AP Calculus: Facts, Figures, and FAQs

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1 AP Calculus: Facts, Figures, and FAQs Stephen Kokoska Bloomsburg University Chief Reader, AP Calculus August, /

2 Objectives. The AP Calculus Exam and the Reading.. The AP Calculus Exam is graded fairly, accurately, and consistently. We award points for good calculus work. 3. Please complete a Reader application. A unique professional development opportunity. /

3 The AP Calculus Exam AP Calculus Exams Operational: North, Central, and South America (includes Alaska and Hawaii) Form A: Alternate Exam, late test Form I: International, operational Form J: International, alternate Section I: Multiple Choice. Section II: Free Response Calculator and Non-calculator Sections AB and BC Exams Common Problems Multiple choice: rights only scoring 3 /

4 The AP Calculus Exam Free-Response Questions Six questions on each exam (AB and BC) Three questions in common to AB and BC Two calculator active questions on each exam Nine points allotted to each problem We award credit for complete and correct work. Scoring rubric (standard) is used to assign partial credit. 4 /

5 The AP Calculus Exam Exams Number of AP Calculus Exams AB Exams BC Exams Total Exams Totals AB: 57,54 BC: 85,647 Year Since 955: > 4, 93, 3 5 /

6 The Reading Background Information Score the free-response questions Kansas City: Convention Center (versus college campus) Westin Hotel (versus college dorms) Previous locations: Louisville, Colorado State University, Clemson University, Rider University, Trenton State Seven day Reading (five day pre-reading preparation) Total Participants: 857 High School: 49% College: 5% 5 states, DC, and other countries Everyone reads three questions over seven days 6 /

7 The Reading Positions Chief Reader Exam Leaders (AB, BC, Alternate, International) Question Leaders Question Team Members Table Leaders Readers (8 per room, TLs) 7 /

8 Free Response AP Calculus AB Version. AB: Particle Motion For t 6, a particle is moving along the x-axis. The particle s position, xt, is not explicitly given. t 4 The velocity of the particle is given by vt sine. The acceleration of the particle is given by t 4 t at e cose 4 and x. (a) Is the speed of the particle increasing or decreasing at time t 5.5? Give a reason for your answer. (b) Find the average velocity of the particle for the time period t 6. (c) Find the total distance traveled by the particle from time t to t 6. (d) For t 6, the particle changes direction exactly once. Find the position of the particle at that time. (a) v , a : conclusion with reason The speed is increasing at time t 5.5, since velocity and acceleration have the same sign. 8 /

9 (b) acceleration Find the average have velocity the same of sign. the particle for the time period t 6. (a) (c) Find v5.5the total.45337, distance atraveled by.3585 the particle from time t to t : 6. conclusion with reason the particle.949 : changes direction exactly once. Find the position : integral : answer of the particle at that time. The speed is increasing at time t 5.5, since velocity and acceleration have the same sign. (a) v , a : conclusion with reason 6 (b) Average velocity vt dt : : integral : answer The speed is increasing at time t 5.5, since velocity and acceleration have 6 the same sign. (c) Distance vt dt.573 : : integral 6 (b) Average velocity vt dt : : answer integral : answer (b) Average velocity vt dt (d) For Free t 6, Response 6 6 : : integral : : answer integral (c) Distance vt dt (b) Average velocity vt dt (d) vt when t Let b vt changes sign from positive to negative at time t b. 6 (c) Distance b vt dt.573 xb vt dt4.34 or 4.35 (d) vt when t Let b vt changes sign from positive to negative at time t b. 6 (c) Distance b vt dt.573 xb vt dt4.34 or 4.35 : answer : considers vt 3 : : integral : answer : answer : : integral : : integral : : answer answer (d) vt when t Let b vt changes sign from positive to negative at time t b. b xb vt dt4.34 or 4.35 : considers vt 3 : : integral : considers vt 3 : : integral : answer 9 /

10 Free Response AP Calculus AB 3 Version. AB3: Tangent Line/Area/Volume Let R be the region in the first quadrant enclosed by the graphs of and g x sin x, as shown in the figure above. f x 8x 3 (a) Write an equation for the line tangent to the graph of f at x. (b) Find the area of R. (c) Write, but do not evaluate, an integral expression for the volume of the solid generated when R is rotated about the horizontal line y. (a) f f x 4 x, so f 6 An equation for the tangent line is y 6 x. : f : : answer /

11 f x 4 x, so f 6 (a) An equation for the tangent line is y x f x 4 x, so f 6 (a) f An equation for the tangent line is y x f x 4 x, so f 6 f Free Response g x f x dx An equation for the tangent line is y x (b) Area (b) Area gx fx4 dx cos x x x 3 sin x 8x dx 8 x (b) Area gx fx4 dx cos x x x 3 sin x 8x dx 8 x cos 4 x x (c) fx gx dx 8 3 8x sinx dx (c) fx gx dx 3 sin x 8x dx 3 x : answer : f : : answer : f : : answer : integrand 4 : : antiderivative : answer : integrand 4 : : antiderivative : answer : integrand 4 : : antiderivative : answer : limits and constant 3 : : integrand : limits and constant 3 : : integrand /

12 Scores (Operational Exam) Operational Score AB BC 5: Extremely well qualified.% 47.% 4: Well qualified 6.3% 6.3% 3: Qualified 8.5% 7.% : Possibly qualified.8% 5.9% : No recommendation 33.4% 3.6% Total 57,54 85,647 Notes Equate items from previous years Statisticians from the College Board and ETS Test development specialists from ETS College comparability study /

AP CALCULUS AB 2007 SCORING GUIDELINES (Form B)

AP CALCULUS AB 2007 SCORING GUIDELINES (Form B) AP CALCULUS AB 27 SCORING GUIDELINES (Form B) Question 2 A particle moves along the x-axis so that its velocity v at time 2 t is given by vt () = sin ( t ). The graph of v is shown above for t 5 π. The