As shown in the (x,y,z) coordinate space below, the cube with vertices L through S has edges that are 2 coordinate units long. The coordinates of Q are (0,0,0), and S is on the positive x-axis. What are the coordinates of O?
(F) (2,0,2)
(G) (2,2,2)
(H)
(J)
(K)
RST is a right triangle with side lengths of r, s, and t, as shown below. What is the value of cos2 S + cos2 R?
(F) 1 (G) (H) (J) (K)
Correct Answer: F
A rectangular solid consisting of 18 smaller cubes that are identical is positioned in the standard (x,y,z) coordinate system, as shown below. Vertex M has coordinates of (-1,3,0) and point O on the y-axis has coordinates of (0,3,0). What are the coordinates of vertex N?
(F) (3,0, 2) (G) (2,2, 0) (H) (3,0,-1) (J) (0,2, 2) (K) (2,0, 2)
Correct Answer: K
For all xy ≠ 0, and when both x and y are greater than 1, the expression equals which of the following?
(A) (B) (C) 1 (D) (E)
Correct Answer: D
More ACT Math Exam Questions
- 1
Alfred and Rani both picked different two-digit numbers. If you multiply Alfred’s number by 5 and double Rani’s number, the sum is 300. If you double Alfred’s number and multiply Rani’s number by 3, the sum of the two numbers is 252. What is the sum of their two numbers?
- 2
Which of the following expressions is equivalent to the expression given below?
(2x3 – x - 1) - 3(x4 + 2x3 - 2x2 – x + 3)
- 3
To this questions below, use the following graph, which provides information about the number of new clients five salespeople registered last month.
What percentage of the new clients did Yolanda register?
- 4
A rock band, The Young Sohcahtoans, is trying to design a t-shirt logo. The measurements they have chosen are represented on the figure below. The angle to the right of the logo "TYS" has a degree measure of 35°, and the side of the figure has a measure of 10 in. Which of the following expressions gives the measure, in inches, of the diagonal top side of the figure?
- 5
In the figure below, ∠ ABC ≅ ∠ DFE, ∠ BAC ≅ ∠ FDE, D and F are on AB, AD ≅ FB, and distances in centimeters are as shown. What is the length of AD, in centimeters?