What Types of Math Problems Are on the College Placement Test?

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The math college placement tests are university-specific exams required by colleges aside from SAT or ACT tests. The math problems you will find in the college placement test fall into three main categories: arithmetic, algebra and advanced algebra. The problems range from simple addition and subtraction operations to solving logarithmic functions and quadratic equations. This test aims to cover the overall math knowledge a student should be acquainted with after graduating high school. The test, however, is not necessarily used as an admission requirement by colleges, but to determine the appropriate math level placement for students entering college.


The math college placement test is typically administrated by the college or university that requires it or via Accuplacer. Accuplacer is a computer-based exam developed by the College Board that is used in various educational institutions in the United States. The scoring system used for the math college placement test differs from the score criteria used in the SAT or ACT tests. The math portion of the college placement test sets specific scoring criteria to determine students' placement in math courses and each might vary from college to college. It is recommended for students to contact the college admissions department to find specific details about the test.


Arithmetic problems are the first you will find in the test. The first two portions of this section include questions and world problems related to adding, subtracting, multiplying and dividing fractions and whole numbers, estimating and solving percent problems and division of decimals. The third portion includes solving problems related to basic geometry, measurements, rate and distribution of quantities into fractional parts. Examples of questions in this section include: "A football team played 60 games this season and lost 30 percent of them. How many games did the team win?" "Find 6 to the third power," "What percent of 20 is 25?" and "A man owed $2,467 on his car. After making 36 payments of $68 each, how much does he have left to be paid?"

Elementary Algebra

The problems presented in the second section will test your knowledge of elementary algebra. The first two portions of this section involve operations with rational numbers, absolute values, basic algebraic expressions, monomials, polynomials and evaluation of exponents and positive rational roots. Examples of problems you will find in this section are: "Simplify (5 - 6) - (14 - 19 + 3)," "What is |-25 |?" Solve for x: 2x - y = (3/4)x + 6" and "Factor 6y(x - 6) -4(x - 6)." This section of the test is computer-based, presented in multiple-choice format and consists of a total of 12 questions.

Advanced Algebra

The advanced algebra section or college-level mathematics will evaluate you on six main areas. These include algebraic operations, which consist of rational algebraic expressions, factoring polynomials and expanding polynomials; solutions of equations and inequalities, including problems that deal with linear and quadratic equations and inequalities; coordinate geometry, consisting of plotting points on graphs based on algebraic functions and plane geometry; other algebraic topics, such as series and sequences, permutations, combinations word problems and complex numbers; and functions, such as logarithmic, polynomial, exponential and algebraic functions. Examples of problems include: "If f(x) = 7x + 2 and f1 denotes the inverse function of f, then f1(9)," "How many different ways can teams of two ping-pong players be selected from a group of 5 players?" and "Find the coefficient of x² when (3x² + 2x) is multiplied by (x² -4x-1)." There are 20 questions in this section of the test.


The scores you get in the math placement exam will determine if you need to take preparatory math courses in college. For example, a score of 20 to 64 in the arithmetic section might require you to take two semesters of college preparatory math. A score of 72 or higher in elementary algebra will exempt you from preparatory courses. Math placement scores are generally valid for three years. Prepare for the exam by taking math preparatory courses prior to the test date or take free practice tests online. The math problems presented in the practice exams will vary from those in the official placement test. Use the practice exams to evaluate your skills on each section and narrow down the areas you need to improve. Study those areas aside, then retake the exam once you feel confident with your progress.


About the Author

Emilio Alvarez has a Bachelor of Science in computer science from San Diego State University and a minor in music composition from Southwestern College, San Diego. He has been writing since 2002 and has published short stories with Editorial Dunken (Buenos Aires, Argentina), where his work is part of a Spanish anthology: "El libro de talleres."

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