Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Choose the correct response.
1)
Which expression represents the monetary value of x 5–dollar bills?
1)
A)
x
5 dollars
B)
5x dollars
C)
5
x dollars
D)
5+ x dollars
2)
Suppose that x ounces of a 25% acid solution are mixed with y ounces of a 35% solution to obtain 99
ounces of a 32% solution. One equation in a system for solving this problem is x + y =99. Which of
the following is the other equation?
2)
A)
25x + 35y = .32(99)
B)
35x + 25y = 32
C)
.25x + .35y = .32(99)
D)
.35x + .25y = .32(99)
C
3)
What is the speed of a plane that travels at a rate of 504 mph into a wind of r mph?
3)
A)
504 – r mph
B)
504
r mph
C)
504 + r mph
D)
r –504 mph
A
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
4)
Why could (–4, –8) not be a solution of the system that is graphed?
4)
B
5)
Explain why the solution of a system of equations is the point of intersection of the graphs
of the equations.
5)
6)
Describe the three possible outcomes when graphing a system of equations, and relate each
to the type of solution(s) each system has.
6)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Graph the system of inequalities. Indicate the solution by shading.
7)
2x + 3y 6
x – y 3
y 2
7)
A)
B)
2
C)
D)
Clear fractions then solve by substitution.
8)
7x
3+5y
4= 4
5x
6– 2y = 21
8)
A)
{(–6, 8)}
B)
(x, y)|7x
3+5y
4= 4
C)
{(6, –8)}
D)
Solve the system by the elimination method.
9)
5x – 26 = – 7y
2x + 2y =12
9)
A)
{(8, –1)}
B)
{(8, –2)}
C)
D)
{(7, –1)}
Solve by the substitution method.
10)
x – 3y = – 24
8x – 2y = – 16
10)
A)
{(–8, 0)}
B)
{(0, 8)}
C)
D)
{(1, 7)}
Graph the system of inequalities. Indicate the solution by shading.
11)
2x + 3y 6
x – y
3
x
1
11)
A)
B)
C)
D)
Solve by the substitution method.
12)
x + y =8
7x + 7y =56
12)
A)
{(x, y)| x + y =8}
B)
{(6, 2)}
C)
{(0, 0)}
D)
Attending concerts is a favorite form of entertainment for many people. The graph shows concert attendance gradually
increased from 1994 to 2004 for concerts at a small town’s outdoor concert venue. In 1994, the average attendance was 935,
as represented by the point P(1994, 935). In 2004, the average attendance was 2350, as represented by the point
Q(2004, 2350). We can find an equation of the line segment PQ using a system of equations, and then we can use the
equation to approximate the attendance in any of the years between 1994 and 2004.
13)
The line segment has an equation that can be written in the form y = ax + b. Use the coordinates of
point P with x = 1994 and y = 935, write an equation in the variables a and b.
13)
A)
y = 1994a + b
B)
y = 935a + b
C)
1994 = 935a + b
D)
935 = 1994a + b
5
Solve the problem.
14)
In a recent school board election, the two candidates for president received 2715 votes. The loser
received 207 fewer votes than the winner. How many votes did the winner receive?
14)
A)
1254 votes
B)
2508 votes
C)
834 votes
D)
1461 votes
Attending concerts is a favorite form of entertainment for many people. The graph shows concert attendance gradually
increased from 1994 to 2004 for concerts at a small town’s outdoor concert venue. In 1994, the average attendance was 935,
as represented by the point P(1994, 935). In 2004, the average attendance was 2350, as represented by the point
Q(2004, 2350). We can find an equation of the line segment PQ using a system of equations, and then we can use the
equation to approximate the attendance in any of the years between 1994 and 2004.
15)
The line segment has an equation that can be written in the form y = ax + b. Use the coordinates of
point P with x = 2004 and y = 2350, write an equation in the variables a and b.
15)
A)
y = 2004a + b
B)
2350 = 2004a + b
C)
y = 2350a + b
D)
2004 = 2350a + b
Solve the system by the elimination method.
16)
3x +4y =11
12x +16y =44
16)
A)
{(x, y)| 3x +4y =11}
B)
C)
{(6, 1)}
D)
{(0, 4)}
Graph the system of inequalities. Indicate the solution by shading.
6
17)
2x + 3y 6
x – y 3
x
1
17)
A)
B)
C)
D)
7
Solve the problem.
18)
Regrind, Inc. regrinds used typewriter platens. The cost per platen is $2.00. The fixed cost to run the
grinding machine is $225 per day. If the company sells the reground platens for $7.00, how many
must be reground daily to break even?
18)
A)
30 platens
B)
45 platens
C)
25 platens
D)
112 platens
Indicate whether the statement is true or false.
19)
A system of linear inequalities can have solutions in only one quadrant.
19)
A)
True
B)
False
Graph the system of inequalities. Indicate the solution by shading.
20)
2x + 3y 6
x – y
3
x
1
20)
A)
B)
8
C)
D)
Solve the system of equations by graphing. If the system is inconsistent or the equations are dependent, say so.
21)
4x + y =23
4x + y =31
21)
A)
{(x, y)|4x + y =23} (dependent equations)
B)
{(19, –53)}
C)
{(16, 7)}
D)
(inconsistent system)
Solve the system by the elimination method.
22)
x – 4y =28
3x – 5y =42
22)
A)
{(–4, –5)}
B)
{(4, –6)}
C)
D)
{(3, –5)}
Solve the problem.
23)
Ellen wishes to mix candy worth $1.52 per pound with candy worth $3.23 per pound to form 31
pounds of a mixture worth $2.57 per pound. How many pounds of the more expensive candy
should she use?
23)
A)
12 pounds
B)
14 pounds
C)
24 pounds
D)
19 pounds
D)
Without graphing, answer the following questions for the linear system.
(i) Is the system inconsistent, are the equations dependent, or neither?
(ii) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line?
(iii) Does the system have one solution, no solution, or an infinite number of solutions?
24)
2x + 3y = 6
4x + 9y = – 12
24)
A)
(i) inconsistent
(ii) parallel lines
(iii) no solution
B)
(i) neither
(ii) intersecting lines
(iii) one solution
C)
(i) dependent
(ii) one line
(iii) infinite number of solutions
Write an expression that illustrates the quantity described.
25)
The cost of z pounds of mixed spices that sell for $1.17 per pound
25)
A)
$1.17z
B)
$1.17
C)
$1.18z
D)
$z
D)
Solve the system by the elimination method.
26)
4x +4y = – 4
–16x – 16y =16
26)
A)
B)
{(3, –5)}
C)
{(2, 3)}
D)
{(x, y)| 4x +4y = – 4}
Solve the system of equations by graphing. If the system is inconsistent or the equations are dependent, say so.
27)
2x + y =7
4x + 2y =14
27)
A)
{(5, –3)}
B)
(inconsistent system)
C)
{(x, y)|2x + y =7} (dependent equations)
D)
{(0, 7)}
Solve the problem.
28)
A plane makes a 240–mile trip against a head wind in 1 hour and 30 minutes and returns, with a
tail wind of the same speed, in 1 hour. What is the speed of the wind?
28)
A)
200 mph
B)
80 mph
C)
160 mph
D)
40 mph
Provide an appropriate response.
29)
When two linear equations are solved for y, the slopes are equal and the y–intercepts are different,
the lines are _____.
29)
A)
the same line
B)
intersecting lines
C)
parallel lines
Solve the problem.
30)
A woman made a deposit of $254. If her deposit consisted of 78 bills, some of them one–dollar bills
and the rest being five–dollar bills, how many one–dollar bills did she deposit?
30)
A)
44 one–dollars
B)
24 one–dollars
C)
29 one–dollars
D)
34 one–dollars
Solve by the substitution method.
31)
8x – 5y =10
6x – 2y =4
31)
A)
B)
{(0, –2)}
C)
{(–1, –1)}
D)
{(0, –1)}
Solve the problem.
32)
Joe has a collection of nickels and dimes that is worth $6.70. If the number of dimes were doubled
and the number of nickels were increased by 14, the value of the coins would be $11.10. How many
dimes does he have?
32)
A)
18 dimes
B)
37 dimes
C)
14 dimes
D)
60 dimes
33)
A company manufactures three products. The graph shows the production from 1986 to 1996. In
what year did the production of C equal the production of A?
33)
A)
1991
B)
650,000
C)
1996
D)
600,000
Clear fractions then solve by substitution.
34)
x +1
2y = y – 3
1
3x – y =5x – y
34)
A)
{(0, 6)}
B)
C)
{(1, 6)}
D)
{(5, 0)}
Solve the problem.
35)
Mrs. Boyd has a desk full of quarters and nickels. If she has a total of 25 coins with a total face value
of $4.85, how many of the coins are nickels?
35)
A)
7 nickels
B)
9 nickels
C)
18 nickels
D)
23 nickels
36)
A canoeist who took 6 hours to paddle 6 miles upstream was able to return to his starting spot in 45
minutes. What was the rate of the current?
36)
A)
4.5 mph
B)
3.5 mph
C)
5 mph
D)
4 mph
Decide whether or not the ordered pair is a solution of the system.
37)
(5, 1)
x + y = – 4
x – y = – 6
37)
A)
Yes
B)
No
Solve the problem.
38)
Gloria collected 27 fantail and comet goldfish. There were 7 fewer fantails than comets. How many
comets did Gloria have?
38)
A)
10 comets
B)
17 comets
C)
20 comets
D)
12 comets
Graph the solution of the system.
13
39)
3x – 2y –6
x – 1 < 0
39)
A)
B)
C)
D)
14
Write an expression that illustrates the quantity described.
40)
The cost of m student tickets and n adult tickets for a play if a student ticket costs $6.50 and an
adult ticket costs $7.50
40)
A)
$6.50m + $7.50n
B)
$14.00
C)
$14.00(m + n)
D)
$(m + n)
Solve the problem.
41)
Chuck and Dana agree to meet in Chicago for the weekend. Chuck travels 176 miles in the same
time that Dana travels 164 miles. If Chuck’s rate of travel is 3 mph more than Dana’s, and they
travel the same length of time, at what speed does Chuck travel?
41)
A)
37 mph
B)
44 mph
C)
51 mph
D)
41 mph
Solve by the substitution method.
42)
0.2x +0.04y =0.12
5x + y =3
42)
A)
{(0, 3)}
B)
3
5, 0
C)
{(x, y)| 0.2x +0.04y =0.12}
D)
Solve the problem.
43)
An airplane travels 700 miles against the wind in 4 hours, and makes the return trip with the same
wind in 2 hours. Find the speed of the wind.
43)
A)
350 mph
B)
87.5 mph
C)
175 mph
D)
262.5 mph
Attending concerts is a favorite form of entertainment for many people. The graph shows concert attendance gradually
increased from 1994 to 2004 for concerts at a small town’s outdoor concert venue. In 1994, the average attendance was 935,
as represented by the point P(1994, 935). In 2004, the average attendance was 2350, as represented by the point
Q(2004, 2350). We can find an equation of the line segment PQ using a system of equations, and then we can use the
equation to approximate the attendance in any of the years between 1994 and 2004.
44)
What is the equation of the segment PQ?
44)
A)
y = 141.5x – 281,216
B)
y = 92.0x + 34,590
C)
y = 103.5x – 204,239
D)
y = 145.7x – 239,394
Solve the system by the elimination method.
45)
6x – 5y =5
18x – 15y =25
45)
A)
{(5, 25)}
B)
C)
5
4, –3
2
D)
{(3, 5)}
Solve by the substitution method.
46)
x + y =7
x + y =5
46)
A)
{(x, y)|x + y =5}
B)
{(0, 12)}
C)
D)
{(7, 5)}
16
Indicate whether the statement is true or false.
47)
When graphing a linear inequality, the origin can always be used as a test point for determining
which side of a boundary line should be shaded.
47)
A)
True
B)
False
Without graphing, answer the following questions for the linear system.
(i) Is the system inconsistent, are the equations dependent, or neither?
(ii) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line?
(iii) Does the system have one solution, no solution, or an infinite number of solutions?
48)
x + y =4
x + y =8
48)
A)
(i) inconsistent
(ii) parallel lines
(iii) no solution
B)
(i) neither
(ii) intersecting lines
(iii) one solution
C)
(i) dependent
(ii) one line
(iii) infinite number of solutions
Clear fractions then solve by substitution.
49)
3
4x + y =1
4+ 2y
5x – 4 +y
4= – 3 +6x
49)
A)
–17
13 , –16
13
B)
7
19 , –7
13
C)
(x, y)| 3
4x + y =1
4+ 2y
D)
50)
2x +4
5y =10
3x +3
2y =27
2
50)
A)
{(8, –6)}
B)
{(–7, –6)}
C)
{(7, –5)}
D)
Solve the problem.
51)
Jill is 9 kilometers away from Joe. Both begin to walk toward each other at the same time. Jill walks
at 2 kilometers per hour. They meet in 2 hours. How fast is Joe walking?
51)
A)
2 kilometers per hour
B)
4.5 kilometers per hour
C)
3.5 kilometers per hour
D)
2.5 kilometers per hour
Graph the solution of the system.
52)
2x + y
4
x – 1
0
52)
A)
B)
18
C)
D)
Clear fractions then solve by substitution.
53)
3x
2–y
3= – 18
3x
4+2y
9= – 9
53)
A)
{(–12, 0)}
B)
(x, y)|3x
2–y
3= – 18
C)
{(12, 0)}
D)
Without graphing, answer the following questions for the linear system.
(i) Is the system inconsistent, are the equations dependent, or neither?
(ii) Is the graph a pair of intersecting lines, a pair of parallel lines, or one line?
(iii) Does the system have one solution, no solution, or an infinite number of solutions?
54)
3x = y + 3
6x – 2y = 3
54)
A)
(i) neither
(ii) intersecting lines
(iii) one solution
B)
(i) dependent
(ii) one line
(iii) infinite number of solutions
C)
(i) inconsistent
(ii) parallel lines
(iii) no solution
Solve the problem.
55)
A lumber yard has fixed costs of $4907.10 a day and variable costs of $1.00 per board–foot
produced. The company gets $2.10 per board–foot sold. How many board–feet must be produced
daily to break even?
55)
A)
1582 board–feet
B)
4461 board–feet
C)
2974 board–feet
D)
4907 board–feet
56)
Tim and Judy mix two kinds of feed for pedigreed dogs. They wish to make 19 pounds of feed
worth $.39 per pound by mixing one kind worth $.20 per pound with another worth $.81 per
pound. How many pounds of the cheaper kind should they use in the mix? (Round to the nearest
whole number)
56)
A)
11 pounds
B)
6 pounds
C)
15 pounds
D)
13 pounds