Download Math 103 Practice Exam 3 Exam 3 Monday, December

Math 103
Practice Exam 3
Exam 3 Monday, December 3rd
Professor Busken
Name:
Directions: Box off your final answer or write it on an answer line if one is provided. Work
together! You may not use a calculator, unless you are working the problems on page 10.
Show all your work in a neat, organized fashion to receive full credit on the exam. The exam
is a two-part exam. After you complete and turn in part 1 of the exam, you will be allowed
to use your scientific calculator to complete part 2. The use of graphing calculators or phones
are prohibited.
For questions 1—6, simplify each expression as much as possible. Assume all variables represent nonnegative numbers.
1.
√
− 81
1.
2.
√
− 3 −27
2.
3.
−811/4
3.
4.
163/4
4.
5.
27−4/3
5.
6.
√
5
32a15 b65
6.
For questions 7—9, use the properties of exponents to simplify each expression. Assume all
bases represent positive numbers.
7.
x3/2 · x−1/2
7.
8.
2
x3/2 · y −1/2
8.
9.
x2/3 y 3
x1/4 y 1/3
9.
10.
Multiply (x3/2 − 3)2
11.
Divide
28x5/6 + 14x7/6
7x1/3
10.
11.
For questions 12—15, write each expression in simplified form for radicals. Assume all variables represent nonnegative numbers.
12.
√
24
12.
13.
√
400
13.
14.
√
3
16
14.
15.
√
3
72a7 b5
15.
For questions 16—18, rationalize the denominator in each expression.
16.
3
√
13
16.
17.
3
√
3
2
17.
18.
3
√
5−2
18.
For question 19, write the given expression in simplified form. Assume all variables represent
nonnegative numbers.
19.
s
48x3
7y
19.
For questions 20—22, write each expression in simplified form for radicals. Assume all variables represent nonnegative numbers.
20.
√
√
√
8x 8 − 14x 50 + x 18
20.
21.
√
√
12 − 52
21.
22.
√
p
3
2x 3 xy 3 z 2 − 6y x4 z 2
22.
For questions 23—24, multiply.
23.
√ √ √
2·
3−2 2
23.
24.
√
√
x−5 ·
x−9
24.
For questions 25—31, solve the given equations for x. Solutions may take on either real or
complex (number) values.
√
25.
4x + 1 = 1
25.
26.
√
3x + 1 − 3 = 1
26.
27.
√
√
x+4= x−2
27.
28.
√
3
3x − 8 = 1
28.
29.
(2x − 5)2 = 25
29.
30.
(3x − 4)2 = −49
30.
31.
(2x − 5)3 = −27
31.
32.
3−
1
2
+ 2 =0
x x
32.
33.
1
1
+
=1
x−3 x+2
33.
For questions 34—35, solve each quadratic equation by completing the square.
34.
x2 + 4 = 4x
34.
35.
3x2 + 15x = −18
35.
For questions 36—37, solve each quadratic equation using the Quadratic Formula.
36.
5x2 + 2x = 3
36.
37.
100x2 − 200x = 100
37.
For questions 38—39, use the definition of the logarithm to write each equation in logarithmic
form.
38.
0.01 = 10−2
39.
2−3 =
1
8
38.
39.
For questions 40—41, use the definition of the logarithm to write each equation in exponential
form.
40.
log3 (9) = 2
40.
41.
log4 (4) = 1
41.
For questions 42—44, solve each of the following equations for x.
42.
log5 x = 3
42.
43.
log3 (81) = x
43.
44.
logx (25) = 2
44.
For questions 45—49, sketch the graph of the solution set of each equation. Identify or label
any intercepts or vertex points, if applicable, for full credit. Please state the domain and range
of each equation as well.
y
45.
2
5
y = x + 4x − 5
4
3
2
1
x
−5
−4
−3
−2
−1
1
2
3
4
5
1
2
3
4
5
1
2
3
4
5
−1
−2
−3
−4
−5
46.
f (x) =
x
1
3
y
5
4
3
2
1
x
−5
−4
−3
−2
−1
−1
−2
−3
−4
−5
y
47.
y = log 21 x
5
4
3
2
1
x
−5
−4
−3
−2
−1
−1
−2
−3
−4
−5
y
48.
f (x) = 2
x
5
4
3
2
1
x
−5
−4
−3
−2
−1
1
2
3
4
5
1
2
3
4
5
−1
−2
−3
−4
−5
y
49.
y = log2 (x)
5
4
3
2
1
x
−5
−4
−3
−2
−1
−1
−2
−3
−4
−5
For questions 50—53, simplify each of the following expressions.
50.
log3 3
50.
51.
log6 1
51.
52.
log2 64
52.
53.
log 12 (8)
53.
For questions 54—56, expand the given logarthimic expression using the properties of logarithms.
54.
log2 ( x4 )
54.
55.
56.
log3
8a
b
log2
y3
√
5
x
55.
56.
For question 57, write the given expression as a single logarithm.
57.
2 log7 (x) − 5 log7 (y) +
1
log7 (z)
2
57.
For questions 58—59, solve each equation for x.
58.
log2 (x) + log2 (4) = 3
58.
59.
log6 (x − 1) + log6 (x) = 1
59.
For questions 60—62, use the definition of the natural logarithm to simplify each logarithmic
expression.
60.
ln(e2 )
60.
61.
ln(1)
61.
62.
ln(e−1 )
62.
For questions 63—65, use a calculator to find the following common logarithms. Round to
four decimal places.
63.
log(0.741)
63.
64.
log(741)
64.
65.
ln(741)
65.
For questions 66—68, find x in the following equations. You may use your calculator. Round
to four decimal places.
5
3
66.
log(x) =
67.
log(x) = −4
68.
ln(x) =
2
3
66.
67.
68.
For questions 69—70, use a calculator to evaluate each expression. Round your answers to
four decimal places.
69.
log 4
log 3
69.
70.
4
log
9
70.
For questions 71—72, solve the given equation for x. You may use a calculator to approximate
the solution at the end. Round your answers to four decimal places.
71.
4x = 3
71.
72.
7−x = 8
72.