1. No category

Algebra 1
Practice Final
Fall Semester Practice Final
Multiple Choice
Identify the choice that best completes the statement or answers the question.
Solve the equation. Then check your solution.
1
−16 − 10.2g = −14.7g + 16.85
A 147.825
B 7.3
C –7.3
D 3.65
2
6 = −2 (10n + 7)
A 1
B –1
C 0.05
D 0.4
3
−7m + 20 = −17m − 10
A –3
1
B 14
C
D
4
Identify the hypothesis and conclusion of the
statement. Then write the statement in if-then
form.
David goes swimming when he finishes mowing
the lawn.
A H: David has finished all of his chores
C: he is going swimming
If David has finished all of his chores, then
he is going swimming.
B H: David is going swimming
C: he has finished mowing the lawn
If David is going swimming, then he has
finished mowing the lawn.
C H: he has finished mowing the lawn
C: David is going swimming
If he has finished mowing the lawn, then
David is going swimming.
D H: he is going to play tennis
C: David has finished mowing the lawn
If he is going to play tennis, David has
finished mowing the lawn.
7
f(x) = 5x + 2 , find f(3) .
A 15
B 17
C 13
D 12
8
Jan and David began riding their bicycles in
opposite directions. Jan travels at 10 miles per
hour and David rides at 12 miles per hour. When
will they be 11 miles apart?
1
A 5 2 hours
1
3
Sam’s test score is 12.5 more than Nicole’s
score. The sum of twice Sam’s score and three
times Nicole’s score is 195. What are Sam and
Nicole’s test scores?
A Sam’s score: 46.5; Nicole’s score: 59
B Sam’s score: 21.5; Nicole’s score: 34
C Sam’s score: 34; Nicole’s score: 46.5
D Sam’s score: 46.5; Nicole’s score: 34
Use substitution to solve the system of equations.
5
6
−9 = x − 3y
−2x + 6 = 6y
A infinitely many solutions
B (–3, 2)
C (–9, 0)
D (3, 4)
1
B
1
2
C
D
2 hours
11
hour
20
hour
Algebra 1
Practice Final
Write a direct variation equation that relates x
and y. Assume that y varies directly as x. Then
solve.
9
Solve the equation. Then check your solution.
13
–4.2 = –2.1n
A 2
B 2.1
C –2
D –6.3
14
4
5
If y = 5 when x = –10, find y when x = 1.
1
1
A
y = − 2 x; − 2
B
y = − 10 x; − 10
C
y = 2 x;
D
y = − 2 x; − 5
7
1
1
7
1
2
3
Name the property used in the equation. Then
find the value of n.
10
11n = 11
A Multiplicative Identity; 1
B Multiplicative Identity; 0
C Additive Identity; 1
D Multiplicative Inverse; 1
15
13
A
− 35
B
−2
C
13
35
D
1 35
1
8
−2x − 10y = 10
−3x + 10y = −10
A (–20, –5)
B (0, 1)
C (20, 5)
D (0, –1)
y = 7x + 6; {(5, 41), (6, 44), (4, 39), (7, 42)}
A {(4, 39)}
B {(7, 42)}
C {(5, 41)}
D {(6, 44)}
16
Determine the best method to solve the system of
equations. Then solve the system.
12
3
7
Use elimination to solve the system of equations.
Find the solution set for the equation, given the
replacement set.
11
+x=
−4x + 5y = 9
4x − 5y = −7
A elimination using subtraction; (−2, 2)
B elimination using addition; no solution
C substitution; (7, 7)
D elimination using addition; (0,16)
2
For a certain orchid to grow, the temperature
around it must be kept within 12 degrees of 78°F.
Write the range of suitable temperatures.
A {x| 66 ≤ x ≤ 90}
B {x| x ≤ 66 or x ≥ 90}
C {x | x ≤ 90}
D {x | 66 ≤ x }
Algebra 1
Practice Final
Solve the compound inequality and graph the
solution set.
17
20
u + 8 ≥ 1 and u − 3 < 3
A 0≤u<9
B
−7 ≤ u < 6
C
−7 ≤ u < 6
A
B
C
D
18
0≤u<9
22
Distance (miles)
60
120
180
240
300
23
Write an equation to describe the relationship.
A
B
C
D
d
d
d
d
= 60 ÷ t
= 60t
= 60 − t
= 60 + t
The sum of one-fifth p and 38 is as much as
twice p.
1
A 5 p × 38 = 2p
B
1
4
p + 38 = 2p
C
1
5
p + 38 = 2p
D
1
5
p + 38 = 2 + p
Three times the sum of a and b is equal to five
times c.
A 3(a + b) = 5c
B 3 + a + b = 5c
C 3a + b = 5c
D 3(a − b) = 5c
Name the sets of numbers to which each number
belongs.
Find the next three terms of the arithmetic
sequence.
19
−5(3z + 3) < −3(5z − 4)
A −30z < 27
B z < 27
C ∅ (the empty set)
D ò (all real numbers)
Translate the sentence into an equation.
The table below shows the distance traveled by a
person driving at the rate of 60 miles per hour.
Hours
1
2
3
4
5
y = x+3
infinitely many
no solution
two
one
Solve the inequality.
21
D
Graph the following equations and then
determine how many solutions there are for this
system.
2x = 2y − 6
24
55, 47, 39, 31, . . .
A 36, 41, 46
B 29, 27, 25
C 23, 15, 7
D 26, 21, 16
A
B
C
D
3
34
Real and rational
Real and irrational
Real, rational, and integer
Real, rational, integer, and whole
Algebra 1
Practice Final
Simplify the expression.
25
Write the slope-intercept form of an equation of
the line that passes through the given point and
is parallel to the graph of the equation.
3 ÊÁË 1.2x + 2.2y ˆ˜¯ + 2 ÊÁË 3.2x + y ˆ˜¯
A
B
C
D
8.6x + 10y
8.8x + 8.6y
10x + 8.6y
10x + 7.6y
28
Express the relation shown in each table,
mapping, or graph as a set of ordered pairs.
Then write the inverse of the relation.
A
B
C
D
y
5
2
3
6
29
Relation: {(3, 5), (4, 2), (2, 6)}
Inverse: {(5, 3), (2, 4), (6, 2)}
Relation: {(3, 5), (4, 2), (3, 3), (2, 6)}
Inverse: {(3, 5), (2, 4), (3, 5), (6, 2)}
Relation: {(3, 5), (4, 2), (3, 3), (2, 6)}
Inverse: {(5, 3), (2, 4), (3, 3), (6, 2)}
Relation: {(5, 3), (2, 4), (3, 3), (6, 2)}
Inverse: {(3, 5), (4, 2), (3, 3), (2, 6)}
13
4
y = 4x +
B
y=
C
y = 4x –
D
y = −5 x +
13
4
x+
5
5
4
13
4
4
13
5
ÊÁ −3, − 4 ˆ˜ , m = 3
Ë
¯
A y = 3x + 13
B y = 3x + 5
C y = 3x − 5
D y = −3x + 5
4
(4, 4), 2x – y = 4
1
A
y = −2 x + 6
B
y = 2x + 6
C
D
y = 4x + 2
y = 2x + 2
1
30
Evaluate the following expression if x = 12, y =
8, and z = 6.
x 2 y − 2z
4
A 285
B 1140
C 1296
D 21
31
A board is leaning against a building so that the
top of the board reaches a height of 18 feet. The
bottom of the board is on the ground 4 feet away
from the wall. What is the slope of the board as a
positive number?
9
A 2
Write an equation of the line that passes through
each point with the given slope.
27
5
A
Write the slope-intercept form of an equation that
passes through the given point and is
perpendicular to the graph of the equation.
26
x
3
4
3
2
(–5, –3), 5x – 4y = 8
B
2
9
C
D
undefined
9
−2
Algebra 1
32
Practice Final
Write each equation in standard form.
A hotel has 150 rooms. The charges for a double
room and a single room are $270 per night and
$150 per night respectively. On a night when the
hotel was completely occupied, revenues were
$33,300. Which pair of equations can be used to
determine the number of double room, d, and the
number of single room, s, in the hotel?
A d + s = 33,300
B
270d + 150s = 33,300
d + s = 33,300
C
270d + 150s = 150
d + s = 150
D
270s + 150d = 33,300
d + s = 150
33
y + 6 = (x + 4)
A x + y = –2
B x–y=2
C y=x–2
D x – y = 10
270d + 150s = 33,300
Year
Birth Rate
(per 1000)
United States Birth Rate
1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000
2001
16.7
14.5
16.3
15.9
15.5
15.2
14.8
14.7
14.5
14.6
14.5
14.7
Source: National Center for Health Statistics, U.S. Dept. of Health and Human Services
34
Let x represent the number of years since 1990 with x = 0 representing 1990. Let y represent the birth rate per
1000 population. Write the slope-intercept form of the equation for the line of fit using the points representing
1992 and 2000.
A y = −0.15x − 15.6
C y = −0.15x + 16.2
B y = 0.15x + 16.2
D x = −0.15y + 16.2
35
Predict the birthrate in 2005. Round your answer to the nearest tenth, if necessary.
A 14.5
C 15.1
B 14.0
D 13.1
5
Algebra 1
36
Practice Final
Graph f(x) = |4x + 4| .
A
C
B
D
6
Algebra 1
Practice Final
A student can buy notebooks for $0.40 each and pens for $0.25 each. Ben needs to have at least 8 notebooks. He
has a total of $5.00 to spend.
37
Make a graph showing the number of notebooks and pens Ben can purchase.
C
A
B
D
7
Algebra 1
Practice Final
Solve the system of inequalities by graphing.
38
y ≤ −x + 4
y > −2x − 4
A
C
B
D
8
Algebra 1
Practice Final
Express each relation as a graph and a mapping. Then determine the domain and range.
39
{(1, 1), (–2, 3), (2, 4), (3, 1)}
C
A
D = {–2, 1, 3}; R = {1, 3, 4}
B
D = {–2, 1, 2, 3}; R = {1, 3, 4}
D
D = {–2, 1, 2, 3}; R = {1, 3, 4}
D = {–2, 1, 2, 3}; R = {1, 3, 4}
9
Algebra 1
Practice Final
Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely
many solutions. If the system has one solution, name it.
40
y = −x + 5
y = 6x − 2
A one solution; (1, 4)
C
infinitely many
B
D
one solution; (4, 1)
no solution
10
Algebra 1
Practice Final
Constructed Response
41
Statistics show that the average number of people who bought CD players in a particular state in
February of the year 2000 was 50 million and the average number of people who bought Ipods was 14.25
million. During the next several years, it is assumed that the number of CD players would decrease at an
average of 4 million per year and the number of Ipods would increase at an average of 2.5 million per
year.
a. Write an expression that would represent the number of CD players sold, using x to represent the number of
year since 2000.
b. Write an expression, that would represent the number of Ipods sold, using x to represent the number of year
since 2000.
c. Write an equation that could be used to determine the number of years it would take for the number of CD
players sold to equal the number of Ipods sold.
d. Explain how an equation can be used to determine when the two populations are equal.
e. Include the steps for solving the equation and the year when the number of CD players sold will equal the
number of Ipods sold according to the model. What year and month would this be?
f. Explain why this method can be used to predict the events.
42
James wants to make 11 ml of a 28% sugar solution by mixing together a 10% sugar solution and a 30%
sugar solution.
a. Define your variables for this situation.
b. Write a system of equations that could be used to solve this problem. Explain what each equation represents.
c. Which method for solving systems of equations would be the best to use in the situation.
d. How much of the 10% sugar solution would he need?
e. How much of the 30% sugar solution would he need?
11
ID: C
Fall Semester Practice Final
Answer Section
MULTIPLE CHOICE
1
B
2
B
3
A
4
D
5
B
6
C
7
B
8
B
9
A
10
A
11
C
12
B
13
A
14
A
15
D
16
A
17
B
18
B
19
C
20
A
21
D
22
C
23
A
24
B
25
C
26
C
27
B
28
A
29
A
30
A
31
A
32
D
33
B
1
ID: C
34
C
35
B
36
A
37
B
38
C
39
D
40
A
ESSAY
41
42
a. 50 - 4x
b. 14.25 + 2.5x
c. 50 − 4x = 14.25 + 2.5x
d. Equations can be useful when two populations are equal as we have the variable x on each side of the
equation.
e. (1) Add 4x to each side.
(2) Subtract 14.25 from each side.
(3) Solve for x.
35.75 = 6.5x
x = 5.5 years
July of 2005
f. This method can be used to predict events by putting the value of x in the equation, we can find the respective
data for x years.
Use the Addition and/or Subtraction Properties of Equality to get the variables on one side of the equals sign and
the numbers without variables on the other side of the equals sign.
Simplify the expressions on each side of the equals sign.
Use the Multiplication or Division Property of Equality to solve.
a. x = the amount of the 10% sugar solution. y = the amount of the 30% sugar solution.
b.
x + y = 11 represents the total amount of liquids for the 3 solutions
0.1x + 0.3y = 3.08 represents the amount of sugar in each of the solutions.
c. Elimination with multiplication
d. 1.1 mL of the 10% sugar solution.
e. 9.9 mL of the 30% sugar solution
2