Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Answer the question.
1)
Suppose that a problem asks you to find the height of a triangle, and that the problem leads to a
quadratic equation. If h represents the height of the triangle, which of the following solutions to the
equation cannot be an answer to the problem?
1)
A)
h =2–13
B)
h =13
4
C)
h =2+13
D)
h =13
2
Provide an appropriate response.
2)
The line of symmetry of a parabola is called the ? of the parabola.
2)
A)
vertex
B)
axis
C)
y–intercept
D)
x–intercept
Answer the question.
3)
Which one of the following methods cannot be used to solve the equation x2– 4x – 2 = 0?
3)
A)
Factoring
B)
Completing the square
C)
Quadratic formula
D)
All of the methods can be used.
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
4)
Without graphing, explain the differences between the graphs of y =x2, y = – x2.
4)
Answer the question.
5)
Give a definition of function.
5)
6)
How does one decide whether a set of points is included in the domain of a function? In
the range?
6)
7)
Describe the graph of the function f(x) = x +3 if the domain is the set of real numbers
(–, ). Give examples of points that are on the graph.
7)
(2, 5), (3, 6), (4, 7), (5, 8).
Provide an appropriate response.
8)
Without graphing, explain the differences between the graphs of y =x2,y =x2–3,
y =x2+3, y = (x –3)2, and y = (x +3)2.
8)
Answer the question.
9)
Use the equation 5x2– 2x = c to explain how to solve a quadratic equation by completing
the square.
9)
10)
The equation of a circle can be written in the form x2+y2=r2. Is this a function? Why or
Why not?
10)
11)
To complete the square of 2x2+ 4x = 8, is it ever a good idea to divide by the coefficient of
x2?
11)
12)
What is the first step in order to solve the equation 3x2– 7x =7 by completing the square?
12)
13)
To complete the square from an equation in the form x2– ax = b, is it ever appropriate to
subtract a positive number from each side?
13)
14)
The equation y =x2 is satisfied by the points (2,4) and (–2,4). A horizontal line may be
drawn between these two points. Is y =x2 a function? Why or why not?
14)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Determine whether the graphed relation is a function.
15)
15)
A)
function
B)
not a function
16)
16)
A)
function
B)
not a function
3
Solve the problem.
17)
Solve the formula V =1
3r2h +1
3hrR +1
3hR2 for r.
17)
A)
r =–R ± – 3R2
2
B)
r =–hR ±32h2R2– 12hV
h
C)
r =–hR ±12hV – 32h2R2
2h
D)
r = ± 12hV + 32h2R2
Solve the equation by completing the square.
18)
4x2+ 12x = – 6
18)
A)
B)
–3+3
2, –3–3
2
C)
–3+15
2, –3–15
2
D)
–3+3
8, –3–3
8
Determine whether the relation is a function. Give the domain and range.
19)
{(4, –4), (3, –1), (10, 12), (3, –8), (9, 8)}
19)
A)
function; domain: {–8, –4, –1, 8, 12}; range: {3, 4, 9, 10}
B)
not a function; domain: {3, 4, 9, 10}; range: {–8, –4, –1, 8, 12}
Solve the equation. Express radicals in simplest form.
20)
1
3m2= – 1
6m +1
2
20)
A)
–3
2
B)
3
2, –1
C)
–3
2, 1
D)
Determine whether the relation is a function. Give the domain and range.
21)
{(–4, 3), (1, 10), (–4, –4), (–1, –6)}
21)
A)
not a function; domain: {–4, –1, 1}; range: {–6, –4, 3, 10}
B)
function; domain: {–6, –4, 3, 10}; range: {–4, –1, 1}
22)
{(9, 9), (–6, –3), (6, 2), (1, –3), (–6, 9)}
22)
A)
function; domain: {–3, 2, 9}; range: {–6, 1, 6, 9}
B)
not a function; domain: {–6, 1, 6, 9}; range: {–3, 2, 9}
Solve the equation. Express radicals in simplest form.
23)
x2– x =20
23)
A)
{–4, –5}
B)
{4, 5}
C)
{–4, 5}
D)
{1, 20}
Solve the problem.
24)
This chart shows the number of meals served in a restaurant during each of the past 4 months.
Write the information in the chart as a set of ordered pairs.
Month Number
January 1500
February 1557
March 1541
April 1562
24)
A)
{(January, 1500), (February, 1557), (March, 1541), (April, 1562)}
B)
{(1500, January), (1557, January), (1541, January), (1562, January)}
C)
{(1500, January), (1557, February), (1541, March), (1562, April)}
D)
{(January, 1500), (February, 1500), (March, 1500), (April, 1500)}
Solve the equation. Express radicals in simplest form.
25)
5n2= – 12n – 1
25)
A)
–6+31
5, –6–31
5
B)
–6+41
5, –6–41
5
C)
–6+31
10 , –6–31
10
D)
–12 +31
5, –12 –31
5
26)
y2
3–y
12 =1
24
26)
A)
2 + – 28
16 , 2 – – 28
16
B)
–1
4, 1
2
C)
D)
1
2
27)
(x + 3)2=20
27)
A)
{–3+ 2 10, –3– 2 10}
B)
{2 5– 3, 2 5+ 3}
C)
{–3+ 2 5, –3– 2 5}
D)
{2 5, –2 5}
Is the following correspondence a function?
28)
Domain Range
28)
A)
function
B)
not a function
Solve the problem.
29)
This chart shows the number of meals served in a restaurant during each of the past 4 months.
Assume that the information in the chart defines a function with the name g. State the range of g.
Month Number
January 2000
February 2057
March 2041
April 2062
29)
A)
{2000, 2057, 2041, 2062}
B)
{(2000, January), (2057, February), (2041, March), (2062, April)}
C)
{January, February, March, April}
D)
{(January, 2000), (February, 2057), (March, 2041), (April, 2062)}
Write the equation in the standard form ax2+
bx +
c = 0. Then identify the values of a, b, and c. Do not actually solve the
equation.
30)
x = – 0.8x2+7.3
30)
A)
a =0.8, b = – 1, c = – 7.3
B)
a = – 0.8, b = – 1, c = – 7.3
C)
a = – 0.8, b =7.3, c = – 1
D)
a = – 0.8, b = – 1, c =7.3
D
Solve the equation. Express radicals in simplest form.
31)
–8k2– 15 = – 47
31)
A)
{2}
B)
{–2, 2}
C)
{–4, 4}
D)
{–23.5}
B
Solve the equation by completing the square.
32)
a2+ 10a = – 9
32)
A)
{1, 9}
B)
{ 9, –9}
C)
{18, –9}
D)
{–1, –9}
D
7
A
Solve the problem.
33)
Given f(x) =3x + 6 , find f –5 .
33)
A)
–5
2
B)
–9
C)
–1
D)
9
Solve the equation. Express radicals in simplest form.
34)
(2x + 5)2=49
34)
A)
{0, 1}
B)
{1, 6}
C)
{27, –27}
D)
{1, –6}
Provide an appropriate response.
35)
On the graph of the equation y =2x2– 3x + 8, the vertex is the ? point.
35)
A)
middle
B)
axis
C)
lowest
D)
highest
Decide whether the statement is true or false. If it is false, tell why.
36)
If k is a positive integer, then x2= k will have one rational and one irrational solution.
36)
A)
True
B)
False; there will be either two rational solutions or two irrational solutions.
C)
False; there will always be two rational solutions.
Solve the problem.
37)
The cross section of a piece of a roller coaster having a width of 220 feet and a depth of 105 feet is
depicted below.
What is the equation of this parabola?
37)
A)
Not enough information
B)
y =21
4840 x2
C)
y =21
22 x2
D)
y =21
2420 x2
Solve the equation by completing the square.
38)
p2+ 5p – 5 = 0
38)
A)
{–5+3 5, –5–3 5}
B)
–5– 3 5
2
C)
5+ 3 5
2
D)
–5+3 5
2, –5–3 5
2
9
Solve the problem.
39)
The distance d, in feet, a bomb falls in t seconds is given by d =16t2
1 + 0.06t . How many seconds are
required for a bomb released at 12,000 feet to reach its target? (If necessary, round your answer to
two decimal places.)
39)
A)
662.06 seconds
B)
1854.20 seconds
C)
57.94 seconds
D)
115.89 seconds
Answer the question.
40)
If we apply the quadratic formula and find that the value of b2– 4ac is positive, what can we
conclude about the solutions?
40)
A)
The equation has two irrational solutions.
B)
The equation has exactly one rational solution.
C)
The equation has no real number solutions.
D)
The equation has two real number solutions.
D
Solve the problem.
41)
This chart shows the fees for an 18 hole round of golf for each of the last 5 years at a local municipal
golf course. Write the information in the chart as a set of ordered pairs.
Year Fee
1995 $21
1996 $24
1997 $26
1998 $26
1999 $30
41)
A)
{(21, 1995), (24, 1996), (26, 1997), (26, 1998), (30, 1999)}
B)
{21, 24, 26, 30}
C)
{(1995, 1996), (1996, 1997), (1997, 1998), (1998, 1999)}
D)
{(1995, 21), (1996, 24), (1997, 26), (1998, 26), (1999, 30)}
D
C
42)
Solve S =rh +r2 for r.
42)
A)
r =–±2+ 4S
2
B)
r =–h ±h + 4S
2
C)
r =–h ±2h2+ 4S
2
D)
r =–h ±2h2– 4S
2
Graph the equation and give the coordinates of the vertex.
43)
y =x2– 1
43)
A)
(0, –1)
B)
(0, 1)
C)
(–1, 0)
D)
(1, 0)
D)
Solve the problem.
44)
Solve the formula S =1
3r2h + 4rh for r.
44)
A)
r =–6h ±362h2+ 3hS
h
B)
r =–12h ±362h2+ 3hS
2h
C)
r =12h ±362h2+ 3hS
h
D)
r =–6h ± 2 362h2+ 3hS
h
45)
This chart shows the number of meals served in a restaurant during each of the past 4 months.
Assume that the information in the chart defines a function with the name g. State the domain of g.
Month Number
January 1500
February 1557
March 1541
April 1562
45)
A)
{(1500, 1557, 1541, 1562)}
B)
{January, February, March, April}
C)
{(January, 1500), (February, 1557), (March, 1541), (April, 1562)}
D)
{(1500, January), (1557, February), (1541, March), (1562, April)}
D)
Decide whether the statement is true or false. If it is false, tell why.
46)
The equation (x + 13)2= 0 has exactly one real solution.
46)
A)
True
B)
False; the equation has two real solutions.
C)
False; the equation has no real solutions.
12
D)
Solve the problem.
47)
This chart shows the fees for an 18 hole round of golf for each of the last 5 years at a local
municipal golf course. Assume that this chart defines a function with the name of f. State the range
of f.
Year Fee
1995 $21
1996 $23
1997 $25
1998 $25
1999 $29
47)
A)
{(1995, 21, (1996, 23), (1997, 25), (1998, 25),(1999, 29)}
B)
{(21, 1995), (23, 1996), (25, 1997), (25, 1998),(29, 1999)}
C)
{1995, 1996, 1997, 1998, 1999}
D)
{21, 23, 25, 29}
Determine whether the relation is a function. Give the domain and range.
48)
{(3, 4), (–2, –2), (–6, 8), (3, –2)}
48)
A)
not a function; domain: {–6, –2, 3}; range: {–2, 4, 8}
B)
function; domain: {–2, 4, 8}; range: {–6, –2, 3}
A
Solve the equation. Express radicals in simplest form.
49)
2x2=14
49)
A)
{8}
B)
{–7, 7}
C)
{–7, 7}
D)
{7}
B
Graph the equation and give the coordinates of the vertex.
50)
y = – x2+ 2x + 3
50)
13
D
A)
(1, 2)
B)
(1, 4)
C)
(1, –4)
D)
(–1, –4)
Is the following correspondence a function?
51)
Domain Range
51)
A)
function
B)
not a function
Complete the trinomial so it is a perfect square.
52)
16x2+?+49
52)
A)
392x
B)
56x
C)
28x
D)
14x
14
Solve the problem.
53)
Given f(x) =4x – 1, find f(–4).
53)
A)
–16
B)
17
C)
–17
D)
–5
Determine whether the graphed relation is a function.
54)
54)
A)
function
B)
not a function
Solve the equation by completing the square.
55)
k2–10k +25 = 0
55)
A)
{5, –3, 3}
B)
{5}
C)
{–5, 3}
D)
{–5, 5}
Solve the equation. Express radicals in simplest form.
56)
m2=20.25
56)
A)
{–5.25, 5.25}
B)
{4.5}
C)
{–4.5, 4.5}
D)
Solve the problem.
57)
The position of an object moving in a straight line is given by s =t2– 8t, where s is the distance in
feet and t is the time in seconds the object has been in motion. How long (to the nearest tenth) will it
take the object to move 12 feet?
57)
A)
9.3 sec
B)
9.1 sec
C)
4.8 sec
D)
13.0 sec
58)
Given f(x) =x2+ 2x + 2, find f(0).
58)
A)
4
B)
2
C)
–2
D)
0
Solve the equation by completing the square.
59)
10d2+ 23d + 12 = 0
59)
A)
–2
3, –4
5
B)
–3
2, –4
5
C)
2
3, 5
4
D)
3
2, 4
5
Solve the problem.
60)
A rock falls from a tower that is 304 feet high. As it is falling, its height is given by the formula
h =304 – 16t2. How many seconds will it take for the rock to hit the ground (h=0)? Round to the
nearest tenth, if necessary.
60)
A)
17 sec
B)
4.4 sec
C)
17.4 sec
D)
5776 sec
Solve the equation. Express radicals in simplest form.
61)
x2=9
64
61)
A)
–9
128, 9
128
B)
81
4,096
C)
9
32
D)
–3
8, 3
8
Decide whether the equation defines y as a function of x.
62)
x =y2– 6
62)
A)
function
B)
not a function
Solve the equation. Express radicals in simplest form.
63)
4z2+ 4 =788
63)
A)
{394}
B)
{–15, 15}
C)
{–14, 14}
D)
{14}
64)
n2= – 361
64)
A)
{–19}
B)
{–19, 19}
C)
D)
{19}
Solve the equation by completing the square.
65)
–x2+ 2x = – 1
65)
A)
{–1 +2, –1 –2}
B)
1 +2
2, 1 –2
2
C)
{1, 2}
D)
{1 +2, 1 –2}
Is the following correspondence a function?
66)
Domain Range
66)
A)
function
B)
not a function