PSAT PRACTICE MATH WORKSHEET 5

(1)  [(2/3) + (1/4)]  ÷ 2  =

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

(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

(3)  How many terms are in the sequence

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

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

(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

(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

(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%

(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

(8)  What is the prime factorization of 752 ?

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

 (D) 2⁴ ⋅ 47  (E) 3⁴ ⋅ 47

(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)  ∞

(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

(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

(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)  ∞

(13)  

What is the area of the shaded region ?

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

(D)  48 - 6π  (E)  16π

(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

(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°

(16)

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

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

(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

(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

(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

(20)  3[9 ÷ (-3)]  + [-3 - (-8)]  =

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