CALCULUS AB - Section I, Part A - Number of questions-28 - Time-55 Minutes

Sep 20, 2026

Practice examination for Calculus AB, Section I, Part A, with 28 multiple-choice questions to be solved in 55 minutes. Instructions require selecting the best answer choice and marking the corresponding oval on the answer sheet, with no credit for writing in the test book. The exam includes guidance on function domains being all real numbers unless otherwise specified, plus problems involving derivatives, integrals, continuity and differentiability conditions, tangent line slopes, normal line equations, and average value of functions.

LanguageEnglish

CategoryExam

FormatPDF

Pages20

Reading Time50 min

AccessFree to download

Number of questions—28

Section I, Part A

Directions and assumptions

Problem set (1–25)

CALCULUS AB SECTION I,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 answersheet.No credit will be given for anything writen 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 of all real numbers x forwhich f(x)is a real number. 1. ,then f'(8)= (D)80 (E) (C)40 (A)10 (B) 2. (D) (E)∞ (C) (A)0 (B) THE PRINCETON REVIEW APCALCULUS AB PRACTICE TEST 1翻535 (A)1 (B) (C) (D)(E) 4.If the function fis continuous for all real numbers and if(B)8(A)1(C)-1(D)0(E)undefined (A) (B) (C) (D) (E) 6.Which of the following integrals correctly corresponds to the area of the shaded region in the figure above?(C)(D)(E) 7.Iff(x)=secx+cscx,thenf(x)=(A)0 (B)sec²x+csc²x.(C)cscx-secx (D)sec x tan x+cscx cot x(E):sec x tan x-cscx cot x 8.An equation of the line normal to the graph of y=√(3x²+2x)at(2,4)is(A)-4x+y=20 (B)4x+7y=20(C)-7x+4y=2 (D)7x+4y=30 (E)4x+7y=36 9. (A)0 (B)π (C)1 (D)2π (E)2 10.If f(x)=cos²x,thenf"(π)=(E)2π(A)-2(B)0(C)1(D)2 (E) (A)-3 (B) (C)3 (D)5 12. (A) (B) (C) (D) (E) 13.The slope of the line tangent to the graph of 3x²+5lny=12at(2,1)is (E)-7 (D)12 (C) (B) (A) 14.The equation (E)2π (D)8 (B) (C) (A) ,for all real numbers x,which of the following must be true? I.f(x)is continuous everywhere. I.f(x)is differentiable everywhere.Ⅲ.f(x)has a local minimum at x =2 (A)I only (B)I and Ⅱ only (C)II and I only(D)I and IⅢ only (E)I,II,and Ⅲ 16.For what value of x does the function f(x)=x³-9x²-120x+6 have a local minimum?(A)10(B)4(C)3(D)-4(E)-10 17.The acceleration of a particle moving along the x-axis at timetis given by a(t)=4t-12.If the velocity is 10whent=0 and the position is 4 whent=0,then the particle is changing direction at(A)t=1(B)t=3(C)t=5(D)t=1 andt=5(E)t=1 andt=3 andt=5 18.The average value of the function f(x)=(x-1)²on the interval fromx=1 to x=5 is (E) (D) (C) (B) (A) 19. (A) (B) (C). (D) (E) GO ON TO THE NEXT PAGE 20.If f(x)=√(x³+5x+121)(x²+x+11)then f(0)=(A)(B)(C)22(D)(E) 21.If f(x)=53×thenf(x)=(A)5³×(ln125)(B)(C)3(5²x)(D)3(53x)(E)3x(5³x-1) 22.A solid is generated when the region in the first quadrant enclosed by the graph ofy=(x²+1)³,the line x=1,the x-axis,and the y-axis is revolved about the x-axis.Its volume is found by evaluating which of thefollowing integrals? (A) (B) (C) (D) (E) 23. (A)2 (B) (B)±√66 (A)18 25. (A) (B) (C) (D) (E) (C)○ (C)58 (D)0 (E)undefined (E)±√58 (D)±√74 GO ON TO THE NEXT PAGE

FAQs

How many questions are in this Calculus AB practice section, and what is the time limit?

This section has 28 questions and a time limit of 55 minutes.

Are calculators allowed for this part of the examination?

No. A calculator may not be used on this part of the examination.

What is the default assumption about the domain of a function unless otherwise specified?

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

Sep 20, 2026

Uploaded by Emma Wilson