PSAT MATH TEST WORKSHEET

(1)  The circle that is inscribed in the square below has a radius of 2. What is the length of diagonal of the square ?

(A)  2  (B)  4  (C)  16  (D)  4√2  (E)  2√2

Solution

(2)  What is the absolute value of the difference between the number of integers between 0 and 5 inclusive and the number of integers between 1 and 6 exclusive ?

(A)  0  (B)  1  (C)  2  (D)  3  (E)  5

Solution

(3)  Corey is walking on a path. Every three steps he take, he makes a 30 degree rotation to counterclockwise, if he took 18 steps in total, how many full revolutions was he able to make altogether ?

(A)  0.25  (B)  0.5  (C)  1  (D)  2  (E)  5

Solution

(4)  What is 20% of 20% of 20 ?

(A)  0.2  (B)  0.8  (C)  2  (D)  8  (E)  8000.

Solution

(5)  What is the difference between the largest and lowest integer in the sequence of consecutive odd integers whose sum is 15 ?

(A)  2  (B)  4  (C)  5  (D)  9  (E)  12

Solution

(6)  The half life of a substance is the time it takes for a substance to decrease to half its initial amount. If John initially had 100 pounds of goo and ten days later, he only had 25 pounds of goo, what is the half life of the goo ?

(A)  10 days  (B)  5 days   (C)  7.5 days 

(D)  20 days   (E)  25 days

Solution

(7)  What is the value of (9⁴ - 8⁴)/(9² + 8²) ?

(A)  1  (B)  16  (C)  17  (D)  18  (E)  155

Solution

(8)  Jack fills a jug with water continuously. It takes him 2 minutes to fill up 50% of the empty space in the jug with water. After every 2 minutes, he puts a penny into a jar to celebrate. How many pennies will he have in the jar at the instant the jug has less tan 30% empty space left ?

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

Solution

(9) 

In the figure above, there are two balance beams that have triangles, circles and squares on them. Both beams are fully balanced. How many circles are needed to balance 70 squares ?

(A)  10  (B)  12  (C)  35  (D)  70  (E)  140

Solution

(10)  0.7 bar + (2/9)  = 0.6 bar + ____

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

Solution

(11)  The distinct prime factors of 232 are

(A)  2, 2, 2, 29  (B)  116, 2  (C)  2, 29 

(D)  2, 2, 58  (E)  2, 58 

Solution

(12)  If the pattern continues, what will be the 438th symbol ?

Solution

(13)  Find the value of t. 

t/32  =  x/p

(A)  32p/x (B)  xp/32  (C)  32/px  (D)  32x/p  (E)  32px

Solution

(14)  What is the largest integer greater than 52/3 ?

(A)  16   (B)  17  (C)  18  (D)  19  (E)  20

Solution

(15)  If 5⁵ + 5⁵ + 5⁵ + 5⁵ + 5⁵  =  5^{a + 1}, what is a ?

(A)  3  (B)  4  (C)  5  (D)  6  (E)  7

Solution

(16)  If (x + y)²  =  x² + y², then what condition must be true?

(A)  x  =  y  =  0  (B)  x + y  =  0  (C)  2x  =  0

(D)  2y  =  0  (E)  xy  =  0

Solution

(17)  What is the maximum number of points that two distinct circles intersect at ?

(A)  1  (B)  2  (C)  3  (D)  4  (E) Undefined

Solution

(18)  A cumulative product of a set {a, b, c, ............} is the sequence a, ab, abc,.............. What is the mean of the terms in cumulative product of {1, 2, 3, 0} ?

(A)  0  (B)  2  (C)  2.25  (D)  3.5  (E)  6

Solution

(19)  How many integers are in the set of non positive, non negative  integers?

(A)  0  (B)  1  (C)  2  (D)  3  (E)  Undefined

Solution

(20)  How many chords are in the circle below ?

(A)  0  (B)  1  (C)  2  (D)  3  (E)  7

Solution

Question 11 :

In an experiment, a student uses the thermometer that can read temperatures from -94° F to 172° F. The student also converts measurements from  °F to kelvins (K) and degree Rankine (°R) using the following approximate formulas.

T_K = (5x/9) + 255

where x is the temperature in °F and T_k is the temperature in K.

T_R = x + 460

where x is the temperature in °F and T_R is the temperature R.

If the temperature was recorded as 500°R, which of the following is closest to the reading of the thermometer ?

(A)  40°F      (B)  120°F      (C)  710°F     (D)  960°F

Solution

Question 12 :

If  √[17 + (x - y)³] = 9, what is the value of (x - y)³

(A)  4      (B)  9      (C)  16     (D)  25

Solution

Question 13 :

The boiling point of water at sea level is 212 degree Fahrenheit (°F). For every 550 feet above sea level, the boiling point of water is lowered by about 1°F. Which of the following equations can be used to find the boiling point B water, x feet above sea level ?

(A)  B = 550 + (x/212)      (B)  B = 550 - (x/212)

(C)  B = 212 + (x/550)      (D)  B = 212 - (x/550)

Solution

Question 14 :

In the xy-plane, the graph of the quadratic function g intersects the x-axis at x = 5 and x = 9. Which of the following could be an equation of g ?

A) g(x) = (x - 5)(x - 9)     B) g(x) = (x + 5)(x + 9)

C) g(x) = (x - 7)² + 4     D) g(x) = (x + 7)² - 4

Solution

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