solve for the variable by transforming equations · 2017-04-27 · solve for the variable by...

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

2

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)

_____________________________________________________________________________________


3

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.

_____________________________________________________________________________________


4

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)

_____________________________________________________________________________________


5

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

_____________________________________________________________________________________


6

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⋅ __________________________________________________________________________


7

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+ −= ____________________________________________________________________

_____________________________________________________________________________________


8

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) ___________________________________________________________________


9

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)

_________________________________________________________________________________


10

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= −


11

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)

_________________________________________________________________________________


12

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


13

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

_________________________________________________________________________________

_________________________________________________________________________________


14

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__________________________________________________________________


15

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


16

138. y< x + 3

Graph the following systems of inequalities.

139. y – x <2

3x + 2y > – 6

140. y > 2x – 1

y < 2x + 2


17

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⋅ _______________________________________________________________________


18

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 _________________________________________________________________

____________________________________________________________________________________


19

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.


20

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.


21

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:

solve for the variable by transforming equations · 2017-04-27 · solve for the variable by...

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