AP Calculus Exam Format and Calculator Tips: Exam Format: The exam is 3 hours and 15 minutes long and has two sections multiple choice and free response. A graphing calculator is required for parts of the exam (see below). You may not take both the Calculus AB and Calculus BC exams within the same year.
Multiple Choice Questions (all are AP-like and calculator allowed) 1. f( x) x(cos x)(ln x)( e x ); f 1 (A) 0 (B) 1 (C) 1.31 (D) 1.406 (E) 1.469 Calculus with the Graphing Calculator. Let ln x f ( x) cosx for 1 x 6. On what intervals is f concave down? x e (A) (1.481, 4.76) (B) (1, 3.105) (C) (3.105, 6) (D) (1, 4.76) (E) (1, 1.481) (4.76, 6) 3. Given f ( x) sin x, use the tangent line at x 1 to estimate f (1.1). (A) 0 (B) 0.540 (C) 0.841 (D) 0.896 (E) 1
Calculus with the Graphing Calculator 4. Two particles start at the origin and move along the x-axis. For 0 t 4, their respective position functions are given to be x1 ln t and acceleration of x 1 equal the velocity of x? (A) 1.060 (B) 0.470 (C) 3.960 (D).039 (E) None x ( 5) t. For what value of t does the 5. The average value of the function f x ( ) cos( x ) 0, is on the closed interval (A) 0.31 (B) 0.461 (C) 0.780 (D) 0.977 (E) 1.53 t 6. Water is pumped out of a pond at the rate Rt () 6 cubic meters per minute, where t is t 1 measured in minutes. How much water is pumped from time t 0 to t 3? (A) 0.17 cubic meters (B).147 cubic meters (C) 5.196 cubic meters (D) 1.88 cubic meters (E) 5.456 cubic meters 7. If c satisfies the conclusion of the Mean Value Theorem for 0 x 1, then c is f ( x) sin 1 x on the interval (A) 0.500 (B) 0.771 (C) 0.785 (D) 1 (E) 1.186
Calculus with the Graphing Calculator 8. A particle moves along the x axis in a way such that the velocity of the particle for t 1 is sin t given by vt (). The total distance traveled by the particle from t to t 4 is t (A) 0.094 (B) 0.094 (C) 0.153 (D) 0.47 (E) 0.340 9. An object traveling in a straight line has position x() t at time t. If the initial position is x(0) 3 and the velocity of the object is time t 4? (A) 0.403 (B) 5.78 (C) 6.877 (D) 8.78 (E) 9.877 vt () 1 3 t, what is the position of the object at x 10. The area of the region bounded by the curves y e, y ln x, and the line x 1 is (A) 0.04 (B) 0.054 (C) 0.096 (D) 0.78 (E) 1.686
11. Let g( x ) be the function given by true? I. g is decreasing on (0,1) II. g is decreasing on (1,) III. g() 0 (A) I only (B) II only (C) IIIonly (D) I and III only (E) I, II, and III x t ( ) ( 1). 0 Calculus with the Graphing Calculator gx e t dt Which of the following must be 4 1. Let R be the region in the first quadrant enclosed by the graphs y x 1 and y x 16. The volume of the solid generated by revolving R about the x-axis is (A) 5.616 (B) 80.475 (C) 507.539 (D) 1594.480 (E) 3188.959 x t 13. Given f ( x) dt; f (1) 1 t ( e 1)(sin t) (A) 0 (B) 0.00 (C) 0.30 (D) 0.341 (E) does not exist
Free Response Questions (all are AP or AP-like and calculator allowed) Calculus with the Graphing Calculator 14. t (minutes) 0 4 9 15 0 W() t( degrees Fahrenheit) 55.0 57.1 61.8 67.9 71.0 The temperature of water in a tub at time t is modeled by a strictly increasing, twicedifferentiable function W, where W (t) is measured in degrees Fahrenheit and t is measured in minutes. At time the temperature of the water is 55 F. The water is heated for 30 minutes, beginning at time Values of W (t) at selected times t for the first 0 minutes are given in the table above. (a) Use the data in the table to estimate Show the computations that lead to your answer. Using correct units, interpret the meaning of your answer in the context of this problem. (b) Use the data in the table to evaluate Using correct units, interpret the meaning of in the context of this problem. (c) For the average temperature of the water in the tub is Use a left Riemann sum with the four subintervals indicated by the data in the table to approximate Does this approximation overestimate or underestimate the average temperature of the water over these 0 minutes? Explain your reasoning. (d) For the function W that models the water temperature has first derivative given by W () t = 0.4 t cos(0.06). t Based on the model, what is the temperature of the water at time
Calculus with the Graphing Calculator 15. A particle travels on the x axis so its velocity at time t is given by for 0 t. The particle is at position x at time t 0. 1 vt ( ) cost, (a) For what values of t is the particle moving to the left? (b) What is the particle's final position? (c) What is the total distance traveled by the particle over the interval 0 t? (d) When t, is the speed of the particle increasing or decreasing? Justify your answer. 6
Calculus with the Graphing Calculator 16 16. Let R be the region bounded by the graphs of y 1 x and y 3. Set up and evaluate an integral expression for each of the following: (a) the area of R (b) the volume of the solid generated by revolving R about the x -axis (c) The region R is the base of a solid. For this solid, the cross sections perpendicular to the x-axis are semicircles. Determine the volume of this solid.