Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the graph with its function using the x–intercepts.
1)
1)
A)
y =x–2+x–1+ 2
B)
y =x–2–x–1+ 2
C)
y =x–2–x–1– 2
D)
y =x–2+x–1– 2
2)
2)
A)
y =x4+ 2x2+ 1
B)
y =x4– 2x2+ 1
C)
y =x4+ 2x2– 1
D)
y =x4– 2x2– 1
3)
3)
A)
y =x1/2 + 2x1/4 + 1
B)
y =x1/2 + 2x1/4 – 1
C)
y =x1/2 –3x1/4 –4
D)
y =x1/2 +3x1/4 –4
Match the correct viewing rectangle dimensions with the figure.
4)
4)
A)
[–1, 8, 1] by [–1, 8, 1]
B)
[–10, 5, 1] by [–10, 5, 1]
C)
[–1, 8, 1] by [–4, 5, 1]
D)
[–4, 5, 1] by [–1, 8, 1]
C
D
Match the graph with its function using the x–intercepts.
5)
5)
A)
y =2(x – 2)2+ 3(x – 2) – 5
B)
y =2(x – 2)2– 3(x – 2) – 5
C)
y =2(x + 2)2– 3(x + 2) – 5
D)
y =2(x + 2)2+ 3(x + 2) – 5
6)
6)
A)
y =x1/3 –13x1/6 –14
B)
y =x1/3 +13x1/6 +14
C)
y =x1/3 –13x1/6 +14
D)
y =x1/3 +13x1/6 –14
7)
7)
A)
y =x–2+ 2x–1– 3
B)
y =x–2+ 2x–1+ 3
C)
y =x–2– 2x–1– 3
D)
y =x–2– 2x–1+ 3
Match the story with the correct figure.
8)
The amount of rainfall as a function of time, if the rain fell more and more softly.
8)
A)
B)
C)
D)
Match the correct viewing rectangle dimensions with the figure.
9)
9)
A)
[–4, 4, 2] by [–4, 4, 2]
B)
[–20, 20, 2] by [–20, 20, 2]
C)
[–16, 16, 4] by [–4, 4, 2]
D)
[–4, 4, 2] by [–80, 80, 8]
D
C
Match the graph with its function using the x–intercepts.
10)
10)
A)
y =x4+5x2+4
B)
y =x4–5x2–4
C)
y =x4–5x2+4
D)
y =x4+5x2–4
11)
11)
A)
y =(x – 2)2– 7(x – 2) + 6
B)
y =(x – 2)2+ 7(x – 2) + 6
C)
y =(x – 2)2– 3(x – 2) – 4
D)
y =(x – 2)2+ 3(x – 2) – 4
Match the correct viewing rectangle dimensions with the figure.
12)
12)
A)
[–5, 40, 5] by [–5, 40, 5]
B)
[–50, 25, 5] by [–50, 25, 5]
C)
[–5, 25, 5] by [–20, 40, 5]
D)
[–50, 150, 50] by [–2000, 2500, 500]
The table of values was generated by a graphing utility with a TABLE feature. Use the following table to solve.
13)
Which equation corresponds to Y2 in the table?
13)
A)
y2=3x –2
B)
y2= 2x + 3
C)
y2=3–2x
D)
y2= x +3
B
D
Match the correct viewing rectangle dimensions with the figure.
14)
14)
A)
[–50, 25, 5] by [–50, 25, 5]
B)
[–5, 5, 5] by [–5, 5, 5]
C)
[–25, 25, 10] by [–25, 25, 10]
D)
[–25, 25, 5] by [–25, 25, 5]
Match the story with the correct figure.
15)
The height of an animal as a function of time.
15)
A)
B)
C)
D)
A
D
16)
Mark started out by walking up a hill for 5 minutes. For the next 5 minutes he walked down a steep
hill to an elevation lower than his starting point. For the next 10 minutes he walked on level
ground. For the next 10 minutes he walked uphill. Determine which graph of elevation above sea
level versus time illustrates the story.
16)
A)
B)
C)
D)
Match the graph with its function using the x–intercepts.
17)
17)
A)
y = 6x–2– 5x–1+ 1
B)
y = 6x–2– 5x–1– 1
C)
y = 6x–2+ 5x–1+ 1
D)
y = 6x–2+ 5x–1– 1
18)
18)
A)
y =x4–29x2+10
B)
y =x4–29x2+100
C)
y =x4+29x2–10
D)
y =x4+29x2+100
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Solve the problem.
19)
Solve the formula r =3V
h for V.
19)
20)
Solve the formula r =2A
for .
20)
Explanation:
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
21)
A certain store has a fax machine available for use by its customers. The store charges $2.25 to send
the first page and $0.60 for each subsequent page. Use an inequality to find the number of pages
that can be faxed for $5.25.
21)
A)
50 pages or fewer
B)
6 pages or fewer
C)
2 pages or fewer
D)
9 pages or fewer
Explanation:
Perform the indicated operations and write the result in standard form.
22)
( 3 – – 36)( 3+ – 36)
22)
A)
39
B)
3–36i
C)
–33
D)
3– 6i
Explanation:
Solve the radical equation, and check all proposed solutions.
23)
x + 5 =7
23)
A)
{144}
B)
{54}
C)
{49}
D)
{44}
Explanation:
11
Explanation:
First, write the value(s) that make the denominator(s) zero. Then solve the equation.
24)
7
x +1+3
x –1=6
(x +1)(x –1)
24)
A)
x –1, 1; {2}
B)
x –1; {1}
C)
No restrictions; {1}
D)
x –1, 1;
Find all values of x satisfying the given conditions.
25)
y1=1
x + 4 , y2=1
x – 4 , y3=1
x2– 16 , and the difference between 4 times y1 and 2 times y2 is the
product of 6 and y3.
25)
A)
{30}
B)
{15}
C)
{3 2}
D)
{–15}
Solve and check the equation.
26)
(5x +2)1/2 =4
26)
A)
14
5
B)
10
C)
16
5
D)
–2
5
Write the English sentence as an equation in two variables. Then graph the equation.
27)
The y–value is one decreased by the square of the x–value.
27)
12
A)
y =1– x
B)
y =x2–1
C)
y =1–x2
D)
y = x –1
Determine whether the equation is an identity, a conditional equation, or an inconsistent equation.
28)
4(4x – 15) =16x – 60
28)
A)
Identity
B)
Conditional equation
C)
Inconsistent equation
A
Solve and check the equation.
29)
5x5/2 –25 = 0
29)
A)
55
B)
525
C)
D)
2
B
C
Solve the formula for the specified variable.
30)
S = 2rh + 2r2for h
30)
A)
h =S
2r– 1
B)
h = 2(S – r)
C)
h = S – r
D)
h =S – 2r2
2r
Find the product and write the result in standard form.
31)
(–9– 3i)(2+ i)
31)
A)
–21 – 15i
B)
–15 – 3i
C)
–21 – 3i
D)
–15 – 15i
D
Solve the equation by completing the square.
32)
x2+ 8x =7
32)
A)
{–1–11.5, –1+11.5}
B)
{–4–11.5, –4+11.5}
C)
{–4–111.5, –4+111.5}
D)
{4 +11.5}
B
Solve the polynomial equation by factoring and then using the zero product principle.
33)
x3+8x2– x –8= 0
33)
A)
{1, –8, 8}
B)
{64}
C)
{–8, 8}
D)
{–1, 1, –8}
D
Divide and express the result in standard form.
34)
6+ 3i
5+ 2i
34)
A)
12
7+1
7i
B)
8
7+1
7i
C)
36
29 +3
29 i
D)
24
29 –27
29 i
C
D
Solve the problem.
35)
When a number is subtracted from –7, the absolute value of the difference is more than 3. Use
interval notation to express the set of all numbers that satisfy this condition.
35)
A)
(–10, –4)
B)
( , –10] [–4, )
C)
( , –4) (10, )
D)
( , –10) (–4, )
Solve the absolute value equation or indicate that the equation has no solution.
36)
2x2– x – 1 = 3
36)
A)
–1 –33
4, –1 +33
4
B)
1 –33
4, 1 +33
4
C)
1 –33
4, –1 +33
4
D)
B
Use graphs to find the set.
37)
(–10, 0) [–1, 5]
37)
A)
(–10, –1]
B)
[–1, 0)
C)
(0, 5]
D)
(–10, 5]
D
Solve the problem.
38)
Andrea is having her yard landscaped. She obtained an estimate from two landscaping companies.
Company A gave an estimate of $230 for materials and equipment rental plus $65 per hour for
labor. Company B gave an estimate of $335 for materials and equipment rental plus $50 per hour
for labor. Determine how many hours of labor will be required for the two companies to cost the
same.
38)
A)
10 hours
B)
7 hours
C)
6 hours
D)
11 hours
B
D
Find the x–intercepts of the graph of the equation.
39)
y =2x + 5 –x – 2 – 3
39)
A)
2
B)
2, 38
C)
–2
D)
3, 8
Solve the equation.
40)
x – 16
–8+x + 7
7= x + 5
40)
A)
–448
55
B)
–224
55
C)
–112
55
D)
–336
55
Solve the absolute value inequality. Other than , use interval notation to express the solution set and graph the solution
set on a number line.
41)
|x + 6| <4
41)
A)
(–10, –2)
B)
(–, –10) (–2, )
C)
D)
[–10, –2]
16
Solve the problem.
42)
Inclusive of a 6.8% sales tax, a diamond ring sold for $2029.20. Find the price of the ring before the
tax was added. (Round to the nearest cent, if necessary.)
42)
A)
$1900
B)
$1891.21
C)
$137.99
D)
$2167.19
Divide and express the result in standard form.
43)
9+ 3i
9+ 8i
43)
A)
21
29 –9
29 i
B)
57
29 –99
29 i
C)
21
17 –9
17 i
D)
57
17 –9
17 i
A
Use graphs to find the set.
44)
(–7, 0)
[–4, 2]
44)
A)
(0, 2]
B)
[–4, 0)
C)
(–7, –4]
D)
(–7, 2]
B
Solve the equation by factoring.
45)
12x2+ 23x + 10 = 0
45)
A)
5
4, –2
3
B)
5
4, 2
3
C)
–5
4, –2
3
D)
–5
12 , –1
5
C
Perform the indicated operations and write the result in standard form.
46)
(–8– – 49)2
46)
A)
113 + 112i
B)
64 –49i
C)
64 +49i
D)
15 +112i
D
A
Solve the formula for the specified variable.
47)
A =1
2h(a + b) for a
47)
A)
a=2Ab– h
h
B)
a=2A – hb
h
C)
a=hb – 2A
h
D)
a=A – hb
2h
Graph the equation.
48)
y = x – 5
48)
A)
B)
C)
D)
Solve the radical equation, and check all proposed solutions.
49)
2x +10 = x + 6
49)
A)
–4, 4
3
B)
{8}
C)
{–4}
D)
{2, 8}
Solve the problem.
50)
Suppose a cost–benefit model is given by y =2771x
100 – x , where y is the cost for removing x percent of
a given pollutant. What percent of pollutant can be removed for $36,000? Round your answer to the
nearest tenth of a percent.
50)
A)
9.3%
B)
565.1%
C)
92.9%
D)
108.3%
Solve the absolute value inequality. Other than , use interval notation to express the solution set and graph the solution
set on a number line.
51)
|x – 7| < 0
51)
A)
(–7, 7)
B)
(–7, )
C)
(–, 7)
D)
Find all values of x satisfying the given conditions.
52)
y =(x2–2x)2–18(x2–2x) and y = – 45
52)
A)
– 1, – 3, 3, 5
B)
3, 5
C)
3, 15
D)
– 1, – 3, 3, 15, 3, 5
Solve the equation by making an appropriate substitution.
53)
x1/2 –12x1/4 + 27 = 0
53)
A)
{3, 9}
B)
{81, 6561}
C)
{–3, –9}
D)
{9, 81}
B
Find all values of x satisfying the given conditions.
54)
y1=x
x –3+8, y2=6x
x –3 , and y1=y2
54)
A)
–16
5, –4
B)
4, 6
C)
16
5, 4
D)
4, 2
C
Add or subtract as indicated and write the result in standard form.
55)
(6 – 2i) + (8+ 7i)
55)
A)
14 + 5i
B)
–14 – 5i
C)
14 – 5i
D)
–2+ 9i
A
20
A