Mathematics Test

Arithmetic Test

The 17 arithmetic questions administered by the ACCUPLACER™ Tests are divided into three types.
• Operations with whole numbers and fractions : topics included in this category are addition,
subtraction , multiplication, division, recognizing equivalent fractions and mixed numbers, and
estimating.
• Operations with decimals and percents: topics include addition, subtraction, multiplication, and
division with decimals. Percent problems, recognition of decimals, fraction and percent
equivalencies, and problems involving estimation are also given.
• Applications and problem solving: topics include rate, percent, and measurement problems,
simple geometry problems, and distribution of a quantity into its fractional parts.

Questions from all three categories are always presented to the student although the number of
questions from each category varies with the student’s skill level. For example, if the student's
responses show minimal arithmetic skills, presenting too many applications problems is pointless. On the
other hand, a student exhibiting good skills with whole numbers and fractions will be presented with more
of these types of problems. Thus, the proportion of questions in the various categories will automatically
vary according to the student's responses. In this sense, this test and the other ACCUPLACER™Tests
are truly adaptive in nature.

Elementary Algebra Test

A total of 12 questions, divided into three types, are administered in this test. The first type involves
operations with integers and rational numbers , and includes computation with integers and negative
rationals, the use of absolute values, and ordering. These questions test minimal skill levels of the
student.

A second type, which involves operations with algebraic expressions tests minimal skill levels using
evaluation of simple formulas and expressions, and adding and subtracting monomials and polynomials .
At all skill levels, questions are provided involving multiplying and dividing monomials and polynomials,
the evaluation of positive rational roots and exponents, simplifying algebraic fractions, and factoring.

The third type of question involves the solution of equations , inequalities, and word problems. As with
the Arithmetic Test, few questions from this category are presented to the student unless he or she
shows skill in this area. When a high degree of competence is indicated, questions from this category
include solving linear equations and inequalities , the solution of quadratic equations by factoring, solving
verbal problems presented in an algebraic context, including geometric reasoning and graphing, and the
translation of written phrases into algebraic expressions.

College-Level Mathematics Test

A total of 20 questions are administered in the College-Level Mathematics Test (CLM). CLM assesses
proficiency in intermediate algebra through Pre-calculus. This test therefore enables institutions to place
students into intermediate algebra, college algebra, Pre-calculus, and introductory calculus courses.

Questions administered in this test, representing six general categories, are as follows:
• Algebraic Operations including simplifying rational algebraic expressions, factoring and
expanding polynomials, and manipulating roots and exponents.
• Solutions of Equations and Inequalities category including the solution of linear and quadratic
equations and inequalities, systems of equations, and other algebraic equations.
• Coordinate Geometry involving plane geometry, the coordinate plane, straight lines, conics , sets
of points in the plane, and graphs of algebraic functions.
• Applications and other Algebra Topics category including complex numbers , series and
sequences, determinants, permutations and combinations , factorials, and word problems.
• Functions including questions involving polynomial, algebraic, exponential, and logarithmic
functions.
• Trigonometry category including trigonometric functions.

Summary Of Test Specifications For Core Tests

Use of Calculators

In February 2004, new items were added to the Arithmetic and Elementary Algebra test item pools.
Some of these new items have pop-up calculators for students to use when answering the question. The
new items were written so that the use of a calculator will not help the student answer the question, it is
simply provided as a tool for the student to use. For example, if a student is asked to calculate the area
of a rectangle, (s)he must know the formula (length times width) for calculating the area. The calculator
is available in this case as a tool for multiplying the length times the width. It does will not help the
student who does not know the formula.

Calculators are not available for all items. For example, if a student is asked to estimate the value of
9.755 times 5.688, the calculator is not available, because the question is asking the student to round
9.755 to 10, and 5.688 to 6 and multiple 10 times 6 in their head. The use of the calculator would “help”
the student answer this type of question; therefore, it is not available.

In Setup ACCUPLACER™ it is possible to turn the pop-up calculator off. It is recommended that
students be provided with the pop-up calculator because item difficulty levels were calculated from data
where students were using the pop-up calculators.

If the pop-up calculator is turned off, caution should be used when interpreting student scores, and
adjustments may be necessary to the required cut scores for placement into various math courses.