Algebra I Formula Sheet
Geometric Formulas
b
l
h
h
h
h
b
b
A=
1
2
bh
A = bh
s
l
r
1
3
w
V = lwh
S.A.= 2(lw + lh + wh)
r
b1
s
h
h
h
p = 4s
A = s2
V = 13 Bh
S.A.= 12 lp + B
b2
A=
1
2
h(b1 + b2 )
w
a
r
l
c2 =
p = 2(l + w)
A = lw
c
b
a2 + b2
Pi
Abbreviations
milligram
gram
kilogram
milliliter
liter
kiloliter
millimeter
centimeter
meter
kilometer
square centimeter
cubic centimeter
mg
g
kg
mL
L
kL
mm
cm
m
km
cm2
cm3
ounce
pound
quart
gallon
inch
foot
yard
mile
square inch
square foot
cubic inch
cubic foot
oz
lb
qt
gal.
in.
ft
yd
mi.
sq in.
sq ft
cu in.
cu ft
volume
total surface area
area of base
V
S.A.
B
year
month
hour
minute
second
yr
mon
hr
min
sec
Copyright © 2006 by the Commonwealth of Virginia Department of Education
l
B
22
7
Quadratic Formula
x=
–b
b2 – 4ac
2a
Algebra I
Directions
Read each question and choose the best answer. For this test you may assume that the value
of the denominator is not zero.
SAMPLE
If f (x) = x2 + 2 x + 3, what is the value of f (x) when x = 6?
A
B
C
D
27
42
51
60
3
1
What value of x will make the equation 3(x + 15) − 6 x = − 6(x − 3) true?
A
B
C
D
2
−
−
9
6
2
3
Which describes the graph of g(x) = − 3 x + 5 ?
F
G
H
J
A
A
A
A
line
line
line
line
with
with
with
with
a slope of − 3 and a y-intercept of − 5.
a slope of − 3 and a y-intercept of 5.
a slope of 3 and a y-intercept of − 5.
a slope of 3 and a y-intercept of 5.
4
3
What is most likely the slope of the line graphed on the coordinate plane?
y
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 O
-1
-2
1
-3
-4
-5
-6
-7
-8
-9
A
B
C
D
−
3
0
3
Undefined
5
2
3
4
5
6
7
8
9
x
4
Which ordered pair represents the solution to the system of equations?
⎧⎪⎪ 2 x − 7 y = 0
⎨
⎪⎪⎩ x − 6 y = −5
5
F
(7, 2)
G
(2, 7)
H
(1, 1)
J
(−11, −1)
What is the solution to the following inequality?
3(x − 3) ≤ 3
A
B
C
D
x ≤2
x ≥2
x≤4
x≥4
6
6
Which equation best models line n ?
y
n
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 O
-1
-2
1
2
3
4
5
6
7
8
9
-3
-4
-5
-6
-7
-8
-9
F
G
H
J
7
x=8
y=8
x = 8y
y = x+8
Which quadratic equation has solutions of 5 and 7 ?
A
B
C
D
x2 − 5x = 0
x 2 − 2 x − 35 = 0
x 2 − 3 x − 28 = 0
x 2 − 12 x + 35 = 0
7
x
8
Which graph best represents the equation y =
y
9
8
7
6
5
4
3
2
F
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
1
-1
2
3
4
5
6
7
8
9
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
1
2
3
4
5
6
7
8
9
x
-2
-3
-4
-5
-6
-7
-8
-9
y
9
8
7
6
5
4
3
2
G
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
x
-3
-4
-5
-6
-7
-8
-9
y
9
8
7
6
5
4
3
2
H
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
-3
x
-4
-5
-6
-7
-8
-9
y
9
8
7
6
5
4
3
2
J
1
-9 -8 -7 -6 -5 -4 -3 -2 -1
-1
-2
x
-3
-4
-5
-6
-7
-8
-9
8
3
x −2 ?
4
9
This is the graph of a system of linear equations.
y
5
4
3
2
1
-5
-4
-3
-2
-1
1
O
2
3
4
5
x
-1
-2
-3
-4
-5
Based upon the graph, which is the apparent solution to the system
of equations?
10
A
(2, 5)
B
(3, 4 )
C
( 4, 3)
D
(5, 2)
Which is an example of the distributive property?
F
G
H
J
10 + 5 x = 5 x + 10
5(x + 2) = 5 x + 10
5 x + 10 = 5 x + 10
(5 + 10)x = x (5 + 10)
9
11
Which graph best represents the equation of the line y =
y
A
5
4
3
2
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
1 2 3 4 5
x
1 2 3 4 5
x
1 2 3 4 5
x
1 2 3 4 5
x
y
B
5
4
3
2
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
y
C
5
4
3
2
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
y
D
5
4
3
2
1
-5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
10
−
1
x +2 ?
3
12
A school play cost $1,200 to produce. If tickets sold for $5 each, the profit, p,
made on the play by selling x tickets is given by the equation shown.
p = 5 x − 1,200
What is the slope of the line representing this equation?
F
G
H
J
13
1, 200
−
240
1
5
Which of the following is a solution to 2 x2 + 2 x − 12 = 0 ?
A
B
C
D
14
−
−
−
12
3
−
2
0
Which is an equation for the line that contains (1, 2) and has a slope of 4 ?
F
G
H
J
y = 2x − 4
y = −2 x + 4
y = 4x − 2
y = −4x + 2
11
15
Which inequality is equivalent to 4 x − 2 y ≤ 8 ?
A
B
C
D
16
What is the slope of the line that passes through (−2 , 5) and (3, 9) ?
F
G
17
y ≤ 2x − 4
y ≥ 2x − 4
y ≤ −2 x − 4
y ≥ −2 x − 4
−
5
4
−
4
5
H
4
5
J
5
4
In addition to an $80 bonus, Joan earned $8 per hour working last week.
Joan’s total earnings last week were $240. How many total hours did she
work last week?
A
B
C
D
10
20
30
40
12
18
Tommie paid $17.50 to buy 6 youth tickets and 1 adult ticket to a school
carnival. Susan paid $22.50 to buy 3 youth tickets and 3 adult tickets at the
carnival. What was the price of an adult ticket?
F
G
H
J
19
What is the value of
A
B
C
D
20
$2.00
$2.90
$5.50
$7.50
6x − 3y
xy
when x = 6 and y = − 4 ?
−
2
−
1
2
3
Which equals (2.3 ×103 )(3.6 ×103 ) ?
F
G
H
J
8.28 ×109
8.28 ×106
5.90 ×109
5.90 ×106
13
21
Which expression is equivalent to
(4 x2 − 3 x + 9) + (7 x2 − 11) + (− x2 + 7 x − 2) ?
A
B
C
D
22
10 x 2 + 4 x − 4
10 x 2 − 10 x − 22
10 x 6 + 4 x 2 − 4
11x 2 + 4 x + 4
In simplest radical form,
F
13
G
13 2
H
13 3
J
13 5
845 is equal to —
14
23
24
Which polynomial is equivalent to
A
4 x2 + 6
B
4 x2 + 6 x
C
4 x 2 + 12 x
D
4 x 4 + 6 x2
What is the complete factorization of x2 − 5 x − 14 ?
F
G
H
J
25
8 x3 + 12 x
when x ≠ 0 ?
2x
(x − 2)(x + 7)
(x + 2)(x − 7)
(x − 1)(x + 14 )
(x + 1)(x − 14 )
Which statement could be represented by the expression n2 + 4 n ?
A
B
C
D
The
The
The
The
square of a number increased by four
square of the product of a number and four
sum of two times a number and four times a number
square of a number increased by four times the number
15
26
Which expression is equivalent to 4 x(2 x2 − x − 3) ?
F
G
H
J
27
6 x2 − 5x − 7
6 x3 − 5x2 + 7x
8 x 2 − 4 x + 12
8 x 3 − 4 x 2 − 12 x
Which labeled point on the number line is closest to
WX
5
A
B
C
D
28
40 ?
YZ
6
7
8
W
X
Y
Z
−
A computer chip has two pins on one side. One pin is 4.0 ×10 3 inches long
−
and the other is 2.5 ×10 3 inches long. What is the difference in the lengths of
the pins?
F
G
H
J
6.5 ×109 in.
−
6.5 ×10 3 in.
−
1.5 ×10 3 in.
−
1.5 ×10 6 in.
16
29
Which represents the complete factorization of 3v2 + 9v ?
A
B
C
D
30
Lincoln High School earned $5,100 in ticket sales for a play. The cost per
ticket was $12. Let t represent the number of tickets sold to the play. Which
of the following equations could be used to determine how many tickets were
sold to the play?
F
G
H
J
31
v(3 v + 9)
3(v2 + 3 v )
3 v (v + 3)
3 v2 (1 + 3 v )
12 = 5,100t
12t = 5,100
t = 5,100 − 12
t = 5,100 i 12
The function f (x) = 35 + 15 x represents the amount of money, in dollars,
Mr. Lewis earns for working x hours. How much money does Mr. Lewis earn
for working 25 hours?
A
B
C
D
$75
$375
$410
$1,250
17
32
Which equation represents the relationship between time, t, and distance, d ?
Distance Traveled
Time Distance
(hours) (miles)
2
90
3
135
4
180
5
225
F
d = t + 45
G
d = 45t
H
t = 45d
J
t = 45
d
18
33
What is the domain of the relation shown in the table?
y
x
–5
–2
–23
–14
0
–8
3
1
6
10
A
{ − 5,
B
{ − 23,
−
14,
−
8, 1, 10 }
C
{ − 23,
−
14,
−
8,
D
{ (− 5, − 23), (− 2, −14), (0, − 8), (3, 1), (6, 10) }
−
2, 0, 3, 6 }
−
5,
−
2, 0, 1, 3, 6, 10 }
19
For every dollar that Stacy earns,
her dad deposits twice that amount
into a savings account for her.
Which graph illustrates this example
of direct variation?
F
Dad’s Deposits
Stacy’s Savings
10
9
8
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10
Stacy’s Earnings
G
Dad’s Deposits
Stacy’s Savings
10
9
8
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10
Stacy’s Earnings
H
Dad’s Deposits
Stacy’s Savings
10
9
8
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10
Stacy’s Earnings
Stacy’s Savings
J
Dad’s Deposits
34
10
9
8
7
6
5
4
3
2
1
0
1 2 3 4 5 6 7 8 9 10
Stacy’s Earnings
20
35
36
Which of the following sets of ordered pairs is a function?
A
{(3, 4), (2, 3), (3,
B
{(2, 5), (
−
1, 9), (6, 3), ( − 1, − 2)
C
{(1, 3), (
−
2, 5), (4, 5), (3, − 2)
D
{(5, 6), (
−
−
}
}
}
2, 3), (10, 1), ( − 2, − 9)
What is g(2) for g(x) =
F
G
H
J
}
2), (4, 1)
1 3
x +2x ?
2
5
7
8
12
21
37
What is the domain of the function shown?
y
9
8
7
6
5
4
3
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 O
-1
-2
1
-3
-4
-5
-6
-7
-8
-9
A
B
C
D
−
2≤ x ≤6
−
5≤ x ≤3
−
2≤ y≤6
−
5≤ y≤3
22
2
3
4
5
6
7
8
9
x
38
Which graph best represents a direct variation?
y
5
4
3
2
1
F
-5
-4
-3
-2
-1
O
1
2
3
4
5
x
1
2
3
4
5
x
1
2
3
4
5
x
1
2
3
4
5
x
-1
-2
-3
-4
-5
y
5
4
3
2
1
G
-5
-4
-3
-2
-1
O
-1
-2
-3
-4
-5
y
5
4
3
2
1
H
-5
-4
-3
-2
-1
O
-1
-2
-3
-4
-5
y
5
4
3
2
1
J
-5
-4
-3
-2
-1
O
-1
-2
-3
-4
-5
23
39
What are the range values of the function f (x) = −3 x2 + 5 for the domain
values
{
−
}
2, 0, 1 ?
A
{
−
31, − 4, 5
}
B
{
−
7, 2, 5
C
{5, 8, 17}
D
{5, 14, 41}
}
24
40
Which of the following tables indicates that x and y vary directly?
F
G
H
J
x
y
1
2
2
4
3
4
4
5
5
8
x
y
1
1
2
4
3
9
4
16
5
25
x
y
1
5
2
4
3
3
4
4
5
5
x
y
1
3
2
6
3
9
4
12
5
15
25
41
The table shows the cost of a 12-inch pizza for different numbers of toppings.
Pizza Pricing
Number of
toppings
Cost of
pizza
0
$15.50
1
$17.35
2
$19.20
3
$21.05
4
$22.90
Which equation gives C, the cost of a pizza with t toppings?
A
B
C
D
C = 1.85t
C = 17.35t
C = 15.50 + 1.85t
C = 22.90 − 1.85t
26
42
Which graph best represents the function g(x) = (x − 2)(x + 4) ?
y
9
8
7
6
5
4
3
F
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 O
-1
-2
1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
x
1
2
3
4
5
6
7
8
9
x
-3
-4
-5
-6
-7
-8
-9
y
9
8
7
6
5
4
3
G
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
-6
-7
-8
-9
y
9
8
7
6
5
4
3
H
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
-6
-7
-8
-9
y
9
8
7
6
5
4
3
J
2
1
-9 -8 -7 -6 -5 -4 -3 -2 -1 O
-1
-2
-3
-4
-5
-6
-7
-8
-9
27
43
What is the sum of these matrices?
⎡ 2
⎢−
⎢ 4
⎢−
⎢ 3
⎣
A
⎡ −3
⎢
⎢ −11
⎢
⎢ −8
⎣
7 ⎤⎥
2 ⎥⎥
− ⎥
4⎦
−
B
⎡ 10
⎢
⎢ − 28
⎢
⎢ −15
⎣
C
⎡7
⎢
⎢3
⎢
⎢2
⎣
D
⎡ 7
⎢
⎢ −3
⎢
⎢ −2
⎣
1 ⎤ ⎡⎢ 5
⎥
0 ⎥ + ⎢⎢ 7
⎥
− ⎥
3 ⎦ ⎢⎣ 5
−
6 ⎤⎥
0 ⎥⎥
− ⎥
3⎦
5 ⎤⎥
2 ⎥⎥
− ⎥
2⎦
−
5 ⎤⎥
2 ⎥⎥
− ⎥
2⎦
−
28
6 ⎤⎥
2 ⎥⎥
1 ⎥⎦
−
44
The table shows high temperatures for four Virginia cities during one week
in March.
March High Temperatures
(degrees Fahrenheit)
Arlington
Norfolk
Roanoke
Virginia
Beach
Sunday
52
52
63
50
Monday
70
71
70
73
Tuesday
74
75
65
78
Wednesday
66
70
57
68
Thursday
56
53
59
55
Friday
50
70
48
71
Saturday
63
73
54
72
Day
Which city had the greatest mean high temperature during this week?
F
G
H
J
Arlington
Norfolk
Roanoke
Virginia Beach
29
45
Which equation most closely represents the line of best fit for the data in
this table?
A
−
y = 5 x +3
B
−
y = 4 x +3
C
y = 4 x +3
D
y = 5 x +3
x
y
1
2
3
4
5
6
4
6
7
9
10
10
4
5
5
4
30
46
Collin caught 15 fish in each of the two ponds on his ranch. The box-andwhisker plots summarize the lengths in inches of the fish from each pond.
0
5
10
15
Taylor Pond
20
0
5
10
15
Willow Pond
20
The lengths of the fish from Willow Pond have a —
F
G
H
J
greater range than the lengths of those from Taylor Pond
median equal to 12 inches
mean equal to 20 inches
lower quartile equal to the lower quartile for Taylor Pond
31
47
⎡ 5
⎢
What is ⎢⎢ 2
⎢ 2
⎣
A
⎡ 3
⎢
⎢ 5
⎢
⎢ 6
⎣
B
⎡ 7 −7 ⎤
⎥
⎢
⎢ −1 8 ⎥
⎥
⎢
⎢ − 2 10 ⎥
⎦
⎣
C
⎡ 7
⎢−
⎢ 1
⎢−
⎢ 2
⎣
D
⎡ 10 12 ⎤
⎢−
⎥
⎢ 6 12 ⎥
⎢−
⎥
⎢ 8 24 ⎥
⎣
⎦
−
3 ⎤⎥ ⎡⎢ −2
6 ⎥⎥ − ⎢⎢ 3
6 ⎥⎦ ⎢⎣ 4
4 ⎤⎥
− ⎥
2⎥?
− ⎥
4⎦
1⎤
⎥
4⎥
⎥
2 ⎥⎦
1⎤
⎥
4⎥
⎥
2 ⎥⎦
32
48
Which is most likely the equation of the line of best fit for the set of
data points?
y
9
8
7
6
5
4
3
2
1
0
F
y= 5x+6
G
y= 2x+6
H
−
y= 2x+6
J
−
y= 5x+6
1 2 3 4 5 6 7 8 9
2
5
5
2
33
x
49
Jake worked part-time at a restaurant. The amount of money Jake earned for
each of six weeks is shown.
$40 , $80 , $38 , $40 , $32 , $65
Jake then earned $25 for working a seventh week. How were the mean and
median affected?
A
B
C
D
The
The
The
The
mean decreased and the median remained the same.
median decreased and the mean remained the same.
median and the mean both remained the same.
mean and the median both decreased.
34
50
A sports league charges $60 per person to register and participate for each
sport. The table shows the actual numbers of people registered for soccer and
football by age range.
Sports League Registration
Age
Soccer
Football
7–8
9–10
11–14
350
320
180
280
165
120
Which product represents the registration fees paid for soccer and football by
age range?
F
⎡280 ⎤
⎢
⎥
60 ⎢165 ⎥
⎢120 ⎥
⎣
⎦
G
⎡350 ⎤
⎢
⎥
60 ⎢320 ⎥
⎢180 ⎥
⎣
⎦
H
⎡ 7−8 ⎤
⎥
⎢
60 ⎢ 9 − 10 ⎥
⎢11 − 14 ⎥
⎦
⎣
J
⎡350 280 ⎤
⎥
⎢
60 ⎢320 165 ⎥
⎢180 120 ⎥
⎦
⎣
35