PSAT MATH QUIZ ONLINE PRACTICE

(1)  The perimeter of a square is four times the circumference of a circle with radius of 1 m. What is the area of the square ?

(A)  4π  (B)  8π  (C)  4π²  (D)  8π²  (E)  16π²

Solution

(2)  

(A)  24  (B)  66  (C)  67  (D)  68  (E)  1120

Solution

(3)  Convert 3/40 to a decimal.

(A)  0.0075  (B)  0.075  (C)  0.06  (D)  0.75  (E)  7.5

Solution

(4)  For what value of q is 6(q + 3)  =  2(q + 4) ?

(A)  -1/2  (B)  -4/9  (C)  -5/2  (D)  -3  (E)  -2/5

Solution

(5)  

What is angle x of the circle O?

(A)  45 degree  (B)  60 degree (C)  75 degree 

(D)  150  degree  (E)  90 degree

Solution

(6) For how many values of x is -3x²/4 > 0 ?

(A)  0  (B)  1   (C)  3  (D)  5  (E)  6

Solution

(7)  x is 40% of y and y is the square of x, which is x?

(A)  √x  (B)  0.4√x  (C)  0.4x²  (D)  x²  (E)  0.4x

Solution

(8)  If x  =  7 and 4x(3y - 2x)  =  112, what is the value of y ?

(A)  4  (B)  6  (C)  7  (D)  28  (E)  84

Solution

(9) If x ⟩ y  =  (x + y)/(x - y), what is a ⟩ (a - b) ?

(A)  2a/b  (B)  (2a - b)/2a  (C)  (2a - b)/b 

(D)  (2a - b)/2b  (E)  (a + b)/(a - 2b)

Solution

(10)  What is the value of √25 + √64?

(A)  10  (B)  13  (C)  14  (D)  89  (E)  100

Solution

(11) On a certain map that is drawn to scale, 1.5 centimeters is equivalent to 2 miles. If two cities are 35 miles apart, how many centi-meters apart should they be on this map? 

(A) 24.75     (B) 26.00   (C) 26.25   (D) 45   (E) 46.33

Solution

(12) Jose needs a 5/8-meter length of copper pipe to complete a project. Which of the following lengths of pipe can be cut to the required length with the least length of pipe left over?

(A) 9/16 meter      (B) 3/5 meter     (C) 3/4 meter

(D) 4/5 meter       (E) 5/6 meter

Solution

(1)  What is the value of r in the equation 2r  =  10² ?

(A)  5  (B)  10  (C)  25  (D)  50  (E)  100

Solution

(2)  What is the area of a square with a perimeter of 16 ?

(A)  4  (B)  8  (C)  12  (D)  16  (E)  24

Solution

(3)  What is 10% of a number whose square is 81 ?

(A)  0.81  (B)  0.9  (C)  8.1  (D)  9  (E)  10

Solution

(4)  What is the range of the set {1, 2, 5, 10, 6, 12} ?

(A)  -16  (B)  -11  (C)  3  (D)  11  (E)  22

Solution

(5)  Nancy found a formula for the area of a square in terms of its perimeter. Let A stand for the area and P for perimeter. What is the formula Nancy found ?

(A)  p²  (B)  p²/8  (C)  p²/4  (D)  p²/16  (E)  4p

Solution

(6)  Anayet is driving to work from home and realizes he left his wallet at home when he is at workplace. He turns back to retrieve his wallet. His workplace and home are 45 miles apart and it takes him twice as long to get to workplace from his home than the other way around. It is a 30 minutes drive from his workplace to home. What is the average speed for the round trip in miles per minute ?

(A)  0.75   (B)  1.5  (C)  1  (D)  2  (E)  0.5

Solution

(7)  Given that a vector  =  a² + a, what is a vector ÷ a ?

(A)  a  (B)  a + 2  (C)  1  (D)  a + 1  (E)  2a

Solution

(8)  Sarah has a trick coin that has heads on both sides. She asks he friend John, who believes the coin is fair, to guess what face it will land on. If they flip the coin 100 times, how many times bigger is Sarah's expected probability of the coin landing on heads than John's expected probability of the coin landing on heads ?

(A)  0.25  (B)  0.5  (C)  1  (D)  2  (E)  4

Solution

(9)  What is the square of a number that when added to any number does not change that number's value ?

(A)  0  (B)  0.5  (C)  1  (D)  4  (E)  undefined

Solution

(10)  How many non zero numbers are between 3 and 5 ?

(A)  0  (B)  2  (C)  8  (D)  9  (E)  undefined

Solution

(11) A company has a newsletter. In January 2018, there were 1,300 customers subscribed to the newsletter. For the next 24 months after January 2018, the total number of customers subscribed to the newsletter each month was 7% greater than the total number subscribed the previous month. Which equation gives the total number of customers, c, subscribed to the company’s newsletter m months after January 2018, where m ≤ 2 ?

a) c = 1,300 (0.07)^m      b) c = 1,300 (1.07)^m

c) c = 1,300 (1.7)^m         d) c =1,300(7)^m

Solution

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