MAT 102 UNIT 3 TEST Part B – Fall 2015 – Version 6
Name _______________________________
Instructions:
Show your work in order to receive credit.
Date ________________
Draw a box around your final answer.
Scientific calculators are permitted on this portion of the test.
Use a pencil, not a pen.
Each question on the test counts 4 points unless otherwise specified (for a total of 100 points).
Use your calculator to find the value of the radical expression
accurate to four decimal places. (2 pts each)
Simplify the following expression. Assume that each variable
is positive.
14.
4
9.
√81𝑥 21 𝑦 5
√39
10.
3
√−216
15.
3
√54𝑥 17 𝑦 4
11.
−1 + 7√2
Simplify the following expression. Assume that each variable
is positive.
Rationalize the denominator and simplify if possible. Assume
that all variables represent positive numbers.
16.
12.
√
78𝑥 13
2𝑧
√3𝑦
81𝑦 4
13.
3
√
13𝑥 13
8𝑦 3
17.
√𝑥
√𝑥 + 5
Rationalize the denominator and simplify if possible. Assume that all variables represent positive numbers.
18.
3
√
7
3𝑧
Solve the following radical equation or if there is no solution write "No Solution". Remember to check your answer(s). (6 pts each)
19.
20.
√−8 + 2𝑧 + 4 = 6
3
√6 + 4𝑡 = −4
2
Solve the following radical equation or if there is no solution write "No Solution". Remember to check your answer(s).
21.
(6 pts)
√𝑥 + 6 + √𝑥 + 22 = 8
Simplify the following expression. Assume all variables are positive. Write the solution using rational exponents. Assume that the
variables are positive.
22.
8𝑥 3 · 𝑦 2
−1⁄
3
(𝑥 −1 · 𝑦4 )
(4 pts)
𝑦 2⁄7 · 𝑦 2⁄3
(2pts)
23.
3
24.
For the following functions, use interval notation to indicate the domain. Note: Round any decimal values to two decimal
places. (2 pts each)
a.
g(x) = √−5𝑥 + 3.6
3
b. y = √−2𝑥 + 9.2
25.
For the function 𝑦 = √𝑥 − 2,
a. Determine the domain expressing your answer in interval notation.
b. Determine at least 3 ordered pair solutions.
c. Sketch the graph.
d. Determine the range expressing your answer in interval notation.
Domain: _______________________
Range: ________________________
4
(2 pts)
(6 pts)
(2 pts)
(2 pts)
Review Problems:
26.
Solve the following quadratic equation:
3𝑥 2 = −7𝑥 + 20
27.
Simplify the following:.
𝑥+3
𝑥+2
+
𝑥−2
𝑥−3
5