PSAT 10 Practice

Multiple Choice Math Questions for the New PSAT 10


This quiz illustrates the range of difficulty expected by the PSAT 10 test:

Question 1: A store sells N refrigerators at a price of $x and then discounts the product and sells M of the same refrigerators at a price of $y. What quantity does the following expression represent?

Question 2: If a < 0, b < 0 and (a/b) > (b/a), which of the following expressions must be positive?

Question 3: Find the set of real numbers (x,y) which is a solution to both equations x2 + y2 = 4 and (x - 3)2 + y2 = 1.

Question 4: A square S of side l is divided into four identical squares of sides l/2. One of the four squares is divided again into four smaller identical squares and the same process continues until the initial square S is divided n times.
Write the mathematical relation between l, n and A, where A is the area of the smallest square resulted after n divisions.

Question 5: A bacterial colony doubles its size every 24 hours. Write an equation that describes the number of bacteria in the colony at the end of the nth day, S(n), in terms of the number of bacteria in the colony at the end of day (n-4), S(n-4).

Question 6: Which of the following could be the function of a real variable x whose graph is shown below?

Questions 7 and 8: The ticket prices advertised by an airline agency are given in the table below:

Distance D (miles)Fare F ($)

Assuming a linear relation between the distances traveled and fares, if F = a·D + b, then:

a = 0.08 b = 250
a = 0.1 b = 280
a = 0.15 b = 290
a = 0.2 b = 300
a = 0.25 b = 320

Questions 9: Triangle ABC in the figure below is inscribed in circle C of center O. Suppose D is the midpoint of segment AC and E is the midpoint of segment BC. What is the circumference of the circle if the segment OD measures 2 cm?

Question 10: A box contains 5 blue marbles, 4 red marbles and 6 green marbles. How many additional blue marbles must be added in the box so that the probability of randomly drawing a blue marble is 1/2?

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