Algebra 1
Midterm Review Packet
Name ____________________
Date______________________
CHAPTER 1
Match the following with the appropriate property.
1. x  y  y  x
A.
Distributive Property
2.
6u  2v   6u  12v
B.
Commutative Property of Multiplication
3.
5m  n   5  m n
C.
Associative Property of Addition
4.
gx  xg
D.
Commutative Property of Addition
5.
2a  3b  4c  2a  3b  4c
E.
Associative Property of Multiplication
Simplify
6. 47+  28 
7.
 27.9  36
6.__________________
7.__________________
8.
14   8 
9.
-15 + 6
8.__________________
9.__________________
10. 5(-3) + 4(6)
11. 12  3  2  9
10._________________
11._________________
12. 6  8  22  1
13. (6  2)  (3  1)
12._________________
13._________________
14.
10  5
3 42
15. 12  3  4  1
14._________________
15._________________
16.
2
1  2 3
17.
1
(19 + 11 - 3)
2
16._________________
17._________________
18. 5  3  2  2
19. 17  28  2  4
18._________________
19._________________
20. 3  6  9  3  6
21. 6  8 8  3  9  3  2
20._________________
21._________________
22.
 81
 27
23.
1 3

2 2
22._________________
23._________________
24.
2 1

3 6
25.
3  5
  
4  4
24._________________
25._________________
26. 
1 3
 
4 2
27.
1 2

3 5
26._________________
27._________________
28.
5

6
4

2
29.
4
3
3
28._________________
29._________________
30.
2  1
  
5  6
31. 
2
6
3
30._________________
31._________________
 9
32.  8    
 14 
33. 
40
8
32._________________
33._________________
Rewrite the following using exponents.
34. 2 2  a  a  b
35. 37  x  x  x  z  z  z  z
34._________________
35._________________
Rewrite the following without using exponents.
3
36. a 2 b 3
37. 4 y 
36._________________
37._________________
Evaluate the following expressions when x = 3 and y = 5.
38. ( y  x) 3
39. 2x 2  y
38._________________
39._________________
40. 7 y  25  x
41. 2 y 2  3x  y 
2
40._________________
41._________________
Check whether the given number is a solution of the equation or inequality. Write “Yes” or “No”
42. 2x  3  17 ; 7
43. x  5  7 ; 12
42._________________
43._________________
44. x 2  7  10;
45. 6x  1  8x  7 ;
2
2
44._________________
45._________________
Match the following phrases with their algebraic expression.
46. Six times a given number
47. Six less a number
48. Six less than a number
49. Fourteen is less than seven
times a given number
50. Fourteen less than a given
number is seven
51. 14 less the product of a given
number and seven
52. Six less a number z is less
than 21
53. Six less than a number z is
less than 21
54. The product of six and a number
z is less than 21
A.
6–x
B.
x–6
C.
6x
D.
14 < 7x
E.
14 – 7x
F.
x – 14 = 7
G.
6 - z < 21
H.
z – 6 < 21
I.
6z < 21
Write an equation that correctly models the situation. Then solve.
55. You are 72 inches tall. You are 15 inches taller than your younger sister. How tall is your sister?
55._____________________
55._____________________
56. Your teacher gave you 10 days to read a 290-page book. How many pages a night will you have to read?
Let p be the number of pages read.
56._____________________
56._____________________
57. A movie theater charges $8 admission. The total sales on a given day were $560. How many
admission tickets were sold that day?
57._____________________
57._____________________
Use the Chapter 1 Formulas to help solve the following application problems.
58. An airplane travels at a rate of 500
59. A car travels at 120 kilometers
miles per minute for 13 minutes.
per hour for 4 hours. How far
How far does the plane travel?
does the car travel?
58._________
59._________
60. Find the perimeter of the triangle
below if x = 6.
2x
61. Find the area of a triangle with
a height of 7 inches and a base
of 12 inches.
60._________
x
3x
62. Find the volume of a cubic package with
a base of 3 feet.
61._________
63. Find the area of a rectangular pig
pen with a length of 17 feet and a
width of 11 feet.
62._________
63._________
Algebra 1
Midterm Review Packet
CHAPTER 2
In 1-4, replace the ?
7
1.
?
-7
3
with >, < or = to make each sentence true.
4
5
2.
?
5
9
Name ____________________
Date______________________
1.__________________
2.__________________
3.
 11
5
?
 17
8
4.
2
3
?
3
7
3.__________________
4.__________________
5.
Write
6 9 7
,
,
in order from least to greatest:
11 14 13
5.__________________
6.
5
4
Write  4,  ,  ,  1.5 in order from greatest to least:
4
5
6.__________________
Evaluate the following expressions.
7. 18
8.  18
9.  18
Evaluate the following when a = -13 and b = 7
11. a  b
12. b  42  a
10.   18
11._________________
12._________________
Use the Distributive Property to help simplify the following.
4
13. 2 x  10 
14. 5r  2   7 r
5
13._________________
14._________________
15. 2x  8x
16. 12  2x  5  10
15._________________
16._________________
17. 64a  3b
18.  36a  9b 
17._________________
18._________________
19. 3 x  4   2 x  5
20. 4 x  2 x  5
19._________________
20._________________
21. 3 p  6 p   2 p
22.
3
2x  3x  4 x
7
7
21._________________
22._________________
23. 32 y  4  5 y  3
24.
15a  20b
5
23._________________
24._________________
25.
 2x  8
4
26. 3ab  2a  7b  6ab
25. _________________
26._________________
2t 2 3n
27.

4 2t
28. (5xy - x - 7) + (2xy + 3x + 4)
27. _________________
28._________________
29.  b  9  2  b
30. 11m  7n  2m  6n
29._________________
30._________________
31. On February 13th you deposit $150 into your bank account. On April 12th
you withdraw $125 and on May 6th you deposit $25. How much money do
you have in your bank account?
31._________________
32. One quarter will give 40 minutes at a parking meter. If you will be gone
2 hours (120 minutes), how many quarters do you need to deposit?
32._________________
Algebra 1
Midterm Review Packet
CHAPTER 3
Solve the following equations.
1. x  4  12
2.
x 13  5
Name ____________________
Date______________________
1.__________________
2.__________________
3.
2 3
 x
7 4
4.  288  16u
3.__________________
4._________________
5.

x
7
2
6.
4
8
y
5.__________________
6.__________________
7.
x3
 7
5
8.
7
14   x
2
7.__________________
8.__________________
9.
8 x
 4
3
10.
2a  4
5
6
9.__________________
10._________________
11.
2
x  5  14
3
12. 2 x  12  20
11._________________
12._________________
13. 2(a + 3) = 16
14.  3b  8  5  9b  2  1
13._________________
14._________________
16. 3 y 1  3 y  3
15. 2 x  3  4 x  5
15._________________
16._________________
17.  3d  4  4d 10
18.
1
2
x 7 x
3
3
17._________________
18._________________
20.  3   4 x   4 x  5
19. 8a  9  8a
19._________________
20._________________
21.  10  y   3 y  12
22. 22x  3  4x  6
21._________________
22._________________
Solve the following formulas for the indicated value.
23. y  mx b ; x
24. A  bh ;
h
23._________________
24._________________
25. P  2 L  2W ;
L
1
26. V  Bh ;
3
h
25._________________
26._________________
Solve the following proportions.
x 4

27.
18 3
28.
9 3

2 y
27._________________
28._________________
29.
2x 4

3 5
30.
3
5

5 x2
29._________________
30._________________
Convert each of the following units.
31. 4 years to months
32. 156 inches to feet
31._________________
32._________________
Solve each of the following percentage questions.
33. What percent of 80 is 72?
34. What is 35% of 80?
33._________________
34._________________
35. 45% of what is 9?
36. What is 100% of 232?
35._________________
36._________________
37. 20% of what is 15?
38. What percent of 20 is 30?
37._________________
38._________________
39. What is 200% of 54?
40. 45% of what is 10?
39._________________
40._________________
Algebra 1
Midterm Review Packet
CHAPTER 4
Write the ordered pairs that correspond to points A, B, C, and D
1.
2.
A
A
B
B
C
C
D
D
3.
Label the quadrants, axes, and the origin on the coordinate plane to the right.
4.
List the quadrant that each of the points is in
DO NOT PLOT THE POINTS
A. (-5, 22)
B. (0, -7)
C. (2, 16)
D. (12, -80)
E. (10, 0)
F. (-30, -60)
Identify the Ordered Pair that IS a solution to the equation
5. 3x  y  18
6. y  18
A. (-1, 21)
C. (3, -9)
A. (0, -18)
B. (1, -21)
D. (9, 3)
B. (18, 0)
7.
x  8
A. (-8, 1)
B. (1, -8)
9.
8.
C. (8, -1)
D. (-1, 8)
Find the range of y 
Name ____________________
Date______________________
 y  4 x  23
A. (3, 5)
B. (5, 3)
2x  1
if the domain is {0, 1, 2, 3}
3
5.__________________
C. (0, 18)
D. (-18, 0)
6.__________________
7.__________________
C. (3, -5)
D. (5, -3)
8.__________________
9.__________________
10. Find the range for y = 2x – 1 if the domain is {-1, 0, 1}
10._________________
11. Find the output values for y = 7 – 3x if the input values are {-2, -1, 0, 1, 2}
11._________________
Use the following tables to a) List the Domain; b) List the Range; c) Does it represent a function?
12.
13.
14.
x
y
x
y
x
y
0
1
2
3
2
4
6
8
7
9
10
10
7
9
8
10
1
3
5
7
1
2
3
1
Domain:_________________
Domain:_________________
Domain:_________________
Range:__________________
Range:__________________
Range:__________________
Function?________________
Function?________________
Function?________________
Determine whether each of the relations below is a function.
15. {(2, -6), (3, 4), (-2, -6), (5, 0)}
16. {(1, 2), (3, 6), (1, -4), (5, 0), (8, -3)}
15._________________
16._________________
17.
18.
17._________________
18._________________
Write an equation for the graphs shown below.
19.
20.
21.
22.
23. Which of the following equations has a graph that is vertical?
A. y = 2x + 3
B.
y=3
C.
x=4
D. y = x
24. Which of the following equations has a graph that is horizontal?
A. y = 2x + 3
B.
y=3
C.
x=4
D. y = x
Use the graph below to find the x-intercept and the y-intercept.
25.
26.
27.
x-int_______
x-int_______
y-int_______
x-int_______
y-int_______
y-int_______
Find the x-intercept and the y-intercept of the following equations. Use the intercepts to graph the equation.
28. 3x + 2y = 6
29. 4x – 2y = 10
28. x:_______________
y:_______________
29. x:_______________
y:_______________
30. y 
3
x 3
5
31.  3 y  5 x  9
30. x:_______________
y:_______________
31. x:_______________
y:_______________
Rewrite the equation in Slope-Intercept Form:_____________________
32.  6 x  y  18
33. 3x  y  14
32._________________
33._________________
34.  3x  6 y  24
35.  4 y  6x  12
34._________________
35._________________
36. Find the slope of the line
passing through the points
(2, -1) and (3, 4)
37. Find the slope of the line
passing through the points
(0, 8) and (-1, 8)
36._________________
38. Find the slope of the line
passing through the points
(2, 4) and (5, 0)
39. Find the slope of the line
passing through the points
(3, 4) and (3, -2)
38._________________
40. Sketch the graph of a line with:
A. a positive slope
B. a negative slope
C. no-slope (undefined )
Identify the slope and y-intercepts, then graph the line.
41. y  3x  2
2
42. y   x  4
3
slope:
slope:
y-int:
y-int:
37._________________
39._________________
D. zero-slope
43. Write the equation of a line
44. Write the equation of a line
3
with a slope of and a
5
y-intercept of -4. Then graph.
with a slope of -2 and a
y-intercept of 6. Then graph.
Match the following picture with the correct equation.
45.
43._________________
44._________________
46.
A.
y  2x  1
A.
B.
y  x2
B.
C.
y  x  2
C.
D.
y  2x  2
D.
y  2 x 
1
2
1
y  x2
2
1
y  x2
2
y  2x  2
Evaluate.
47. g x   8x  2
when
x  2
48. hx  
3
x6
4
when
x8
47._________________
48._________________
49. Given f(x) = 2x – 8, find f(3)
50. Given f(x) = 17 – 3x + 9, find f(-1)
49._________________
50._________________
51. The cost of a one day car rental from City Wide Rentals is given by the
function Cx  0.18x  35 where x is the number of miles driven. What is
the cost of the car rental if 587 miles are driven in one day?
51._________________
Algebra 1
Midterm Review Packet
Name ____________________
Date______________________
CHAPTER 5
1. Write the equation of the line in slope-intercept form
given the following graph.
2.
1.__________________
Which of the following lines is the graph of 4x + 2y = 8
A.
B.
C.
2 x  5 y  10
3.
Rewrite in slope-intercept form:
3.__________________
4.
Write the equation of the line through (10, 8) with slope
1
in point-slope form.
2
4.__________________
5.
Write the equation of the line through (1, -3) with slope -2 in point-slope form.
4.__________________
6.
Write the equation of the line through (7, 6) with slope
3
in point-slope form.
5
6.__________________
7.
Write the equation of the line through (2, 5) with slope 6 in slope-intercept form.
8.
Write the equation of the line through (4, 5) with slope
7.__________________
1
in slope-intercept form. 7.__________________
2
9. Determine the slope of the line passing through (-4, 5) and (3, -2).
9.__________________
10. Write the equation of the line that passes through the points (-4, 5) and (3, -2).
10._________________
11. Write the equation of the line that passes through the points (-8, -4) and (6, 3)
11._________________
12. Write the equation of the line that passes through the points (-3, 5) and (1, 5)
12._________________
13. Write the equation of the line that passes through the points (2, -1) and (4, 5)
13._________________
Rewrite the following equations in Standard Form.
14.  3x  2 y  7
15. 2 y  4 x  6
14._________________
15._________________
1
16. y   x  3
2
17. 3 y 
2
x4
5
16._________________
17._________________
18. What is the slope of a line
parallel to the line with the
equation y  2 x  7
19. What is the slope of a line
parallel to the line with the
3
equation y  x
2
18._________________
19._________________
20. What is the slope of a line
perpendicular to the line with the
equation y  2 x  7
21. What is the slope of a line
perpendicular to the line with the
3
equation y  x
2
20._________________
21._________________
Determine whether the following sets of lines are Parallel, Perpendicular, or Neither.
22. 2y = -6x
23. y = 3x + 1
22._________________
-12y = -4x
4y = 3x + 1
23._________________
24.
y = 3x + 6
-2y = 6x – 4
25.
y = -½ x + 3
2y = -x + 4
24._________________
25._________________
26. Write an equation of a line that passes through the point (4, -1)
1
and is parallel to the line y  x  1
2
26._________________
27. Write an equation of a line that passes through the point (2, -3)
and is parallel to the line y  3x  6
27._________________
28. Write an equation of a line that passes through the point (-4, 6)
and is perpendicular to the line y  2x  3
28._________________
29. Write an equation of a line that passes through the point (0, 11)
and is perpendicular to the line y   x  6
29._________________
Algebra 1
Midterm Review Packet
CHAPTER 6
Solve the following inequalities and graph their solutions.
1. 12 + x < 18
2. -3a > 18
Name ____________________
Date______________________
1.__________________
2.__________________
3.
15 
x
4
4.
y
 7  5
3
3.__________________
4.__________________
5.
 15 
c
4
6.
4n  6  6n  20
5.__________________
6.__________________
7.
3  2 y  15
8.
52  3x   46
7.__________________
8.__________________
9.
7x  2  3x  2
10. 3 y  2  2 y  51
9.__________________
10._________________
Write the inequality for each graph shown below.
11.
12.
-5
-4 -3
-2 -1
0
1
2
3
4
-5
5
13.
11._________________
-4 -3
-2 -1
0
1
2
3
4
5
14.
-5
-4 -3
-2 -1
0
1
2
3
4
5
15.
13._________________
-5
-4 -3
-2 -1
0
1
2
3
4
5
16.
-5
-4 -3
-2 -1
0
1
2
3
4
5
12._________________
14._________________
15._________________
-5
-4 -3
-2 -1
0
1
2
3
4
Solve the following compound inequalities and graph the solution.
17. -14 < 7x < 21
18. 3 < x – 3 ≤ 5
5
16._________________
17._________________
18._________________
19. -3 ≤ 2x + 1 < 9
20. 6 + 2x > 20 or 8 + x ≤ 0
19._________________
20._________________
21.
x
 3 or  5  6  x
3
22. 2x + 1 > 13 or -18 > 7x + 3
21._________________
22._________________
23. You earn $8.75 per hour at your math tutoring job. Write and solve an inequality to show how many
full hours h you need to work to save at least $650 so that you can buy Ms. Kurtz something awesome!
Inequality:_______________________
Solution:________________________
24. A membership to the “Math Is Cool Club” has an initiation fee of $90. Each month you are billed an
additional $30. Write and solve an inequality to find the maximum amount of time you can be a member
for $600.
Inequality:_______________________
Solution:________________________
Algebra 1
Midterm Review Packet
Name ____________________
Date______________________
PRACTICE STORY PROBLEMS
Define your variable(s), write an equation, and solve. Be sure to include units!!
1. The sum of two numbers is 18. The less of the two is 6,
what is the greater number?
2.
1.__________________
The difference of two numbers is 8. The greater number is 2,
what is the lesser number?
2.__________________
For $1.89, you can buy 75 square feet of plastic wrap. At this rate, how much
does 125 square feet of plastic wrap cost?
3.__________________
Lisa is 7 years older than Claire. The sum of their ages is 51.
What is Claire’s age?
4.__________________
5.
Jack drove 260 miles in 4 hours. How fast was he driving?
5.__________________
6.
Manny can average 16 mi/hr on his bicycle in a race. How long will a
44 mile race take?
6.__________________
3.
4.
Midterm Review Chapter 1 Answers
Algebra 1
1. D
2. A
3. E
9. -9
17.
4. B
10. 9
27
25. −
11. 9
18. 6
2
1
26. −
2
7
27.
4
34. 22 𝑎2 𝑏
41. 46
42. Yes
52. G
20. 15
2
28. −
15
35. 31 71 𝑥 3 𝑧 4
5
59. 480
30. −
9
23. 2
12
44. No
45. Yes
62. 27
46. C
1
5
6
32.
9
39. 13
8. 22
15. 17
24.
31. −
5
36. 𝑎 ∙ 𝑎 ∙ 𝑏 ∙ 𝑏 ∙ 𝑏 37. 4𝑦 ∙ 4𝑦 ∙ 4𝑦 38. 8
43. Yes
60. 36 61. 42
14. 3
22. 3
4
29.
3
7. 8.1
13. 1
21. 7
53. H 54. I 55. a) x + 15 = 72 b) 57 inches
58. 6500
6. 19
12. 5
19. 25
33. -5
5. C
112
9
40. 103
47. A 48. B 49. D 50. F 51. E
56. a) 10p = 290 b) 29
57. a) 8x = 560 b. 70
63. 187
Midterm Review Chapter 2 Answers
Algebra 1
1. > 2. > 3. < 4. > 5.
7
8
13. 𝑥 − 8
12. -48
20. 2x – 10
3𝑡𝑛
28. 7xy + 2x – 3
4
6
,
9
4
5
5
4
6. − , − , −1.5, −4
14. 12r + 10
5
19. 5x – 9
27.
,
13 11 14
22. −
21. 11p
15. 10x
11
7
𝑥
8. -18
16. -2x + 32
23. 11y + 3
30. 9m – 13n
29. -11
7. 18
10. -18
11. 20
18. -18a – 27b
17. 24a + 18b
1
24. 3a – 4b
31. $50
9. 18
26. 9ab – 2a + 7b
25. 𝑥 − 2
2
32. 3 quarters
Midterm Review Chapter 3 Answers
Algebra 1
1. 8
2. 8
14. 0
15. -1
23. 𝑥 =
𝑦−𝑏
𝑚
33. 90%
3.
29
4. -18
5. -14
6. 2
7. -32
16. All real #’s
17. -2
18. 7
19. No sol.
28
24. ℎ =
34. 28
𝐴
𝑏
35. 20
25. 𝐿 =
𝑃−2𝑊
36. 232
2
26. ℎ =
37. 75
3𝑉
𝐵
38. 150
8. -4
9. 20
20. 1
10. 13
11. -13.5
28.
39. 108
40.
2
29.
3
13. 5
31. 48
32. 13
22. All real #’
21. -11
27. 24
12. 4
6
5
30.
31
3
200
9
Midterm Review Chapter 4 Answers
Algebra 1
1. A(5, 1) B(0, 4) C(-3, -1) D(0, 0) 2. A(-4, 0) B(2, 3) C(1, -1) D(-3, -5)
3. On graph
4. A. Quad 1, B. y-axis, C. Quad 1, D. Quad 4, E. x – axis, F. Quad 3
5. A
1
5 7
3
3 3
9. , 3, ,
6. C
7. A 8. D
10. -3, -1, 1 11. 13, 10, 7, 4, 1 12. D: 0, 1, 2, 3 R: 2, 4, 6, 8 yes 13. D: 7, 9, 10 R: 7, 9, 8, 10, no
16.
2
9
14. D: 1, 3, 5, 7 R: 1, 2, yes
22. y = -3.5
23. C
24. B
15. Yes 16. No 17. Yes 18. No 19. x = 2
25. x: (3, 0) y: (0, 3)
26. x: (-1, 0) y: (0, 3)
20. y = 4 21. x = -3.5
27. x: (2, 0) y: (0, -2)
5
9
2
5
28. x: (2, 0) y: (0,3) 29. x: ( , 0) y: (0, -5) 30. x: (5, 0) y: (0, -3) 31. x: (− , 0) y: (0, -3)
1
33. 𝑦 = 3𝑥 − 14
40. positive
3
34. 𝑦 = 𝑥 + 4
35. 𝑦 = 𝑥 + 3
negative undefined
zero
2
44.
2
45. B
36. 5
38. −
37. 0
41.
46. B
4
32. 𝑦 = 6𝑥 + 18
39. Undefined
3
42.
43.
47. 14
48. 0
49. -2
y = -2x +6
50. 29
3
y= x-4
5
51. $140.66
Midterm Review Chapter 5 Answers
Algebra 1
3
1. 𝑦 = 𝑥 + 1
2
1
8. 𝑦 = 𝑥 + 3
2
2
1
2. A
3. 𝑦 = − 𝑥 − 2
4. 𝑦 = 𝑥 + 3
9. -1
10. 𝑦 = −𝑥 + 1
11. 𝑦 = 𝑥 − 6
15. 4𝑥 + 2𝑦 = 6
5
16. 𝑥 + 2𝑦 = −6
22. perpendicular
23. Neither
1
28. 𝑦 = − 𝑥 + 4
5. 𝑦 = −2𝑥 − 1
2
1
12. 𝑦 = 5
2
17. 2𝑥 − 15𝑦 = −20
24. neither 25. Parallel
18. -2
1
9
5
5
13. 𝑦 = 3𝑥 − 7
19.
26. 𝑦 = 𝑥 − 3
2
3
6. 𝑦 = 𝑥 +
3
2
20.
1
7. 𝑦 = 6𝑥 − 7
14. 3𝑥 + 2𝑦 = 7
21. −
2
2
3
27. 𝑦 = 3𝑥 − 9
29. 𝑦 = 𝑥 + 11
2
Midterm Review Chapter 6 Answers
Algebra 1
1. x < 6 2. a < -6 3. x ≤ 60
10. y ≤ -9
17. -2 < x < 3
11. x ≥ -2
4. y ≤ 6
12. x > 2
18. 6 < x ≤ 8
22. x > 6 OR x < -3
5. c > 60
13. x ≤ -3
19. -2 ≤ x < 4
23. 8.75x ≥ 650, x ≥ 75
6. n < 7
7. y ≥ -6
14. 0 < x ≤ 3
8. x ≥ -2.4
9. x ≤ 2
15. x ≤ -2 OR x ≥ 4
16. -3 < x < 1
20. x > 7 OR x ≤ -8
21. x < -9 OR x > -1
24. 90 + 30x ≤ 600,
x ≤ 17
Midterm Review Story Problems Answers
Algebra 1
1. 12
2. -6
3. $3.15
4. 22
5. 65 mph
6. 2.75 hours