Princeton Review BC Exam 1 - Cracking the AP Calculus AB & BC Exams - Section I, Part A

Sep 20, 2026

Uploaded by Hazel

Section I, Part A of an AP Calculus AB/BC practice examination (Time: 55 minutes; 28 questions) presents multiple-choice problems and detailed directions for answering on an answer sheet. The test covers core calculus skills including function domains, volumes of revolution, tangent and normal line concepts, periodic curve identification, derivative zero conditions, differential approximations, series interval of convergence, and average value. Additional questions compute related rates with a ladder, arc length for parametric curves, velocity from position vectors, inflection points, and volumes generated by rotation.

LanguageEnglish

CategoryExam

FormatPDF

Pages23

Reading Time58 min

AccessFree to download

A Calculator May Not Be Used on This Part of the Examination

Directions and Assumptions

Key Calculus Problem Sections (Multiple Choice)

SECTIONI,Part A Time—55 Minutes Number of questions—28 # A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAMINATION Directions:Solve each of the following problems,using the available space for scratchwork.After examining theform of the choices,decide which is the best of the choices given and fillin the corresponding oval on the answer.sheet.No credit will be given for anything written in the test book.Do not spend too much time on any one problem. In this test:Unless otherwise specified,the domain of a functionfis assumed to be the set ofall real numbers x forwhich f(x)is a real number. (A)x-e (C) (B)y-e× (E) 2.The volume of the solid that results when the area between the curvey=e and the line y=0,from x=1 tox=2,is revolved around the x-axis is(B)(C)(E)2πe²(A)2π(e⁴-e²)(D)2π(e²-e) (A) (B) (C) (D) (E) (E) (C) (D) (B)10tlnt+4t (A) 726■CRACKING THE AP CALCULUS AB&BC EXAMS 5. (D)-6 (E)6 (C)0 (B) (A) 6.The tangent line to the curvey=x³-4x+8at the point (2,8)as an x-intercept at (D)(0,8) (E)(8,0) (C)(0,-8) (B)(1,0) (A)(-1,0) The graph in the xy-plane represented byx=3sin(t)andy=2cos(t)is(C)a hyperbola (D)a parabola(E)a line(A)a circle(B)an ellipse 8. (A) (B) (C) (D) (E) 9. (B)2 (A)0 728■ CRACKING THE AP CALCULUS AB&BC EXAMS (C)4 (E)nonexistent (D)4π 10.The position of a particle moving along the x-axis at time t is given by x(t)=ecos²8),0≤t≤π.For which of thefollowing values of t will x'(t)=0? I.t=0II.III.t=π (B)I only (C)I and II only(D)I and II only (E)I,II,and III (A)I only (A)-1 (E)√2 (C) (B)0 (D)1 12.Use differentials to approximate the change in the volume of a cube when the side is decreased from 8 to 7.99 cm.(in cm³)(A)-19.2(B)-15.36(C)-1.92(D)-0.01(E)-0.0001 13.The radius of convergence ofis(A)(a-2)≤x≤(a+2)(B)(a-2)x>(a-2)(D)(a-2)>x>(-a-2)(E)(a-2)≤x≤(-a-2) 14. (A)0 (B) (C) 15.The equation of the line normal to(A)81x-60y =142(B)81x+60y=182(C)20x+27y=49(D)20x+27y=31(E)81x-60y=182 (D) (E) 16.If c satisfies the conclusion of the Mean Value Theorem for derivatives forf(x)=2 sinx on the interval [0,π],then c could be(A)0(B)(C)(D)π(E)There is no value of c on[0,π] 17.The average value of f(x)=x Inx on the interval [1,e]is (A) (C) (D) 18.A 17-foot ladder is sliding down a wall at a rate of-5 feet/sec.When the top of the ladder is 8 feet from theground,how fast is the foot of the ladder sliding away from the wall (in feet/sec)? (A) (D)-16 (E) (D) (E) (A)8e3sinx (B)8e³cosx (C)8e3sinx+3 20.The length of the curve determined by x=3t and y=2t²from t=0 tot=9 is(A)(B)(C)(D)(E) 21.If a particle moves in the xy-plane so that at timet>0 itsposition vector is (e²,e),then its velocityvector at time t=3 is(A)(In6,ln(-27))(B)(In9,In(-27))(C)(e⁹,e-27)(D)(6e⁹,-27e-27)(E)(9e⁹,-27e-27) 22.The graph of f(x)=√11+x²has a point of inflection at(A)(0,√11)(B)(-√11,0)(c)(0,-√11)(D)(E)There is no point of inflection. 23.What is the volume of the solid generated by rotating about the y-axis the region enclosed byy=sinx and the x-axis,from x=0 to x=π? (E)4 (D)2 (C)4π² (B)2π² (A)π² 24. (E)Undefined (D)2 (C)-1 (B)0 (A)1 25.A rectangle is to be inscribed between the parabola y=4-x²and the x-axis,with its base on the x-axis.Avalue of x that maximizes the area of the rectangle is (E) (D) (C) (B) (A)0

FAQs

How long is Section I, Part A and how many questions does it contain?

Time is 55 minutes and there are 28 questions.

What are the main rules for answering the multiple-choice questions?

Solve using the provided scratch space, select the best choice from each problem, and mark the corresponding oval on the answer sheet; no credit is given for work written in the test book.

What general domain assumption is used unless stated otherwise?

The domain of a function f is assumed to be all real numbers x for which f(x) is real.

Sep 20, 2026

Uploaded by Hazel