ࡱ> b 0bjbjyy .J$ vvvT.@ 2+2+2+Z+nnnlnnnnnn$ͥvnc nnn2+Z+7n^2+(vZ+lnl80xZ+ ޱ2LU)oHh$X0gqv:gHgv nnnnnnn|nnnnnnngnnnnnnnnn :   Ch 3 TEST AP Calculus BC Name:  Part A No Calculator  1. If  EMBED Equation.3 , when a > 0 and b > 0 then  EMBED Equation.3  (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E)  EMBED Equation.3   The line tangent to the graph of  EMBED Equation.3  at ( 0 , 1 ) intersects the x-axis at x = (A) -1 (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D) 1 (E) 2  3. If  EMBED Equation.3 , then  EMBED Equation.3  (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E)  EMBED Equation.3    Part A No Calculator  Questions 4-5 refer to the table below. The function f is continuous and differentiable for x > 0 and  EMBED Equation.3  and  EMBED Equation.3  have the indicated tabular values. 4. The equation of the line normal to  EMBED Equation.3  at x = 2 is: (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E)  EMBED Equation.3   5. If f and  EMBED Equation.3  (the inverse of f ) exist, are continuous and differentiable for x > 0, then  EMBED Equation.3  at x = 1 is (A) -4 (B) -2 (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E) 2  6. If  EMBED Equation.3 , then  EMBED Equation.3   (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E)  EMBED Equation.3   Part A No Calculator  7. If  EMBED Equation.3 , then  EMBED Equation.3  is (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E) nonexistent  8. If  EMBED Equation.3 , then  EMBED Equation.3  (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E)  EMBED Equation.3   9. If  EMBED Equation.3 , then  EMBED Equation.3  (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E)  EMBED Equation.3    Part A No Calculator  Questions 10-11 refer to the following graph.        10. If  EMBED Equation.3 , then  EMBED Equation.3  (A) -4 (B) -2 (C) 2 (D) 4 (E) 6  11. If  EMBED Equation.3 , then  EMBED Equation.3  (A) -4 (B) -2 (C) 2 (D) 4 (E) 6  12. If  EMBED Equation.3  and  EMBED Equation.3  and if  EMBED Equation.3 , then  EMBED Equation.3   (A) -2 (B) -1 (C) 0 (D) 1 (E) Does not exist  Part A No Calculator  13. If  EMBED Equation.3 , then a vertical tangent to its curve exists at the point (A) (  EMBED Equation.3  ,  EMBED Equation.3  ) (B) (  EMBED Equation.3  ,  EMBED Equation.3  ) (C) (  EMBED Equation.3  ,  EMBED Equation.3  ) (D) (  EMBED Equation.3  ,  EMBED Equation.3  ) (E) ( EMBED Equation.3  ,  EMBED Equation.3  )  14. Using local linearization for  EMBED Equation.3  about x = 0, the approximate value of  EMBED Equation.3  (A) 3 (B) 3.005 (C) 3.025 (D) 3.05 (E) 3.1  15. If  EMBED Equation.3 , then the slope of a tangent line to  EMBED Equation.3  equals -1 at x = (A)  EMBED Equation.3  (B) 0 (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E)  EMBED Equation.3    Part A No Calculator  16. If  EMBED Equation.3 , then at y =1 ,  EMBED Equation.3  (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E)  EMBED Equation.3   17. If the derivative of  EMBED Equation.3  equals 4 when x = -1 , what is the derivative of  EMBED Equation.3  when x = 4 ? (A) -2 (B) -1 (C) 1 (D) 2 (E) 4  18. What is the slope of the line tangent to the curve  EMBED Equation.3  at ( 1 , 2 ) ?  (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E)  EMBED Equation.3   Part A No Calculator  19. Let f be a function whose line tangent at the point ( 1 , 5 ) passes through the point ( -2 , -1 ). Which of the following would be equal to  EMBED Equation.3 ? (A) 2 (B) 1 (C) -2 (D) 0 (E) undefined  20. If  EMBED Equation.3 , then which of the following is an equation of the line tangent to the graph of f at the point where x = 1 ? (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E)  EMBED Equation.3    Stop! You may use your graphing calculator for the remainder of the test.   Part B Graphing Calculator Required  21. For the differential equation  EMBED Equation.3 ,  EMBED Equation.3 , then  EMBED Equation.3  (A) -1 (B)  EMBED Equation.3  (C) 1 (D)  EMBED Equation.3  (E)  EMBED Equation.3   22. If  EMBED Equation.3  and  EMBED Equation.3  is the inverse of  EMBED Equation.3 , then  EMBED Equation.3  (A) 0.5 (B) 0.003 (C) 0.077 (D) 0.25 (E) 0.417  23. If the line  EMBED Equation.3  is tangent to  EMBED Equation.3  at the point ( 2 , 6 ) , then  EMBED Equation.3   (A) 2 (B) 2.5 (C) 3 (D) 4 (E) 6  Part B Graphing Calculator Required  24. If  EMBED Equation.3  then a horizontal tangent line to  EMBED Equation.3  exists at x = (A) e (B) 1 (C) 0 (D)  EMBED Equation.3  (E)  EMBED Equation.3   25. The balance, B , in a savings account t years after a deposit of $10,000 is given by the formula  EMBED Equation.3 . At what rate, measured in dollars per year, is the balance in the account changing at t = 10 years? (A) 1000.91 (B) 1091.24 (C) 1587.75 (D) 8412.25 (E) 21,170.00          26. For the function  EMBED Equation.3  shown above, the Mean Value Theorem for Derivatives would be satisfied by which x-coordinate over the interval  EMBED Equation.3 ? (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E)  EMBED Equation.3    Part B Graphing Calculator Required  27. If  EMBED Equation.3 ,  EMBED Equation.3 , and  EMBED Equation.3  are continuous on [ a , b ], then there is a number c in ( a , b ) with (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D) the instantaneous rate of change of f at x = c equal to the average rate of change of f on the interval [ a , b ] (E)  EMBED Equation.3  is the maximum value of f on the interval [ a , b ]  28. The function  EMBED Equation.3  is continuous for the closed interval [ -3 , 2 ] and differentiable for the open interval ( -3 , 2 ). If  EMBED Equation.3  and  EMBED Equation.3 , then which of the following is true? I. There exists c , where  EMBED Equation.3 , such that  EMBED Equation.3  II. There exists c , where  EMBED Equation.3 , such that  EMBED Equation.3  III. There exists c , where  EMBED Equation.3 , such that  EMBED Equation.3  (A) I only (B) II only (C) III only (D) I and II only (E) I, II, and III  29. The function  EMBED Equation.3  is continuous for the closed interval [ -3 , 2 ] and differentiable for the open interval ( -3 , 2 ). If  EMBED Equation.3  and  EMBED Equation.3 , then which of the following is true? I. There exists c , where  EMBED Equation.3 , such that  EMBED Equation.3  II. There exists c , where  EMBED Equation.3 , such that  EMBED Equation.3  III. There exists c , where  EMBED Equation.3 , such that  EMBED Equation.3  IV. There exists c , where  EMBED Equation.3 , such that  EMBED Equation.3  (A) I only (B) II only (C) III only (D) I and III only (E) I, III, and IV   Part B Graphing Calculator Required  30. If  EMBED Equation.3 , then  EMBED Equation.3  (A)  EMBED Equation.3  (B)  EMBED Equation.3  (C)  EMBED Equation.3  (D)  EMBED Equation.3  (E)  EMBED Equation.3   JFF 31. Suppose  EMBED Equation.3 ,  EMBED Equation.3 ,  EMBED Equation.3 , and  EMBED Equation.3  . Find the equation of the tangent lines of  EMBED Equation.3 ,  EMBED Equation.3 , and  EMBED Equation.3  at x = 2. (a) If  EMBED Equation.3 . (b) If  EMBED Equation.3 .  Part B Graphing Calculator Required  (c) If  EMBED Equation.3 .     PT PT x EMBED Equation.3  EMBED Equation.3 121/2231/331-2 PT PT 5 4 3 2 1 g (x) f (x) 1 2 3 4 5 PT PT PT PT PT y f (x) a c c c c c b x 1 2 3 4 5 PT PT PT This review has more 3.1 to 3.3 material. Be sure to study the AP Free Response style problems from every worksheet, especially problems from 3.4. Also remember that anything on any worksheet is fair game. SO STUDY EVERYTHING! 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