College Level Advanced Math

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

The problems below are from our Asset 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.

The Asset Test for Advanced Math - Problems:

1) Simplify the following equation: (x + 3y)2
A) 2(x - 3y)
B) 2x + 6y
C) x2 + 6xy - 9y2
D) x2 - 6xy + 9y2
E) x2 + 6xy + 9y2

2) (x - 4)(3x + 2) = ?
A) 3x2 - 10x - 8
B) 3x2 - 10x + 8
C) 3x2 + 14x - 8
D) 3x2 + 14x + 8
E) 3x2 - 14x - 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


The Asset Test for Advanced Math - Solutions and Explanations:

1) Simplify the following equation: (x + 3y)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 + 3y)2 =
(x + 3y)(x + 3y)

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

x   x  x = x2

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

x   x   3y = 3xy

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

3y   x   x = 3xy

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

3y   x   3y = 9y2

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

x2 + 9y2 + 3xy + 3xy =

x2 + 6xy + 9y2

2) (x - 4)(3x + 2) = ?

The correct answer is: A

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

FIRST: x   x   3x = 3x2
OUTSIDE: x   x   2 = 2x
INSIDE: - 4   x   3x = - 12x
LAST: - 4   x   2 = - 8

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

3x2 + 2x + - 12x + - 8 =
3x2 + 2x - 12x - 8 =
3x2 - 10x - 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 (x1, y1) and (x2, y2), the midpoint is:

(x1 + x2) / 2 , (y1 + y2) / 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



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