PERT Practice Test (Math)

Question 1

If 4x + 3x − 2(x + 5) = −9, then x = ?

Accepted Answer

1/5

Answer

To solve the equation, first distribute the -2: 4x + 3x - 2x - 10 = -9. Combine the x terms: 5x - 10 = -9. Add 10 to both sides: 5x = 1. Finally, divide by 5 to find x: x = 1/5.

Question 2

What is 181.5% of 18?

Accepted Answer

32.67

Answer

To find a percentage of a number, convert the percentage to a decimal by dividing by 100. So, 181.5% becomes 1.815. Then, multiply this decimal by the given number: 1.815 * 18 = 32.67.

Question 3

In a coordinate plane, triangle ABC has coordinates: (−2,7), (−3,6), and (4,5). If triangle ABC is reflected over the y-axis, what are the coordinates of the new image?

Accepted Answer

(2,7), (3,6), (−4,5)

Answer

When a point (x, y) is reflected over the y-axis, its x-coordinate changes sign, while its y-coordinate remains the same. Applying this rule to each vertex: (-2, 7) becomes (2, 7); (-3, 6) becomes (3, 6); and (4, 5) becomes (-4, 5).

Question 4

David purchased new shoes that were on sale for $45.44. The original price was $60.59. What percentage discount was the sale price?

Accepted Answer

25%

Answer

First, calculate the discount amount by subtracting the sale price from the original price: $60.59 - $45.44 = $15.15. Then, divide the discount amount by the original price to find the decimal percentage: $15.15 / $60.59 ≈ 0.25. Multiply by 100 to convert to a percentage: 0.25 * 100 = 25%.

Question 5

ABC is a triangle with coordinates (3, 1), (6, 1), and (1, 3). It is translated to points A′(−3, 3), B′( 0, 3), and C′(−5, 5). Find the rule for the translation.

Accepted Answer

6 units left and 2 units up

Answer

The correct answer is 6 units left and 2 units up. The rule of translation is the rule, which when applied to the first set of points, yields the second set of points. The difference between the x values of the non-translated and translated points is:

(x2 − x1) = (−3 − 3) = (0 − 6) = (−5 − 1) = −6

This corresponds to a shift of 6 units to the left.

Likewise, for the y values:

(y2 − y1) = (3 − 1) = (3 − 1) = (5 − 3) = 2