PSAT Math Practice Test

Welcome to your PSAT Math Practice Test

The free PSAT Math practice test is specifically designed to ensure that the test-taker is knowledgeable about the PSAT and is able to know what to expect when it is time to take the Math portion of the PSAT.

The diagram shows the outline of a racetrack for skaters, which consists of two long straight sections and two semi-circular turns. Given the dimensions shown, which of the following most closely measures the perimeter of the entire track?


This question is based on the following table:

The table shows the cost of renting a bicycle for 1, 2, or 3 hours. Which of the following equations best represents the data, if represents the cost and represents the time of the rental?

What is the value of a if (2a + 3) − (4a − 8) = 7 ?

An airplane leaves Atlanta at 2 PM and flies north at 250 miles per hour. A second airplane leaves Atlanta 30 minutes later and flies north at 280 miles per hour. At what time will the second airplane overtake the first?

A sailboat is 19 meters long. What is its length in inches?


Tyra subscribes to an online gaming service that charges a monthly fee of
$5.00 and $0.25 per hour for time spent playing premium games. Which of
the following functions gives Tyra’s cost, in dollars, for a month in which
she spends x hours playing premium games?
A) C(x) = 5.25x
B) C(x) = 5x + 0.25
C) C(x) = 5 + 0.25x
D) C(x) = 5 + 25x

If x + y > 0 when x > y, which of the following cannot be true?

A babysitter earns $8 an hour for babysitting 2 children and an additional
$3 tip when both children are put to bed on time. If the babysitter gets the
children to bed on time, what expression could be used to determine how
much the babysitter earned?
A) 8x + 3, where x is the number of hours
B) 3x + 8, where x is the number of hours
C) x(8 + 2) + 3, where x is the number of children
D) 3x + (8 + 2), where x is the number of children

If 12/X 30/6 , what is the value of ?

In a certain game, a player can solve easy or hard puzzles. A player earns
30 points for solving an easy puzzle and 60 points for solving a hard
puzzle. Tina solved a total of 50 puzzles playing this game, earning 1,950
points in all. How many hard puzzles did Tina solve?
A) 10
B) 15
C) 25
D) 35

Which of the following is a solution to the inequality  4x − 12 < 4?

The question bellow is based on the following diagram:


Find the length of the side labeled . The triangle represented in the figure is a right triangle, as shown.

The equation above is used to model the relationship between the number
of cups, n, of hot chocolate sold per day in a coffee shop and the average
daily temperature, T, in degrees Fahrenheit. According to the model, what
is the meaning of the 3 in the equation?
A) For every increase of 3°F, one more cup of hot chocolate will be sold.
B) For every decrease of 3°F, one more cup of hot chocolate will be sold.
C) For every increase of 1°F, three more cups of hot chocolate will be sold.
D) For every decrease of 1°F, three more cups of hot chocolate will be sold
p(x) = 3(x2 + 10x + 5) − 5(x − k)
In the polynomial p(x) defined above, k is a constant. If p(x) is divisible by
x, what is the value of k?
A) −3
B) −2
C) 0
D) 3

A motorcycle manufacturer offers 3 different models, each available in 6 different colors. How many different combinations of model and color are available?

The figure shows an irregular quadrilateral and the lengths of its individual sides. Which of the following equations best represents the perimeter of the quadrilateral?


Your new question!
A car traveled at an average speed of 80 miles per hour for 3 hours and
consumed fuel at a rate of 34 miles per gallon. Approximately how many
gallons of fuel did the car use for the entire 3-hour trip?
A) 2
B) 3
C) 6
D) 7

Mrs. Patterson’s classroom has sixteen empty chairs. All the chairs are occupied when every student is present. If 2/5 of the students are absent, how many students make up her entire class?

In the xy-plane, if the parabola with equation y = ax2 + bx + c, where a, b,
and c are constants, passes through the point (−1, 1), which of the
following must be true?
A) a − b = 1
B) −b + c = 1
C) a + b + c = 1
D) a − b + c = 1
If x − 2 is a factor of x2
− bx + b, where b is a constant, what is the value of
b ?
A high school basketball team won exactly 65 percent of the games it
played during last season. Which of the following could be the total
number of games the team played last season?
A) 22
B) 20
C) 18
D) 14

Which of the following expressions is equivalent to x3x5?

Boyd grows only tomatoes and raspberries in his garden. Last year, he
grew 140 pounds of tomatoes and 60 pounds of raspberries. This year, the
production, by weight, of tomatoes declined by 20 percent, and the
production, by weight, of raspberries declined by 50 percent. By what
percentage did the total yield, by weight, of Boyd’s garden decline?
A) 29 percent
B) 30 percent
C) 35 percent
D) 70 percent

If a = -6 and = 7, then 4 a( + 5) + 2 = ?

A soda company is filling bottles of soda from a tank that contains 500
gallons of soda. At most, how many 20-ounce bottles can be filled from the
tank? (1 gallon = 128 ounces)
A) 25
B) 78
C) 2,560
D) 3,200
Janice puts a fence around her rectangular garden. The garden has a
length that is 9 feet less than 3 times its width. What is the perimeter of
Janice’s fence if the area of her garden is 5,670 square feet?
A) 342 feet
B) 318 feet
C) 300 feet
D) 270 feet
To cut a lawn, Allan charges a fee of $15 for his equipment and $8.50 per
hour spent cutting a lawn. Taylor charges a fee of $12 for his equipment
and $9.25 per hour spent cutting a lawn. If x represents the number of
hours spent cutting a lawn, what are all the values of x for which Taylor’s
total charge is greater than Allan’s total charge?
A) x > 4
B) 3 ≤ x ≤ 4
C) 4 ≤ x ≤ 5
D) x < 3

Rachel spent $24.15 on vegetables. She bought 2 lbs of onions, 3 lbs of carrots, and 1 ½ lbs of mushrooms. If the onions cost $3.69 per lb, and the carrots cost $ 4.29 per lb, what is the price per lb of mushrooms?

In a college archaeology class, 78 students are going to a dig site to find
and study artifacts. The dig site has been divided into 24 sections, and each
section will be studied by a group of either 2 or 4 students. How many of
the sections will be studied by a group of 2 students?

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