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College Placement Math Test - Algebra

Free practice for the College Placement Math Test in Algebra. Below you will find a sample algebra test for the College Placement Test in Math.

The college placement math test in algebra is one part of the CPT exam. The algebra part of the College Placement Math Test contains twelve questions.

Our online college placement practice tests contain algebra questions just like those on the real college placement test.

Here is a free sample from our College Placement Math Test download in Algebra:

Example 1:

Polynomials are algebraic expression that contain more than one term. You will definitely have questions on the CPT Math Test about multiplying polynomials.

(2a - 3b)² = ?

Solution 1:

When multiplying polynomials, you should use the F-O-I-L method.

This means that you multiply the variables two at a time from each of the two parts of the equation in the parentheses in this order:

First - Outside - Inside - Last

(2a - 3b)² =

(2a - 3b)(2a - 3b)

So, the first variables in each set of parentheses are 2a and 2a

FIRST: 2a x 2a = 4a²

The variables on the outside of each set of parentheses are 2a and 3b

OUTSIDE: 2a x - 3b = -6ab

The variables on the inside of each set of parentheses are -3b and 2a

INSIDE: -3b x 2a = -6ab

The last variables in each set of parentheses are -3b and -3b

LAST: - 3b x - 3b = 9b²

Then we add all of the above parts together to get:

4a²- 6ab - 6ab + 9b² =

4a²+ 9b² - 12ab

Example 2:

This is a question on inequalities. Inequalities contain the less than or greater than signs. Algebra questions on the College Placement Test will also include inequalities problems.

35 - 1/4X > 31, then X < ?

Solution 2:

First, deal with the whole numbers on each side of the equation first:

35 - 1/4X > 31 =

(35 - 35) - 1/4X > (31 - 35) =

-1/4X > - 4

Then deal with the fraction:

-1/4X > - 4 =

4 x -1/4X > - 4 x 4 =

-X > -16

Then, deal with the negative number:

-X > -16 =

-X + 16 > -16 + 16 =

-X + 16 > 0

Finally, isolate the unknown variable as a positive number:

-X + 16 > 0 =

-X + X + 16 > 0 + X =

16 > X =

X < 16

Example 3:

You will also see exam problems on the division of polynomials. In order to solve this type of problem, you must do long division of the polynomial:

(a² + a - 12) / (a - 3) =

Solution 3:

Remember, you must to long division of the polynomial until you have no remainder:

              a + 4
a - 3)a² + a - 12

     -(a² - 3a)
     _______

            4a - 12

          -(4a - 12)
            ______

                    0

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