Next Generation Arithmetic Study Guide for the ACCUPLACER Test

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General Information

This is a test of basic math ability. Of the 20 questions on it, there are 3 to 5 related to each of these mathematical procedures:

  • operations with whole numbers
  • operations with fractions
  • operations with decimal numbers
  • working with percentages
  • comparing numbers and finding equivalent numbers

Some questions simply present an equation to solve or ask a question about a number or group of numbers. Other questions include a real-world scenario in which there is a mathematical problem to be solved. For these, you need to construct a problem using the numbers and information given, then calculate the answer.

As you can see from the initial description, the questions cover very basic math operations and types of problems. Usually, only a few of the problems have more than one step. You do need to know the meaning of basic math terms, such as sum and product to understand some questions.

Note: It would be best to check with your testing center for confirmation, but our information indicates that no handheld calculators are allowed during any Accuplacer tests. Apparently, there are some questions that allow calculator use and, for those questions, only, an on-screen calculator will appear.

Whole Numbers

Some of the questions on the Accuplacer Next Generation Arithmetic Test involve working with whole numbers only. These are the counting numbers, beginning with 1, and you should be able to easily perform all four basic operations with them. They do not include any “parts” of numbers, like fractions or decimals. You may also need to work with some whole numbers in questions that deal mostly with fractions or decimals and some of the same principles apply, so be sure you are very good at this and that you strive for accuracy. During practice, check all of your answers with a calculator, just to be sure.

You have been doing these operations for years, but careless mistakes are easy to make. Here are some tips in order to avoid errors when working with whole numbers:

Addition and Subtraction

  • Know the basic addition and subtraction facts up to 9 + 9. This will speed up the process and make you less likely to get so involved in simple computation that you forget where you are in the problem-solving process.

  • When adding or subtracting columns of numbers, be sure to keep your columns straight. Use light lines if you need to, or use notebook paper turned sideways for instant columns.

  • When you think you have the correct answer, reverse the operation and see if you end up with the number you started with. If you added first, now subtract and vice versa.

  • Be sure you are concentrating while calculating. It’s easy to get so involved that you look at 6 - 3 and think 6 + 3.

  • If the addition columns are really long, add the numbers twice to see if you get the same answer. Start at the top the first time and work from the bottom the second time.

  • Don’t hesitate to lightly write numbers that you regroup (“carry” over to the next place in addition or “borrow” to use in subtraction). This will help you remember to use them.

Multiplication and Division

  • Know the basic multiplication facts up to 9 x 9. Knowing them up to 12 x 12 will help in some instances, but generally, you multiply and divide 1 digit numbers as part of a bigger process. Knowing the facts will speed things up here, too, and let you focus on the big picture of finding the final answer.

  • Maintaining correct columns is also important for these operations. See hints under Addition and Subtraction, above. Be especially careful with columns when doing long division or multiplying by a number with more than one digit.

  • If you need to use a zero to mark a place, do so. Here’s an example:

\(\quad \quad \; \; 1\)
\(\begin{align} \quad \quad \; \; 74& \\ \underline{x\quad 31}& \\ \quad \quad \; \; 74& \\ \underline{ 2220}& \\ 2294& \\ \end{align}\)

Note the 1 carried and the 0 used as placeholder in 2220.


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