## College Level Advanced Math – Practice Problems

Here are some college level advanced math problems and solutions for the college-level advanced math part of the exam.

The problems below are from our Asset Test College-Level Advanced Math download.

Our **Asset Advanced Math download **shows step-by-step solutions and explanations to help you understand all of the advanced math formulas that you need in order to be successful on your test.

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**College Level Advanced Math – Problems:**

1) Simplify the following equation: (*x* + 3*y*)^{2}

A) 2(*x* – 3*y*)

B) 2*x* + 6*y*

C) *x*^{2} + 6*xy* – 9*y*^{2}

D) *x*^{2} – 6*xy* + 9*y*^{2}

E) *x*^{2} + 6*xy* + 9*y*^{2}

2) (*x* – 4)(3*x* + 2) = ?

A) 3*x*^{2} – 10*x* – 8

B) 3*x*^{2} – 10*x* + 8

C) 3*x*^{2} + 14*x* – 8

D) 3*x*^{2} + 14*x* + 8

E) 3*x*^{2} – 14*x* – 8

3) State the *x* and *y* intercepts that fall on the straight line represented by the following equation:

*y* = *x* + 6

A) (0,6) and (-6,0)

B) (-6,0) and (0,6)

C) (6,0) and (0,-6)

D) (0,-6) and (6,0)

E) (0,6) and (6,0)

4) Find the midpoint between the following coordinates: (2, 2) and (4, -6)

A) (3,4)

B) (3,-4)

C) (3,2)

D) (3,-2)

E) (3,-8)

5) A rectangular box has a base that is 5 inches wide and 6 inches long. The height of the box is 10 inches. What is the volume of the box?

A) 30

B) 110

C) 150

D) 300

E) 3000

**College Level Advanced Math – Solutions and Explanations:**

1) Simplify the following equation: (*x* + 3*y*)^{2}

The correct answer is: E

This type of algebraic expression is known as a binomial. When multiplying binomials, 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 this order:

First – Outside – Inside – Last

(*x* + 3*y*)^{2} =

(*x* + 3*y*)(*x* + 3*y*)

FIRST: Multiply the first variable from the first set of parentheses with the first variable from the second set of parentheses.

*x* x *x* = x^{2}

OUTSIDE: Multiply the first variable from the first set of parentheses with the second variable from the second set of parentheses.

*x* x 3*y* = 3*xy*

INSIDE: Multiply the second variable from the first set of parentheses with the first variable from the second set of parentheses.

3*y* x *x* = 3*xy*

LAST: Multiply the second variable from the first set of parentheses with the second variable from the second set of parentheses.

3*y* x 3*y* = 9*y*^{2}

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

*x*^{2} + 9*y*^{2} + 3*xy* + 3*xy* =

*x*^{2} + 6*xy* + 9*y*^{2}

2) (*x* – 4)(3*x* + 2) = ?

The correct answer is: A

Remember to use the F-O-I-L method when you multiply:

FIRST: *x* x 3*x* = 3*x*^{2}

OUTSIDE: *x* x 2 = 2*x*

INSIDE: – 4 x 3*x* = – 12*x*

LAST: – 4 x 2 = – 8

Then add all of the above once you have completed F-O-I-L:

3*x*^{2} + 2*x* + – 12*x* + – 8 =

3*x*^{2} + 2*x* – 12*x* – 8 =

3*x*^{2} – 10*x* – 8

3) State the *x* and *y* intercepts that fall on the straight line represented by the following equation:

*y* = *x* + 6

The correct answer is: A

To solve problems like this one, begin by substituting 0 for *x*.

*y* = *x* + 6

*y* = 0 + 6

*y* = 6

Therefore, the coordinates (0, 6) represent the *x* intercept.

Now substitute 0 for *y*: *y* = *x* + 6

0 = *x* + 6

0 – 6 = *x* + 6 – 6

– 6 = *x*

So, the coordinates (-6, 0) represent the *y* intercept.

4) Find the midpoint between the following coordinates:

(2, 2) and (4, -6)

The correct answer is: D

For coordinate geometry questions like this one, remember that you need to use the following formula:

For two points on a graph (*x*_{1}, *y*_{1}) and (*x*_{2}, *y*_{2}), the midpoint is:

(*x*_{1} + *x*_{2}) / 2 , (*y*_{1} + *y*_{2}) / 2

Now calculate for *x* and *y*:

(2 + 4) / 2 = midpoint *x*, (2 – 6) / 2 = midpoint *y*

6 / 2 = midpoint *x*, -4 / 2 = midpoint *y*

3 = midpoint *x*, -2 = midpoint *y*

5) A rectangular box has a base that is 5 inches wide and 6 inches long. The height of the box is 10 inches. What is the volume of the box?

The correct answer is: D

The volume of a box is calculated by taking the length times the width times the height.

So 5 x 6 x 10 = 300