PSAT MATH PRACTICE WORKSHEET

(1) In the figure given below, there is a function plotted and there are 5 points tabled A through E drawn. For how many points is y(x) equal to 0 ?

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

Solution

(2) At what time on a clock will the hands form an acute angle formed of 60 degree?

(A) 1 : 00 PM (B) 1 : 15 PM (C) 2 : 00 PM

(D) 2 : 30 PM (E) 3 : 00 PM

Solution

(3) A jar contains only red and blue marbles. The probability of picking a red marble is 20% . One blue marble is added to the jar. What is the probability of picking a blue marble ?

(A) 1/3 (B) 1/2 (C) 4/5 (D) 1/6

(E) cannot be determined from the information given.

Solution

(4) If a = 35, what is, (-6)² (-6)(-6) + 6(-6) in terms of a ?

(A) a + 1 (B) a² (C) a² + 1 (D) a² + a (E) 35a

Solution

(5) A circle and an octagon share the same perimeter (circumference of the circle). If the side length of the octagon is a, the radius of the circle is r, then what is the radius in terms of the side length of the octagon ?

(A) 4a (B) a/π (C) 4/π (D) 4a/π (E) 4π

Solution

(6) What is the least integer greater than the greatest integer less than 1.5?

(A) 2 (B) 1.5 (C) 0.5 (D) 1 (E) 0

Solution

(7) What is the area of a semicircle in terms of "t" with radius r. "t" is double the value of π

(A) t² r (B) tr² (C) tr/4 (D) tr/2 (E) tr²/4

Solution

(8) If F = - kx and greater than 0, then what happens to the value of k if F triples in value and x remains constant.

(A) increases (B) Doubles (C) Decreases (D) Remains constant

(E) cannot be determined from the information given.

Solution

(9) If the length of the side of a square is 7^a, what is the area ?

(A) 7^a (B) 2 ⋅ 7^a (C) 49^a (D) 7^2a (E) 7a^a

Solution

(10) What is the circumference of the dotted section of the circle whose center is O below ?

(A) 6π (B) 12π (C) 24π (D) 48π (E) 64π

Solution

(11) Given that 0 < x < 1, and set A = {x, x², x³, x⁴}, what is the smallest value in set A ?

(A) x (B) x² (C) x³ (D) x⁴

(E) cannot be determined

Solution

(12) Sammy has a faulty clock. Every 15 degrees that one of the hands moves, 5 minutes passes. If a hand is initially 5 : 35 PM, in how long will be the hand be at that same position ?

(A) 65 minutes (B) 2 hours (C) 1 hour

(D) 45 minutes (E) 1 hour and 15 minutes

Solution

(13) If (x - 2) (x + 2) = ax² + bx + c, what is the sum of a, b and c ?

(A) -4 (B) -3 (C) 0 (D) 1 (E) 5

Solution

(14) Natalie walks in a special way. After every 2 steps she takes, she takes 1 step in the opposite direction. She starts at point A and walks forward. When she is 7 steps away from the point A, she has reached her destination point B. How many steps in total did she take to get from point A to B.

(A) 7 (B) 8 (C) 17 (D) 15 (E) 18

Solution

(15) If Cmn = C(m + n), for what value of n is Cmn neither positive nor negative ?

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

Solution

(16) Two sides of a triangle at 6 and 8. What is the length of the third side ?

(A) 2 (B) 4 (C) 5 (D) 10 (E) Cannot be determined

Solution

(17) 2 + (1/3) = 14/b, what is b ?

(A) 3 (B) 6 (C) 7 (D) 9 (E) 28

Solution

(18) The radius of circle A is x and the radius of circle B is 2. If the circumference of circle A is two times the circumference of the circle B, find the value of x.

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

Solution

(19) In the formula V = r²h, if h is doubled and r is tripled, then V is multiplied by ?

(A) 6 (B) 9 (C) 12 (D) 18 (E) 36

Solution

(20) Max A returns the largest value in the set A, min A returns the lowest value in the set A. For example, max {1, 2, 3} = 3 and min {0, 4, 5} = 0. What is max {min{x, 2x, 3x}, max{x/2, x/4,x/8}} ?

(A) x (B) 2x (C) x/2 (D) 3x

(E) cannot be determined.

Solution