PSAT Math Multiple-Choice Practice Test 23

1. An architect is building a scale model of the Statue of Liberty. The real statue measures 305 feet, 6 inches from the bottom of the base to the tip of the torch. The architect plans to make her model 26 inches tall. If Lady Liberty's nose on the actual statue is 4 feet, 6 inches long, how long in inches should the nose on the model be?

A.

B.

C.

D.

2. If f(x) = 3x + 5, what is f(6) - f(2) ?

3.

The United States Fish and Wildlife Service classifies animals whose populations are at low levels as either threatened or endangered. Endangered species are animals that are currently on the brink of extinction, whereas threatened species have a high probability of being on the brink in the near future. Since 1990, the Northern Spotted Owl has been listed as threatened. The figure above shows the populations of the Northern Spotted Owl in a certain region in Oregon from 1994 to 2014. Based on the line of best fit shown in the figure, which of the following values most accurately reflects the average change per year in the number of Northern Spotted Owls?

4. The x-coordinates of the solutions to a system of equations are - 4 and 2. Which of the following could be the system?

A.

B.

C.

D.

5.

The white-footed mouse, named for its darker body fur and white feet, is primarily found on the east coast of the United States, living in warm, dry forests and brushland. A scientist in Virginia studied a sample of 200 white-footed mice to see how many offspring they had per birth. The results of the study are recorded in the figure above. Based on the data, given a population of 35,000 female white-footed mice living in Virginia, how many would you expect to have a litter of seven or more pups?

6. Human beings have a resting heart rate and an active heart rate. The resting heart rate is the rate at which the heart beats when a person is at rest, engaging in no activity. The active heart rate rises as activity rises. For a fairly active woman in her 20s, eight minutes of moderate exercise results in a heart rate of about 90 beats per minute. After 20 minutes, the same woman's heart rate will be about 117 beats per minute. If the human heart rate increases at a constant rate as the time spent exercising increases, which of the following linear models represents this same woman's heart rate, r, after t minutes of moderate exercise?

7. Chantal buys new furniture using store credit, which offers five-year no-interest financing. She sets up a payment plan to pay the debt off as soon as possible. The function 40 x + y = 1,400 can be used to model her payment plan where x is the number of payments Chantal has made and y is the amount of debt remaining. If a solution to the equation is (21, 560), which of the following statements is true?

8.

Which of the following equations best represents the trend of the data shown in the figure above?

9. The graph of f(x) passes through the point (5, 1). Through which point does the graph of -f(x + 3) - 2 pass?

10. When a certain kitchen appliance store decides to sell a floor model, it marks the retail price of the model down 25 percent and puts a "Floor Model Sale" sign on it. Every 30 days after that, the price is marked down an additional 10 percent until it is sold. The store decides to sell a floor model refrigerator on January 15th. If the retail price of the refrigerator was $1,500 and it is sold on April 2nd of the same year, what is the final selling price, not including tax?

11. When New York City built its 34th Street subway station, which has multiple underground levels, it built an elevator that runs along a diagonal track approximately 170 feet long to connect the upper and lower levels. The angle formed between the elevator track and the bottom level is just under 30 degrees. What is the approximate vertical distance in feet between the upper and lower levels of the subway station?