# FREE PSSA Mathematics Questions and Answers

#### Mary was three times as old as Mark was five years ago. If Mark is 10 years old now, how old is Mary?

Explanation:

Mary was three times as old as Mark five years ago.

Mark is 10 years old now. Therefore, 5 years ago Mark was just 5 years old.

Five years ago, Mary was:

A = 3 × 5 = 15

15 + 5 = 20

So Mary is 20 years old now.

#### A math teacher goes shopping and sets his budget using the following:

{x | x > 50 and x < 75} where x is the amount he will spend.

Which of the following is within his budget?

Explanation:

The amount must be greater than 50, and less than 75. $55 is the only number that meets the parameters.

#### ABC Car Rentals charges $100 upfront, plus 10 cents per mile.

Orange Car Rentals charges 25 cents per mile with no upfront fee.

Which of the following best represents the situation If TC represents the total cost for the car, and N represents the number of miles?

Explanation:

We will be solving for the total cost of the rental (TC) when we set up the equations for the two companies. We will obtain a single value for both equations—the point at which both businesses charge the same amount—by using a system of equations.

#### Which of the following best describes a linear equation with steps starting at 5 and increasing by 8?

Explanation:

The number in front of the x is the slope, which indicates how much it increases with each step, and the number by itself is the y-intercept, or where it begins when using the slope-intercept form. Therefore, the number in this problem must be 5, and the number in front of the x must be 8.

#### When resolving a 1-variable absolute value inequality, which rule should you remember?

Explanation:

You have to flip the inequality symbol on the negative solution when solving a 1-variable absolute value inequality and undoing an absolute value.

#### In the shape below, what is the area of the shaded region?

Explanation:

Find the area of the entire shape by breaking it into two rectangles:

6*2 + 5*4 = 32

Break the inner shape into two rectangles:

5*2 - 1*2 = 8

Subtract the inner shape from the entire shape:

32 - 8 = 24

#### Solve for the value of X:

8x - 7 = 5x + 8

Explanation:

Solving for x, you will get:

8x - 7 = 5x + 8

3x = 15

x = 15 / 3 = 5

#### Using a substitution method to solve this system of equations, which of the following is a valid first step?

2x - y = 7

x = 2y - 1

Explanation:

The value of x is provided by the second equation, therefore the first step would be to substitute that value for x, which is 2(2y - 1)- y = 7.

#### How long was your nap on Tuesday if you napped 1 1/6 hours on Monday and 2 1/2 times as long on Tuesday?

Explanation:

Convert the mixed numbers to improper fractions:

1 1/6 = 7/6 and 2 1/2 = 5/2

Now, multiply these two improper fractions together:

7/6 * 5/2 = 35/12

Simplifying, you get 2 11/12 hours.

#### Which of the following statements would an inequality represent?

Explanation:

The roller coaster requirement to be at least four feet tall introduces a range of possible values. Anyone who is four feet tall or taller can therefore ride.

#### Which of the following points is included in the graph of f(x) = 2x - 2?

Explanation:

Point (3, 4) is included.