PSAT MATH PRACTICE TEST ONLINE FREE

(1)  [(2/3) + (1/4)]  ÷ 2  =

(A)  22/12  (B)  1/12  (C)  11/24  (D)  1/3  (E)  12

Solution

(2)  Michelle bought a dress that costs $103.00, a pair of shoes that costs $73.00 and a bag that costs $111.00. There is a 7% sales tax on all items priced at $90.00 and higher. There is no sales tax on items under $90.00. How much did Michelle spend on the following items, including tax ?

(A)  $287.00  (B)  266.00  (C)  295.47 

(D)  300.60  (E)  $301.98

Solution

(3)  How many terms are in the sequence

0, 3, 6,.............57, 60 ?

(A)  20  (B)  21  (C)  23  (D)  30  (E)  60

Solution

(4)  The larger of two consecutive even integers is two times the smaller. What is their sum ?

(A)  2  (B)  3  (C)  4  (D)  6  (E)  8

Solution

(5)  3^x  =  27 ^a+b and (a² - b²) / (a-b)  =  5, what is x ?

(A)  6  (B)  9  (C)  12  (D)  15  (E)  27

Solution

(6)  In Mr.Farmer's class there are 30 kids. If there are twice as many boys as there are girls in the English club, then what percentage of the English club are boys ?

(A)  33.3%  (B)  10%  (C)  30%  (D)  20%  (E)  66.6%

Solution

(7)  a⊗b  =  a³- 3a²b + 3ab² - b³ and a ⊕b  =  (a-b)(a-b), what is (a⊗b) / (a⊕b)

(A)  a² + b²  (B)  a - b  (C) a² + 3b² + 3ab

(D)  a² - b²  (E)  b² + 3a

Solution

(8)  What is the prime factorization of 752 ?

(A) 2³ ⋅ 48  (B) 2³ ⋅ 49  (C) 3³ ⋅ 49 

 (D) 2⁴ ⋅ 47  (E) 3⁴ ⋅ 47

Solution

(9)  If x can be any integer, what is least possible value of the expression 4x² - 10 ?

(A)  -10  (B)  -4  (C)  4  (D)  10  (E)  ∞

Solution

(10)  There is a total of 5 bicycles and tricycles in a park. There are 12 wheels.How many tricycles are there ?

(A)  2  (B)  3  (C)  6  (D)  7  (E)  8

Solution

(11)  What is the least possible value of (x² - 1)/x if x ≥ 1 ?

(A)  -1  (B)  0  (C)  3  (D)  3/4  (E)  2/3

Solution

(12)  What is the maximum number of points in which a circle and triangle can intersect ?

(A)  3  (B)  5  (C)  6  (D)  8  (E)  ∞

Solution

(13)  

What is the area of the shaded region ?

(A)  48 - 10π  (B)  64 - 22π  (C)  10π 

(D)  48 - 6π  (E)  16π

Solution

(14)  There are 45 plastic ducks in a bag. If there are black, green, blue and purple plastic ducks and 1/3 of the plastic ducks are black, 1/5 of the plastic ducks are blue, one third of the number of black plastic ducks are green, then how many purple plastic ducks are in the bag ?

(A)  6  (B)  15  (C)  16  (D)  21  (E)  39

Solution

(15)  

In the figure above, point B is on the line segment DC. If AB  =  BC, what is the measure of the angle ABE ?

(A)  20°  (B)  40°  (C)  80°  (D)  90°  (E)  100°

Solution

(16)

According to the figure given above, what is the value of y ?

(A)  3  (B)  6  (C)  12  (D)  15  (E)  18

Solution

(17)  A painter needs 4 gallons of paint to paint each room. If a house has 8 rooms in total, how many quarts of paint is he going to need ?

(A)  12  (B)  32  (C)  128  (D)  200 (E)  512

Solution

(18)  A rectangle is inscribed in a circle. The rectangle is tangent at the points A, B, C and D. If the diagonal of the rectangle is 20 inches long. What is the are of the circle ?

(A)  10π  (B)  15π  (C)  20π  (D)  100π  (E)  400π

Solution

(19)  The prices in the table given below  show the different types of gas offered at a gas station and the prices of gas per gallon. If Emily has $50, what is the least amount of gas, in gallons, she can purchase subtracted from the greatest amount of gas, in gallons, she can purchase ?

(A)  2  gallons  (B)  3 gallons  (C)  5 gallons  

(D)  20 gallons  (E)  25 gallons

Solution

(20)  3[9 ÷ (-3)]  + [-3 - (-8)]  =

(A)  -20  (B)  -4  (C)  -2  (D)  2  (E)  14 

Solution

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