Here are some free algebra questions for the Accuplacer.

Example 1:

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

(2x - 3y)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

(2x - 3y)² =

(2x - 3y)(2x - 3y)

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

FIRST: 2x x 2x = 4x²

The variables on the outside of each set of parentheses are 2x and 3y

OUTSIDE: 2x x - 3y = -6xy

The variables on the inside of each set of parentheses are -3y and 2x

INSIDE: -3y x 2x = - 6xy

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

LAST: - 3y x - 3y = 9y²

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

4x²- 6xy - 6xy + 9y² =

4x²+ 9y² - 12xy

Example 2:

Algebra questions on the Accuplacer Test will also include inequalities problems. Inequalities contain the less than or greater than signs.

31 - 2/3X > 27, then X < ?

Solution 2:

In order to solve inequalities, deal with the whole numbers on each side of the equation first:

31 - 2/3X > 27 =

(31 - 31) - 2/3X > (27 - 31) =

- 2/3X > - 4

Then deal with the fraction:

- 2/3X > - 4 =

3 x - 2/3X > - 4 x 3 =

-2X > -12

Then deal with the remaining whole numbers:

-2X > -12 =

-2X ÷ 2 > -12 ÷ 2 =

-X > -6

Then, deal with the negative number:

-X > -6 =

-X + 6 > -6 + 6 =

-X + 6 > 0

Finally, isolate the unknown variable as a positive number:

-X + 6 > 0 =

- X + X + 6 > 0 + X =

6 > X =

X < 6

Example 3:

You will also be asked to divide polynomials on the Accuplacer Test. In order to solve this type of problem, you must do long division of the polynomial:

(x² - x - 6) ÷ (x - 3) =

Solution 3:

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

               x + 2
x - 3)x² - x - 6

  -(x² - 3x)
    _______

            2x - 6

            2x - 6
            ______

                    0

Go to the Accuplacer Algebra Test Page