Accuplacer Math Sample Problems and Solutions from Math Course

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Problems:

1)   7.23 + .004 + .513 = ?

2)   8.13 x 3.1 = ?

3)   Two people are going to give money to a foundation for a project. Person A will provide one-half of the money. Person B will donate one-eighth of the money. What fraction represents the unfunded portion of the project?

When you buy the Math Course, you will see Arithmetic questions 4 to 50 here.

51)   If 5x - 2(x + 3) = 0, then x = ?

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

53)   (x + 3y)(x - y) = ?

When you buy the Math Course, you will see Algebra questions 54 to 100 here.

101)   5⁸ ÷ 5² = ?

102)   How many 3 letter permutations can be made from the following five letter set: F U N K Y?

103)   Find the coordinates (x, y) of the midpoint of the line segment on a graph that connects the points (-5, 3) and (3, -5).

When you buy the Math Course, you will see Arithmetic questions 104 to 150 here.

Our math course includes solutions and explanations for each problem. Here is an example of the solutions we provide with the math course:

Solutions ans Explanations:

1)   7.23 + .004 + .513 = ?

The correct answer is: 7.747

When you add on your scratch paper, be sure to line all of the decimals up in a column like this:

7.230
0.004
0.513
_____
7.747

As you can see, you should add zeros where necessary at the beginning or end of the numbers in order to make the decimal points line up.

2)   8.13 x 3.1 = ?

The correct answer is: 25.203

Tip: Be sure to put the decimal point in the correct position after you do the long multiplication.

We know that the decimal point has to be three places from the right on the final product because 8.13 has 2 decimal places and 3.1 has 1 decimal place, so 1 plus 2 equals 3 places.

Solution:

      8.13

´     3.1

     .813

24.390

25.203

3)   Two people are going to give money to a foundation for a project. Person A will provide one-half of the money. Person B will donate one-eighth of the money. What fraction represents the unfunded portion of the project?

The correct answer is: 3/8

The sum of all contributions must be equal to 100%, simplified to 1. Let's say that the variable U represents the unfunded portion of the prject. So the equation that represents this problem is:

A + B + U = 1

Now substitute with the fractions that have been provided: 1/2 + 1/8 + U = 1

Now, find the lowest common denominator of the fractions:

4/8 + 1/8 + U = 1

5/8 + U = 1

U = 1 - 5/8

U = 3/8

51)   If 5x - 2(x + 3) = 0, then x = ?

The correct answer is: 2

To solve this type of problem, do multiplication of the items in parentheses first:

5x - 2(x + 3) = 0
5x - 2x - 6 = 0

Then deal with the integers by putting them on one side of the equation as follows:

5x - 2x - 6 + 6 = 0 + 6
3x = 6

Then solve for x:

3x = 6
x = 6 ÷ 3
x = 2

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

The correct answer is: x² + 6xy + 9y²

(x + 3y)² =
(x + 3y)(x + 3y)

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

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

x ´ x = x²

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

x ´ 3y = 3xy

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

3y ´ x = 3xy


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

3y ´ 3y = 9y²

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

x² + 9y² + 3xy + 3xy =

x² + 6xy + 9y²

53)   (x + 3y)(x - y) = ?

The correct answer is: x² + 2xy - 3y²

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

FIRST: x ´ x = x²

OUTSIDE: x ´ - y = - xy

INSIDE: 3y ´ x = 3xy

LAST: 3y ´ - y = 3y²


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

x² - xy + 3xy - 3y² =

x² + 2xy - 3y²

101)   5⁸ ÷ 5² = ?

The correct answer is: 5⁶

This question tests your knowledge of exponent laws. First look to see whether your base number is the same on each part of the equation. (5 is the base number for each part of this equation.) If the base number is the same, and the problem asks you to divide, you simply subtract the exponents:

5⁸ ÷ 5² =
5^{8 - 2} =
5⁶

102)   How many 3 letter permutations can be made from the following five letter set: F U N K Y?

The correct answer is: 60

Permutations are like combinations, except permutations take into account the order of the items in each group. In order to calculate the number of permutations of size S taken from N items, you should use this formula:

N! ÷ (N - S)! =

For the question above:

N = 5 and S = 4

N! ÷ (N - S)! =
(5 ´ 4 ´ 3 ´ 2 ´ 1) ÷ (5 - 3) =
(5 ´ 4 ´ 3 ´ 2) ÷ 2 =
120 ÷ 2 =
60

103)   Find the coordinates (x, y) of the midpoint of the line segment on a graph that connects the points (-5, 3) and (3, -5).

The correct answer is: (- 1, - 1)

This question covers coordinate geometry. Remember that in order to find midpoints on a line, 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:

(-5 + 3) ÷ 2 = midpoint x, (3 + - 5) ÷ 2 = midpoint y
-2 ÷ 2 = midpoint x, -2 ÷ 2 = midpoint y
- 1 = midpoint x, - 1 = midpoint y