Download Algebra 1 First Semester Final Exam Study Guide 1. Write an

Algebra 1 First Semester Final Exam Study Guide
1. Write an expression for the following. Define your own variables:
 Ten more than the sum of a number and its opposite.
 Twice a number added to 7.
2. Evaluate the expression for a = 2 and b = 6:
 (a3 + b2) ÷ a
 2(7a – b)
3. Simplify:
 3[4(8 – 2) + 5]
 4 + 3(15 – 23)
 5(32 + 2) – 2(62 – 52)


3
1
 3 1
4
2
1  3
  
4  4
 |3.7 – (-6.8)|
 8 – (-4) – (-5)

3
4
3

7
 -(-4)3
4. Write 16% as a decimal and as a fraction in lowest terms.
5. Write
7
as a percent.
10
6. Simplify each expression. Justify your steps!

1
12n  8
2
 4 x  32 x  5

7. Write an expression for the following phrases. Define your own variables.
 “5 times the quantity x plus 6”
 “-8 times the quantity 4 decreased by w”
8. Name the property represented by the following:
 8  7  6  8  7  6
 16 + 0 = 16
 (x) + (-x) = 0

23
  1
32
9. Fill in the reasons for the following “proof”:
8w – 4(7 – w) =
8w – 28 + 4w
8w + (-28) + 4w
8w + 4w + (-28)
12w + (-28)
____________________________________
____________________________________
____________________________________
____________________________________
10. Simplify.
 160
 3-3

9
2 1
 -6 ∙ 3-4

a 2 b 1
cd 3
11. Which set(s) of numbers do the following numbers belong?
 7_____________________________________________________________________
 -7.34__________________________________________________________________
12. Order the numbers from least to greatest:
5 1 2
 , ,
6 2 3
13. Compare:
|-18| _____ |-17|
14. Simplify:
-7 + (-4) = __________
15. A diver dives 47 ft below the surface of the water and then rises 12 ft. Use addition to find the
diver’s depth.
16. Simplify:
2 – (-9) = __________
17. Simplify:
|-11 – (-8)| = ___________
x

y

z for x = 3, y = -4, and z = -6.
18. Evaluate
19. Evaluate a  c  c for a = -2 and c = -4.
20. Evaluate m  p   n for m = -4, n = 3, and p = -1.
21. Simplify  5 1 = ____________
4
2
22. Simplify  5  3 = ____________
3
23. Evaluate 8  6 x  4 y  
3z
for x = -2, y = 3, and z = 3.5.
y
3
r
1
24. Evaluate
for r   and s  .
4
8
 3s
25.
26.
27.
28.
Write 0.09 as a percent.______________________
Write 250% as a decimal_____________________
Write 16% as a fraction in simplest form____________________
Write an algebraic expression for each statement. You may choose your own variables:
 a number minus 11________________________
 The sum of 13 and twice a number________________________
29. Write an equation that models the situation (you do not have to solve!):
 The total length of rope, in feet, used to put up tents is 60 times the number of tents.
30. Write an algebraic expression for the statement:
 The quotient of 3 times b and 4.5______________________
 2 times the quantity 3 times c plus 9________________________


2
31. Simplify: 10  4  8  8  9
32. Simplify: 4  8  1  5  8
3
33. You stopped on your way to basketball practice and bought four bottles of Powerade for $.69 each.
How much did you spend in all?
34. Simplify:
2
5w  10 
5
35. Fill in the reasons for the problem:
1
4 x  8  3x
4
 x  2  3x
 x  (2)  3 x
 x  3 x  (2)
 4 x  (2)
 4x  2
36. Simplify: 9  4t  6 y  3t  10

Given
_____________________________
_____________________________
_____________________________
_____________________________
Definition of Subtraction
4r  8  52r  1
37. Simplify, and justify your steps:
38. Name the property that justifies each equation:
 (-7 + 4) + 1 = -7 + (4 + 1) ______________________________________
 9(7.3) = 7.3(9)
______________________________________
 -0.5 ∙ (-2) = 1
______________________________________
3 2 7
39. Simplify: 2 x z
7 s 0 t 5
40. Simplify: 1 2
2 m
4 3 2
41. Evaluate 2 r s for r = -3 and s = 5.
1
 1 
1
42. Simplify: 2   2  5 2 
3
2 
43. Write 9,040,000,000 in scientific notation:_________________________
44. Write 4.8 x 10-3 in standard notation:__________________________

5
2

6

x y x y
45. Simplify:
46. Simplify, and write your answer in scientific notation:
47. Simplify:
c  c
2 3
12
48. Simplify:
32 m 3t 6
35 m 7 t 5
49. Simplify:
 4n 
 2
 2n 
50. Solve each equation:
m
7 3
9
 5z  9  21
1
x  8  3

2

3
0.7 10 0.3 10 
12
8
42a  2  17  15
 0.52 x  4  17
1
51. Solve A  bh for h.
2
52. Solve 5r  3  2r  6 for r. Justify your steps!

53. Solve
54. Solve
55. Solve
56. Solve
57. Solve
2
3 3
a   a for a. Justify your steps!
3
4 4
7  2n  n  14 for n. Justify your steps!
4s  12  5s  51 for s. Justify your steps!
k 7

for k.
3 10
x 3
 for x.
15 4
m
 7  3 for m. Justify your steps!
9
59. Solve 5z  9  21 for z. Justify your steps!
60. Solve  c  2  5 for c. Justify your steps!
58. Solve
61. To mail a first class letter, the US Postal Service charges $.34 for the first ounce and $.21 for each
additional ounce. It costs $1.18 to mail your letter. How many ounces does
your letter weigh?
62. Solve  4x  32x  5  31 for x. Justify your steps!
63. Solve 2b  6  3b  14 for b. Justify your steps!
1
12n  8  26 for n. Justify your steps!
2
1
1
65. Solve x  for x. Justify your steps!
3
2
66. Solve 3n  1  5n  3  2n for n. Justify your steps!
2
67. Solve 6 x  3  4 x  2 for x. Justify your steps!
3
64. Solve
68. A pound of coffee costs $14.99. What is the cost per ounce?
z 7

4 8
s 7
70. Solve 
3 10
3 x3
71. Solve 
6
8
x  2 x 1

72. Solve
6
12
69. Solve
73. Your car averages 18 miles per gallon on the highway. If gas costs $3.14 per gallon, how much
does it cost in dollars per mile to drive your car on the highway?
74. May rides her bike the same distance that Leah walks. May rides her bike 10 mph faster than Leah
walks. If it takes May 1 hour and Leah 3 hours to travel that distance, how fast does each travel?
75. The length of a rectangle is 4 inches greater than the width. The perimeter of the rectangle is 24
inches. Find the dimensions of the rectangle.
76. Find three consecutive integers whose sum is 126.
77. Find the percent of change:
 $90 to $84.50
 58 to 76
78. The United States imported 6,909,000 barrels of oil per day in 1980. In 2000, the United States
imported 11,459,000 barrels of oil per day. What is the percent of change from 1980 to 2000?
79. In 1990, Atlanta, GA, failed to meet air quality standards on 42 days. In 1999, Atlanta failed to
meet air quality standards on 61 days. What is the percent of change from 1990 to 1999?
80. Find the greatest possible error and the percent error for a measurement of 16 inches.
81. Are these numbers solutions of n(n – 3) < 54?
 9
 3
 10
82. Write an inequality to model the situation: A bus can seat at most 48 students.
83. Solve w – 3 + 1 ≥ 9 and graph the solution.
1
 1 and graph the solution.
2
85. Solve  7  2q and graph the solution.
84. Solve h 
86.
87.
88.
89.
Solve -18d < 12 and graph the solution.
Solve  2h  2  14 and graph the solution.
Solve 32  r   15  2r and graph the solution.
Are the following numbers a solution of 7 x  14  6x  16 ?
 0
 -4
 2
90. Solve 7  b  13 and graph its solution.
91. Solve 2v 
92. Solve
93. Solve
94. Solve
95. Solve
96. Solve
3
1
 1 and graph its solution.
4
4
a
 1 and graph its solution.
4
1
1
 p  and graph its solution.
9
3
2c  4  10  c
1
2t  8  4  6t
2
3
3 1
k  k
4
4 4
34 g  6  6g  2
 6  9  3 y  6 and graph the solution.
7  2a  9 or  4a  8 and graph the solution.
97. Solve
98. Solve
99. Solve
100. The crowd that heard the President speak was estimated to be 10,000 people. The actual crowd
could be 750 people more or less than this. What are the possible values for the actual crowd size
(written as an inequality)?
101. Solve | 2k | 8 and graph its solution.
102. Solve d  25  13 .
103. Solve  4 7  d  44
104. Solve 3 b  4  21  27 and graph its solution.
105. The average number of cucumber seeds in a package is 25. The number of seeds in the package
can vary by three. Find the range of acceptable numbers of seeds in each package.
106. Members of the track team can run 400m in an average time of 58.2 s. The fastest and slowest
times vary from the average by 6.4 s. Find the range of times for the track team.
107. Leona was in a golf tournament last week. All four of her rounds of golf were within 2 strokes of
par. If par was 72, find the range of scores that Leona could have shot for each
round of the golf
tournament.
108.
109.



Solve  2 h  2  2 and graph the solution.
Find the slope of the following:
of a line through (3,-6) and (-7,-1)
of the line y = -5
of the line:
 of the line x = 3
 of the line y – 3 = 5(x + 3)
 of the line y = ½ x – 4
110. Write the equation of the line in slope-intercept form for the following:
 with slope 2 and y-intercept of -5
 through (1,-3) and with slope of ½
 through (0,1) and (-3,0)
111. Write the equation in standard form of the line that goes through (-1,-4) and has slope of 1/3.
(start with point-slope form, then go to slope-intercept, then to standard)
112. Write the equation of the line in slope-intercept form for the following:
 with slope -3 and y-intercept of 1/2
 through (0,3) and with slope of 3/4
 through (2,1) and (1,0)
113. Write the equation in standard form of the line that goes through (1,4) and has slope of 3. (start
with point-slope form, then go to slope-intercept, then to standard)
114. Find the rate of change for the data given. What does the rate of change mean?
People
Cost ($)
2
7.90
3
11.85
4
15.80
5
19.75
6
23.70
115. What is the slope between (5,6) and (3,2)?
116. What is the slope and the y-intercept of y = -x – 7?
117. Write the slope-intercept form of the line shown in the graph.
2
3
119. Graph y  4 x  3
118. Graph y   x  1
120. What is the x-intercept and the y-intercept of -6x + 3y = -9?
121. Is x = -2 a horizontal, vertical, or sloped line?
122. Graph x + y = 2
123. Graph y = 3
124. Write an equation in point-slope form, slope-intercept form, and standard form for the line that
passes through (-1,0) and (1,2).
 point-slope form:
 slope-intercept form:
 standard form:
125. Write an equation in standard form for a line that passes through (4,2) with a slope of 
5
3
126. Write an equation in slope-intercept form for a line with slope -2 and y-intercept 4.
127. Write an equation in slope-intercept form for a line that passes through (6,-3) and (-2,-3).
128. Suppose an elevator is 400 feet above the ground. It descends at a steady rate. After 15 seconds,
it is 250 feet above the ground. Write a linear function for the height of the elevator as a function of
time. Graph the function.
3

 y  4 x  4
129. Are the following lines parallel, perpendicular, or neither: 
y   1 x  4

4
2 x  y  2
130. Are the following lines parallel, perpendicular, or neither: 
2 x  y  5
131. Write an equation for the line parallel to y = 5x – 2 through (2,-1).
132. Write an equation for the line perpendicular to y = -3x + 7 through (3,5).
133. You start a pet-washing service. You spend $30 on supplies. You plan to charge $5 to wash each
pet. Write an equation to relate your profit y to the number of pets you wash x.
134. A car rental company charges $19.95 per day plus $.15 per mile. Calculate the cost in dollars to
travel 250 miles over a 2-day period.
135. Tara’s car travels about 25 miles on one gallon of gas. She has between 10 and 12 gallons of gas
in the tank. List the following:
 Independent quantity_______________________________________________________
 Dependent quantity________________________________________________________
 Domain_________________________________________________________________
 Range__________________________________________________________________
136. Are the following relations functions?
 [(3,7),(3,8),(3,-2),(3,4),(3,1)]
__________________________________
 [(0.04,0.2),(0.2,1),(1,5),(5,25)]
__________________________________
 [(4,2),(1,1),(0,0),(1,-1),(4,-2)]
__________________________________
137. Find the range for the function f(x) = 5x – 2 with the domain {-5,-1,0,2,10}.
138. Model the rule f(x) = 2x – 7 with a table of values and a graph.
139. Model the rule f ( x) 
1 2
x with a table of values and a graph.
4
140. Write a function rule for the table:
Ears of Corn Total Cost
1
$0.20
2
$0.40
3
$0.60
4
$0.80
141. Sketch a graph to show the number of apples on a tree over one year. Label each section of the
graph.
142. Find the range of the function y = 6x – 5 for the domain {-4,-1,0,3}.
143. Is the relation [(1,2),(2,3),(3,4),(4,5),(5,6)] a function?
144. Find the range of the function f(x) = |x| - 2 for the domain {-4,-1,0,3}.
145. Graph the function y 
2
x.
3
146. Is the relation [(5,2),(1,3),(4,7),(5,6),(0,4)] a function?
147. Graph the function y  x 2  3x  1 .
148. Write the function rule for the table:
x
f(x)
-3
-1
-1
1
1
3
3
5
149. Graph the direct variation that includes the point (5,4). Write the equation.
150. Find the constant of variation for the inverse variation in which y = 10 and x = 7.
151. Find the second and fifth terms of the sequence with the rule: A(n) = 22 + (n – 1)11
152. Find the range for the function y 
1 2
x with a domain of {-4,-2,0,2,4}.
4
153. A supermarket sells string beans for $2 a pound. The function A(n) = 2n relates the total cost of
string beans to the number of pounds n bought. Is the data continuous or discrete?
154. Graph the function y  x  4
155. Graph the function y 
1
x
2
156. The amount of blood in a person’s body varies directly with body weight. A person who weighs
160 lb has about 5 qt of blood.
 What is the constant of variation?__________________________
 Write an equation relating quarts of blood to weight.________________________
 Estimate the number of quarts of blood in your body._________________________