Free PSSA Mathematics Questions and Answers — Questions and Answers
Question 1: Mary was three times as old as Mark was five years ago. If Mark is 10 years old now, how old is Mary?
- 25
- 20 (Correct answer)
- 15
- 10
Correct answer: 20
Explanation: <br> Mary was three times as old as Mark five years ago. <br> Mark is 10 years old now. Therefore, 5 years ago Mark was just 5 years old. <br><br> Five years ago, Mary was: <br> A = 3 × 5 = 15 <br> 15 + 5 = 20 <br><br> So Mary is 20 years old now.
Question 2: 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?
- 1 1/2 hours
- 2 1/2 hours
- 2 1/12 hours
- 2 11/12 hours (Correct answer)
Correct answer: 2 11/12 hours
Explanation: <br> Convert the mixed numbers to improper fractions: <br> 1 1/6 = 7/6 and 2 1/2 = 5/2 <br><br> Now, multiply these two improper fractions together: <br> 7/6 * 5/2 = 35/12 <br><br> Simplifying, you get 2 11/12 hours.
Question 3: Which of the following best describes a linear equation with steps starting at 5 and increasing by 8?
- y = -5x + 8
- y = 5x + 8
- y = 8x + 5 (Correct answer)
- 5x + y = 8
Correct answer: y = 8x + 5
Explanation: <br> 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.
Question 4: ABC Car Rentals charges $100 upfront, plus 10 cents per mile. <br> Orange Car Rentals charges 25 cents per mile with no upfront fee. <br><br> Which of the following best represents the situation If TC represents the total cost for the car, and N represents the number of miles?
- TC = 100 - 0.10n <br> TC = 0.25 - n
- TC = 100 + 0.10n <br> TC = 0.25n (Correct answer)
- TC = 100 + 0.10 / n <br> TC = 0.25 / n
- n = 100 + 0.10 / TC <br> n = 0.25 / TC
Correct answer: TC = 100 + 0.10n <br> TC = 0.25n
Explanation: <br> 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.
Question 5: Using a substitution method to solve this system of equations, which of the following is a valid first step? <br><br> 2x - y = 7 <br> x = 2y - 1
- x= 2(2x-y) - 1
- 2x - (2y - 1) = 7
- 2(2y - 1)- y = 7 (Correct answer)
- 2x-y = 2y - 1
Correct answer: 2(2y - 1)- y = 7
Explanation: <br> 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.
Question 6: Which of the following points is included in the graph of f(x) = 2x - 2?
- (3, 4) (Correct answer)
- (-3, -4)
- (-4, 3)
- (4,-3)
Correct answer: (3, 4)
Explanation: <br> Point (3, 4) is included.
Question 7: Solve for the value of X: <br> 8x - 7 = 5x + 8
- -5
- 5 (Correct answer)
- -3
- -1/3
Correct answer: 5
Explanation: <br> Solving for x, you will get: <br> 8x - 7 = 5x + 8 <br> 3x = 15 <br> x = 15 / 3 = 5 <br>
Question 8: Which of the following statements would an inequality represent?
- Each ticket for the concert is $75.
- It is a 12-foot-long fence.
- It takes precisely four hours to roast the turkey.
- You have to be at least four feet tall to ride the roller coaster. (Correct answer)
Correct answer: You have to be at least four feet tall to ride the roller coaster.
Explanation: <br> 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.
Question 9: A math teacher goes shopping and sets his budget using the following: <br> {x | x > 50 and x < 75} where x is the amount he will spend. <br><br> Which of the following is within his budget?
- $40
- $45
- $55 (Correct answer)
- $75
Correct answer: $55
Explanation: <br> The amount must be greater than 50, and less than 75. $55 is the only number that meets the parameters.
Question 10: When resolving a 1-variable absolute value inequality, which rule should you remember?
- You have to invert the inequality symbol on the positive solution in order to undo an absolute value.
- You must flip the inequality symbol for one of them but leave the other two positive in order to undo an absolute value.
- The inequality symbol needs to be reversed when dividing or multiplying both sides by a negative value.
- When undoing an absolute value, you must flip the inequality symbol on the negative solution. (Correct answer)
Correct answer: When undoing an absolute value, you must flip the inequality symbol on the negative solution.
Explanation: <br> You have to flip the inequality symbol on the negative solution when solving a 1-variable absolute value inequality and undoing an absolute value.
Question 11: In the shape below, what is the area of the shaded region?
- 20
- 24 (Correct answer)
- 27
- 32
Correct answer: 24
Explanation: <br> Find the area of the entire shape by breaking it into two rectangles: <br> 6*2 + 5*4 = 32 <br><br> Break the inner shape into two rectangles: <br> 5*2 - 1*2 = 8 <br><br> Subtract the inner shape from the entire shape: <br> 32 - 8 = 24
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?