AP Calculus AB - Practice Exam - Part A - Calculators Not Allowed

Sep 20, 2026

Uploaded by Aditya

AP Calculus AB Practice Exam - Part A focuses on core calculus concepts including tangency and slope, forming differential equations from real-world relationships, and analyzing concavity and graph behavior. The exam also tests continuity versus differentiability, interpreting derivative tables to determine increasing intervals, and understanding inverse and slope-related formulations. Additional questions evaluate continuity, differentiability, second-derivative inflection points, horizontal asymptote implications, and reasoning with derivatives from given diagrams and expressions. Suitable for timed assessment and skill review.

LanguageEnglish

CategoryExam

FormatPDF

Pages46

Reading Time1 h 56 min

AccessFree to download

Section 1, Part A

Directions and exam notes

Problems 3-16

AP Calculus AB Practice Exam Calculus AB Section 1, Part A Time-55 minutes Number of questions-28 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM Directions: Solve all of the problems that follow. Available space on the page may be used for scratch work. In this exam: (1) The domain of a function in this exam is assumed to be all real numbers for which the function is defined, unless specified otherwise. (2) The inverse notation or the prefix “arc” may be used to indicate an inverse function. For example, the inverse tangent of x may be written as arcsin(x) or as . Copyright © 2015 by Lucid Education Calculus AB 3. A line through the point (2, -2) is tangent to function f at the point ( -2, 6) . What is ? A) -8 B) -2 C) D) 6 E) Undefined 4. Grain is pouring out of an opening in the bottom of a grain silo. The rate at which the height, h, of the grain in the silo is changing with respect to time, t, is proportional to the square root of the height. Which of the following is a differential equation describing this situation? A) ~~ ~~ B) ~~ ~~ ~~ ~~ C) ~~ ~~ D) E) Calculus AB 5. Where is the graph of concave up? A) B) C) D) E) 6. Shown is a graph of function f. At which value of x isf continuous but not differentiable? A) a B) b C) c D) d E) e Calculus AB 7. The table shows values of , the derivative of function f. Although is continuous over all real numbers, only selected values of are shown. | x | -2 | -1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | | | 4.1 | 2.3 | 1.2 | 0 | -0.6 | -0.8 | -2 | 0 | 1.5 | If has exactly two real zeros, then f is increasing over which of the following intervals? A) B) C) only D) E) 8. . A) B) C) D) E) Calculus AB 9. At each point (x, y) on a graph of function f, the graph has a slope equal to . If the graph of f goes through the point (2, 3), then A) B) C) D) E) 10. The derivative of function g is given by . When is g increasing? A) B) C) D) E) Calculus AB 11. Function f is defined as Which of the following statements is true: I. f is continuous at . II. exists. III. f is differentiable at A) None of the statements are true. B) I only C) II only D) I and II only E) I, II, and III 12. Calculus AB 13. Shown is a graph of , the second derivative of function . The curve is given by the equation . The graph of has inflection points at which values of x ? A) b only B) c only C) a and d D) a and c E) d only 14. Function f is defined such that for all , the line is a horizontal asymptote. Which of the following must be true? A) is undefined. B) for all . C) D) All of the above. E) None of the above. Calculus AB 15. Shown in the diagram is a graph of , the derivative of function . If , then ? 16. A) B) C) D) E)

FAQs

What is the allowed tool for Part A of this practice exam?

A calculator may not be used on this part of the exam.

What does the exam state about the function domain (unless specified otherwise)?

The domain is assumed to be all real numbers for which the function is defined, unless specified otherwise.

How is increasing behavior determined in questions that use a derivative table?

The function is increasing on intervals where the derivative values shown are positive (and using all stated derivative information, not only the selected values).

What type of question asks for a differential equation describing a changing quantity?

The exam includes a grain-silo scenario where the height rate of change is proportional to the square root of the height; the task is to choose the option that matches the required differential equation form.

Sep 20, 2026

Uploaded by Aditya