Name: _______________________
Date: __________________
Algebra: Midterm Review Sheet
Unit 1 - Expressions, Equations & Single Variable Inequalities
1.
Fill in each circle of the following flow diagram with one of the letters C for
Commutative Property (for either addition or multiplication), A for Associative Property
(for either addition or multiplication), or D for Distributive Property.
2
2.
2
1
 5
Evaluate the expression: 4    x     when x 
3
3
 9
1
3.
Translate and solve the following word problem:
Six more than three times a number is negative thirty-six.
4.
Solve the following equations; if appropriate write identity or no solution:
a) 62k  5  3k  66
c)

b) 0.2x  50  6  0.43x  20
3
 x  8  1 6 x  10
4
2
d) 36  4 x  26 x  9
e) 23x  5  52x  4  4x
f) Solve for b1:
1
A  hb1  b2 
2
2
5.
Solve the following inequalities, graph the solutions.
a)  11 p  20  35
b)  1 
2
x33
3
Unit 2 - Graphs & Functions
6.
Which graph below most likely represents each of the following? – Multiple Choice
a)
a person’s body temperature as he enters a sauna and then cools off in a Jacuzzi
b)
the rise and fall of an elevator as it carries passengers from the ground floor to an
observation tower
c)
the cost to mail a package based on weight categories
a) II; IV; I
b) II; III; IV
c) I; III; II
d) II; I; IV
3
7.
8.
Which diagram represents a function? – Multiple Choice
(1)
(2)
(3)
(4)
The equation f x   x  6 is an example of which type of function? – Multiple Choice
a) linear
9.
b) exponential
c) step
d) absolute value
Find the range of the function for the given domain. Show all work.
y = –x2; {–3, –1, 1}
4
10.
Use the table below to answer the following questions.
a)
Plot the points (x,y) in this table on a graph (except when x is 5).
y
24
22
20
18
16
14
12
10
8
6
4
2
1
b)
11.
2
3
4
5
6
7
8
9
10
x
The y-values in the table follow a regular pattern that can be discovered by computing the
differences of consecutive y-values. Find the pattern and use it to find the y-value when x
is 5.
Which function identifies the graph below? – Multiple Choice
a) f x   x 2
b) f  x   x
c) f x   x 3
5
d) f  x   3 x
12.
Graph the following equations on the same graph:
1
2
y x
y
8
y  x2 4
7
6
5
Describe how graph (2) can be
obtained from graph (1) using
transformations.
4
3
2
1
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
–2
–3
–4
–5
–6
–7
–8
Unit 3 - Linear Relationships
13.
Find the common difference of the arithmetic sequence and then find the next two
numbers in sequence. Write the function.
-5,
14.
-2,
1,
4,
_______,
_______
Find the rate of change. Explain what the rate of change means for the situation.
6
7
8
x
15.
Complete the table.
Identify the slope, y-intercept, and write a function rule for the table.
16.
Find the equation of the line that passes through the pair of points:
A (2,  1) and B (3, 2)
17.
Hans needs to rent a moving truck. The information is provided in the following table.
Complete the table.
total cost, C
days, d
$60
0
$100
1
$140
2
3
4
Write an algebraic equation for the total cost, C, based on the number of days, d.
Truck Rental Company: _____________________
7
18.
A trainer for a professional football team keeps track of the amount of water players
consume throughout practice. The trainer observes that the amount of water consumed is
a linear function of the temperature on a given day. The trainer finds that when it is 90°F
the players consume about 220 gallons of water, and when it is 76°F the players consume
about 178 gallons of water.
Write a linear function to model the relationship between the gallons of water consumed
and the temperature. Explain the meaning of the slope in the context of the problem.
19.
20.
2
Is (9, -1) a solution to the equation y   x  5 ?
3
The functions below represent pricing plans for car rentals, where d is the number of days
and c is the cost. Order the car rentals from least to greatest based on their rate of change.
Avis
14
3
7
d 2
4
c 100 130 250 460
Enterprise
Total cost is $30 plus $25 per day.
Hertz
7d  0.25c  10
8
Unit 4 - Systems of Equations & Linear Inequalities
21.
3

y  x
2

6 x  4 y 1
Solve the system of equations algebraically, find the solution:
What is the solution to the following system of linear equations?
If there is no solution or infinitely many, explain why.
y
22.
 y  2x  7

y  x  2
8
7
6
5
4
3
2
1
–8
–7
–6
–5
–4
–3
–2
–1
–1
–2
–3
–4
–5
–6
–7
–8
9
1
2
3
4
5
6
7
8
x
23.
Solve the system of linear inequalities by graphing.
y
 2 x  3 y  3

 y  3x  1
8
7
6
5
4
3
2
1
–8
–7
–6
–5
–4
–3
–2
–1
–1
1
2
3
4
5
6
7
8
x
–2
–3
Name one point in the solution set.
–4
–5
–6
–7
–8
24.
Shopping at Savers Mart, Lisa buys her children four shirts and three pairs of pants for
$85.50. She returns the next day and buys three shirts and five pairs of pants for $115.00.
What is the price of each shirt and each pair of pants? Only an algebraic solution will be
accepted.
10
Math 8 Material
25.
Point D (2, 4) is rotated 180° about the origin, and then reflected over the y-axis. What is
the coordinate of D”?
26.
Complete the table below by marking the properties that change under each
transformation with an “X”.
Transformation
Size
Shape
Rotation
Reflection
Translation
Dilation
11
Location in
the Plane
Orientation
27.
Polygon ABCDE is plotted on the grid below.
Part A
On the graph, draw the translation of polygon ABCDE eight units to the right and four
units up. Label the image A’B’C’D’E’.
Part B
What would the coordinates of A” be after a reflection over the x-axis?
Answer ______________
12
28.
If the m13  61 and m 9  46 .
Complete the table below for each angle and explain.
Angle
Measure
Reason
11
8
2
1
7
13