Midterm Exam Review Questions Free Response Non Calculator

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1 Name: Dae: Block: Miderm Eam Review Quesions Free Response Non Calculaor Direcions: Solve each of he following problems. Choose he BEST answer choice from hose given. A calculaor may no be used. Do no spend oo much ime on any one problem. In his es: Unless oherwise specified, he domain of he funcion f is assumed o be he se of all real numbers for which f() is a real number.. The graph of y = 3 3 has a relaive maimum a (A) (0,0) only (B) (,) only (C) (,) only (D) (, 6) only (E) (0,0) and (,). lim (A) 0 (B) (C) (D) /0 (E) /0 y B B A C E 3. The figure above shows he graph of he velociy of a moving objec as a funcion of ime. A which of he marked poins is he speed he greaes? (A) A (B) B (C) C (D) D (E) E D AP Calculus AB Miderm Eam Revision 0-03

2 . Wha are all values of for which he graph of y = (A) No values of (B) < (C) > (D) < (E) > is concave downward? 5. The equaion of he angen line o he curve + y = 69 a he poin (5, ) is (A) 5y = 0 (B) 5 y = 9 (C) 5 y = 69 (D) + 5y = 0 (E) + 5y = If he graph of (A) (B) (C) 0 (D) (E) f ( ) k has a poin of inflecion a, hen he value of k is 7. A paricle moves along he -ais in such a way ha is posiion a ime is given by he acceleraion of he paricle a ime = 0? (). Wha is (A) (B) (C) 3/5 (D) (E) 8. If dy d y, hen d y d = (A) (B) (C) (D) (E) y 3 3 y y 3 y y y y 3 AP Calculus AB Miderm Eam Revision 0-03

3 9. y g() g() f () f () Piecewise funcions f and g are shown above. If h() = f() g, ( ) hen h (3) = (A) 8/3 (B) /3 (C) 0 (D) /3 (E) 8/3 0. The average rae of change of he funcion f ( ) cos on he closed inerval [, 0] is (A) sin() (B) sin() (C) cos() (D) cos() sin() (E). If 6 ( ) 0 d is approimaed by hree inscribed recangles of equal widh on he -ais, hen he approimaion is (A) (B) 6 (C) 8 (D) 8 (E) 76 AP Calculus AB Miderm Eam Revision 0-03

4 Name: Dae: Block: Miderm Eam Review Quesions Free Response Calculaor Acive Direcions: Solve each of he following problems. Choose he BEST answer choice from hose given. A calculaor may be used. Do no spend oo much ime on any one problem. In his es: () The eac numerical value of he correc answer may no always appear among he choices given. When his happens, selec from among he choices he number ha bes approimaes he eac numerical value. () Unless oherwise specified, he domain of he funcion f is assumed o be he se of all real numbers for which f() is a real number.. Le f be he funcion given by f() = an and le g be he funcion given by g() =. A wha value of in he inerval 0 do he graphs of f and g have parallel angen lines? (A) 0 (B) (C).083 (D).9 (E) Le f() for > 0. For wha value of is f () equal o he average rae of change of f on he closed inerval [a, b]? (A) (B) (C) (D) (E) ab ab ab ab b a AP Calculus AB Miderm Eam Revision 0-03

5 R() C B A The figure above shows a road running in he shape of a parabola from he boom of a hill a A o poin B. A B, i changes o a line and coninues o on o C. The equaion of he road is R ( ) a, From A ob b c, From BoC B is,000 fee from A and 00 fee higher. Since he road is smooh, R () is coninuous. Wha is he value of b? (A) 0. (B) 0.0 (C) 0.00 (D) (E) y f () 5. The figure above shows he graph of he derivaive of a funcion f. How many poins of inflecion does f have in he inerval shown? (A) None (B) One (C) Two (D) Three (E) Four AP Calculus AB Miderm Eam Revision 0-03

6 6. The amoun A() of a cerain iem produced in a facory is given by A() = ( 3) ( 3) 3 Where is he number of hours of producion since he beginning of he workday a 8:00 a.m. A wha ime is he rae of he producion increasing mos rapidly? (A) 8:00 a.m. (B) 0:00 a.m. (C) :00 a.m. (D) :00 noon (E) :00 p.m. 7. A how many poins on he curve he origin? 5 y will he line angen o he curve pass hrough (A) One (B) Two (C) Three (D) Four (E) Five 8. Suppose ha f() is an even funcion and le (A) 5 (B) (C) 0 (D) (E) 5 0 f ( ) d 5 and 7 0 f ( ) d. Wha is 7 f ( ) d? 9. The graph of he derivaive of a wice differeniable funcion is shown below. y 3 y f () If f () =, which of he following mus be rue? (A) f () < f () < f () (B) f () < f () < f () (C) f () < f () < f () (D) f () < f () < f () (E) f () < f () < f () AP Calculus AB Miderm Eam Revision 0-03

7 0. Le f be a funcion ha is everywhere differeniable. The value of f () is given for several values of in he able below f () 0 If f () is always increasing, which saemen abou f () mus be rue? (A) f () has a relaive min a = 0. (B) f () is concave down for all. (C) f () has a poin of inflecion a (0, f (0)) (D) f () passes hrough he origin (E) f () is an odd funcion. The able below gives he values of a differeniable funcion f. wha is he approimae value of f ()? f () (A) (B) 0.89 (C) 0.7 (D).30 (E) f () can no be approimaed from he informaion given.. The funcion f () = an(3 ) has a zero in [0,.]. The derivaive a his poin is (A) 0. (B).0 (C) 3.5 (D) (E) undefined 3. The edge of a cube is increasing a he rae of 0.05 cenimeers per second. In erms of he edge of he cube, s, wha is he rae of change of he volume of he cube, in cubic cenimeers per second? (A) (B) 0.05s (C) 0.05s 3 (D) 0.5s (E) 3s AP Calculus AB Miderm Eam Revision 0-03

8 . Which graph bes represens he posiion of a paricle, s(), as a funcion of ime, if he paricle s velociy and acceleraion are boh posiive? s() s() s() (A) (B) (C) (D) s() (E) s() 5. Le f be a funcion such ha f (7 h) f (7) lim. Which of he following mus be rue? h 0 h I. f is coninuous a = 7 II. f is differeniable a = 7 III. The derivaive of f is coninuous a = 7 (A) I only (B) II only (C) I and II only (D) I and III only (E) II and III only MC Answer Key Non-Calculaor Calculaor. C 6. E. B. C 7. A. C. A 7. E 3. B 8. B 3. D 3. D 8. E. A 9. A. C. E 9. C 5. E 0. A 5. C 5. C 0. D 6.C. D AP Calculus AB Miderm Eam Revision 0-03