By William Ma
An interesting new sequence of research courses that shall we each one pupil layout a process examine pitched to his or her person wishes and studying style
Each yr, a couple of million U.S. highschool scholars take a number of complicated placement (AP) assessments, and, based on respectable projections, that quantity will proceed to upward thrust within the years forward. that's simply because AP tests confer very important merits on those that do good on them. excessive AP ratings are quintessential to gaining admission to so much elite faculties. they supply scholars with a aggressive part whilst competing for gives you and scholarships. they usually permit scholars to avoid required college survey classes, saving on skyrocketing university fees.
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Additional resources for AP Calculus AB
Draw a possible graph of f ′ on (a, b). Figure D-2 y 10. If h( x) = f x ∫π 2 sin t dt , find h′(π). 11. What is the average value of the function y = e−4x on [−ln 2, ln 2]? a c 0 d e f b x 12. The graph of f consists of four line segments, for −1 ≤ x ≤ 5 as shown in Figure D-3. What is the value of ∫ f ( x)dx ? 5 −1 y Figure D-1 6. If f ( x) = 2xe x , what is the value of lim f ′( x) ? f x → 0+ 7. Evaluate 8. If ∫ 1 − x2 dx. x2 ∫ (2x − 3)dx k −1 –1 0 1 2 3 = 6, find k. 9. The graph of the velocity function of a moving particle is shown in Figure D-2.
Set v(t ) = 0 ⇒ t (t − 1) = 0 ⇒ t = 0 or t = 1 16. From Chapter 8 Let u = 3x; du = 3dx or ∫ g(3x)dx a(t ) = v ′(t ) = 2t − 1 du = dx 3 Set a(t ) = 0 ⇒ 2t − 1 = 0 or t = du 1 g(u) = ∫ g(u)du 3 3 = ∫ = 1 1 f (u) + c = f (3x) + c 3 3 ∫0 g(3x)dx = Since the graph of g is decreasing and then increasing, It is not monotonic. Thus only statements II and III are true. At x = 0, y = cos( xy) = cos(0) = 1; (0, 1) 2 d ( tan x) x 4 dx π = sec2 = 4 15. From Chapter 6 y = cos( xy) ; ∆x 1 Since v(t ) < 0 and a(t ) > 0 on , 1 , 2 the speed of the particle is decreasing on 2 1 1 1 f (3x)]0 = f (6) − f (0) [ 3 3 3 1 , 1 .
Org/ap/calculus. What Are the Advanced Placement Exam Grades? Advanced Placement Exam grades are given in a 5-point scale with 5 being the highest grade. The grades are described below: 5 4 3 2 1 Extremely Well Qualified Well Qualified Qualified Possibly Qualified No Recommendation 0267-02/Part II 12/18/2001 17:23 Page 14 14 • What You Need to Know About the AP Calculus AB Exam How Is the AP Calculus AB Exam Grade Calculated? • The exam has a total raw score of 108 points: 54 points for the multiple-choice questions in Section I and 54 points for the free-response questions for Section II.
AP Calculus AB by William Ma