PSAT/NMSQT Math: Heart of Algebra Questions and Answers

Question 1

A cell phone company offers a data plan that costs $25 per month plus $15 for every gigabyte of data used.
This relationship is modeled by the function C(g) = 15g + 25, where C is the total monthly cost and g is the number of gigabytes used.
What does the number 25 in the function represent?

Accepted Answer

The flat monthly fee, regardless of data usage.

Answer

The cost for every gigabyte of data used.

Answer

The total number of gigabytes a customer can use per month.

Answer

The total cost for a customer who uses zero gigabytes of data and makes no calls.

Question 2

At a local fair, a combo meal that includes a hot dog and a soda costs $8. A family buys 4 combo meals. A different family buys 3 hot dogs and 5 sodas for a total of $30. If h is the cost of a hot dog and s is the cost of a soda, which of the following systems of equations can be used to determine the price of a hot dog and a soda?

Accepted Answer

h + s = 8
3h + 5s = 30

Answer

4h + 4s = 8
3h + 5s = 30

Answer

h + s = 8
5h + 3s = 30

Answer

4(h + s) = 8
3h + 5s = 30

Question 3

If 5x - 6 = 14, what is the value of 2x + 7?

Accepted Answer

15

Answer

4

Answer

8

Answer

23

Question 4

A car rental company charges a flat fee of $50 plus an additional $0.75 for every mile driven. Which of the following inequalities represents the maximum number of miles, m, a person can drive if they have a budget of no more than $200?

Accepted Answer

50 + 0.75m ≤ 200

Answer

50 + 0.75m < 200

Answer

50 + 0.75m > 200

Answer

50m + 0.75 ≤ 200

Question 5

If 2a + b = 10 and a - b = 2, what is the value of a?

Accepted Answer

4

Answer

2

Answer

6

Answer

8

Question 6

A line in the xy-plane passes through the origin and the point (3, 12). Which of the following is an equation of the line?

Accepted Answer

y = 4x

Answer

y = 3x + 12

Answer

y = 1/4 x

Answer

y = 12x + 3