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)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
D)
Match the correct viewing rectangle dimensions with the figure.
2)
2)
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)
C
Match the graph with its function using the x–intercepts.
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
4)
4)
A)
y =x4+5x2–4
B)
y =x4+5x2+4
C)
y =x4–5x2+4
D)
y =x4–5x2–4
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
Match the correct viewing rectangle dimensions with the figure.
6)
6)
A)
[–50, 25, 5] by [–50, 25, 5]
B)
[–25, 25, 5] by [–25, 25, 5]
C)
[–5, 5, 5] by [–5, 5, 5]
D)
[–25, 25, 10] by [–25, 25, 10]
B
D
Match the graph with its function using the x–intercepts.
7)
7)
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
8)
8)
A)
y =x4+ 2x2– 1
B)
y =x4– 2x2– 1
C)
y =x4– 2x2+ 1
D)
y =x4+ 2x2+ 1
The table of values was generated by a graphing utility with a TABLE feature. Use the following table to solve.
9)
Which equation corresponds to Y2 in the table?
9)
A)
y2= 2x + 3
B)
y2= x +3
C)
y2=3x –2
D)
y2=3–2x
Match the graph with its function using the x–intercepts.
10)
10)
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 correct viewing rectangle dimensions with the figure.
11)
11)
A)
[–50, 150, 50] by [–2000, 2500, 500]
B)
[–5, 25, 5] by [–20, 40, 5]
C)
[–5, 40, 5] by [–5, 40, 5]
D)
[–50, 25, 5] by [–50, 25, 5]
Match the graph with its function using the x–intercepts.
12)
12)
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
B
A
Match the story with the correct figure.
13)
The height of an animal as a function of time.
13)
A)
B)
C)
D)
Match the graph with its function using the x–intercepts.
14)
14)
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
Match the story with the correct figure.
15)
The amount of rainfall as a function of time, if the rain fell more and more softly.
15)
A)
B)
C)
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 correct viewing rectangle dimensions with the figure.
17)
17)
A)
[–20, 20, 2] by [–20, 20, 2]
B)
[–4, 4, 2] by [–80, 80, 8]
C)
[–4, 4, 2] by [–4, 4, 2]
D)
[–16, 16, 4] by [–4, 4, 2]
Match the graph with its function using the x–intercepts.
18)
18)
A)
y =x4–29x2+10
B)
y =x4+29x2–10
C)
y =x4–29x2+100
D)
y =x4+29x2+100
C
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)
11
B
20)
Solve the formula r =2A
for .
20)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Find all values of x satisfying the given conditions.
21)
y1=1
x + 3 , y2=4
x – 3 , y3=9
x2– 9 , and y1–y2=y3
21)
A)
{24}
B)
{–8}
C)
{2}
D)
{8}
Solve the equation.
22)
2x
5=x
3+5
22)
A)
{75}
B)
{150}
C)
{–75}
D)
{–150}
Solve the equation by making an appropriate substitution.
23)
x –10 x+24 = 0
23)
A)
{–2, 2, –6, 6}
B)
{16, 36}
C)
{–4, 4, –6, 6}
D)
{4, 6}
Solve the equation by completing the square.
24)
x2+ 4x – 9 = 0
24)
A)
{–2–113 , –2+113}
B)
{–1–13 , –1+13}
C)
{–2–13 , –2+13}
D)
{2 +13}
12
Solve the equation by the square root property.
25)
4x2+ 5 =789
25)
A)
{–14, 14}
B)
{394.5}
C)
{14}
D)
{–15, 15}
Find all values of x satisfying the given conditions.
26)
y1=x + 6
5, y2=x + 8
7, and y1=y2
26)
A)
{–2}
B)
{1}
C)
{–1}
D)
{2}
Solve the linear inequality. Other than , use interval notation to express the solution set and graph the solution set on a
number line.
27)
5(x +2) 4(x – 1) + x
27)
A)
B)
[4, )
C)
( , 4]
D)
( , )
13
The line graph shows the recorded hourly temperatures in degrees Fahrenheit at an airport.
28)
At what time was the temperature 72°?
28)
A)
10 a.m.
B)
9 a.m. and 10 a.m.
C)
9 a.m.
D)
6 p.m.
Solve the equation by completing the square.
29)
x2+ 8x =7
29)
A)
{–4–11.5, –4+11.5}
B)
{–4–111.5, –4+111.5}
C)
{4 +11.5}
D)
{–1–11.5, –1+11.5}
Solve the equation by making an appropriate substitution.
30)
x – 32 x–2048 = 0
30)
A)
{3072}
B)
{8192}
C)
{4096}
D)
{2048}
Find all values of x satisfying the given conditions.
31)
y1=7x, y2= (6x – 1), and y1 exceeds y2 by 2.
31)
A)
–1
B)
–1
13
C)
1
13
D)
1
Solve the problem.
32)
On the first four exams, your grades are 78, 90, 65, and 79. There is still a final exam, and it counts
as two grades. You are hoping to earn a C in the course. This will occur if the average of your six
exam grades is greater than or equal to 70 and less than 80. What range of grades on the final exam
will result in earning a C?
32)
A)
[54, 84]
B)
[38, 88]
C)
[38, 88)
D)
[54, 84)
D
Solve the equation by the method of your choice.
33)
7x2–13x –3= 0
33)
A)
13 ±i71
14
B)
13 ±253
14
C)
–13 ±97
14
D)
13 ±97
14
D
Add or subtract as indicated and write the result in standard form.
34)
(6 – 2i) + (8+ 7i)
34)
A)
14 – 5i
B)
14 + 5i
C)
–2+ 9i
D)
–14 – 5i
B
15
D
Solve the equation.
35)
80 –x
9=x
7
35)
A)
1280
63
B)
{5}
C)
{315}
D)
640
Find the product and write the result in standard form.
36)
(8 – 6i)(–5– 4i)
36)
A)
–16 – 62i
B)
–16 – 2i
C)
–64 – 2i
D)
–64 – 62i
C
Solve the formula for the specified variable.
37)
P = 2L + 2W for W
37)
A)
W= P –L
B)
W=P – 2L
2
C)
W=P –L
2
D)
W= P – 2L
B
Use the five–step strategy for solving word problems to find the number or numbers described in the following exercise.
38)
One number exceeds another by –5. The sum of the numbers is –1. What are the numbers?
38)
A)
–4 and 3
B)
–3 and 2
C)
3 and 3
D)
No solution
B
First, write the value(s) that make the denominator(s) zero. Then solve the equation.
39)
16
8x –8+1
8=2
x – 1
39)
A)
x 1; {1}
B)
x 1;
C)
x –1, 8; {1, 8}
D)
x 8; {1}
B
C
Solve the absolute value equation or indicate that the equation has no solution.
40)
11x +22
2=11
40)
A)
{–4, 0}
B)
{4, 0}
C)
{–4, 4}
D)
Solve the problem.
41)
The revenue for a small company is given by the quadratic function r(t) =4t2+3t +810 where t is
the number of years since 1998 and r(t) is in thousands of dollars. If this trend continues, find the
year after 1998 in which the company’s revenue will be $855 thousand. Round to the nearest whole
year.
41)
A)
2004
B)
2001
C)
2002
D)
2003
Solve the equation by the method of your choice.
42)
x2+ 12x + 15 = 0
42)
A)
{6 +21}
B)
{6 –15, 6+15}
C)
{–12 +15}
D)
{–6–21, –6+21}
Perform the indicated operations and write the result in standard form.
43)
(6 + – 3) (6+ – 7)
43)
A)
57 +252i
B)
(36 –21 )+ (6 7 +6 3)i
C)
15 –12 21i
D)
(36 +21 )–57i
17
Solve the problem.
44)
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.)
44)
A)
$2167.19
B)
$137.99
C)
$1900
D)
$1891.21
Solve the absolute value inequality. Other than , use interval notation to express the solution set and graph the solution
set on a number line.
45)
|x – 7| < 0
45)
A)
(–7, )
B)
(–7, 7)
C)
(–, 7)
D)
Solve the absolute value equation or indicate that the equation has no solution.
46)
x2– 1x= 0
46)
A)
{–1, 0}
B)
{–1, 0, 1}
C)
{0, 1}
D)
Find the x–intercept(s) of the graph of the equation. Graph the equation.
18
47)
y =x2+ 4x – 7
47)
A)
x–intercepts: –4 and 3
B)
x–intercepts: none
C)
x–intercept: 4
D)
x–intercepts: –2 ±11
19
Solve the equation by the method of your choice.
48)
5x2=65
48)
A)
{–13 , 13}
B)
{14}
C)
{32.5}
D)
{–13, 13}
Solve the equation.
49)
x
2=x
3+7
2
49)
A)
–7
2
B)
1
21
C)
0
D)
21
Solve the radical equation, and check all proposed solutions.
50)
6x +55 = x
50)
A)
{–5, 11}
B)
C)
{11}
D)
– 11
20