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AP Calculus BC Practice Quiz: Ratio Test for Convergence

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 7 questions to check your progress.

Question 1 of 7

According to the provided text, what is the primary function of the ratio test?

All Questions (7)

According to the provided text, what is the primary function of the ratio test?

A) To find the sum of a series

B) To determine whether a series converges or diverges

C) To calculate the limit of a sequence

D) To find the derivative of a function represented by a series

Correct Answer: B

The provided content explicitly states that the ratio test is a method 'to determine whether a series of numbers converges or diverges.'

A student is given an infinite series and asked to analyze its behavior. Which of the following tasks is the ratio test designed to accomplish?

A) Determining if the series has a finite sum or not

B) Calculating the exact value to which the series converges

C) Finding the interval of convergence for a power series

D) Approximating the value of the series using a partial sum

Correct Answer: A

The content specifies that the ratio test's purpose is to 'determine whether a series converges or diverges.' A series that converges has a finite sum, while one that diverges does not. Therefore, the test helps determine if the sum is finite.

The provided text indicates that the ratio test is a topic exclusive to a specific AP Calculus course. Which course is it?

A) AP Calculus AB

B) AP Calculus BC

C) Both AP Calculus AB and AP Calculus BC

D) AP Statistics

Correct Answer: B

The content includes the specific note '(BC ONLY)' in its description of the ratio test, indicating it is a topic for the AP Calculus BC exam.

The ratio test is a method applied to what kind of mathematical object?

A) A function of a single variable

B) A sequence of numbers

C) A series of numbers

D) A definite integral

Correct Answer: C

The text states that the ratio test is used to 'determine whether a series of numbers converges or diverges,' identifying a 'series of numbers' as the object of the test.

Which of the following questions about a series can be answered using the ratio test?

A) What is the rate of change of the series?

B) What is the value of the 10th term in the series?

C) Does the sum of the terms in the series approach a specific finite value?

D) What is the average value of the terms in the series?

Correct Answer: C

The ratio test determines convergence or divergence. A series converges if the sum of its terms approaches a specific finite value. Therefore, the ratio test helps answer this fundamental question about the series's behavior.

The outcome of applying the ratio test to a series provides information about its...

A) convergence or divergence.

B) periodicity.

C) continuity.

D) differentiability.

Correct Answer: A

Based on the provided text, the sole purpose of the ratio test described is to 'determine whether a series converges or diverges.'

Based on the provided information, which statement is a correct description of the ratio test?

A) It is a method for finding the sum of a geometric series.

B) It is a tool used exclusively in AP Calculus AB to test for divergence.

C) It is a method for determining if a series converges, and it is a topic in AP Calculus BC.

D) It is a test that can only be applied to series with positive terms.

Correct Answer: C

The content confirms two facts: the ratio test is used to 'determine whether a series converges or diverges,' and it is a '(BC ONLY)' topic. Option C correctly combines these two pieces of information.