College Algebra (MATH 1314) Pre-Test
Name: _______________________________
Write the solution set using interval notation.
1.
1. ________
2(𝑥𝑥 + 8) ≤ 3(𝑥𝑥 − 6)
A) (−∞, −2]
B) (−∞, 34)
C) [34, ∞)
D) (−2, ∞)
Use the properties of exponents to simplify the expression. Write with positive exponents.
2.
3
�−2𝑥𝑥 4/5 �
𝑥𝑥 −1/2
A) −2𝑥𝑥 19/10
2. ________
B) −8𝑥𝑥 19/10
C) −2𝑥𝑥 29/10
D) −8𝑥𝑥 29/10
Solve the compound inequality.
3.
12𝑥𝑥 − 8 < 4𝑥𝑥 or −3𝑥𝑥 ≤ −9
3. ________
Multiply or divide as indicated. Simplify completely.
4.
𝑥𝑥 2 +5𝑥𝑥−6
𝑥𝑥 2 +9𝑥𝑥+18
A)
𝑥𝑥+4
𝑥𝑥−1
÷
𝑥𝑥 2 −1
𝑥𝑥 2 +7𝑥𝑥+12
B)
𝑥𝑥+1
𝑥𝑥+4
4. ________
C)
𝑥𝑥+4
𝑥𝑥+1
D)
𝑥𝑥−1
𝑥𝑥+4
Find the domain of the rational function.
5. 𝑓𝑓(𝑥𝑥) =
1−6𝑥𝑥
𝑥𝑥 2 −16𝑥𝑥+28
5. ________
A) {𝑥𝑥|𝑥𝑥 is a real number and 𝑥𝑥 ≠ −14, 𝑥𝑥 ≠ 2}
1
6
B) {𝑥𝑥|𝑥𝑥 is a real number and 𝑥𝑥 ≠ 14, 𝑥𝑥 ≠ 2, 𝑥𝑥 ≠ , 𝑥𝑥 ≠ 0}
C) {𝑥𝑥|𝑥𝑥 is a real number and 𝑥𝑥 ≠ 14, 𝑥𝑥 ≠ 2}
1
D) �𝑥𝑥|𝑥𝑥 is a real number and 𝑥𝑥 ≠ −14, 𝑥𝑥 ≠ 2, 𝑥𝑥 ≠ �
6
Simplify the radical expression. Assume that all variables represent positive real numbers.
6.
3
√−64𝑎𝑎14 𝑏𝑏10
A) 4√𝑎𝑎10 𝑏𝑏14
6. ________
3
B) 4𝑎𝑎𝑎𝑎 √𝑎𝑎4 𝑏𝑏 5
3
C) −4𝑎𝑎4 𝑏𝑏3 √𝑎𝑎2 𝑏𝑏
3
D) 4𝑎𝑎2 𝑏𝑏 √𝑎𝑎4 𝑏𝑏 3
SHORT ANSWER: Write the word or phrase that best completes each statement or answers the
question.
Perform the indicated operation. Simplify if possible.
7.
𝑥𝑥
8
− 2 +5𝑥𝑥+4
𝑥𝑥 2 −16
𝑥𝑥
7. ______________________________
√43 − 𝑥𝑥 = 𝑥𝑥 − 1
8. ______________________________
Solve.
8.
Factor the polynomial completely.
9.
12𝑥𝑥 2 𝑦𝑦 2 − 11𝑥𝑥𝑦𝑦 2 − 15𝑦𝑦 2
9. ______________________________
Solve the equation.
4𝑥𝑥 2 + 36𝑥𝑥 + 81 = 0
10.
Answers:
1) C
2) D
3) A
4) C
5) C
6) C
7)
𝑥𝑥 2 −7𝑥𝑥+32
(𝑥𝑥+4)(𝑥𝑥−4)(𝑥𝑥−1)
8) 𝑥𝑥 = 7 𝑜𝑜𝑜𝑜𝑜𝑜𝑜𝑜
9) 𝑦𝑦 2 (3𝑥𝑥 − 5)(4𝑥𝑥 + 3)
10) 𝑥𝑥 =
−9
2
10. _____________________________