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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)

The Correct Answer
Explanation

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

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