Cantwell Sacred Heart of Mary High School
Math Department
Study Guide for the Algebra 1 (or higher) Placement Test
Name: ______________________________________________ Date: _______________________
School: ___________________________________________________________________________
Solve for the variable by transforming equations:
1. 2y + 3 = 9
_____________________________________________________________________________________
2. 1
3 52x− =
_____________________________________________________________________________________
3. 2
43
x−=
_____________________________________________________________________________________
4. 4w – w = - 12
_____________________________________________________________________________________
5. 6(x – 4) + 5 = 11
_____________________________________________________________________________________
6. 10n = 36 – 2n
_____________________________________________________________________________________
7. 2
125x x+ =
_____________________________________________________________________________________
Simplify:
8. 2x – y + 3x – 2y ______________________________________________________________________
9. Add 2 2 2 22 5 6 8 6x xy y and x xy y+ − + +
_____________________________________________________________________________________
Add.
10. (4c2
- 3cd – 5d2
) + ( -c2
+ 6cd – 2d2
)
_____________________________________________________________________________________
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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11. 2 2 2(6 2 ) ( 2 5 )a ab a ab b− + − + −
_____________________________________________________________________________________
Subtract.
12. (4c2
- 3cd – 5d2
) - (-c2
+ 6cd – 2d2
)
_____________________________________________________________________________________
13. 2 2 2(6 2 ) ( 2 5 )a ab a ab b− − − + −
_____________________________________________________________________________________
Simplify.
14. 3 4(4 )(3 )x x ______________________________________________________________________
15. 2 2(6 )(2 (3 )x y xy x _________________________________________________________________
16. 2 3 3( )( 5 )( 2 )a b ab ab− − − ____________________________________________________________
17.
2 3 26 20
5 3
h k hk
_________________________________________________________________
18. 2 22 1
(3 )3 2
y y y
_______________________________________________________________
19. 5 3 3(3 )(4 ) (5 )(2 )x x x x− _____________________________________________________________
20. ( )325a __________________________________________________________________________
21. ( )256y− _________________________________________________________________________
Simplify.
22. ( )2 2 24 5 3 4x y x xy y− + _____________________________________________________________
23. ( )2 2 216 12 9
3x y x xy y− + ____________________________________________________________
24. ( )2 2 2 2110 6 8
2x y x xy y− + ___________________________________________________________
25. 2x(x – 3) + 3x(x + 2)
_____________________________________________________________________________________
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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Solve.
26. y(3-2y) + 2(y2
-6) = 0
_____________________________________________________________________________________
27. 4(3a – 1) – 5(1 – a) = 8
_____________________________________________________________________________________
Simplify.
28. (2a + 3)(51 – 1)
_____________________________________________________________________________________
29. (x – 1)(2x2
+ 3x + 4)
_____________________________________________________________________________________
30. (3x – 4)(2x2
- x + 1)
_____________________________________________________________________________________
Multiply. Arrange the terms in each factor in order of decreasing degree of one of
the variables.
31. (4 + x)(x2
- 4x + 3)
_____________________________________________________________________________________
32. (y – 3x)(2x2
+ y2
- 2xy)
____________________________________________________________________________________
Solve. Explain your answer
33. Two jets leave St. Louis at 8:00 A.M., one flying east at a speed km/h greater than the other, which
is traveling west. At 10:00 A.M. the planes are 2480 km apart. Find their speeds.
_____________________________________________________________________________________
34. A rectangular flower garden is 8 ft longer than it is wide. It is surrounded by a brick walk 2 ft wide.
The area of the walk is 176 ft2
. Find the dimensions of the flower garden.
_____________________________________________________________________________________
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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Simplify.
35.
2 3
3 3 3
x yz
x y z___________________________________________________________________________
36.
2 3
2
6
9
x y
xy
− __________________________________________________________________________
37. ( )3
3
2
2
x
x___________________________________________________________________________
38. ( )7
7
xy
xy
−___________________________________________________________________________
Find the missing factor.
39. 8t4
= (2t)(____) ___________________________________________________________________
40. ( )2 4 228 7 (____)x y x y− = ___________________________________________________________
Divide. Assume that no denominator equals zero.
41.
28 12
4
xy x
x
−_______________________________________________________________________
42.
2 26 12
4
ab a b
ab
−
_______________________________________________________________________
Simplify.
43. (a – 2b)(a + b)
_____________________________________________________________________________________
44. (x + 3y)(x + 2y)
_____________________________________________________________________________________
45. 3 3( 2 )( 1)x x x− +
_____________________________________________________________________________________
46. (x – 5)(x + 5)
_____________________________________________________________________________________
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47. (2x – 6y)(2x + 6y)
_____________________________________________________________________________________
Factor.
48. b2
- 16 ___________________________________________________________________________
49. 9a2
- 25b2
________________________________________________________________________
Simplify. Write each square as a trinomial.
50. (x + 5)2
_____________________________________________________________________________________
51. (ab – 3) 2
_____________________________________________________________________________________
Decide whether each trinomial is a perfect square. If it is, factor it. If it is not,
write not a perfect square.
52. k2
+ 10k + 25
_____________________________________________________________________________________
53. y2
- 8y + 16
_____________________________________________________________________________________
54. 81k2
+ 180k + 100
_____________________________________________________________________________________
Factor. Check by multiplying the factors. If the polynomial is not factorable, write
prime.
55. a2
+ 10a + 30
_____________________________________________________________________________________
56. x2
- 19x + 60
_____________________________________________________________________________________
57. a2
+ 12a – 45
_____________________________________________________________________________________
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58. y2
- 14y – 72
_____________________________________________________________________________________
59. 2x2
- 3x – 9
_____________________________________________________________________________________
60. 4u2
- 8u – 5
_____________________________________________________________________________________
61. ax – 2x + ay – 2y
_____________________________________________________________________________________
Solve:
62. (x – 1)(x + 3) = 0
_____________________________________________________________________________________
63. 2x(x – 10) = 0
_____________________________________________________________________________________
64. x2
- 7x + 12 = 0
_____________________________________________________________________________________
65. Find two consecutive positive odd integers whose product is 143.
_____________________________________________________________________________________
Simplify. Give any restrictions on the variables.
66. 3 3
9
x y−_________________________________________________________________________
67.
2
2
5 36
81
a a
a
− −−
______________________________________________________________________
68. ( )( )( ) ( )
7 4
7 2
x x
x x
− −
− +____________________________________________________________________
_____________________________________________________________________________________
Multiply. Express each product in simplest form.
69.
3
2
8
4
x
x⋅ __________________________________________________________________________
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70.
2 2
2
2
5 4
de f
e f d⋅ ________________________________________________________________________
71. 2 2
3 2
9
x x
x x
−⋅
−______________________________________________________________________
72.
2
4
a
____________________________________________________________________________
73.
234
5
b −
_________________________________________________________________________
Divide. Give your answers in simplest form.
74. 4
ab a
b÷ ___________________________________________________________________________
75. 2
3 1
4 12
n
m mn÷ ______________________________________________________________________
76.
2 2
2 2
9 6
4 6
x x x
x x x
− − −÷
− + −________________________________________________________________
_____________________________________________________________________________________
Simplify.
77. 4
15 15
x x+ __________________________________________________________________________
78. 2
1 5
3 6x x+ __________________________________________________________________________
Solve.
79. 3
30 5
x= ___________________________________________________________________________
80. 1 2
6 3
x−= _________________________________________________________________________
81. 3 4 9
3 5
x x+ −= ____________________________________________________________________
_____________________________________________________________________________________
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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82. 5
2 3 3
w w+ = ________________________________________________________________________
_____________________________________________________________________________________
83. 3 3
10 5 2
n n+ = ________________________________________________________________________
_____________________________________________________________________________________
84. 1 1
25 3
x x+ −− =− ___________________________________________________________________
_____________________________________________________________________________________
85. 2 1 3
4 4x+ = _________________________________________________________________________
_____________________________________________________________________________________
86. 24 is 20% of what number?___________________________________________________________
87. What percent of 60 is 45?____________________________________________________________
Simplify.
88. 13− _______________________________________________________________________________
89. 05 ________________________________________________________________________________
90. 3(3 )x −
____________________________________________________________________________
91. ( ) 32ab−−
_________________________________________________________________________
Simplify. Write your answers in scientific notation.
92.
6
2
4.8 10
3.0 10
××
_________________________________________________________________________
93. ( )( )4 24 10 7 10−× × ________________________________________________________________
State whether each ordered pair is a solution of the given equation. Show why or
why not.
94. x – y = 5
a. (6, 1) ___________________________________________________________________
b. (3, - 2) ___________________________________________________________________
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95. 2m – 3n = 6
a. (6, 2) ___________________________________________________________________
b. (9, 4) ___________________________________________________________________
Solve for y in terms of x.
96. 3x + y = 6___________________________________________________________________
97. xy + x = 4___________________________________________________________________
Solve each equation if x and y are whole numbers.
98. 3x + y = 7___________________________________________________________________
99. xy + 2 = 9___________________________________________________________________
Graph each equation.
100. x – y = 4
101. 2x – 3y = 6
Find the slope of the line through the given points.
102. (5, – 6), (2, – 4)
_________________________________________________________________________________
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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103. (1, 4) (– 3, 0)
_________________________________________________________________________________
Find the slope of each line.
104. 6x + 2y = 3
_________________________________________________________________________________
105. 2x – 5y = 10
_________________________________________________________________________________
State the slope and the y-intercept.
106. y = - x + 5
_________________________________________________________________________________
107. 3x + 2y = 6
_________________________________________________________________________________
Graph the following equations.
108. y = - x + 3
109. 2
43
y x= −
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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State whether the lines whose equations are given are parallel. State why or why
not.
110. 2x – y = 5
2x – y = 8
_________________________________________________________________________________
111. 2x – y = 6
2y – x = 6
_________________________________________________________________________________
Write an equation in slope-intercept form of each line described.
112. slope 2; passes through (3, - 1)
_________________________________________________________________________________
113. slope -1, passes through (3, 1)
_________________________________________________________________________________
114. (4, 5), (2, 1)
_________________________________________________________________________________
115. (- 2, 8), (1, 2)
_________________________________________________________________________________
116. y – intercept – 1; x – intercept 4
_________________________________________________________________________________
Find the values for each given function with the set of real numbers as the
doman.
117. f(x) = 3x – 2 a. f(2) b. f(-2) c. f(-4)
_________________________________________________________________________________
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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118. g(x) = x2
- 1 a. g(4) b. g(-4) c. g(0)
_________________________________________________________________________________
Graph each linear function.
119. f(x) = - x + 3
120. g(x) = 5
Find the vertex and axis of symmetry of the graph of each equation. Then use the
vertex and at least four other points to graph the equation.
121. y = 2 - x2
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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122. y = x2
- 3x
Systems of equations.
Solve by the graphing method.
123. x – y = 3
x + y = 5
Solve by the substitution method:
124. y = x + 2
x + y = 6
_________________________________________________________________________________
_________________________________________________________________________________
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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Solve by elimination
125. x + y = 4
2x + y = 5
_________________________________________________________________________________
_________________________________________________________________________________
126. 2x – y = 1
3x + 2y = - 2
_________________________________________________________________________________
_________________________________________________________________________________
Solve each inequality. Graph the solution set.
127. 2 3x− ≥ _____________________________________________________________________
128. 6 2 3b b− > − ________________________________________________________________
129. 2r – 3<3r + 1__________________________________________________________________
130. x – 1< - 4 or x – 1 > 5____________________________________________________________
131. -3< y + 1 ≤ 2__________________________________________________________________
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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Solve.
132. |x + 2|= 6 ______________________________________________________________________
133. |x – 5| = 2 _____________________________________________________________________
Solve and graph the solution set.
134. |x + 2|≤ 4____________________________________________________________________
135. |t – 2|> 3______________________________________________________________________
Graph the following inequalities.
136. 2x – y ≥ - 4
137. y > 3
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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138. y< x + 3
Graph the following systems of inequalities.
139. y – x <2
3x + 2y > – 6
140. y > 2x – 1
y < 2x + 2
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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Find the indicated square root.
141. 144
625___________________________________________________________________________
142. 200
162− _________________________________________________________________________
143. 50
72± __________________________________________________________________________
Simplify. Leave your answers in simplest radical form.
144. 8 50 ___________________________________________________________________________
145. 4 98 ___________________________________________________________________________
146. 281x __________________________________________________________________________
147. 2 2121x y− ______________________________________________________________________
148.
3 2
2
32
2
m n
mn_______________________________________________________________________
Solve.
149. x2
= 16__________________________________________________________________________
150. x2
– 9 = 0 ________________________________________________________________________
151. 0 = 45x2
– 125____________________________________________________________________
Use the Pythagorean Theorem to solve for the missing side.
152. a = 3, b = 4, c = ? __________________________________________________________________
153. a = 7, b = ?, c = 13__________________________________________________________________
154. a = ?, b = 16, c = 20. _______________________________________________________________
Simplify.
155. 6 2 3 2⋅ ______________________________________________________________________
156. 11 99⋅ ________________________________________________________________________
157. 5 3
3 20⋅ _______________________________________________________________________
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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158. 3
5___________________________________________________________________________
159. 1
6___________________________________________________________________________
160. 1 21 46 3⋅ _____________________________________________________________________
161. 3 10 7 10− + __________________________________________________________________
162. 5 13 3 2 2 13 8 2− + + ________________________________________________________
163. 4x = _________________________________________________________________________
164. 12 3a= _______________________________________________________________________
165. 3 2 7x− = ______________________________________________________________________
166. 25 36 2m m− = __________________________________________________________________
167. 5 3
47
c−= _____________________________________________________________________
Solve. Express irrational solutions in simplest radical form. If the equation has no
solution write No solution.
168. 5x2
= 125_________________________________________________________________________
169.2x2
= 18 _________________________________________________________________________
170. x2
= 25
36__________________________________________________________________________
171. (x – 3)2
= 0________________________________________________________________________
172. 3x2
- 9 = 33 ______________________________________________________________________
173. 2(x + 3)2
- 4 = 68 _________________________________________________________________
Use the Quadratic Formula to solve each equation. Give any irrational roots in
simplest radical form.
174. 3x2
+ 5x – 2 = 0 _________________________________________________________________
____________________________________________________________________________________
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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175. x2
+ 3x – 10 = 0 _________________________________________________________________
____________________________________________________________________________________
176. 2x2
= 8x – 5 _________________________________________________________________
____________________________________________________________________________________
177. 3x2
+ 2x = 2 _________________________________________________________________
____________________________________________________________________________________
178. A landscaper wants to design a formal garden which is rectangular. The length will be 6m longer
than the width. If the area of the garden is to be 135 m2
, find the length and width. Draw a diagram to
illustrate the solution.
___________________________________________________________________________________
____________________________________________________________________________________
Diagram:
Geometry
179. Find the area of the triangle in square feet.
__________________________________
__________________________________
180. What is the volume of a cube that has an edge of 3 centimeters?
________________________________________________________________________________
181. The perimeters of the two rectangles are equal. What is the width of the second rectangle?
_______________________________
_______________________________
_______________________________
3.5 ft.
4 ft.
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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182. A shoe box is most like a
A. Cone
B. Cylinder
C. Rectangular Prism
D. Sphere
183. Which item is most like a cylinder?
A. basketball
B. box of cookies
C. can of soup
D. desk
184. The strings of a guitar are most like
the following types of line segments.
a. parallel
b. intersecting
c. collinear
d. perpendicular
For questions 185-189
Using the diagram describe the
following:
185. A point:
186. A line:
187. The point where two lines intersect:
188. Three collinear points:
189. The point where a line and a plane
intersect.
CSHM Study Guide for Algebra 1 Placement Test Spring 2017
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Vocabulary. Define the following
terms. Try to give answers that are
not straight textbook or internet
answers
190. Equation:
191. Expression:
192. Term:
193. Power:
194. Exponent
195. Coefficient:
196. Factor:
197. Slope:
198. Variable:
199. Simplify:
200. Root:
201: Zeros (of a quadratic equation):
202. Solution:
203. Absolute Value:
204. Outlier:
205. Vertical line:
206. Horizontal line: