Algebra 1 College Prep Midterm REVIEW
What is an algebraic expression for the word phrase?
1. 2 times the sum of y and k
2. The quotient of 6 and the difference of c and n
3. The table shows how the height of a stack of DVDs depends on the number of DVDs.
the height?
Number
of DVDs
2
3
4
n
What is a rule for
Height
(cm)
14
21
28
?
What is the simplified form of each expression?
4.
5.
6. Evaluate
, for u = 18, x = 5, y = 8, and z = 3.
What is the simplified form of each expression?
7.
8. A square field has an area of 121 ft2. What is the approximate length of a side of the field?
answer to the nearest foot.
9. Give an example of a rational and an irrational number.
types?
Give your
What is the difference between the two
10. What is the square root of 96 to the nearest integer?
11. What is the order of
, 0.3,
1
, 0.4,
9
from least to greatest?
What property is illustrated by each statement?
12. 10 + 6.9 = 6.9 + 10
13. –2 + (7 + 9) = (–2 + 7) + 9
Simplify each expression.
14.
15. (2 + 4f) + 4
16. You made two deposits to your bank account this month. One deposit was $18.15, and the second
deposit was $16.03. Your balance at the end of the month is $72.31, and you made no withdrawals.
Write and evaluate an expression for your balance at the beginning of the month.
What is the simplified form of each expression?
17.
2
(–6m + 12)
3
18.
What sum or difference is equivalent to the expression?
19.
What is the simplified form of each expression?
20.
What is the solution of the equation?
21. 4.7x + 4.3 = 13.7
22.
5
x–3=7
8
23. Steven wants to buy a $600 bicycle. Steven has no money saved, but will be able to deposit $35 into a
savings account when he receives his paycheck each Friday. However, before Steven can buy the bike,
he must give his sister $65 that he owes her. For how many weeks will Steven need to deposit money
into his savings account before he can pay back his sister and buy the bike?
What is the solution of the equation?
24.
25. Angela and Neil are going to the movies. They each bought a medium popcorn, and Neil got a small soft
drink. Angela had a $20 gift certificate to put toward the cost, and Neil paid the rest, which came to
$7.00. A movie ticket costs $7.50 and a medium popcorn costs $4.70. How much does a small soft drink
cost at the theater?
What is the solution of the equation?
26. 3x + 7 = 6x – 2
27.
28.
29. What equation do you get when you solve
for x?
30. You are shopping for jeans. City Express sells 3 pairs of jeans for $53. Denim Planet sells 2 pairs of jeans
for $78. New Threads sells 4 pairs of jeans for $105. Which store has the best deal?
What is the solution of the proportion?
31.
32.
33.
34. A van travels 320 miles on 16 gallons of gas. Find how many gallons the van needs to travel 360 miles.
35. A dress that normally costs $57.50 is on sale for 40% off. What is the sale price of the dress?
36. You deposited $1800 dollars in a savings account that earns a simple interest rate of 2.25% per year.
How many years do you need to keep the money in the account to earn $81 in interest?
37. The viewership of a television show has decreased from 5.3 million viewers to 3.3 million viewers per
episode. Find the percent of decrease in viewership to the nearest percent.
38. Sarah is currently making $34,000 a year at her job and has been offered a raise to $38,420 per year.
What would be the percent increase in her salary?
What inequality represents the graph?
39.
40.
–10 –8
–6
–4
–2
0
2
4
6
8
10
–5
–3
–2
–1
0
1
2
3
4
5
–4
What inequality describes the situation?
41. Let t = the amount Thomas earned. Thomas earned $44 or more.
What are the solutions of the inequality? Graph the solutions.
42.
43. Your class hopes to collect at least 450 cans of food for the annual food drive.
donated the first week and 130 more the second week.
There were 126 cans
Write an inequality that describes this situation. Let c represent the number of cans of food that must
be collected by the end of the third week for your class to meet or surpass your goal. How many cans
are needed to meet or surpass your goal?
What are the solutions of the inequality?
Graph the solutions.
44. –9b < –18
What are the solutions of the inequality?
45.
–
1
7
x–7<
4
12
What are the solutions of the inequality?
46.
Check the solutions.
What are the solutions of the inequality?
47.
48.
What compound inequality represents the phrase?
Graph the solutions.
49. All real numbers that are greater than –6 and less than 6
50. All real numbers x that are less than 4 or greater than 10
What are the solutions of the compound inequality?
Graph the solutions.
51. –1 < 4x – 5 < 15
What are the solutions of the compound inequality?
Graph the solutions.
52.
53. The table shows the amount of money made by a summer blockbuster in each of the first four weeks of
its theater release. Draw a graph that could represent the data listed.
Week
1
2
3
4
Money ($)
20,000,000
10,000,000
5,000,000
2,500,000
What are the variables in each graph? Describe how the variables are related at various points on the
graph.
54. The graph shows the number of handbags that Jenny made in one day.
Describe how the variables are related at various points on the graph.
number of handbags
Jenny's Handbags
time
Find the slope of the line.
y
55.
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
What is the slope of the line that passes through the pair of points?
56. (4, 5), (7, –3)
Write an equation of a line with the given slope and y-intercept.
57. m = 2, b = 5
What are the variables?
58. What is an equation of the line in slope intercept form that passes through the given points?
(2, 1) and (6, 9)
Graph the equation.
59. y = x – 5
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
1
2
3
4
5
x
–2
–3
–4
–5
60. y = –5x – 2
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
Find the x- and y-intercept of the line.
61. –3.4x + 1.1y = 22.44
What is the graph of the equation?
62. y = –4
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
x
5
–2
–3
–4
–5
63. x = –2
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
64. Write y =
1
x + 8 in standard form using integers.
5
65. A paint store sells exterior paint for $27.75 a gallon and paint rollers for $8.00 each. Write an equation
in standard form for the number of gallons p of paint and rollers r that a customer could buy with $130.
Write an equation for the line that is parallel to the given line and passes through the given point.
66. y =
1
x + 6; (–2, 2)
2
Tell whether the lines for each pair of equations are parallel, perpendicular, or neither.
1
67. y =  x – 10
4
16x – 4y = 24
1
x+5
8
x + 8y = 4
68. y =
1
x – 11
2
9x – 18y = –15
69. y =
Write the equation of a line that is perpendicular to the given line and that passes through the given
point.
70. y =
5
5
x  ; (–4, 5)
8
2
Graph the inequality.
71.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
1
2
3
4
5
x
72.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
x
5
–2
–3
–4
–5
73. An electronics store makes a profit of $72 for every television sold and $90 for every computer sold. The
manager’s target is to make at least $360 a day on sales from televisions and computers. Write a linear
inequality and graph the solutions. What are three possible solutions to the problem?
In the diagram below, what is the relationship between the number of triangles and the perimeter of
the figure they form?
5
7
7
5
1 triangle
7
5
7
5
2 triangles
7
7
5
5
3 triangles
____ 74. Which of the following represents the above relationship?
a.
b.
The perimeter, P, is equal to the length of the base of one triangle multiplied by the
number of triangles in the figure, n, plus two times the length of another side. The
equation for the perimeter is
.
The perimeter, P, is equal to the length of a side of one triangle multiplied by the
number of triangles in the figure, n, plus the length of the base. The equation for the
perimeter is
.
c.
The perimeter, P, is equal to the length of the base of one triangle multiplied by the
number of triangles in the figure, n, plus the length of another side. The equation for
the perimeter is
.
The perimeter, P, is equal to the length of a side of one triangle multiplied by the
number of triangles in the figure, n, plus two times the length of the base. The
equation for the perimeter is
.
d.
____ 75. Suppose you know the perimeter of
triangles?
a.
b.
c.
d.
Add 10 to the perimeter of
Add 5 to the perimeter of
Add 14 to the perimeter of
Add 7 to the perimeter of
triangles. What would you do to find the perimeter of
triangles
triangles
triangles
triangles
76.
5
7
7
5
1 triangle
7
5
7
5
2 triangles
7
7
5
5
3 triangles
Represent the above relationship by filling in the table below.
Number
of
Triangles
Perimeter
1
2
3
77. Represent the above relationship by drawing a graph.
60
55
50
45
Perimeter
40
35
30
25
20
15
10
5
1
2
3
4
5
Number of Triangles
6
7
78. Represent the relationship between the number of triangles and the perimeter of the figure they form
as an equation. How does this equation relate to the method you would use to find the perimeter of
triangles from the perimeter of
triangles?
Let P= perimeter of the figure, and n= number of triangles.
How does it relate to the table you created in question #76:
79. Will and John played a game of basketball together.
Together, they scored a total of 60 points.
a.
b.
Will scored four times as many as John.
Write the equation.
Solve the equation to find out how many points BOTH players scored.
80. A runner ran at a rate of 0.18 miles per minute for a half hour one day.
at a rate of 0.15 miles per minute for 55 minutes.
The next day, the runner ran
Using the d = rt formula, how far did the runner run altogether?
81. Write the function (linear equation) that is represented by these data points:
x
5
6
7
y
7
9
11
82. Give an example of a relation that IS A FUNCTION, and a relation that IS NOT A FUNCTION.
Justify/explain your answer.
What is an equation of the line?
83.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
5
x
–2
–3
–4
–5
84. Solve
for
.
85. The formula for the surface area of a cylinder is
.
What is the formula solved for h?
Algebra 1 College Prep Midterm REVIEW
Answer Section
1. 2(y + k)
2.
3.
4.
5.
6.
h = 7n
196
60
20486
5
7.
11
8. 11
9.
10. 10
1
, 0.3, 0.4,
,
9
12. Commutative Property of Addition
13. Associative Property of Addition
7
14.  4 g
11.
15.
16.
17.
18.
6 + 4f
$72.31 – $18.15 – $16.03; $38.13
4 m + 8
7.4b2 – 0.4f
4
1
19.
x–
7
7
20.
21. 2
22. 16
23. 19 weeks
24. 13
25. $2.60
26. 3
27. infinitely many solutions
28. no solution
29.
30.
31.
32.
33.
34.
35.
36.
37.
City Express
78
–16.8
40
18 gallons of gas
$34.50
2
38%
38. 13%
39. x > 8

40. m
9
2
41.
42.
–20 –16 –12 –8
–4
0
4
8
12
16
20
43. 126 + 130 + c 450; c 194
44. b > 2
–16
–12
45. x > 30
–8
–4
0
4
8
12
16
0
2
4
6
8
1
3
46.
47. all real numbers
48. no solution
49. –6 < x < 6
–8
–6
–4
–2
50. x < 4 or x > 10
–14 –12 –10 –8
–6
–4
–2
0
2
4
6
8
10
12
14
16
18
20
22
51. 1 < x < 5
–10 –8
52.
–6
–4
–2
0
2
4
6
8
10
–6
–4
–2
0
2
4
6
8
or
–12 –10 –8
money
53.
week
54. The variables are the number of handbags and time. The flat parts of the graph show either where Mandy is
working on a handbag or taking a break. As soon as Mandy finishes a bag, the graph jumps up a level to
show that she has completed one more bag.
2
8
56. 
3
57. y = 2x + 5
58. y=2 x-10
59.
55.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
2
4
6
8
10
x
2
4
6
8
10
x
–4
–6
–8
–10
60.
y
10
8
6
4
2
–10 –8
–6
–4
–2
–2
–4
–6
–8
–10
61. x-intercept is –6.6; y-intercept is 20.4
62.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
1
2
3
4
5
x
63.
y
5
4
3
2
1
–5
–4
–3
–2
–1
–1
1
2
3
4
x
5
–2
–3
–4
–5
64. –x + 5y = 40
65. 27.75p + 8r = 130
1
66. y = x + 3
2
67. perpendicular
68. neither
69. parallel
8
7
70. y =  x 
5
5
71.
y
4
–4
O
–4
4
x
72.
y
4
O
–4
4
x
–4
73.
p
Computer
5
4
3
2
1
0
1
2
3
Television
4
5 s
(5, 2), (3, 3), and (1, 4) are three possible solutions.
74. A
75. B
76.
Number of
Perimeter
Triangles
1
19
2
24
3
29
60
55
50
45
Perimeter
40
35
30
25
20
15
10
5
1
2
3
4
5
6
7
Number of Triangles
77.
78. The equation relating the number of triangles to the perimeter of the figure is
of
in this equation is the same value that must be added to the perimeter of
perimeter of
triangles.
79. a) x+4x=60
b) Will=48, John= 12
80. sd;kjlsf
81. y=2x-3
82. no
3
83. y – 2 =  (x + 5)
8
84.
85.
or
. The coefficient
triangles to get the