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1st Semester Final Exam Review ALGEBRA
Mathematician___________
Hour_______
Take your time, do your best, study, ask questions and practice!!!
Finish the SEMESTER STRONG!!
(Chapters 1-2)
1. Write an algebraic expression for the difference of 5
and n cubed.
2. Evaluate 2x + 5y2 - 3z if x = 6, y = 4, and z = 7.
1.
2.
71
3.
{4}
3. Find the solution set for 3b − 4 = 8 if the replacement
set is {1, 2, 3, 4, 5}.
4.
4. Name the property used in the equation 1 = 6n. Then
find the value of n.
5.
7t + 3t
5. 2t2 − 5t2 + 3t
6.
7r + 9t
6. 7(r + 2t) − 5t
7.
23a + 6b
For Questions 5-7, simplify each expression.
7. 5(4a + b) + 3a + b
8. Identify the hypothesis and conclusion of the
statement. Then write the statement in if-then form.
All triangles are polygons.
8.
9.
9. Draw a reasonable graph showing the relationship
between the temperature of a pizza as it is removed
from an oven and placed on a counter at room
temperature, and time.
10.
11.
6x + 12
10. The sides of an equilateral triangle measure (2x + 4)
units. What is the perimeter?
11. Graph {4, 5, 6, 7, 8, …}.
Find each square root.
12.
-6
13.
1.1
12.
13.
14.
14.
For Questions 15-16, replace each with ·, >, or <, to make
each sentence true.
15.
15.
<
16.
=
16.
93
Chapter 2
Glencoe Algebra 1
For Questions 17-18, evaluate each expression if a = 9, b = 16, and c = 81.
17.
18.
19. Name the set or sets of numbers to which
belongs.
20. Write
greatest.
in order from least to
17.
12
18.
16
19.
20.
irrational, real
For Questions 21-27, solve each equation.
21.
-18
22.
-12
23.
42
24.
56
25.
-2
21. m − 5 =-23
22. -4 = 8 + k
23.
24.
25. 5(c + 3) = 15 + 2(2c − 1)
26.
all real numbers
26. 10(a + 1) − 14a = 9 − (4a − 1)
27.
27.
28.
$3.91
29.
v = t − sr
30.
8 lb
28. A magazine is on sale for 15% off the original price. If
the original price of the magazine is $4.60, what is the
discounted price?
29. Solve
for v.
30. How many pounds of peanuts costing $3.00 a pound
should be mixed with 4 pounds of cashews costing
$4.50 a pound to obtain a mixture costing $3.50 a
pound?
Chapter 2
94
Glencoe Algebra 1
(Chapters 1-3)
Part 1: Multiple Choice
Instructions: Fill in the appropriate circle for the best answer.
1. Which vehicle is a counterexample for the statement? If an automobile is a sports
car, then it is red. (Lesson 1-7)
A a red pick-up truck
B a white motor home
C a red sports car
D a yellow sports car
1.
2. Dion owns a delivery service. He charges his customers $15.00 for each
delivery. His expenses include $7000 for the motorcycle he drives and $0.42 for
gasoline per trip. Which equation could Dion use to calculate his profit p for d
deliveries? (Lesson 1-9)
F p = 15 − 0.42d
G p = 7000 + 15d
H p = 14.58d − 7000
J p = 0.42d + 7000
2.
C 63
3.
3. Evaluate 60 ÷ 5 · 6 − 32. (Lesson 1-2)
A -7
B -4
D 4761
4. Jim's new car has 150 miles on the odometer. He takes a trip and drives an
average
of m miles each day for three weeks. Which expression represents the mileage
on
Jim's car after his trip? (Lesson 2-5)
F 150m + 3
G 150 + 3m
H 150m + 21
J 150 + 21m
4.
D s + t = 5(4r)
5.
J -1
6.
5. Translate the sentence into an equation. (Lesson 2-1)
Five times the sum of s and t is as much as four times r.
A 5s + t = 4
B 5s + t = r
C 5(s + t) = 4r
6. Solve 8(x − 5) = 12(4x − 1) + 12. (Lesson 2-5)
F
G
H -2
7. Paul and Charlene are 420 miles apart. They start toward each other with Paul
driving 16 miles per hour faster than Charlene. They meet in 5 hours. Find
Charlene's
speed. (Lesson 2-9)
A 34 mph
B 50 mph
C 40.4 mph
D 68 mph
7.
8. Determine which equation is a linear equation. (Lesson 3-3)
F x2 + y = 4
Gx+y=4
H xy = 4
J
8.
D -11
9.
9. If f(x) = 7 − 2x, find f(3) + 6. (Lesson 3-2)
A 11
B7
C 14
10. Chapa is beginning an exercise program that calls for 30 push-ups each day for
the first week. Each week thereafter, she has to increase her push-ups by 2.
Which week of her program will be the first one in which she will do 50 push-ups
a day? (Lesson 3-4)
F 9th week
G 10th week
H 11th week
J 12th week
60
Chapter 3
10.
Glencoe Algebra
11. Which property of equality is illustrated below? (Lesson 1-4)
If 7 + 9 = 11 + 5 and 11 + 5 = 16, then 7 + 9 = 16.
A Transitive
B Reflexive
C Substitution
D Symmetric
11.
12. Which expression represents the missing second step of simplifying the algebraic
expression? (Lesson 1-5)
Step 1
Step 3
4(x − 3y) + 6 + 5(x + 1)
9x − 12y + 11
F 4x − 3y + 6 + 5x + 1
G 12(x − y) + 6 + x + 5
13. Solve 48= -8r. (Lesson 2-3)
H 4x − 12y + 6 + 5x + 5
J x − 3y + 15 + x + 1
12.
Ar=8
Br=6
C r = -6
D r = -40
13.
H h = -8
J h = -16
14.
14. Solve 4 − (-h) = 12. (Lesson 2-2)
F h = 16
Gh=8
For Questions 15 and 16, use the arithmetic sequence 2, 5, 8, 11, ... .
15. Which is an equation for the nth term of the sequence? (Lesson 3-4)
A an = 2n + 1
B an = 4n − 2
C an = n + 3
D an = 3n − 1
15.
16. What is the 20th term in the sequence? (Lesson 3-4)
F 59
G 60
H 78
J 80
Part 2: Griddable
Instructions: Enter your answer by writing each digit of the answer in a
column box and then shading in the appropriate circle that corresponds to
that entry.
17. The ratio of a to b is
. If a is 16, find the value of b. (Lesson 2-6)
16.
18. The equation
relates the temperature in degrees Fahrenheit F to
degrees Celsius C. If the temperature is 25°C in Rome, Italy, what is the
temperature in degrees Fahrenheit? (Lesson 3-3)
61
Chapter 3
Glencoe Algebra
Part 3: Short Answer
Instructions: Write your anwers in the space provided at the right.
19. Find the solution of
if the replacement set is
19. ____________________
. (Lesson 1-3)
20. ____________________
20. Simplify 5m + 8n + 3m + n. (Lesson 1-6)
21. ____________________
21. Find
. Round to the nearest hundredth. (Lesson 1-8)
22. Translate the following equation into a verbal sentence.
____________________
(Lesson 2-1)
23. Find the discounted price.
22.
clock: $15.00
discount: 15% (Lesson 2-7)
24. Solve -7x + 23 = 37. (Lesson 2-4)
25. Use cross products to determine whether the ratios
form a proportion. Write yes or no. (Lesson 2-6)
23. ____________________
24. ____________________
and
25. ____________________
For Questions 26-27, use the graph.
26. Express the relation as a set of ordered pairs. Then
determine the domain and range. (Lesson 3-1)
26. ____________________
27. Determine whether the relation is a function. (Lesson 3-2)
27. ____________________
28. Find the x-intercept of the graph of 4x = 5 + y. (Lesson 33)
28. ____________________
29.
29. Graph 2x − 3y = 6. (Lesson 3-3)
30. The table below shows the average amount of gas Therese's
truck uses depending on how many miles she drives.
Gallons of
Gasoline
1
Miles Driven
18 36 54 72 90
2
3
4
5
30a.
31.
a. Does the table of values represent a function? Explain.
(Lesson 3-5)
____________________
30b.
b. Is this a proportional relationship? Explain. (Lesson 3-5) ____________________
Chapter 3
62
Glencoe Algebra 1
NAME ___________________________________________________ DATE _______________________
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1 and 2, use the graph to answer each question.
1. What is the domain of the relation?
A. {-1, 0, 1, 3}
B. {-2, 0, 1, 3}
C. {-2, -1, 0, 1, 2, 3}
D. {0, 1, 2, 3}
1. _____
H. {-2, -1, 0, 1, 2, 3}
J. {0, 1, 2, 3}
2. _____
2. What is the range of the relation?
F. {-1, 0, 1, 3}
G. {-2, 0, 1, 3}
3. Where does the graph of y = -3x − 18 intersect the x-axis?
A. (0, 6)
B. (0, -6)
C. (6, 0)
D. (-6, 0)
3. _____
4. Tickets to see a movie cost $5 for children and $8 for adults.
The equation 5x + 8y = 80 represents the number of children
(x) and adults (y) who can see the movie with $80. If no adults
see the movie, how many children can see the movie with $80?
F. 6
G. 10
H. 13
J. 16
4. _____
For Questions 5 and 6, use the arithmetic sequence 12, 15, 18, 21, ... .
5. Which is an equation for the nth term of the sequence?
A. an = 3n + 9
B. an = 9n + 3
C. an = 12n + 3
D. an = n + 3
5. _____
6. What is the 12th term in the sequence?
F. 38
G. 42
H. 45
J. 48
6. _____
7. Which table, mapping, or graph does not show the relation {(-1, 1), (1, 2), (2, -2),
(4, 3)}?
A.
B.
C.
x
-1
1
2
4
y
1
2
-2
3
7. _____
D.
8. What is the inverse of the relation {(0, 1), (1, 0), (3, -4)}?
F. {(0, 0), (1, 1), (3, -4)}
G. {(1, 0), (0, 1), (4, -3)}
H. {(0, 1), (1, 0), (3, -4)}
J. {(1, 0), (0, 1), (-4, 3)}
8. _____
C. {(-1, 2), (0, 3), (1, 4)}
D. {(-1, -1), (0, 0), (-1, 1)}
9. _____
9.
10. Which relation is not a function?
A. {(-3, -1), (0, 0), (3, 1)}
B. {(-1, -3), (0, 0), (1, -3)}
Chapter 3
47
Glencoe Algebra 1
For Questions 10 and 11, use the following information. The distance (d) a car
travels in t hours is given by the function d = 55t.
10. Find d when t = 5.
F. 275
G. 60
H. 50
J. 71
10. _____
11. Write an equation in function notation to describe this relationship.
A. f(t) = 55d
B. f(d) = 55d
C. f(t) = 55t
D. f(d) = 55t
11. _____
12. Which line shown at the right is the graph of y = 2x + 4?
F. ℓ
G. p
H. the x-axis
J. q
12. _____
13. Determine which relation is a function.
A.
C.
13. _____
x 3 4 4 5
y
2 3 6
1
B.
D. {(3, 0), (-2, -2), (7, -2), (-2, 0)}
14. Determine which relation is a function.
F. {(1, 1), (1, 2)}
15. If
A. 12
G. x − 5 = 1
H. y = 9
J. x = 2
14. _____
D. -12
15. _____
, what is the value of h(-9)?
B. 0
C.
16. Determine which sequence is an arithmetic sequence.
F. 3, 6, 12, 24, ...
H. -7, -3, 1, 5, ...
16. _____
G.
J.
17. Find the next three terms of the arithmetic sequence 5, 9, 13, 17, ... .
A. 21
B. 21, 25, 29
C. 41, 45, 49
D. 21, 41, 61
17. _____
18. Find the next two numbers of the sequence 1, 2, 4, 8, 16, ... .
F. 32, 64
G. 24, 32
H. 20, 22
J. 18, 20
18. _____
C.
D. x2 + y2 = 0
19. _____
19. Which equation is a linear equation?
A. 4m2 = 6
B. 3a + 5b = -3
20. Write an equation in function notation for the relation at the right.
F. f(x) = 2x
G. f(x) = x + 1
Bonus
H. f(x) = 1 − x
J. f(x) = -x
20. _____
Graph y = x − 3 by using the x- and y-intercepts.
Chapter 3
47
B:
____________________
Glencoe Algebra 1
Write the letter for the correct answer in the blank at the right of each question.
For Questions 1-4, find the slope of each line described.
1. the line through (3, 7) and (-1, 4)
A.
B.
C.
D.
1. _____
H. 0
J. undefined
2. _____
2. the line through (-3, 2) and (6, 2)
F.
G.
3. the line graphed at the right
A.
C.
B.
D.
3. _____
4. a vertical line
F. 1
G. 0
H. -1
J. undefined
C.
D.
4. _____
5. Which graph has a slope of -3?
A.
B.
5. _____
6. COMMUNICATION In 1996, there were 171 area codes in the United States. In
1999, there were 285. Find the rate of change from 1996 to 1999.
F. 114
G. 38
H.
J. -144
6. _____
For Questions 7-9, find the equation in slope-intercept form that describes each
line.
7. a line through (2, 4) with slope 0
A. y = 2
B. x = 2
C. y = 4
D. x = 4
7. _____
8. a line through (4, 2) with slope
F.
H. y = 2x − 10
G.
J.
8. _____
9. a line through (-1, 1) and (2, 3)
A.
D.
C.
B.
9. _____
10. If 5 deli sandwiches cost $29.75, how much will 8 sandwiches cost?
F. $37.75
G. $29.75
H. $47.60
J. $0.16
10. _____
D. y − 2x = 11
11. _____
11. What is the standard form of y − 8 = 2(x + 3)?
A. 2x + y = 14
B. y = 2x + 14
C. 2x − y = -14
63
Chapter 4
12. Which is the graph of
F.
G.
Glencoe Algebra 1
?
H.
J.
12. _____
13. Which is the point-slope form of an equation for the line that passes through (0, 5) with slope 2?
A. y = 2x = 5
B. y + 5 = 2x
C. y − 5 = x − 2
D. y = 2(x + 5)
13. _____
J. 2x − y = 6
14. _____
14. What is the slope-intercept form of y + 6 = 2(x + 2)?
F. y = 2x − 6
G. y = 2x − 2
H. y = 2x + 6
15. When are two lines parallel?
A. when the slopes are opposite
B. when the slopes are equal
C. when the product of the slopes is
15. _____
1
D. when the slopes are positive 15.
16. Find the slope-intercept form of an equation for the line that passes through (-1,
2) and is parallel to y = 2x − 3.
F. y = 2x + 4
G. y = 0.5x + 4
H. y = 2x + 3
J. y = -0.5x − 4
16. _____
17. Find the slope-intercept form of an equation of the line perpendicular to the graph
of x − 3y = 5 and passing through (0, 6).
A.
B. y = -3 + 6
C.
D. y = 3x − 6
17. _____
For Questions 18 and 19, use the scatter plot at the right.
18. How would you describe the relationship between the x- and y-values in the
scatter plot?
F. strong negative correlation
G. weak negative correlation
H. weak positive correlation
J. strong positive correlation
18. _____
19. Based on the data in the scatter plot, what would you expect the y-value to be for
x = 2010?
A. greater than 80
B. between 80 and 65
C. between 65 and 50
D. less than 50
19. _____
20. Which equation has a slope of 2 and a y-intercept of -5?-F. y = -5x + 2
G. y = 5x + 2
H. y = 2x + 5
J. y = 2x − 5
Bonus Find the value of r in (4, r), (r, 2) so that the slope of the
B:
____________________
line containing them is
64
Chapter 4
20. _____
Glencoe Algebra 1
(Chapters 1-4)
Part 1: Multiple Choice
Instructions: Fill in the appropriate circle for the best answer.
1. If a = 2, b = 6, and c = 4, then
A4
B 0.4
(Lesson 1-2)
C 40
D 0.04
1.
2. If 4 + 7 + 6 = 4 + 7 + 6 + n, what is the value of n? (Lesson 1-4)
F0
G1
H4
J6
2.
3. Lynn has 4 more books than José. If Lynn gives José 6 of her books, how many
more will José have than Lynn? (Lesson 1-2)
A2
B4
C8
D 10
3.
4. If
, which value of x does NOT form a proportion? (Lesson 2-6)
F
G
4.
J
H
5. Two-thirds of a number added to itself is 20. What is the number? (Lesson 2-1)
A 12
B 13
C 30
D 33
5.
J 1600
6.
6. 16% of 980 is 9.8% of what number? (Lesson 2-5)
F 1.6
G 16
H 160
7. For what value(s) of r is 3r − 6 = 7 + 3r? (Lesson 2-7)
A all numbers
B all negative integers
C0
D no values of r
7.
8. The range of a relation includes the integers
.
What could be a value for x in the domain? (Lesson 3-1)
F 20
G 30
H 32
J 40
8.
9. A line with a slope of -1 passes through points at (2, 3) and
(5, y). Find the value of y. (Lesson 4-1)
A -6
B -3
C0
D6
9.
10. If a line passes through (0, -6) and has a slope of -3, what is
an equation for the line? (Lesson 4-4)
F y = -6x − 3
G x = -6y − 3
Chapter 4
H y = -3x − 6
J x = -3y − 6
76
10.
Glencoe Algebra 1
11. If x2 = 16 and y2 = 4, what is the greatest possible value of (x − y)2? (Lesson 1-8)
A6
12. If
F
B 12
C 36
D 64
11.
H2
J4
12.
, x = ? (Lesson 2-4)
G1
13. Find the slope of the line that passes through (2, 2) and (7, 7). (Lesson 4-1)
A -1
B1
C -5
D5
13.
14. What is the equation of the line that passes through (1, 2) and (0, -1)? (Lesson 44)
Fy=x−3
G y = -x + 3
H y = -3x + 1
J y = 3x − 1
Part 2: Griddable
Instructions: Enter your answers by writing each digit of the answer in a
column box and then shading in the appropriate circle that corresponds to
that entry.
15. The formula for the volume of a rectangular solid is V = Bh. A packing crate has a
height of 4.5 inches and a base area of 18.2 square inches. What is the volume
of the crate in cubic inches? (Lesson 2-8)
14.
16. Find the slope of a line parallel to
Chapter 4
. (Lesson 4-7)
77
Glencoe Algebra 1
Part 3: Short Answer
Instructions: Write your answers in the space.
17. Write 2 · r · r · s · s using exponents. (Lesson 1-1)
17. ____________________
18. Evaluate 2xy − y2 if x = 6 and y = 12. (Lesson 1-2)
18. ____________________
Simplify each expression. (Lessons 1-2 through 1-5)
19. 12 − 6 × 5
19. ____________________
20. 6(2 + 3) − 9
20. ____________________
21. (2 · 3)2 − 22
21. ____________________
22. 4 · 9 − 2 · 10
22. ____________________
23. 4(2y + y) − 6(4y + 3y)
23. ____________________
24.
For Questions 25-27, solve each equation. (Lessons 2-2
through 2-4)
24. ____________________
25. 13 − m = 21
25. ____________________
26.
27. 4x + 12 = -16
26. ____________________
28. Solve x − 2y = 12 if the domain is {-3, -1, 0, 2, 5}. (Lesson
3-3)
29. Determine whether {(1, 4), (2, 6), (3, 7), (4, 4)} is a
function, and explain your reasoning. (Lesson 3-2)
30. Write an equation for the relationship between the
variables in the chart. (Lesson 3-5)
x
0
2
4
6
y
2
5
8
11
27. ____________________
28. ____________________
29. ____________________
30. ____________________
31. Determine the slope of the line passing through (2, 7) and
(-5, 2). (Lesson 4-1)
32. Write an equation in slope-intercept form for the line
passing through (2, 6) with a slope of -3. (Lesson 4-3)
33. Write an equation for the line passing through (-6, 5) and
(-6, -4). (Lesson 4-4)
34. Lucy owns a bakery. In 2001, she sold pies for $9.50
each. In 2005, she sold pies for $17.50 each.
a. Find the rate of change for the price of a pie from
2001 to 2005.
31. ____________________
32. ____________________
33. ____________________
34a.____________________
34b.____________________
b. How much do you think Lucy will sell a pie for in
2007?
Chapter 4
78
Glencoe Algebra 1
_____
(Chapters 3-6)
For Questions 1 and 2, use the graph.
1. Express the relation as a set of
ordered pairs. Then determine the
domain and range.
1. ____________________
2. ____________________
2. Determine whether the relation is a
function.
3. Express the relation shown in the
mapping as a set of ordered pairs.
Then write the inverse of the
relation.
3. ____________________
4. Solve 2x − 3 = y if the domain is {2, -1, 0, 3, 5}.
4. ____________________
5.
5. Graph 3x − y = 1.
6. ____________________
6. If g(x) = 2x2 − 3, find g(-4).
7. ____________________
7. Find the 25th term of the arithmetic
sequence with first term 7 and
common difference -2.
8. ____________________
9. ____________________
8. A giraffe can travel 800 feet in 20
seconds.Write a direct variation
equation for the distance traveled
in any time.
10. ____________________
9. Write an equation of the line whose
slope is 2 and whose y-intercept is
9.
11. ____________________
12. ____________________
10. Write an equation of the line that
passes through (-1, -7) and (1, 3).
11. Write
standard form.
in
12. Write the slope-intercept form of an
equation of the line that passes
through (-2, 0) and is parallel to the
graph of y = -3x − 2.
87
Chapter 6
13. The table below shows the distance driven during four different trips
and the duration of each trip. Draw a scatter plot and determine what
relationship exists, if any, in the data. Write an equation for a line of fit
for the data.
14.
Time (hours)
1
2
2.5
4
Distance
(miles)
50
85
120
180
Glencoe Algebra 1