instead of “ Volume = π ∫0 (5x) dx = 225π. ” 3 2 • You are permitted to use the following 4 built-in capabilities of your calculator to obtain an answer: plotting the graph of a function, finding the zeros of a function, finding the numerical derivative of a function, and evaluating a definite integral.

83. Write an equation of the normal line to the graph of y = x3 for x ≥ 0 at the point where f ′(x) = 12. 84. If g( x) = ∫a f (t )dt and the graph of f is shown in Figure D-8, which of the graphs in Figure D-9 on page 23 is a possible graph of g? x y x1 0 x2 x3 x4 x f a 0 Figure D-7 80. How many points of inflection does the graph of y = sin (x2) have on the interval [−π, π]? Figure D-8 b x 0267-02/Part II 12/18/2001 17:24 Page 23 What You Need to Know About the AP Calculus AB Exam • (A) y y (B) (D) a 0 b x b b x a 0 x b y (E) 0 x 0 y y (C) a a 23 a 0 x b Figure D-9 85.