Algebra I - Midterm Review Packet
Name_________________________
Due _________Exam Date________
Teacher___________Block______
Show work where needed. In addition to this packet,remember to review and practice several times in
smaller chunks to help you remember the material.
Unit 1 – Square and Cube Roots
1.
Evaluate :
2. Evaluate:
√49
3
√125
3.) The √17 is between which two positive consecutive integers?
and
4. ) The
-√51 is between which two positive consecutive integers
and
5.) The
3
√434
is between which two consecutive integers?
and
6.) The
3
√−1067
is between which two consecutive integers?
and
7. Explain why √−64 is not possible but
8.
3
√−64 is possible.
Order the following numbers from least to greatest.
3
√−64
3
√425
3
√26
√48
−√100
√26
Simplify:
9.
√75
10.
√98
11.
√48
Unit 2 – Solving Equations
Write an algebraic expression or equation for each phrase or sentence.
12.
14.
13. the quotient of 6 and a number, decreased by 3
6 times a number increased by 3
The difference of twice a number and 7 is 30.
15. The product of six and a number cubed is at least twenty-four.
Simplify.
16.
4(x + 6)
17.
6(x + 3)
18.
(x  7)
19.
5 – 32 + 14
2+3
21.
2x + 4(x  5)
22.
3x  5(x + 4)
23. ½ (6X - 10)
20.
Solve each equation. Show all work.
24.
5x + 7 = 22
25.
26.
3
x  7 = 2
4
27.
28.
7(x + 4) + 2x = 46
29.
x(3x + 7)
3  2x = 13
1
2
x  2
4
3
3x – 7  8x = 18
Find the solution to each equation. If the equation has infinite solutions, please write MANY SOLUTIONS. If the
equation does not have a solution, please write NO SOLUTION. Otherwise, clearly show the value of x. Be sure
and check your answers! You may want to use another sheet of paper!!
30.
6x + 3 = 5x  10
31.
5(x  3) = 8x
32.
8x + 3x =  33
33.
36.
5x + 27 = 2x
34.
7x  (5) - 2x = 5x + 17
35.
4x + 7 = ½ (8x + 12) + 1
Write an equation given the area (A=lw) of the rectangle is 84 sq. feet then solve for x.
7
X+1
Solve for the given variable.
37. a. Given the formula for interest earned,
b. Using the equation in part a,
if you deposited a principal of $5200
and earned $624 in interest at a rate
of 3%, how long did you keep the money in
the bank?
I = prt, solve for t.
38. Given the formula for the area of a trapezoid,
A = ½ h (b1 + b2) solve for b1 .
Unit 3 – Statistics
1.50
Round to hundredths.
Directions: Please
39.
MAD=
4.00
Circle
e
your answer!
40. 𝜎 =
41.
𝜎2 =
42) The average score on a test was 75 with a standard deviation of 6. What is the z-score of a student who
scored a 70 on the test? Round to the tenth.
z-score=
43) Ben’s average yearly electric bill is $210 per month. If Ben’s last bill had a z-score of -1.5 and a standard
deviation of $8, what is the electric bill for the month ? Round to hundredths.
bill= $
44) The speed of a remote control car I got for my birthday is 28mph. When the toy company tested my car, the
researchers reported it had a z-score of 1.2, based on their data set for the cars tested with a standard deviation
of 0.8 mph. Using this information, what was the average speed of the cars tested in this set? Round to tenths.
Average speed=
45) This table shows data on the number of dollars raised during a fundraiser for four different classes and for
one student in each class. Find the amount raised by each student. Round to hundredths.
Number of Dollars Raised
Mean for class
Standard Deviation
Student’s Z-score
Jill
66
4
2.8
Kelly
78
9.5
0.5
Ryan
77
10
1.4
Tim
87
8
-2.5
Jill made _____________
Kelly made____________
__________ made the most.
Ryan made ____________
Tim made ____________
46) The number of points two basketball teams scored is summarized in these box-and-whisker plots.
LA Lakers
20
30
40
50
60
70
80
90
100
Miami Heat
The Lakers scored a different number of points in each of the team’s 14 games.
The Heat scored a different number of points in each of the team’s 20 games.
What is the total number of games that the Lakers and Heat scored 80 or more points?
Round to whole numbers.
_________________________
Units 4 & 5: Functions & Graphing
47.
Choose the ordered pair that is a solution of 2x − 3y = 6.
A.
(5, 1)
B.
(0, 6)
C.
(4, 3)
48 & 49: Given the equation:
5x − 2y = 10
48. Find the x intercept
Find the y intercept:
49.
D.
(6, 2)
50.
What are the x and y-intercepts of the line shown on this graph?
Express as points.
51.
The bowling alley charged $4.50 per game (g) and a shoe rental fee of $3. Write an expression to model
the cost of bowling.
52. If your total charge was $21 for the night, how many games did you play? Use your expression in #51 to
write an equation and solve.
53.
Graph this equation using x/y intercepts:
3x − y = 6
x
y
0
0
54.
Find the slope of the line passing through the points (3, −4) and (−3, 5)
55.
Name the slope of the line shown in the graph.
56. Find the slope of the line from
x
0
1
2
3
the table of points.
57.
y
3
6
9
12
Name the slope of the graph of y = -5x + 8.
(Write in function form, meaning solve for y)
58.
Write in function form: 2y − 2x = 8
59.
Write in function form:
5x − y = 9
60 & 61: Graph each equation two ways. First, use the x/y table to find points to graph if the domain is -1,0,1.
Then use m and b to graph the equation. The graphs should look the same!!
60.
y = x − 3
x
61.
x
62.
graph using points from table
graph using
m=_____b=_____
y
y = −2x + 1
graph using points from table
y
Graph using the method of your choice.
2x - 3y = 6
graph using
m=_____b=_____
63.
Graph x = 2.
64. Graph y = -3
What is the slope?
65. Graph
y
What is the slope?
3
x2
4
66. Compare the following equations
and their slopes to the line in # 65.
Tell whether each line below is parallel,
perpendicular or neither to # 65 by circling the answer.
a.
y
3
x 3
4
b. 4 x  3 y  12
c. 3 x  4 y  6
par
par
par
67. If f(x) = −5x + 2, find f(−2).
perp neither
Remember:
Parallel lines have the
_______ slope.
perp neither
Perpendicular lines
have slopes that are
____________ and
_______________.
perp neither
68. Find the range of f(x) = x + 2 given the domain {0, 1, 2}.
69. Given the function f(x) = ½ x – 3; find the value of x given the value of the function f(x) = 11.
70.
Consider this function: {(2, 3), (3, 4), (4, 5)}. Add a point so that the relation is no longer a function .
71.
Which graph represents a function? Why?
A.
B.
C.
D.
72. Name the zero(s) of the graph.
Unit 6 – Inequalities & Transformations
73. Solve the inequalities then graph on the number line.
a. x + 6 > 1
b. -2y + 4 ≥ 19
c. 2(f – 6) < 2f - 1 + 13
74. Graph the inequalities.
a.
y> -½x+3
b.
6x + 3y > 12
75. Graph f(x) = x then graph g(x) = -4x + 1 . Explain the 3 shifts in the graph.
(slide or translation, rotation and reflection)
c. 2x – 5y > 30