PSAT Math Multiple-Choice Practice Test 41: Heart of Algebra

1. Which ordered pair (x, y) satisfies the pair of equations below?

3x + y = -3

x - 2y = -8

2. The United States primarily uses a 12-hour clock with 12-hour periods for the morning (a.m.) and for the afternoon/evening (P.M.). Much of the rest of the world uses a 24-hour clock. Which of the following inequalities expresses the digits for hours, H, on a 24-hour clock that correspond to the business hours for a restaurant that is open from 7 P.M. until 11 P.M.

3. A video arcade charges a set $5 charge to purchase a game card and then charges $0.50 for each video game played. What expression gives the relationship between the number of games played, G, and the total amount of dollars spent using the game card, T

4. A cardiologist uses the guidelines for maximum recommended heart rate (measured in beats per minute) shown in the table below, which vary based on a patient's age. One of the cardiologist's patients, age 55, wants to start an exercise program. The cardiologist recommends that the patient maintain a heart rate greater than 50% and less than 85% of the maximum recommended heart rate while exercising. Which of the following expressions gives the range in which the patient's heart rate, H, should be during exercise?

5. Hannah has only nickels and dimes in her wallet. She has a total of $2.50 and a total of
30 coins. How many nickels does she have

6. A two-digit number has a tens place, t, and a units place, u. The digits have the following relationships:

t + u = 8

t = 2 + u

What is the value of the two-digit number given by these two digits?

7. 18-karat gold has 18 parts gold for 24 total parts metal (the difference comes from the 6 parts that are metals other than gold). 24-karat gold is pure gold. In order to make a piece of jewelry that is 2.4 ounces in weight and is 20-karat gold, how many ounces of 18-karat gold, X, and of 24-karat gold, Y, are needed to make this piece of jewelry

8. For the equation 3 + 4x - 2 = k + 6x - 2x, what does the constant k need to equal in order for there to be multiple solutions for x

9. What is the value of y in the system of equations below

16x - 4y = 12

8x + 2y = 4

10. What are the solutions for x and y in the equations below?

A.

B.

C.

D.

11. Electrical engineers use Ohm's law, V = IR, to give the relationship among voltage (V), current (I), and resistance (R). Which of the following statements is always true about the relationship among voltage, current, and resistance based on Ohm's law?

If the current increases and the resistance remains the same, the voltage increases.

If the voltage increases, the resistance must increase.

If the resistance increases and the voltage remains the same, the current must decrease.

12. What is the graph of the following function?

3 + y = 2 + 3x

A.

B.

C.

D.