Some Example Questions: Complete these questions without the use of a calculator.
Answers appear at the bottom of the page.
1. The volume of a box with square base is 90 cubic centimeters. If the height of the box is
15 centimeters, what is the length of each side of the base?
(A)
2.
1
1
9𝑥 =
(A)
−
(C) 6
(B) √6
6
32𝑥−1
(D) 9
(E) 36
then 𝑥 =
1
−
(B)
3
1
(C)
4
1
(D)
4
1
(E)
3
1
2
3. What is the equation of the line which passes through the point (5, 3) and is
perpendicular to the line with equation 2𝑥 + 5𝑦 = 10?
2
5
(A) 𝑦 = 𝑥 + 1
4.
𝑦
𝑦+3
(A)
2
5
(B) 𝑦 = − 𝑥 + 5
2
5
5
2
(C) 𝑦 = 𝑥 + 3 (D) 𝑦 = 𝑥 −
19
2
3
+ 𝑦−3 =
1
𝑦−3
(B)
𝑦+3
𝑦−3
(C)
𝑦2 +9
𝑦2 −9
(D)
(C)
15
4
(C) 8
𝑦2
(E)
𝑦+3
2𝑦
(D) 15
(E)
7
4
(D) 9
(E) 100
𝑦 2 −9
5. If 4𝑧 − 5 = 2, then 𝑧 + 2 =
(A)
5
4
(B)
4
5
4
6. If log 3 𝑝2 − log 3 𝑝 = 2, then 𝑝 =
(A)
1
9
3
(B) √9
5
2
(E) 𝑦 = − 𝑥 +
31
2
7. If sec 𝜃 = −√2 and sin 𝜃 > 0, then cot 𝜃 =
(A) −1
(B) 0
(C) −√3
(D) 1
(E) √3
8. (−2𝑥 3 𝑦 2 )(3𝑥𝑦 2 )2 =
(A) −6𝑥 5 𝑦 6
(B) −18𝑥 5 𝑦 6 (C) 6𝑥4 𝑦8
(D) −18𝑥4 𝑦8 (E) −6𝑥 4 𝑦 8
9.
In right triangle ABC shown to the
right, the lengths of AB, BC, and BE
are 20, 15, and 6, respectively. What
is the length of DE?
(A) 6
(B) 8
(C) 9
(D) 12
(E) 15
Answers to Example Problems:
1. (B) 2. (C)
3. (D)
4. (C)
5. (C)
6. (D)
7. (A)
8. (B) 9. (D)