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Midterm Review Questions
Date: ______________
Graph the following numbers on a number line:
1.)
6
2.) 
5
3
Put the following numbers in order:
3.) 9, -3, 10 ,
1
,  5, 
2
4.) Evaluate the following variable
expression where x = 7:
3.) _________________________
5.) Evaluate the following variable
expression where y = -3:
-x + 15
6.) Evaluate the following expression
where n = 4:
12y
7.) Evaluate the following variable
expression where x = 2 and y = 4:
x  32
48
n
3y  2
Solve:
8.) 4x + 7 = 27
9.) 2x – 9 = 0
10.) 15n + 9 = 21
11.) 2b + 11 = 15 – 6b
Solve:
1
5
1
19
12.) x    x 
2
3
2
4
13.) 5n + 11 = 7n - 9
Rewrite the following formulas for the given variable:
14.) Investment at Simple Interest
Solve for P: I=PRT
15.) Area of a Triangle
1
Solve for b: A  bh
2
16.) Volume of a Cone
1
Solve for h: V  r 2 h
3
Identify the five steps to solving a word problem (in order):
17.) Step 1:
18.) Step 2:
19.) Step 3:
20.) Step 4:
21.) Step 5:
Complete the following word problem (showing all five steps), and being sure to answer the
question at the end.
22.) You have borrowed $529 from your parents to buy a mountain bike. Your parents are not
charging you interest, but they want to be repaid as soon as possible. You can afford to pay them
$20 per week. How long will it take you to repay your parents?
Solve and graph the following inequalities:
23.) 5-2x  27
24.) 2(4 – x) > 8
Solve and graph the following inequalities:
25.) x – 8 > -4x -3
26.) 3x – 7 < 5
27.) -7<6x – 1<5
28.) -16  3x  4  2
29.) 3x + 2 < -10 or 2x – 4 > -4
30.) Simplify the expression: 5(n 2  n)  3(n 2  2n)
Solve the following absolute value equations and inequalities:
31.) -|x – 4| = 5
32.) |2x + 1| = 5
33.) |4x – 12| > 16
34.) |3x -+ 2| < 7
35.) Name the quadrants of the following coordinate plane correctly.
36.) Is the following input/output table representative of a function? Explain.
Input
-2
-1
0
1
2
Output
6
8
10
12
12
Evaluate the following functions using the number provided:
37.) f(x) = 5 + 3x – 17; x = 12
38.) f(x) = -x – (5x + 7); x = -2
39.) Find the slope of the line that goes through points (3, -4) and (1, -6). Show all work!
40.) Are the following lines parallel, perpendicular, or neither? Show all work!
Line 1: (4, -3); (-8, 1)
Line 2: (5, 11); (8, 20)
Find the x-intercepts and y-intercepts for the following problems:
41.) y = x - 3
42.) y = 4x + 8
43.) 5y = 2x - 3
44.) Write the equation of the line that has a slope of 3 and goes through the point (1,0).
45.) Write an equation of the line that passes through (1, -1) and is parallel to the line
1
y   x6
2
46.) The variables x and y vary directly. Write an equation that relates the variables. X =
0.8; y = 1.6
47.) Using the equation above, what is the value of y if x = 5?
48.) Draw a scatterplot of the data. Then approximate the best-fitting line by giving me the
line equation.
x
y
-2
4
-1
3
0
2.5
0.5
2.5
1
2
2
0.5
2.5
-1
3.5
-3
Graph the following inequalities. Make sure to shade appropriately.
49.)
y > 3x – 4
50.) y < 
1
x2
2
4
-2.5
5
-2.5
Graph the following inequalities. Make sure to shade appropriately.
51.) y  2
52.) y  2x + 1
53.) In the following absolute value equation, what is the vertex of the graph?
y = |x – 4| + 2
54.) In the following absolute value equation, would the graph open “up” or open “down”?
y = 3|x + 5| - 1
55.) In the following absolute value equation, would the graph be wider, narrower or the
same width as y = |x|?
1
y  | x  3 | 4
2
Graph the following absolute value equations:
56.) y = 2|x|
57.) y = -|x – 3| + 1
Match the following linear equations, linear inequalities and absolute value equations to
the letter of their appropriate graphs:
58.) x  1
__________
63.) y  3
1
59.) y   x  2
3
__________
64.) y = 2|x|
60.) y  -3x + 2
__________
65.) y 
__________
__________
1
x 1
2
__________
61.) y = |x - 2|
__________
66.) y = 2x + 4
__________
62.) y = -|x – 2| + 1
__________
1
67.) y   | x  1 | 2
2
__________
A
B
C
D
E
F
G
H
I
J
68.) Decide if the point (3, 0) is a solution
for the linear system below:
-x + 2y = 3
10x + y = 30
69.) Graph the following linear
system to find the solution:
3x – y = 12
-x + 8y = -4
70.) Find the solution to the following sets of
of linear systems using the substitution
method.
9x – 5y = -30
x + 2y = 12
71.) Find the solution to the following sets
linear systems using the elimination
method.
x + 3y = -2
x+y=2
Graph the system of linear inequalities:
72.)
y  -4
y < -2x + 10
73.)
y > 2x - 7
4x + 4y < -12
Complete the following word problem:
74.) The senior classes at High School A and High School B planned separate trips to New York
City. The senior class at High School A rented and filled 16 vans and 5 buses with 417 students.
High School B rented and filled 10 vans and 8 buses with 480 students. Every van had the same
number of students in it as did the buses. How many students can a van carry? How many
students can a bus carry?
75.) Graph the following quadratic equation using standard form:
y = x 2 – 2x - 1
Axis of symmetry is ___________
Vertex is ____________________
x-intercepts are _______________
y-intercept is _________________
76.) Graph the following quadratic equation using intercept form:
y = -(x + 2)(x – 4)
Axis of symmetry is ___________
Vertex is ____________________
x-intercepts are _______________
y-intercept is _________________
Additional point (if necessary) ______________
77.) Graph the following quadratic equation using vertex form:
y = -(x – 2) 2 - 1
Axis of symmetry is ___________
Vertex is ____________________
x-intercepts are _______________
y-intercept is _________________
Additional point (if necessary) ______________
78.) Write the equation of the quadratic function that has a vertex (0, 0) and contains the
point (4, 8).
Factor the following quadratic expressions completely!
79.) x 2  11x  24
80.) 2 x 2  3x  1
81.) 18 x 2  2
82.) 81x 2  198 x  121
Simplify or solve:
83.)
168
84.)
85.)
6
8
86.) x 2  100
30 2
Also complete the following multiple-choice questions and list the answers here. Show the
work on separate paper and attach by the due date.
Pg 62
Pg 134
Pg 191
1.) __________
1.) __________
1.) ___________
2.) __________
2.) __________
2.) ___________
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6.) ___________
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5.) __________
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6.) __________
7.) __________
7.) __________
8.) __________
8.) __________
9.) __________
9.) __________
10.) _________
10.) _________
11.) _________
11.) _________
12.) _________
On page 192 please complete the following problems and attach the work to the back.
2.) ________
36.) ________
4.) ________
38.) ________
6.) ________
40.) ________
8.) ________
42.) ________
10.) ________
44.) ________
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58.) ________
26.) ________
60.) ________
28.) ________
62.) ________
30.) ________
64.) ________
32.) ________
74.) ________
34.) ________
On page 394 please complete the following problems and attach the work to the back.
44.) ________
58.) ________
46.) ________
60.) ________
48.) ________
62.) ________
50.) ________
64.) ________
52.) ________
66.) ________
54.) ________
68.) ________
56.) ________