ANSWER: D

EXPLANATION: The figure is broken into two identical right triangles, which are each 30–60–90. Use the rule of 30–60–90. AB = 2x, since it is the hypotenuse.

Hence,

so

and

Simply use your calculator to prove this is equal to the answer in D. The answer is D.

3). What set of numbers represents the union of sets A and B?

Set A {1, 2, 7, 10, 11, 17}
Set B {1, 3, 7, 13, 17}

(A) {1, 7, 17}
(B) {1, 7, 10}
(C) {1, 3}
(D) {1, 2, 3, 7, 10, 11, 13, 17}
(E) {1, 1, 2, 3, 7 ,7 10, 11, 13, 17, 17}

ANSWER: D

EXPLANATION: Union means including all numbers that are in either set. Note: numbers appearing in both sets are only included once. The answer is D.

4). If f(x) = 3x² - 6^x, then f(2) =

(A) -12
(B) -24
(C) 0
(D) 10
(E) 18

ANSWER: B

EXPLANATION: Since x = 2 in this question, put in a 2 everywhere you see an x in the equation:
3(2)² – 6². Now simplify: 3(4) – 36, or 12 – 36, which is –24. The answer is B.

5). If a varies directly as b² and a = 36 when b = 3 what is the value of a when b is 7?

ANSWER: E

EXPLANATION: Set up a proportion since this is direct variation. Make sure you use b².

Hence

which becomes

, so a = 196

The answer is E.

6). What is the distance between the points (1, 3) and (2, 11)?

(A)
(B)	9
(C)
(D)	10
(E)	13

ANSWER: C

EXPLANATION: Sketch the line. Now draw a right triangle with vertices of (1, 3), (2, 11) and (1, 12). The lengths of the two sides are 1 (2– 1) and 8 (11– 3). Use Pythagorean Theorem: 1² + 8² = h². Simplify 65 = h². The answer is C.

7). For all

(A)	x + 2
(B)	x2 - 12x - 14
(C)
(D)
(E)

ANSWER: C

EXPLANATION: Factor the top and bottom of the fraction. The top becomes(x + 4) (x – 7) and the bottom becomes (x – 2)(x – 7). Cancel the (x – 7) and you're left with answer C . The answer is C.

8). If,

what is one possible value of x?

(A) 1
(B) 0
(C) 16
(D) 25
(E) 36

ANSWER: C

EXPLANATION: Solve for x. First add 12 to both sides. Now divide both sides by 32 and then square both sides to get: x = 16. The answer is C.

9). What is the y-intercept for the equation 2x + 5y = 10?

(A)	(-10, 0)
(B)	(2, 0)
(C)	(0, 10)
(D)	(0, 2)
(E)

ANSWER: D

EXPLANATION: Rearrange the equation to change it into the y = mx + b form. 5y = –2x + 10. Now divide by 5 to get y on its own. Remember that the b represents the y–coordinate of the y–intercept. The answer is D.

10). Which of the following is the solution set of the equation x² = 3x + 10?

(A) {-2, -5}
(B) {-2, 5}
(C) {-5, 3}
(D) {-3, 5}
(E) {3, 5}

ANSWER: B

EXPLANATION: Set the equation equal to zero so that you can factor. So x² – 3x – 10 = 0.

What are the factors of –10? (1 and –10, –1 and 10, 2 and –5, and –2 and 5). You want the pair to add to –3. So the equation factors to (x – 5)(x + 2) = 0. If that is true, then either x – 5 = 0 or
x + 2 = 0. So x = 5 or –2. The answer is B.