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ACT-math-test

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Ray PK bisects ∠LPM, the measure of ∠LPM is 11x°, and the measure of ∠LPK is (4x + 18)°. What is the measure of ∠KPM ?

Ray PK bisects ∠LPM, the measure of ∠LPM is 11x°, and the measure of ∠LPK is (4x + 18)°. What is the measure of ∠KPM ?

F. 12°

G. 28 2/7°

H. 42°

J. 61 1/5°

K. 66°

Answer(s): 1
Votes: 0

Tags: ACT-math-test, math


For −π/2 ≤θ≤ π/2, |sin θ| ≥ 1 is true for all and only the values of θ in which of the following sets?

For −π/2≤θ≤π/2, |sin θ| ≥ 1 is true for all and only the values of θ in which of the following sets?

A. {−π/2, π/2}

B. {π/2}

C. {θ | -π/2<θ<π/2}

D. {θ | −π/2≤θ≤π/2}

E. The empty set

Answer(s): 1
Votes: 0

Tags: ACT-math-test, math


Given a positive integer n such that i^n = 1, which of the following statements about n must be true?

Given a positive integer n such that in = 1, which of the following statements about n must be true? (Note: i2 = −1)

F. When n is divided by 4, the remainder is 0.

G. When n is divided by 4, the remainder is 1.

H. When n is divided by 4, the remainder is 2.

J. When n is divided by 4, the remainder is 3.

K. Cannot be determined from the given information

Answer(s): 1
Votes: 0

Tags: ACT-math-test, math


For what positive real value of k, if any, is the determinant of the matrix [k 4 3 k] equal to k ?

For what positive real value of k, if any, is the determinant of the matrix  equal to k ? (Note: The determinant of matrix  ad − bc.) A. 3 B. 4 C. 12 D. √12 E. There is no such value of k.

Answer(s): 1
Votes: 0

Tags: ACT-math-test, math


At the school carnival, Mike will play a game in which he will toss a penny, a nickel, and a dime at the same time. He will be awarded 3 points for each coin that lands with heads faceup. Let the random variable x represent the total number of points awarded on any toss of the coins. What is the expected value of x ?

At the school carnival, Mike will play a game in which he will toss a penny, a nickel, and a dime at the same time. He will be awarded 3 points for each coin that lands with heads faceup. Let the random variable x represent the total number of points awarded on any toss of the coins. What is the expected value of x ?

F. 1

G. 3/2

H. 9/2

J. 6

K. 9

Answer(s): 1
Votes: 1

Tags: ACT-math-test, math


One of the following graphs in the standard (x,y) coordinate plane is the graph of y = sin^2 x + cos^2 x over the domain − π/2 ≤ x ≤ π/2. Which one?

One of the following graphs in the standard (x,y) coordinate plane is the graph of y = sin2 x + cos2 x over the domain − π/2 ≤ x ≤ π/2. Which one?

Answer(s): 1
Votes: 0

Tags: ACT-math-test, math


The 3rd and 4th terms of an arithmetic sequence are 13 and 18, respectively. What is the 50th term of the sequence?

The 3rd and 4th terms of an arithmetic sequence are 13 and 18, respectively. What is the 50th term of the sequence?

A. 248

B. 250

C. 253

D. 258

E. 263

Answer(s): 1
Votes: 0

Tags: ACT-math-test, math, Arithmetic-progression, AP


The list of numbers 41, 35, 30, X, Y, 15 has a median of 25. The mode of the list of numbers is 15. To the nearest whole number, what is the mean of the list?

The list of numbers 41, 35, 30, X, Y, 15 has a median of 25. The mode of the list of numbers is 15. To the nearest whole number, what is the mean of the list?

A. 20

B. 25

C. 26

D. 27

E. 30

Answer(s): 1
Votes: 0

Tags: ACT-math-test, math


The graph of a function y = f (x) consists of 3 line segments. The graph and the coordinates of the endpoints of the 3 line segments are shown in the standard (x,y) coordinate plane below. What is the area, in square coordinate units, of the region bounded by the graph of y = f(x), the positive y-axis, and the positive x-axis?

The graph of a function y = f (x) consists of 3 line segments. The graph and the coordinates of the endpoints of the 3 line segments are shown in the standard (x,y) coordinate plane below. What is the area, in square coordinate units, of the region bounded by the graph of y = f(x), the positive y-axis, and the positive x-axis? A. 10 B. 13 C. 14 D. 15 E. 20

Answer(s): 1
Votes: 0

Tags: ACT-math-test, math


A room has a rectangular floor that is 15 feet by 21 feet. What is the area of the floor in square yards ?

A room has a rectangular floor that is 15 feet by 21 feet. What is the area of the floor in square yards ?

A. 24

B. 35

C. 36

D. 105

E. 144

Answer(s): 1
Votes: 0

Tags: ACT-math-test, math