Students Currently in Algebra 2
Maine East Math Placement Exam
Review Problems
NO CALCULATOR!
1) Solve: 4  3x  5  2   x  8  6 x
2) Solve:
1
1
1
x  x
3
4
6
3) The perimeter of a rectangle is 72 cm. The base is three times the height.
Find the area of the rectangle.
4) Find the base of a triangle with a height of 10 cm and an area of 100 cm 2 .
5) Find the height of a parallelogram with a base of 15 cm and an area of 300 cm 2 .
6) The circumference of a circle is 10 cm. Find the area of the circle.
7) A trapezoid has an area of 20 cm 2 and a height of 2 cm. One base is three times the other base.
Find the length of each base.
8) Find the product and report the answer with appropriate units of measure.
 3600 miles  5280 feet  1 hour  1 minute 





 1 hour  1 mile  60 minutes  60 seconds 
9) Convert 360 feet per hour into yards per minute.
10) The width of a water molecule is 0.000000025 meters. Convert this to scientific notation.
11) The distance from Earth to the Andromeda Galaxy is about 18,900,000,000,000 kilometers.
Convert this to scientific notation.
12) Red light has a wavelength of 750 nanometers which is the same as 750 109 meters.
Convert this to scientific notation.
13) If f  x    x2  3x  5 , find f  2 
14) If f  x   x6  x4  x2 , find f  2 
2
15) If f  x    x 2  x  5 , find f  6
3
16) f  x  
x4
3
If f  x   5 , then find x.
17) Determine which of the following represent functions.
D)
A)
x
y
B)
-5
-6
-4
-4
-3
-2
0
-1
3
-2
1,2 ,  1,2 , 3,4
E)
2
C) y  x  5  3
18) Solve for b1: A 
1
1
 b1  b2  h
2
1
19) Solve for h: V   r 2 h
3
20) Solve for h: S  2 rh  2 r 2
21) Solve and graph: 6 x  3  15
22) Solve and graph: 2 x  7  11
23) Solve and graph: 3x  2  8
24) Tell which line is steeper.
Line 1 through  5,0  and
Line 2 through  0, 4  and
3,4
1,6
25) Tell whether the lines are parallel, perpendicular, or neither.
A) Line 1 through 1,5  and  4, 2
Line 2 through  3,0 and
 2, 7 
B) Line 1 through  2, 2  and
Line 2 through  4, 5 and
 2,7 
 5,1
 1 1 
 1 1 
26) Find the slope of the line that contains  ,  and  ,  .
2 3 
 4 6
3
27) A line has a slope of and passes through  2,3 and  6, k  . Find the value of k.
4
28) Graph the following three lines.
2
A) y   x  1
B) x  5
3
C) y  3
3
5
7
29) Write an equation of the line that passes through  3, 4  and has a slope of
30) Write an equation of the line that passes through 1,5  and  4, 2  .
2
.
3
31) Write an equation of the line that passes through  3,2 and is…
A) Perpendicular to the line 3 x  y  2
B) Parallel to the line 3 x  y  2
32) The force, F, of a spring varies directly with its displacement, x.
If a force of 20 lb is applied to the spring, it is displaced 7 inches.
Write an equation that relates these variables.
33) Graph 2 x  y  4
34) Write the inequality whose graph is shown.
35) Graph y  
1
x2 3
2
36) Write the absolute value equation whose graph is shown.
2 x  4 y  13
37) Solve 
4 x  5 y  8
x  2 y  3
38) Shade the region defined by 
 y  3x  4
39) A triangular has vertices of  0,0 ,  0,5 , and  2,0  .
Write a system of three linear inequalities to describe this triangular region.
2 x  3 y  z  10

y  2 z  13
40) Solve: 

z 5

 x yz  9

41) Solve:  x  y  z  1
2 x  y  z  0

 8 2   4 5 
42) Subtract: 


 6 6   1 1
0 4
43) Perform the scalar multiplication: 2 

1 3 
 2 3 
 1 3
44) Perform the matrix multiplication:  1 4 

 2 4

 6 0  
 1 3
45) Evaluate the determinant of 

 2 5
 2 1 3
46) Evaluate the determinant of  2 0 1 


 1 2 4
47) Identify the vertex of the parabola y  
1
2
 x  3  4
2
48) Identify the vertex of the parabola y  2  x  3 x  1
49) Identify the vertex of the parabola y  x 2  6 x  11
50) Write the quadratic function y    x  4 x  9 in standard form.
51) Write the quadratic function y 
1
2
 x  2   3 in standard form.
2
52) Solve: 8 x 2  18 x  9  0 by factoring.
53) Solve:
1
2
 x  5   2  9 by extracting square roots.
3
54) Solve: 2 x 2  x  5 by using the quadratic formula.
55) Given x 2  8 x  c
A) Find the value of c that makes the expression a perfect square trinomial.
B) Then write the expression as the square of a binomial.
56) Find the zeros of f  x   4 x2  4 x  3
57) Plot  3  2i  in the complex plane.
58) Find the absolute value of  2  i 
59) Simplify  4  3i    2  4i 
60) Simplify 4i  6  i 
61) Simplify  1  2i 11  i 
62) Simplify
3i
1  i 
63) Simplify
5  3i
1  2i
64) Simplify 4 5  3 125
65) Complete the square in order to convert y  x 2  8x  11 into vertex form.
66) Complete the square in order to convert y  2 x 2  6 x  7 into vertex form.
67) Evaluate the discriminant of the following and then describe solutions (real/nonreal, different/same)
A) x 2  4 x  10  0
B) x 2  3 x  6  0
C) x 2  14 x  49  0
68) When an object is dropped, the model h  t   16t 2  h0 describes the height (feet) of the object
as a function of time (seconds). The initial height is represented by h0 .
If an object is dropped from a height of 320 feet, in how many seconds will it hit the ground?
69) Use the quadratic formula to solve  x 2  2 x  2 .
70) Solve the quadratic inequality x 2  6 x  5  0
71) Solve the quadratic inequality 2 x 2  7 x  3  0
72) Write a quadratic function in vertex form given vertex  1, 4  and point  2,2 
73) Write a quadratic function in intercept form given x-intercepts 2 & 1 and point  1, 6 
74) Write a quadratic form in standard form given points  0, 4 ,  1, 5 ,  2,10
75) Expand  x  y 
2
76) Factor completely: x 2  12 x  28
77) Factor completely: 4 x 2  4 x  3
78) Factor completely: 9 x 2  24 x  16
79) Factor completely: 6 x 2  15 x  9
80) Factor completely: 2 x 2  54
81) Factor completely: x 3  1
82) Factor completely: 2 x3  4 x 2  3x  6
83) Factor completely: 81x 4  16
84) Evaluate 210 (hint: use fingers and count to 10 as you keep doubling—2, 4, 8, 16, etc.)
85) Simplify x 2  x 2
86) Evaluate 2 2
87) Evaluate  2 
2
88) Evaluate 2 2
89) Evaluate  5 
6
 5
90) Evaluate 42 
91) Evaluate  23 
2
92) Evaluate  
3
4
1
32
2
4
93) Simplify  3x 
3
 xy 9   7 y 
94) Simplify 
2 2  
5 
 20 x y   21x 
 m w
4
95) Simplify
2
m0  w0
96) Subtract  8 x3  3x 2  2 x  9    6 x 2  x  1
97) Multiply
 x  5  5 x 2  3x  1
98) Multiply  x  2 x 1 x  3
99) Solve 3x 4  3x3  6 x 2  6 x  0
100)
Divide  x3  3x 2  7 x  6  by  x  4 
101)
Divide  x3  3x 2  7 x  6  by  x  2 
102)
Factor f  x   3x3  13x2  2 x  8 given that f  4   0
103)
List all the possible rational zeros of f  x   4 x3  5x2  3
104)
State the degree of the following polynomial: f  x   2  x  3 x  2   x  1
105)
A third degree polynomial function has zeros of 3 and  2  4i  .
List the other zero.
106)
3
2
Write a polynomial function of least degree that has a lead coefficient of 1, real coefficients,
and zeros of 4 and 5i .
1
2
 x  4  x  1  x  3
12
107)
Graph the polynomial function f  x  
108)
The graph of a cubic polynomial function has x-intercepts of 3, 2, and 5 .
The graph also passes through the point  0, 15 .
Write the cubic polynomial function in intercept form.
109)
Simplify 93/2
110)
Simplify 32 2/5
111)
Simplify 51/2  51/4
112)
Simplify
3
113)
Simplify
5
114)
Simplify 3 125 y 6
115)
Simplify
116)
Simplify 3 3 5 x5  x 3 40 x 2 (assume all variables are positive)
5
54
3
4
(assume all variables are positive)
5a5b9c13 (assume all variables are positive)
8  75  50
117)
Simplify
118)
Expand 2  3
119)
Expand 2  3 3  2 2
120)
Simplify
121)
Simplify
122)
Let f  x   x2  1




2

1
2
3
2 5
A) Find f  g  x  
g  x   3x
B) Find g  f  x  
1 5 2
x  , find f 1  x  .
6
3
123)
If f  x  
124)
Solve
125)
Solve 2 x3/2  250
126)
Solve
4x  7  2  5
127)
Solve
3x  2  2 x  0
128)
Solve x  4  2 x
129)
Simplify and write in radical form: 5x1/2 y 5/3 (assume all variables are positive)
130)
Simplify and write using rational exponents:
3
x 4 0
3
27x 4 y 2 (assume all variables are positive)