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Free ACCUPLACER Arithmetic Practice

Question #1

Which of the following fractions is equal to 0.12?

a. 1/12

b. 1/120

c. 12/10

d. 12/100

To easily convert a decimal number to a fraction, start by deciding how many digits are after the decimal number. In this case – there are two, meaning the denominator should be 100 (if there was one, it would be 10, three would mean 1,000 and so on).

Now, the nominator is number that is after the decimal point, in this example 12, giving us the correct answer.

Notice, that the answer could also have been 6/50 or 3/25, in this case follow the first footsteps to reach the basic fraction, and then divide both the nominator and denominator by the same number.

Question #2

What is 1,466 + 734.

a. 1,200

b. 1,350

c. 1,555

d. 2,200

While you can perform a full calculation to achieve the correct answer – it is unnecessary at times. In this question, you can immediately eliminate the first 2 answers – by realizing both are smaller than the first number, where the calculation is additive. As for the third answer, you can eliminate it in two ways:

1. The question adds 1,4XX with 7XX, meaning the answer should be at least 2,100.

2. The unit's digit is 6+4 = 10, meaning the answer should be X,XX0. Any answer with another unit's digit can be immediately eliminated.

ACCUPLACER tip – work with the answers: While mostly a time-saving technique, working with the answers is highly useful even when there's no time limit. In both mathematics and English – the answer can help you either better understand the question or can be eliminated before fully answering a question.

The latter is highly important considering the educated guess technique – in which you narrow down as many answers as possible before choosing an answer, increasing the chances of being correct.

Question #3

P, W, Y and  Z are equal to:

Which of the following is true?

In order to place the given equations on a number line, first solve each exercise and compare the results.
To solve and , use long multiplication:

Do not forget to move the decimal point back to the left.

Do not forget to move the decimal point back to the left.

To solve , convert the mixed fraction to an improper fraction, invert the second fraction, and then multiply.

To solve , multiply the fractions, then convert the result to a decimal number.

(Note that this decimal is an infinite number.)

The calculated results of P, W, Y, and Z are: , , , . W is the highest,Y is the lowest, and Z is lower than P:

The correctly coordinated number line corresponds to answer (1).

Question #4

30% of the students in the local college are active in animal rights organizations and 90% of animal rights activists are not active in any other group. How many students are both animal rights activists and active in another group if there are 1200 students in the college?

A. 30

B. 36

C. 120

D. 360

This kind of problem requires an understanding of the relationship between a given percentage and the proportion it represents (and vice versa). This relationship is represented by the following formula:

Specifically, this problem requires finding a portion of a whole. Isolate this variable from the formula:

Method A:

In order to find a proportion from a whole, use the following two steps:
Step 1: Total number of students active in animal rights organizations:

Step 2: Total number of students who are animal rights activists and are also active in another group are 10% of the animal rights activists :

Method B:

Calculate the percentage of students active in both animal rights and another group - out of the all the students:

Now, use the formula to find the number of students 3% represents:

There are 36 students who are both animal rights activists and activists in another group; therefore, the correct answer is (B).

If you chose answer (A), recheck your calculations. If you chose answer (C), you probably forgot to calculate the activists in two groups only from the animal right activists. If you chose answer (D), you probably forgot to subtract the students who are not active in any other group.

The ACCUPLACER Arithmetic Test consists of 20 questions and focuses on computation with basic mathematical operations, using integers, fractions, decimals, and percentages. You will need to be

able to determine the relevant solving methods from given contexts, you must be familiar with the order of operations, and you must be able to make estimations and compare values between different expressions.

Next, is a different type of mathematical section – the QAS (Quantitative Reasoning, Algebra, and Statistics). Let's continue.

ACCUPLACER Quantitative Reasoning, Algebra, and Statistics Practice

Question #1

How many centimeters are in 250 meters? (1 meter = 100 centimeters)

a. 2.5

b. 2,500

c. 25,000

d. 250,000

When converting measurements, first start by deciding whether the required measurement is bigger or smaller than the given (in this case meter is bigger than centimeters, therefore the quantity of centimeters should be greater than meters). By this, answer a is immediately eliminated.

Next, convert by multiplying the number of meters (250) in the conversion ratio (100). In this case, you can simply add two zeros to the provided number of meters, so the answer is: 250X100 = 25,000.

Question #2

If in 2012 the population was 5 million, how many unemployed had a bachelor's degree?

a. 2,500

b. 25,000

c. 250,000

d. 2,500,000

The percentage of unemployed people with a bachelor's degree is 5 out of a population of 5 million people. Therefore, the number of unemployed people with a bachelor's degree is: 5,000,000*0.05= 250,000

ACCUPLACER tip – conversion: Since conversion may be challenging at times, always try to simplify the calculations, even if it means more calculations are needed. As long as you work methodically, writing down each step – it is better to have more simple calculations than a few complicated ones. I.e., when working with percentages, start by calculating how much is 1/10% of the given number, and then multiply by the required amount to achieve the answer.

Question #3

Which of the following is true?

A. Element A is greater than Element B

B. Element B is greater than Element A

C. Element B is equal to Element A

D. There is not enough information to determine the answer

Note that is positive.

The value of is squared, so it must be positive.

Therefore, the correct answer is (B).

If you chose any other answer, you probably did not reduce correctly.
Question #4

Three identical water hoses can fill twenty swimming pools in two hours. How many water hoses are needed in order to fill thirty swimming pools in an hour?

*Assume that all hoses pump at the same constant water flow.

A. 4

B. 9

C. 10

D. 12

To solve the problem, calculate how much water flows through each hose per hour.

Given that in two hours three hoses fill 20 pools, in an hour (half the time), three hoses will fill pools.

Now find how many water hoses are needed to fill 30 pools in an hour, as asked in the problem:

One hour: three hoses can fill ten pools; therefore, in order to fill thirty pools at the same time, multiply the number of hoses:

Therefore, the correct answer is (B).

If you chose answer (A) or (D), you probably did not calculate the correct number of pools filled in one hour. If you chose answer (C), you probably calculated the number of water hoses incorrectly.

The ACCUPLACER QAS Test consists of 20 multiple-choice questions and assesses your knowledge of and competence with a number of related mathematical concepts. The topics include algebraic reasoning, linear expressions and inequalities, plotting and graph

interpretation, ratios, and probability. You will be asked to apply a conceptual understanding of these topics, as well as to determine when they are necessary based on varying contexts that will be described.

Let's move on to the final, and most challenging mathematical section – Advanced Algebra and Functions.

ACCUPLACER Advanced Algebra and Functions Practice

Question #1

y(x) = 6x + 11.
What is the value of y(9)?

a. 43

b. 65

c. 54

d. 20

Substitute x with the number 9: y(9) = 6X9 + 11 y(9) = 54 + 11 y(9) = 65

Once again – you can use elimination for the answers if you are uncertain:

a and d are eliminated since they equals less than 6X9.

c is eliminated since it equals exactly 6X9, but there's an additive portion to the equation.

Question #2

What is the common domain of the two functions?

a.

b.

c.

d. All numbers

e. No common domain

The value under the root sign should be greater or equal to zero. The denominator should not be equal to zero. Therefore, the domain of the functions is defined by the two.

First find the domain of :

Therefore, the domain  of is .

First find the domain of :

Therefore, the domain of is .

The two domains do not overlap; therefore, no common domain exists for the two functions. Accordingly, the correct answer is (E).

If you chose any other answer, review the solution.
Question #3

Given the expression , what is the value of the acute angle that will yield the greatest value of the expression?

A. -330

B. 0

C. 30

D. 60

E. 90

Remember:

Simplify the expression given in the question - :
Note: .
Accordingly:

The most simplified form of the expression is:

Simplify the problem without changing its meaning:
The simplified form: What is the largest value can have? Calculate the acute value of in this case.
Use trigonometric functions definitions and the unit circle to answer the question:
According to cosine definition, the largest value any cosine function can have is .
Therefore, is the largest value of the function above.
Solve the equation:

The solutions to the problem are:
The angle the question is asking about is an acute angle. Therefore is the only possible solution.

Accordingly, the correct answer is (C).

If you chose answer (A), you disqualified the wrong answer. If you chose answer (B), you stopped the solution in the middle. If you chose answer (D) or (E), review your calculations and the cosine function definition.

The ACCUPLACER Advanced Algebra and Functions Test consists of 20 multiple-choice questions that assess your ability to solve problems related to college-level math material. The questions adapt to your level based on your answers. This section covers a wide range of advanced algebraic concepts, and even some geometry and trigonometry.

ACCUPLACER Scores – Each section of the ACCUPLACER test (except the WriterPlacer) provides a score range of 200-300, which is divided into five score bands as such:

1. 200-236

2. 237-249

3. 250-262

4. 263-275

5. 276-300

Since the test is adaptive, the score is not only based on how many questions you got right – but also on how far you've made it in the difficulty level of each section. It is crucial to not only prepare for each section but also study and practice questions of different difficulties.

Our ACCUPLACER Prep Pack contains hundreds of questions for each section (including an essay guide and examples – explained later in this page), with different difficulty levels for you to understand the different approach for different questions, as they increase in difficulty.

Starting at the price of 59\$, you can begin your ACCUPLACER practice today!

We are finally finished with the mathematical portion of the ACCUPLACER test. However, the test is far from over. Let's continue to the ACCUPLACER Reading section.

Question #1 + #2

In February I switched to a new school called E. Heart Coed Union. This was especially difficult for me coming from an all-boys private school, but there were many advantages as well. As part of its new curriculum, the school offered special afternoon music lessons in order to foster musical students. I really enjoy those classes, and I think the others are okay as well. This might come as a surprise to all who hear me refer to the school as the “no education school.”

This is not actually due to any fault of its own, but rather to the sheer misfortune of chance along with my own creative brain. An anagram is formed when letters in a word, name, or phrase are rearranged to create other words; an anagram is even wittier if the newly created words are related to or describe the original ones. I happen to be pretty good at coming up with them: The letters that make up the words ‘the eyes’ can be rearranged to create the words “they see.” That one, though not as impressive, was appreciated by my teachers much more than when I explained how our school’s name could be rearranged to form the words, “no education here.”

1. Which is the best description of the relationship between the second underlined sentence and the first?

A. The second sentence describes an effect of the first.

B. The second sentence illustrates what is explained in the first.

C. The second sentence expands on the first.

D. The second sentence contrasts with the first.

2. Choose the words that can best replace the underlined word “foster” from the passage:

A. Augment

B. Nurture

C. Compliment

D. Deter

The first sentence explains what an anagram is and what makes a good one. The second sentence gives an example of a clever anagram that accomplishes what the sentence describes. Thus, it illustrates the point.

2. The correct answer is (B) nurture, which means to support and encourage, which is similar to the meaning of “foster.”

All other options do not fit the sentence:
To augment means to “enlarge.”
To compliment means to “say something nice to someone.”
To deter means to “discourage someone from acting a certain way.”
To adopt means to “take upon something as your own” or to “assume the care for something or someone.”

ACCUPLACER tip – read the questions before the text: This is also usually a time-saving technique, but it is very useful even when there's no time limit. By reading the question first – you know what you are looking for in the text, and therefore you can put greater emphasis on the required information, rather than getting lost in a lot of data.

Question #3

PDF is a file format that can be used to present documents regardless of which software, hardware, and operating systems one has available. PDF was developed in the early 1990s as a way to share documents among computer users of varying platforms who may not have access to compatible software. Each PDF file includes the text, fonts, graphics, and other information needed to display a document.

This passage is primarily about ____

a. Why people use PDF.

b. How PDF is displayed.

c. PDF and its use.

d. The development of PDF.

The passage discusses PDF files and their use.
Answer (a) is incorrect because while some of the reasons people use PDF are mentioned in the passage, it is not the main idea.
Answer (b) is incorrect because the passage does not mention how PDF is displayed. It does mention what information a PDF file includes in order to display it; however, this is not the main idea of the passage.
Answer (d) is incorrect because while the passage does mention when PDF was developed, it is only mentioned briefly.
Question #4

The industrious bee is often admired for its work ethic and role in pollination. Bees travel from flower to flower, collecting nectar, which they convert into honey, their food source. This process also results in the cross-pollination of plants, a critical step in the reproduction of many types of flora. Without bees, many of the fruits and vegetables humans rely on would fail to reproduce, leading to drastic consequences for global food supplies.

What is the primary role of bees in the ecosystem as described in the text?

a. Producing honey for human consumption

b. Serving as a food source for other animals

c. Facilitating the process of cross-pollination

d. Decorating gardens with their presence

Correct Option (c): The text specifically mentions that bees are critical for the "cross-pollination of plants," which is "a critical step in the reproduction of many types of flora." This indicates that the primary role of bees in the ecosystem, as described, is to facilitate cross-pollination, making option (c) the correct answer.

Incorrect Option (a): While the text does state that bees convert nectar into honey, it does not indicate that this is their primary role in the ecosystem. Honey production is mentioned as a byproduct of their nectar collection, which is primarily for their food source, not specifically for human consumption.

Incorrect Option (b): Although bees can serve as a food source for other animals, the text does not discuss this role. Therefore, it is not the primary role highlighted in the passage.

Incorrect Option (d): The text does not mention anything about bees decorating gardens with their presence. This option is not supported by the information provided in the passage and is therefore incorrect.

There are 20 multiple-choice questions, four of which relate to a single literary text, another four to one informational passage, and the remaining 12 as standalone questions on various types of informational writing. The questions ask you to (a) summarize information and draw conclusions, such as determining main ideas and identifying relationships between characters or pieces of information, (b) interpret rhetoric and analyze elements such as structure, purpose, and argument, (c) analyze connections between different texts, and (d) determine the meaning of words based on context and knowledge of vocabulary.

Let's move on to a different verbal section – the ACCUPLACER Writing section.

Free ACCUPLACER Writing Sample Questions

The ACCUPLACER Writing Test consists of 25 questions spread out over four informational passages and one literary passage. Unlike the reading section, there are no standalone questions, and each passage was written specifically for the test.

The level of the passage and its questions is dependent on your answers to the previous ones. The questions are all multiple choice, and they each ask you to recognize errors and/or make revisions for optimal writing.

The errors you must correct can relate to (a) grammatical norms, (b) the structure of the passage or its sentences, (c) the style and tone for the given purpose or type of writing, (d) logical progression and continuity of the content, and (e) the relevance of the information to the topic or its efficiency in conveying the point or supporting the argument at hand.

Question #1 + #2

1) Despite being known as a popular summer treat around the world, watermelon was once a staple of an individual culture, and it has a surprisingly long history that dates back to ancient times. (2) This fruit was first cultivated in the Nile River Valley in Egypt over 5,000 years ago. (3) It was later introduced to other parts of the world, including the Americas. (4) The ancient Egyptians used watermelons for a variety of purposes, including food, medicine, and even as containers for water. (5) From Egypt, the fruit spread to other parts of the Mediterranean region, such as Greece and Rome. (6) Today, watermelon is grown in more than 100 countries worldwide.

1. Which is the best version of the underlined portion of sentence 2 (reproduced below)?
"This fruit was first cultivated in the Nile River Valley in Egypt over 5,000 years ago."
a.  (as it is now)
b. were first cultivated
c. has been first cultivated

2. Which is the most logical placement for sentence 3 (reproduced below)?
"It was later introduced to other parts of the world, including the Americas."
a. Where it is now
b. After sentence 4
c. After sentence 5
d. After sentence 6

1. a (as it is now)
In sentence 2, the verb "was" is correctly used in the past tense to indicate that watermelon was first cultivated in the Nile River Valley in Egypt over 5,000 years ago. The verb "were" in option B would not be appropriate because the word "fruit" is singular, and "were" is used for plural words. Options C and D use incorrect tenses, "has been" and "had been" respectively, which do not convey the intended meaning of the sentence.

2. c (After sentence 5)

As it appears above, the passage begins with an introduction to the topic, then takes us to ancient Egypt where watermelon originated. We then have our sentence in question which tells us that watermelon spread to other parts of the world. After that, we go back to Egypt and discuss its role there and the different things it was used for. Next, we state again that it spread from Egypt to other areas in the region, closer than the ones we already mentioned. Then we conclude with watermelon in over 100 countries today.

Clearly, this passage is jumping around and out of order, so the sentence in question must not be in the ideal spot. It does not make sense that we should move on to declare how far watermelon spread, then go back to discussing its uses in Egypt, then back again to where it spread from Egypt. Rather, we should finish talking about Egypt (sentence 4 appearing after sentence 2), then discuss how it spread in logical order--first spreading from Egypt to nearby areas (sentence 5), then to the rest of the world (sentence 3), and then finally concluding the passage with its status nowadays (sentence 6). Therefore, the most ideal placement is directly after sentence (5), as in option C.

Question #3 + #4

Text: (1) The concept of urban green spaces has gained significant momentum in city planning discussions around the world. (2) These areas, often consisting of parks, community gardens, and greenways, serve as vital lungs for metropolitan areas, offering residents a respite from the concrete jungle. (3) Beyond their aesthetic value, green spaces are recognized for their role in improving air quality, reducing urban heat islands, and providing habitats for various species. (4) They also offer a venue for physical activity, social interaction, and community events, contributing to the overall well-being of city dwellers. (5) Consequently, many cities are now integrating green spaces into their development plans, acknowledging their multifaceted benefits.

(6) However, the implementation of these green spaces is not without challenges. (7) Land in urban areas is a scarce resource, and dedicating valuable plots to green spaces can be contentious. (8) Furthermore, the maintenance of these areas requires ongoing commitment and resources, which can strain municipal budgets. (9) Despite these hurdles, the push for more green spaces continues, driven by public demand and the growing body of evidence supporting their positive impact on urban life. (10) As cities evolve, the balance between development and the preservation of green spaces remains a critical consideration for urban planners.

3. Which is the best version of the underlined portion of sentence 7 (reproduced below)? Land in urban areas is a scarce resource, and dedicating valuable plots to green spaces can be contentious.

a. (as it is now)

b. can be content

c. could be contentious

d. are contentious

4. Which is the best version of the underlined portion of sentence 4 (reproduced below)? They also offer a venue for physical activity, social interaction, and community events, contributing to the overall well-being of city dwellers.

a. as it is now

b. contributing to city dwellers' overall well-being

c. which contributes to the overall well-being of those living in cities

d. that contributes to the well-being of city dwellers overall

1. a (as it is now)

The sentence correctly uses "can be contentious," indicating that dedicating land to green spaces might lead to disagreements or debates. The phrase is appropriately cautious and reflects the potential for controversy without asserting that contention is inevitable, fitting the context of urban planning challenges.

2. b

This option maintains the clarity and conciseness of the original sentence while slightly rephrasing it for improved readability. It effectively communicates the positive impact of urban green spaces on the well-being of those living in cities without changing the meaning of the original sentence. The possessive form "city dwellers'" before "overall well-being" makes the sentence more direct and personal, emphasizing the benefit to the individuals.

The ACCUPLACER Writing Test consists of 25 questions spread out over four informational passages and one literary passage. Unlike the reading section, there are no standalone questions, and each passage was written specifically for the test. The questions ask you to recognize errors and/or make revisions for optimal writing. The errors you must correct can relate to (a) grammatical norms, (b) the structure of the passage or its sentences, (c) the style and tone for the given purpose or type of writing, (d) logical progression and continuity of the content, and (e) the relevance of the information to the topic or its efficiency in conveying the point or supporting the argument at hand.

As the multiple-choice part of the test is finally completed, it is now time to move to the final part of the ACCUPLACER test – the WriterPlacer Essay.

WriterPlacer Essay

If you are taking the WritePlacer along with the Accuplacer, the last thing you will be asked to do is respond to a prompt in essay form. The prompt may be a short passage to consider and develop an opinion about it, along with guiding questions to address in your response, or reactions to similar stimuli based on careful thought about the subject. You need to show your sophistication of thought and creativity of ideas, your communication skills and ability to express complex ideas in writing, as well as your understanding and proper application of grammatical norms.

The scores range from 1 (low score) to 8 (high score). Different dimensions, such as critical thinking, structure and sentence variety, among others, are measured to provide the overall score.

Let’s see examples of high-score and low-score essays:

Passage: In a rapidly evolving world, the concept of success is often linked to personal achievement and the ability to overcome obstacles. Many argue that success is the result of hard work, determination, and personal responsibility. However, this perspective overlooks the significant impact that external factors such as socioeconomic status, education, and family support can have on an individual's ability to succeed. These external factors can either pave the way for success or create insurmountable barriers that are difficult to overcome.

Assignment: To what extent do external factors influence an individual's ability to achieve success? Plan and write a multi-paragraph essay (approximately 300–600 words) in which you develop your point of view on the above question. Support your position with reasoning and examples taken from your reading, studies, experience, or observations.

Sample Essay #1 - High Score

Success, a concept often defined by personal achievement and the overcoming of obstacles, is not solely the product of an individual's efforts. While hard work and determination play crucial roles, the impact of external factors such as socioeconomic status, education, and familial support cannot be understated. These elements serve as either stepping stones or stumbling blocks on the path to success.

Consider the role of education. It is a gateway to opportunities, offering the knowledge and skills necessary to navigate the complexities of the modern world. However, access to quality education is not universal. Individuals born into communities with underfunded schools face an uphill battle, struggling to attain the same level of preparedness as their peers from more affluent areas. This disparity illustrates how external factors can significantly influence one's chances of success.

Socioeconomic status further exemplifies this point. Those born into wealth have access to resources that can cushion failures and amplify successes. In contrast, individuals from lower-income families often lack this safety net, making each setback potentially devastating. The stress of financial instability can hinder one's ability to focus on long-term goals, thus impacting their overall trajectory towards success.

Family support, both emotional and financial, is another critical external factor. A supportive family can provide encouragement, guidance, and resources that pave the way for success. Conversely, the absence of such support can leave individuals feeling isolated and overwhelmed, making it considerably more challenging to pursue ambitious goals.

In light of these considerations, it becomes clear that external factors play a significant role in shaping an individual's ability to achieve success. While personal responsibility and effort are indispensable, the influence of one's environment and circumstances cannot be ignored. Recognizing this interplay is crucial in developing a more holistic understanding of success and the diverse paths individuals take to achieve it.

Sample Essay #2 - Low Score

success is all about what a person does and nothing else. ppl say that things like money or where you went to school matter but thats not true. you just have to work hard and want it

enough. look at all the stories of ppl who had nothing and made it big they didnt let anything stop them, so why should any1 else?

but some ppl keep saying its not that simple, that things like not having money or going to a bad school can stop you. i don't buy it, like everyone has the same chance if they just try

so it doesnt really matter where you come from or how much money your family has. what really matters is how much you want to succeed and how hard your willing to work for it. all the other stuff is just excuses

How Do You Pass the ACCUPLACER?

Most colleges use a placement exam as a universal measure to ensure students are placed in the correct class. Therefore, you can’t technically pass or fail an ACCUPLACER exam—your score will simply determine which level of math or English course you place into. If you are taking the ACCUPLACER as an admissions exam, the institution to which you are applying will decide what is a sufficient score to their standards.

Why Should I Prepare for the ACCUPLACER?

Without good preparation for the ACCUPLACER exam, you may find yourself in a class that is below your skill level, and perhaps will cost you extra if you could have skipped it altogether. Often, the lower-level courses cover material you will have already learned in high school. Thus, preparation is key to avoiding remedial courses and saving time and money.

For enrollment in special programs, you may need a particular score on the ACCUPLACER. Preparation will help you excel and ensure your spot in your program of choice.

In order to prepare yourself for the material you will encounter on the test, check out TestPrep-Online's ACCUPLACER pack. There you will find over a thousand questions that cover the same subjects and skills that the ACCUPLACER seeks to assess, each complete with an answer and an explanation that details how you should arrive at the correct conclusion. While our packs are not designed exactly like the format of the Next Generation ACCUPLACER, they are designed to get to the root of the concepts of the Next Generation ACCUPLACER and prepare you for the material assessed in it.

Our ACCUPLACER Premium Practice Pack includes:

530 math questions, including three tests for each of the three math subjects, as well as three more extended math practice quizzes for each subject.

480 English questions, including three tests for each of the two English subjects, 10 additional drills for each subject (5 drills per question type), and another 16 drills in English grammar, each one focusing on a different grammatical principle.

Three WritePlacer essay guides

You can also choose to practice only the math or the English tests, depending on your needs.

Practice now to improve your score on ​the ACCUPLACER test!

ACCUPLACER®, WritePlacer®, and ACCUPLACER Practice Test are trademarks and property of COLLEGE BOARD. The trademark holder is not affiliated with TestPrep-Online or this website.