ACCUPLACER® Advanced Algebra and Functions Practice Test

The ACCUPLACER® Advanced Algebra and Functions test is a computer-adaptive test comprised of 20 questions that assess your advanced algebra knowledge. To help you prepare for this section of the ACCUPLACER, this page contains everything you need to know, including what topics are covered, how many questions there are, and how you can study effectively.

Click “Start Test” above to take a free ACCUPLACER Advanced Algebra and Functions practice test!

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What’s on the Test?

ACCUPLACER Advanced Algebra Practice Questions

One of the best ways to test your knowledge is by taking a practice test. Evaluate your algebra skills by trying your hand at the four practice questions below!

Answer each question and read through the answer explanation, whether you got the answer right or wrong. This will help you ensure you’ve got the topic mastered.

Whether you struggled with these questions or aced them on your first try, be sure to take the full practice test to get a better idea of how prepared you really are!

1. Two companies offer monthly cell phone plans, both of which include free text messaging. Company A charges a $25 monthly fee plus five cents per minute of phone conversation, while Company B charges a $50 monthly fee and offers unlimited calling.

At what total duration of monthly calls do both companies charge the same amount?

A. 500 hours B. 8 hours and 33 minutes C. 8 hours and 20 minutes D. 5 hours

The expression representing the monthly charge for Company A is $$25+$0.05m$, where $m$ is the time in minutes spent talking on the phone. Set this expression equal to the monthly charge for Company B, which is $50. Solve for $m$ to find the number of minutes the two companies charge the same amount.

$$25+$0.05m=$50$

$$0.05m=$25$

$m=500$

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2. In the triangle below, which of the following is equal to $\sin \theta$ ?

A. $\frac{a}{2b}$ B. $\frac{2b}{a}$ C. $\frac{a}{2c}$ D. $\frac{b}{ac}$

This problem is most easily solved using the law of sines, which states that the ratio of the sine of each angle in a triangle to the length of the opposite side is equal:

$\frac{\sin ⁡A}{a}=\frac{\sin ⁡B}{b}=\frac{\sin ⁡C}{c}$

In this case, $\angle \theta$ is opposite side $a$, and the angle with a measure of 30° is opposite side $b$, so we can write $\frac{\sin⁡ \theta}{a}=\frac{\sin 30°}{b}$. Since $\sin⁡ 30°=\frac{1}{2}$, this becomes $\frac{\sin \theta}{a}=\frac{\frac{1}{2}}{b}$, or $\sin ⁡\theta=\frac{a}{2b}$.

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3. What is $\log_5⁡(5^3)$ ?

A. −2 B. 1 C. 3 D. 243

For any base $b$, $\log_b⁡ x$ and $b^x$ are inverse functions, so $\log_b⁡(b^x)=b^{\log_b⁡x} =x$. It is also true that $a^c=b$ is equivalent to $\log_a⁡c=b$ for any positive $a$ and $c$.

Therefore, $\log_5 (5^3 )=3$.

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4. If $3^x=2$, then what is the value of $x$ ?

A. 9 B. $\sqrt{3}$ C. $\sqrt[\Large{3}]{2}$ D. $\log_32$

To solve the equation, we need to take the logarithm base three of both sides of the equation. Note that $b^x$ and $\log_b⁡x$ are inverse functions and cancel each other out for any positive base $b$.

Then we have $\log_3⁡(3^x)=\log_3⁡2$, or simply $x=\log_3⁡2$.

Alternatively, just keep in mind that $a^b=c$ is equivalent to $\log_a⁡c=b$ for any positive $a$ and $c$, so $3^x=2$ is equivalent to $\log_3⁡2=x$.

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ACCUPLACER Online Prep Course

If you want to be fully prepared, Mometrix offers an online ACCUPLACER prep course designed to give you everything you need to succeed!

Here’s what you’ll find in the ACCUPLACER course:

70+ Review Lessons Covering Every Topic
Over 1,750 ACCUPLACER Practice Questions
550+ Digital Flashcards
270+ Instructional Videos
Money-back Guarantee
Mobile Access

Everyone learns differently, so we’ve tailored the ACCUPLACER online prep course to ensure every learner has what they need to prepare for the ACCUPLACER exam.

Click below to check it out!

FAQs

Q

How many questions are on the test?

A

There are 20 questions in total on the ACCUPLACER Advanced Algebra and Functions subtest.

Q

How do you pass the ACCUPLACER Advanced Algebra and Functions test?

A

There is no "pass/fail" scoring system for this subtest. Your score will be placed on a score range of 200-300. Your placement on that range will indicate your mathematics knowledge and abilities.

To achieve a high score, you will need to spend an adequate amount of time studying for the test.

Q

What is a good score on the ACCUPLACER Advanced Algebra and Functions test?

A

Your test score will be placed on a score range of 200-300. Within that range are five score bands:

200-236
237-249
250-262
263-275
276-300

A good score to aim for is the 263-275 score band.

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By Lauren Stewart

Lauren graduated from Lamar University with a bachelor’s degree in Interdisciplinary Studies and spent many years in education, primarily teaching math. Lauren recognizes the common struggle with math and has a passion for helping others feel confident in their math abilities. She uses her background in education to help develop K-12 products and create instructional content, practice questions, and videos.

Edited by Aaron Lanni

Aaron is the content manager and lead editor for Mometrix Academy. He regularly produces, updates, proofreads, and edits content to ensure it meets Mometrix’s quality and accessibility standards.

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