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Algebra 1 CP Semester 1 Review 2009
Name:__________________________Hr_____
I. Story Problems
1. A salesman gets a commission of $2.15 on each item sold. One morning he sold 23 calculators
and 5 pocket radios. Find his commission.
2. A taste test is conducted to see how the product is being received. Of those who
participated, 18 said they preferred the new soft drink, 32 preferred the old soft drink, and
25 could not tell any difference. What is the probability that a person in this survey preferred
the old soft drink?
3. You purchased 8 copies of a poster and paid $90. How much did each poster cost?
4. You played tennis for 30 minutes and burned 245 calories. How many calories did you burn
per minute?
5. You rode your bicycle for 46 days this year. This is 12 days more than last year. How many
days did you ride your bicycle last year?
6. In 3 hours a candy maker can produce 90 boxes that each contains 15 pieces of candy. How
many pieces of candy does the candy maker produce in 12 hours?
7. Regina pays $225 in advance on her account at the athletic club. Each time he uses the club,
$5.50 is deducted from the account. Write a linear function that models the value remaining in
his account after x visits to the club. What is the balance in her account after 13 visits?
25 visits? How many times can she go until she must replenish her account?
8. An employee who receives a weekly salary of $300 and a 6% commission is paid according to
the formula p(s)=0.06s + 300, where s represents the total weekly sales. Find the employee’s
weekly salary for the weekly sales of $150?
Of $900?
Of $1525?
How much would he need to sell to earn $1500 for the week?
9. On January 1, Maria had a savings account balance of $2893 and by April 1, her balance had
increased to $5097. Find Maria’s average savings rate in dollars per month for that period.
10. The cost of a banquet is $150 plus $21 per person attending. Write an equation that models
this situation.
11. Victoria pays $135 in advance on her cell phone account. Each time she uses her phone,
$1.75 is deducted from the account. Write an equation that models this situation. How much
will she have in her account after 30 phone calls?
50 calls?
How many calls can she make
without having to replenish her account?
12. In 1990 the average price of a home in Lake County was $64,000. By 1998 the average price
of a home was $89,000. Write a linear model for the price of a home (in terms of the year, t.
Let t = 0 correspond to 1990). If this pattern continued, what would you expect the cost to be
in 2003?
In 2007?
In 2020?
13. The triangle below has a perimeter of 46. Solve for x.
x
x+ 2
8
14. Write an equation or expression to represent the following verbal statements:
a. a number decreased by five squared
b. the product of a number and 6 is 24
c. three times the sum of x and y
d. the sum of a number squared and 2 is 146
II. Simplifying Expressions
15. -6x + 2x
16. n + 5 – 6n
17. 7x + 2 + x
18. -15y – 3y
19. -4(4c – 5) + 3c
21. 10(x – 5) – (8x + 25)
22.
20. 5 – 2(3x – 4)
36  27 x
9
23. (-3)(-k)
24. (-3)(p)2(p)
25. 22(-x)(-x)2(-x)3
26. (-1)5(y)(y)(y)(y)
27. | 21 |
28. -| 21 |
29. | -21 |
30. -| -21 |
III. Check whether the given number is a solution of the equation, inequality, or system.
31. 16x + 3 = 29 – 3x; x = 2
32. 10x  5  20; x = 2.5
33. 6x – 3y = -15 (-2, 1)
IV. Probability and odds. Use the word MATHEMATICS to answer the following questions.
34. P(choosing an M)
35. odds(choosing A)
36. P(not choosing a vowel)
37. odds(not choosing a vowel)
V. Rewrite each equation in function form (slope-intercept form) if necessary. Then, make an
input/output table with a domain of {–2, -1, 0, 1, 2}.
38. y = -3x –2
39. 7x + y = 13
40. x –2y = 6
Input
Output
Input
Output
Input
Output
VI. Solve each equation for x.
41. -12 + x = -10
42. 4x = 2
44. 14x + 3x  40 = 11
45. 3x  8 = -3x + 4
47. 3(x  9) = 3x + -27
48.
2
(x + 4) = 8
3
43. 5x + 7  2x = 22
46. 40  14x = 6x
49. –3x  38
x
–2  9
4
50. 3x – 25  -8x + 30
51.
53. –6 > 3x + 6
54. -(x – 1)  7x – 15
55.
56. x – 3  7 and x – 9  10
57. -12  3x + 3  18
58. 2x + 5  7 or –2x > 6
59. x + 3 = 10
60. x + 4 = 6
61. 3x – 8 = 13
62. 2x  6 + 2 = 9
52. –2x + 17  21
2
x  -22
3
** DON’T FORGET BOTH ANSWERS FOR ABSOLUTE VALUE EQNS!!
For 63-65, the variables x and y vary directly. Write and solve an equation that relates x and y.
63. x = 6 and y = 96
64. x = 15 and y = 3
65.
x = 10 and y = 33
For 66-69 evaluate the expressions when x = 5, y = 3 and z = 9:
66. 2.5x
68. y + z(x + y)2
67. 3x + 7y
69.
xy
x y
VII. For each equation, find the x and y intercepts.
1
xy=5
2
70. 2x + 10y = -30
71. y = -3
72.
x-int = ______
x-int = ______
x-int = ______
y-int = ______
y-int = ______
y-int = ______
VIII. Find the slope of the line passing through the points.
73. (-5, 5) , (-7, -6)
74. (3, 12) , (3, -10)
75. (3, 4) , (7, 4)
X. Find the slope and y-intercept of each equation.
76. y = -2x  5
77. 2x + 3y = 9
78. y = -5
IX. GRAPHING
Graph the numbers on the number line. Then write the numbers in increasing order.
79.
5.2, -3.7, -0.1, 2.5
-4 -3 -2 -1 0 1
2 3 4 5
80.
0, -6, 2, -3.5, 1.9
-7 -6 -5 -4 -3 -2 -1 0 1 2 3
Graph the equations on the given coordinate planes.
81. y =
1
x6
3
82. y = -3x + 2
y
y
x
83. 6x  12y = 36
x
84. 3x  4y = -12
y
y
x-int _____
x-int _____
y-int _____
x
85. x = 2
x
86. y=-5
y
y
x
x
y-int _____
Graph each linear inequality.
87. y > 3
88. y < 2x – 4
y
y
x
x
X. Writing equations of the line.
Write each problem in slope-intercept form and standard form...
1
89. m = 5; (3, -5)
90. m = ; (-12, -7)
91. (2, 5) ; (3, 3)
4
92. (-5, 3) ; (-10, 2)
1
94. - x  2y = 6
3
93. 3x  4y + 12 = 2
95. slope 9 and y-intercept 3
96. Write the equation of the line parallel to the line y = -2x + 7 thru the point (8, -1).
97. Write the equation of the line parallel to the line y =
1
x + 7 thru the point (9, 5)
3
98. Write the equation of the line perpendicular to the line y =
2
x – 8 thru the point (12, 4).
3
Write the equation of each line given two points on the line in point-slope form.
99. (8, -8), (10, 6)
100. (-7, -4), (-2, -7)
Write the equations of the horizontal and vertical lines that pass through the point.
1
101. (-4, 8)
102. (5, )
2
XI. Write the ordered pairs that correspond to the points labeled A, B, C, and D in the
coordinate plane. Label the quadrants on the graph.
y
103. A= _______
A
C


D
B

104. B= _______
x
105. C= _______
106. D= _______
XII. 107. The data in the table shows the forearm lengths and foot lengths (without shoes) of
12 students in an algebra class.
Forearm
Length
22 20 24 21 25 18 20 23 24 20 25 23
(cm)
Foot
Length
24 19 24 23 23 18 21 23 25 22 25 22
(cm)
A) Make a scatter plot of the data.
B) What type of correlation does the data show?
C) Draw the best fit line
D) Write the equation of the best-fit line
(use your calculator).
E) Use the best-fit equation to estimate the foot length of a student whose forearm length is
17cm.
XIII. Graph the solution of each inequality. Label the number line!
108. -3  x
109. x  -4 and x  3
110. x  -1 or x  3
111. –2  x  3
112. x  -6 or x  -8
113. Use the following set of data to find the information below:
6, 9, 9, 8, 4, 3, 8, 9, 4, 9, 7
a. Mean:
b. Median:
d. Range:
e. Make a stem-and-leaf plot
114. Evaluate the function when x = 9 and x = -5:
C. Mode:
f (x )  8  2x