ALGEBRA 2 MIDTERM REVIEW
Evaluating Expressions:
1.) -3 + 3(-2+ 5)2
2.) ( -5 )2
3.) -52
Simplify and evaluate the expression for the given value of the variable:
4.) x2 + x – 8 when x = -2
5.) 3a2 + a – 2a2 when a = 3
6.) 2( n + 1) – 4 (n – 2) when n = -1
Solve the equation:
7.)
1
1
1
x   2x 
2
3
5
8.) 3(2x-1) = -4(-x + 1) + 5
9.) Find three consecutive integers such that if three times the smallest is decreased
by the sum of the other two, the difference will be 46.
Solve the formula for the indicated variable:
10.) Solve for y: 2x – 3y = 6
12.) Solve for h:
A=
1
h(b1  b2 )
2
11.) Solve for l: P = 2l + 2w
Solve the inequality and draw it’s graph :
14.) 2x  3  5x  1
13.) 3x + 1 < 2x + 3
Solve the compound inequality and graph its solution:
15.) 3x + 1 < 2x + 9
16.) - 4 < -2x + 4 < 12
Solve the absolute value equation or inequality.
17.) 3x  5  10
18.) 4 x  2  10
19.) x  2  6
Evaluate the function when x = 5.
20.)
g ( x)   x 2  2
21.) f ( x)  ( x) 2  2
22.) f ( x)  ( x  3) 2  5
Function
Not a Function
Graphically: passes vertical line test
Graphically: fails vertical line test
Each x-value must produce a unique
y output.
(2,4) (3,4) (4,4)
The same x-value produces more
than one y-output
(3,5) (3,6) (4,7)
Find the slope of the line passing through the points.
23.) (4, -3) and (6,5)
24.) (2, 0) and (8,0)
25.) (5, 8) and (5, 14)
Tell whether the two lines are parallel, perpendicular or neither.
26.) Line through (-5,3) and (8,4)
Line through (2,7) and (1,20)
27.) Line through (5,-9) and (-2,5)
Line through (6,3) and (9,9)
Graph the following equations:
28.) y = 
2
x5
3
29.) - 4x + y + 6 = 0
30.) 2x - 4 y = 0
31.) Write the equation of the line that passes through the given point and has the
given slope.
a.) (5, -1); m = 
b.)
1
3
(6,0); m = 0
c.) ( 4, 5); undefined slope
32.) Write the equation of the line that passes through the points ( -2, 5) and (-6, 8).
33.) Write the equation of the line that is parallel to the line y = 2x -1, but passes
through the point ( 6,7,)
34.) Write the equation of the line that is perpendicular to the line y = 2x-1, but
passes though the point (6,7)
35.) The table shows the number p (in thousands) of patents issued to U.S. residents
where t is the number of years since 1985. Draw a scatter plot of the data and
describe the correlation shown. Then approximate the best-fitting line for the data.
t
p
0
43.3
1
42.0
2
47.7
3
44.6
4
54.6
5
52.8
6
57.7
7
58.7
8
61.1
9
64.2
10
64.4
Based on your best-fit line equation, predict the number of patents that will be
issued to U.S. residents in the year 2000.
36.) The table shows the price p (in dollars per pound) of bread where t is the
number of years since 1990. Draw a scatter plot of the data and describe the
correlation shown. Then approximate the best-fitting line for the data.
t
p
0
.70
1
.72
2
.74
3
.76
4
.75
5
.84
6
.87
Based on your best-fit line equation, predict the price of bread per pound in 2006.
Graph the following inequalities:
2
37.) y   x  5
3
38.) y – 5 < -x
39.) x + 4 > -3
Graph the following absolute value inequalities:
40.)  x  3  4
41.) 2 x  2  1
42.) Solve the system of equations by graphing:
x + 2y = -4
3x + 2y =0
43.) Solve the system of equations using the substitution method.
x – 4 y = - 25
2x + 12y = 10
44.) Solve the system of equations using the linear combinations.
2x + 3y = -7
-4x – 5y= 13
Graph the following systems of inequalities:
45.)
x0
y  3 x  3
y  x 1
46.) y  0
 x  2y  8
x  2
x5
47.)
y  1
y3
48.) Perform the indicated operation.
1
6

 3  3
3
2  2
5
0
49.) Solve the matrix equation for x and y.
3
 1

4 y   6

13  8
5  3

0  x
7
13
Find the product of the following matrices.
2
50.) 
 3
15  5

10  1
12
0 
 2
51.) 
8
5
4 
 2
6  
1
 3
4 
 7
Find the determinant of the following matrices.
 9
52.) 
 3
1
2
53.)
 3
1 
6
2

Find the inverse of the following matrices.
2
54.) 
7
3
11
2
55.) 
1
2
3 
Use matrices to solve the following system of equations.
57.) x + 2y – 3z = 10
2x – 3y + 4z =-10
-2x + 3y -5z = 13
56.) -2x + 4y = 22
3x – y = -13
58.) Use a table of values to graph the following quadratic function.
y = x2 - 2x + 1
vertex
x
y
What is the vertex ? ____________
What is the axis of symmetry? _____________
What is the discriminant ?__________
What does the discriminant tell you? ___________
Find the x-intercepts by factoring. ____________
59.) Use a table of values to graph the following quadratic function.
y = -2x2 +8x -5
x
y
What is the vertex ? ____________
What is the axis of symmetry? _____________
What is the discriminant ?__________
What does the discriminant tell you ?
Find the x-intercepts by using the quadratic
formula . ____________________
***************MEMORIZE THE QUADRATIC FORMULA***** **********
 b  b 2  4ac
x
to solve equations in the form 0  ax 2  bx  c for x.
2a
Solve the following equations for x using the quadratic formula.
60.) x2- 8x + 5=0
61.) 9x2 = 1-7x
62.) 3x2 - 5x= -1
Solve the following equations for x by factoring.
63.) x2- 4x -21=0
64.) 2x2 = 200
65.) 2x2 + 3x + 1= 0
66.) The path of a diver is given by
4
24
y   x2 
x8
9
9
where y is the height in feet and x is the horizontal distance x from the end of the
diving board (in feet).
How high is the diving board from the water ? _________________________
Find the maximum height of the diver. ___________________________
How far is the diver from the diving board when he reaches his maximum height ?
How far is the diver from the diving board when he hits the water ? _____________
Write the expression as a complex number in standard form.
67.) (4 – 3i) – (2 + 5i)
68.) ( 7 + 3i)(2 - i)
69.)
Simplify the expression, if possible.
70.)
71.)
72.)
Multiply
73.)
74.)
3  2i
4i
Divide
75.)
76.)
Subtract
77.)
78.)
Simplify
79.)
80.)
Solve the equation
81.)
84.)
82.)
83.)
85.)