Algebra I Regents Exam Questions at Random Worksheet #
1
NAME:__________________________
www.jmap.org
Algebra I Regents at Random Worksheets
1 A ball was launched into the air, and its height above the ground was recorded each second, as shown in the table
below.
Time (sec)
01234
Height (ft)
11 59 75 59 11
Based on these data, which statement is a valid conclusion?
1) The ball lands on the ground at 4
seconds.
3) The ball was launched from a height of 0
feet.
2) The ball reaches a maximum height of 11
feet.
4) The ball reaches its maximum height at 2
seconds.
2 The sum of
2 54
and
26
is
1)
4 60
2)
8 15
3)
76
4)
86
3 A tour bus can seat, at most, 48 passengers. An
adult ticket costs $18 and a child ticket costs $12.
The bus company must collect at least $650 to
make a profit. If a represents the number of adult
tickets sold and c represents the number of child
tickets sold, which system of inequalities models
this situation if they make a profit?
1)
a
+
c
<
48
18a + 12c > 650
2)
a
+
c
≤
48
18a + 12c ≥ 650
3)
a
+
c
<
48
18a + 12c < 650
4)
a
+
c
≤
48
18a + 12c ≤ 650
4 The heights, in inches, of eight football players are
given below.
76, 70, 72, 70, 69, 71, 78, 74
Which box plot represents these data?
1)
2)
3)
4)
5 What is the degree of the polynomial
2x − x
2
+ 4x
3
?
1) 1
2) 2
3) 3
4) 4
Algebra I Regents Exam Questions at Random Worksheet #
2
NAME:__________________________
www.jmap.org
6 On an island, a rare breed of rabbit doubled its
population each month for two years. Which type
of function best models the increase in population
at the end of two years?
1) linear growth
2) linear decay
3) exponential growth
4) exponential decay
7 Graph the system of inequalities on the set of axes
below:
y > 3x − 4
x + 2y ≤ 6
Label the solution set S.
.
Is the point
(2,2)
a solution to the system? Justify
your answer.
8 Use the method of completing the square to
determine the exact values of x for the equation
x
2
+ 10x − 30 = 0
.
9 What is the sum of
3x 7
and
2x 7
?
1)
5x 7
2)
5x
2
7
3)
5x 14
4)
5x
2
14
10 When babysitting, Nicole charges an hourly rate
and an additional charge for gas. She uses the
function
C(h) = 6h + 5
to determine how much to
charge for babysitting. The constant term of this
function represents
1) the additional charge for gas
2) the hourly rate Nicole charges
3) the number of hours Nicole babysits
4) the total Nicole earns from babysitting
11 Use the quadratic formula to determine the exact
roots of the equation
x
2
+ 3x − 6 = 0
.
12 If
f(x) =
30x
2
x + 2
, determine the value of
f
1
2
.
13 If
f(x) = x
2
, then which function represents a shift
of the graph of
f(x)
4 units to the right and 3 units
down?
1)
g(x) = (x + 4)
2
+ 3
2)
j(x) = (x + 4)
2
− 3
3)
h(x) = (x − 4)
2
− 3
4)
k(x) = (x − 4)
2
+ 3
Algebra I Regents Exam Questions at Random Worksheet #
3
NAME:__________________________
www.jmap.org
14 A survey of 150 students was taken. It was determined that
2
3
of the students play video games. Of the students
that play video games, 85 also use social media. Of the students that do not play video games, 20% do not use
social media. Complete the two-way frequency table.
Play Video Games Do Not Play Video Games Total
Social Media
No Social Media
Total
15 Explain why the relation shown in the table below is a function.
x
−
1
012
y
2 445
Complete the table below with values for both x and y so that this new relation is not a function.
x
−
1
012
y
2 445
16 The dot plot below shows the number of goals Jessica scored in each lacrosse game last season.
Which statement about the dot plot is correct?
1) mean > mode 3) mode = median
2) mean = median 4) median > mean
17 Solve
5(x − 2) ≤ 3x + 20
algebraically.
18 Factor
20x
3
− 45x
completely.
Algebra I Regents Exam Questions at Random Worksheet #
4
NAME:__________________________
www.jmap.org
19 When the equation
6
−
ax
=
ax
−
2
is solved for x in
terms of a, and
a ≠ 0
, the result is
1)
4
a
2)
4
a
3)
2
a
4)
2
a
20 The solution to
4(x − 5)
3
+ 2 = 14
is
1) 15
2) 14
3) 6
4) 4
21 One Saturday, Dave took a long bike ride. The
graph below models his trip.
What was Dave's average rate of change, in miles
per hour, on this trip?
1) 10
2) 11
3) 11.6
4) 14.5
22 On the set of axes below, graph
f(x) = x
2
+ 4x + 1
.
State the coordinates of the minimum.
23 The third term in a sequence is 25 and the fifth
term is 625. Which number could be the common
ratio of the sequence?
1)
1
5
2) 5
3)
1
25
4) 25
24 If
x = 4a
2
− a + 3
and
y = a − 5
, then which
polynomial is equivalent to the product of x and y?
1)
−17a
2
− 2a − 15
2)
−17a
2
+ 8a − 15
3)
4a
3
− 21a
2
− 2a − 15
4)
4a
3
− 21a
2
+ 8a − 15
Algebra I Regents Exam Questions at Random Worksheet #
5
NAME:__________________________
www.jmap.org
25 The table below shows the amount of money a popular movie earned, in millions of dollars, during its first six
weeks in theaters.
Week (x)
1 234 5 6
Dollars Earned, in Millions (y)
185 150 90 50 25 5
Write the linear regression equation for this data set, rounding all values to the nearest hundredth. State the
correlation coefficient to the nearest hundredth. State what this correlation coefficient indicates about the linear
fit of the data.
26 Graph the following system of equations on the set
of axes below.
y = x
2
− 3x − 6
y = x − 1
State the coordinates of all solutions.
27 Solve algebraically for x:
0.05(x − 3) = 0.35x − 7.5
28 When solved for x in terms of a, the solution to the
equation
3x − 7 = ax + 5
is
1)
12
3a
2)
12
3− a
3)
3a
12
4)
3
−
a
12
29 Solve the systems of equations algebraically for all
values of x and y:
y = x
2
+ 4x − 1
y = 2x + 7
30 Which expression is equivalent to
3(x
2
− 2x + 3) − (4x
2
+ 3x − 1)
?
1)
−x
2
+ x + 2
2)
−x
2
− 8x + 7
3)
−x
2
− 3x + 8
4)
−x
2
− 9x + 10
Algebra I Regents Exam Questions at Random Worksheet #
6
NAME:__________________________
www.jmap.org
31 The owner of an ice cream stand kept track of the number of ice cream cones that were sold each day of the first
week in June. She compared the ice cream sales to the average daily temperature. The data are shown in the table
below.
Average Daily Temp. (x)
72 75 81 78 77 76 80
Daily Ice Cream Cone Sales (y)
126 183 263 229 200 185 249
State the linear regression equation for these data, rounding all values to the nearest hundredth. State the
correlation coefficient, to the nearest hundredth, for the line of best fit for these data. State what this correlation
coefficient indicates about the linear fit of the data.
32 A bookstore owner recorded the number of books sold and the profit made selling the books.
Books Sold Profit
100 $50.00
250 $275.00
300 $350.00
350 $425.00
What is the average rate of change, in dollars per book, between 100 and 350 books sold?
1) 0.50 3) 1.50
2) 0.67 4) 2.00
33 The zeros of the function
f(x) = x(x − 5)(3x + 6)
are
1) 0,
−
5
, and 2
2) 0, 5, and
−
2
3)
−
5
and 2, only
4) 5 and
−
2
, only
34 The amount of money a plumber charges is
represented by the function
p(h) = 45 + 90h
. The
best interpretation of the y-intercept of this function
is that the plumber charges
1) $45 to come to the house
2) $45 per hour that he works
3) $90 to come to the house
4) $90 per hour that he works
35 Courtney went to a coffee shop to purchase lattes
and donuts for her friends. One day she spent a
total of $15.50 on four lattes and two donuts. The
next day she spent a total of $18.10 on three lattes
and five donuts. All prices included tax. If x
represents the cost of one latte and y represents the
cost of one donut, write a system of equations that
can be used to model this situation. Courtney
thinks that one latte costs $2.75 and one donut
costs $2.25. Is Courtney correct? Justify your
answer. Use your equations to determine
algebraically the exact cost of one latte and the
exact cost of one donut.
Algebra I Regents Exam Questions at Random Worksheet #
7
NAME:__________________________
www.jmap.org
36 Graph the system of inequalities on the set of axes
below.
3y + 2x ≤ 15
y − x > 1
State the coordinates of a point in the solution to
this system. Justify your answer.
37 What is the solution to the inequality
2m − 4 ≤ 3(2m + 4)
?
1)
m
≤
−
2
2)
m
≥
−
2
3)
m
≤
−
4
4)
m
≥
−
4
38 Solve the following systems of equations
algebraically for all values of x and y:
y = x
2
+ 5x − 17
x − y = 5
39 The functions
f(x) = x
2
− 5x − 14
and
g(x) = x + 2
are graphed on the same set of axes. What are the
solutions to the equation
f(x) = g(x)
?
1)
−
14
and 0
2) 0 and 2
3)
−
2
and 8
4)
−
2
and 7
40 The students in Mrs. Smith's algebra class were
asked to describe the graph of
g(x) = 2(x − 3)
2
compared to the graph of
f(x) = x
2
. Which student
response is correct?
1) Ashley said that the graph of
g(x)
is wider and
shifted left 3 units.
2) Beth said that the graph of
g(x)
is narrower and
shifted left 3 units.
3) Carl said that the graph of
g(x)
is wider and
shifted right 3 units.
4) Don said that the graph of
g(x)
is narrower and
shifted right 3 units.
41 At Adelynn's first birthday party, each guest
brought $1 in coins for her piggy bank. Guests
brought nickels, dimes, and quarters for a total of
$28. There were twice as many dimes as nickels
and 12 more quarters than nickels. Which equation
could be used to determine the number of nickels,
x, that her guests brought to her party?
1)
.
0
5
x
+
.
1
0
x
+
.
2
5
x
=
2
8
2)
.
0
5
x
+
.
1
0
(
2
x
)
+
.
2
5
(
x
+
1
2
)
=
2
8
3)
.
0
5
(
2
x
)
+
.
1
0
x
+
.
2
5
(
x
+
1
2
)
=
2
8
4)
.
0
5
(
x
+
1
2
)
+
.
1
0
(
2
x
)
+
.
2
5
x
=
2
8
42 Rationalize:
3
26
Algebra I Regents Exam Questions at Random Worksheet #
8
NAME:__________________________
www.jmap.org
43 What is the y-intercept of the line that passes
through the points
(−1,5)
and
(2,−1)
?
1)
−
1
2)
−
2
3) 3
4) 5
44 A student creates a fourth-degree trinomial with a
leading coefficient of 2 and a constant value of 5.
The trinomial could be
1)
2x
4
+ 3x
2
+ 5
2)
2x
4
+ 5x + 3
3)
4x
2
− 3x + 5
4)
4x
3
− 5x
2
+ 3
45 Nancy has just been hired for her first job. Her
company gives her four choices for how she can
collect her annual salary over the first eight years
of employment. Each function below represents
the four choices she has for her annual salary in
thousands of dollars, where t represents the number
of years after she is hired.
a(t) = 2
t
+ 25
b(t) = 10t + 75
c(t) = 400t + 80
d(t) = 2(t + 1)
2
− 10t + 50
Which pay plan should Nancy choose in order to
have the highest salary in her eighth year?
1)
a
(
t
)
2)
b
(
t
)
3)
c
(
t
)
4)
d
(
t
)
46 Factor
5x
3
− 80x
completely.
47 The equation that represents the sequence
−2,−5,−8,−11,−14,. . .
is
1)
a
n
=
−
3
+
(
−
2
)
(
n
−
1
)
2)
a
n
=
−
2
+
(
−
3
)
(
n
−
1
)
3)
a
n
=
3
+
(
−
2
)
(
n
−
1
)
4)
a
n
=
−
2
+
(
3
)
(
n
−
1
)
48 Which situation can be modeled by a linear
function?
1) A printer can print one page every three
seconds.
2) A bank account earns 0.5% interest each year,
compounded annually.
3) The number of cells in an organism doubles
every four days.
4) The attendance at a professional sports team's
games decreases by 1.5% each year.
49 Which function has a domain of all real numbers
and a range greater than or equal to three?
1)
f
(
x
)
=
−
x
+
3
2)
g(x) = x
2
+ 3
3)
h(x) = 3
x
4)
m(x)
=
x
+
3
|
|
50 What is an equation of the line that passes through
the points
(2,7)
and
(−1,3)
?
1)
y − 2 =
3
4
(x − 7)
2)
y − 2 =
4
3
(x − 7)
3)
y − 7 =
3
4
(x − 2)
4)
y − 7 =
4
3
(x − 2)
Algebra I Regents Exam Questions at Random Worksheet #
9
NAME:__________________________
www.jmap.org
51 An object is launched upward at 64 feet per second
from a platform 80 feet above the ground. The
function
s(t)
models the height of the object t
seconds after launch. If
s(t) = −16t
2
+ 64t + 80
,
state the vertex of
s(t)
, and explain in detail what
each coordinate means in the context of the
problem. After the object is launched, how many
seconds does it take for the object to hit the
ground? Justify your answer.
52 Wayde van Niekerk, a runner from South Africa,
ran 400 meters in 43.03 seconds to set a world
record. Which calculation would determine his
average speed, in miles per hour?
1)
400 m
43.03 sec
⋅
1000 m
0.62 mi
⋅
1 hr
3600 sec
2)
400 m
43.03 sec
⋅
0.62 mi
1000 m
⋅
1 hr
3600 sec
3)
400 m
43.03 sec
⋅
0.62 mi
1000 m
⋅
3600 sec
1 hr
4)
400 m
43.03 sec
⋅
1000 m
0.62 mi
⋅
3600 sec
1 hr
53 A geometric sequence with a common ratio of
−3
is
1)
−
1
0
,
−
7
,
−
4
,
−
1
,
.
.
.
2)
1
4
,
1
1
,
8
,
5
,
.
.
.
3)
−
2
,
−
6
,
−
1
8
,
−
5
4
,
.
.
.
4)
4
,
−
1
2
,
3
6
,
−
1
0
8
,
.
.
.
54 When solving the equation
4x
2
− 16 = 0
, Laura
wrote
4x
2
= 16
as her first step. Which property
justifies Laura's first step?
1) distributive property of multiplication over
addition
2) multiplication property of equality
3) commutative property of addition
4) addition property of equality
55 The expression
5
a + 2b
is equivalent to
1)
5
a
• 5
2
• 5
b
2)
5
a
• 25
b
3)
25
2ab
4)
25
a + 2b
56 In an arithmetic sequence, the first term is 4 and the
third term is
−2
. What is the common difference?
1)
−
1
2)
−
2
3)
−
3
4)
−
6
57 The box plot below summarizes the data for the
amount of snowfall, in inches, during the winter of
2021 for 12 locations in western New York.
What is the interquartile range?
1) 30
2) 50
3) 80
4) 110
58 Given the relation
R = {(−1,1),(0,3),(−2,−4),(x,5)}
. State a value for
x that will make this relation a function. Explain
why your answer makes this a function.
Algebra I Regents Exam Questions at Random Worksheet #
10
NAME:__________________________
www.jmap.org
59 Four quadratic functions are represented below.
Which function has the smallest minimum value?
1) I 3) III
2) II 4) IV
60 Joe is ordering water for his swimming pool. He
determines the volume of his pool to be about 3240
cubic feet. There are approximately 7.5 gallons of
water in 1 cubic foot. A truck load holds 6000
gallons of water. Which expression would allow
Joe to correctly calculate the number of truck loads
of water he needs to fill his pool?
1)
3240 ft
3
1 pool
•
1 ft
3
7.5 gal
•
6000 gal
1 truck load
2)
3240 ft
3
1 pool
•
1 ft
3
7.5 gal
•
1 truck load
6000 gal
3)
3240 ft
3
1 pool
•
7.5 gal
1 ft
3
•
6000 gal
1 truck load
4)
3240 ft
3
1 pool
•
7.5 gal
1 ft
3
•
1 truck load
6000 gal
61 Use the quadratic formula to solve the equation
3x
2
− 10x + 5 = 0
. Express the answer in simplest
radical form.
62 Which function has the zeros
−1
, 3, and
−4
?
1)
f
(
x
)
=
(
x
+
1
)
(
x
−
3
)
(
x
−
4
)
2)
g
(
x
)
=
(
x
−
1
)
(
x
+
3
)
(
x
−
4
)
3)
h
(
x
)
=
(
x
+
1
)
(
x
−
3
)
(
x
+
4
)
4)
k
(
x
)
=
(
x
−
1
)
(
x
+
3
)
(
x
+
4
)
63 Given
g(x) = x
3
+ 2x
2
− x
, evaluate
g(−3)
.
Algebra I Regents Exam Questions at Random Worksheet #
11
NAME:__________________________
www.jmap.org
64 A survey of students at West High School was taken to determine a theme for the prom. The results of the survey
are summarized in the table below.
Beach Party Hollywood Broadway
Girls
86 112 68
Boys
123 77 79
Approximately what percentage of the students who chose the Broadway theme were girls?
1) 26 3) 46
2) 27 4) 68
65 What is the correct factorization of
x
2
+ 4x − 12
?
1)
(
x
+
3
)
(
x
−
4
)
2)
(
x
−
3
)
(
x
+
4
)
3)
(
x
+
2
)
(
x
−
6
)
4)
(
x
−
2
)
(
x
+
6
)
66 Which expression results in an irrational number?
1)
3 ⋅ 3
2)
−
2
3
+
1
4
3)
5 ⋅ 81
4)
1
3
+ 3
67 The expression
−2(x
2
− 2x + 1) + (3x
2
+ 3x − 5)
is
equivalent to
1)
x
2
+ x − 4
2)
x
2
− x − 7
3)
x
2
+ 7x − 4
4)
x
2
+ 7x − 7
68 Which equation is always true?
1)
x
2
• x
3
= x
5
2)
3
x
• 3
2
= 9
2x
3)
−z
2
= z
2
4)
7
a
• 7
b
= 7
ab
69 What is an equation of the line that passes through
(3,7)
and has a slope of 2?
1)
y
−
7
=
2
(
x
−
3
)
2)
y
−
3
=
2
(
x
−
7
)
3)
y
+
7
=
2
(
x
+
3
)
4)
y
+
3
=
2
(
x
+
7
)
70 Which sum is irrational?
1)
−2 12 + 100
2)
− 4 +
1
3
900
3)
1
2
25 + 64
4)
49 + 3 121
Algebra I Regents Exam Questions at Random Worksheet #
12
NAME:__________________________
www.jmap.org
71 Use the method of completing the square to
determine the exact values of x for the equation
x
2
+ 6x − 41 = 0
. Express your answer in simplest
radical form.
72 Which expression is equivalent to
(x − 5)(2x + 7) − (x + 5)
?
1)
2x
2
− 2x − 30
2)
2x
2
− 2x − 40
3)
2x
2
− 4x − 30
4)
2x
2
− 4x − 40
73 Which equation has the same solutions as
x
2
+ 6x − 18 = 0
?
1)
(x + 3)
2
= 24
2)
(x + 3)
2
= 27
3)
(x + 6)
2
= 24
4)
(x + 6)
2
= 27
74 Jen joined the Fan Favorite Movie Club at the local
movie theater. At this theater, the cost of
admission in May and June remains the same. In
May, she saw 2 matinees and 3 regular-priced
shows and spent $38.50. In June, she went to 6
matinees and one regular-priced show and spent
$47.50. Write a system of equations to represent
the cost, m, of a matinee ticket and the cost, r, of a
regular-priced ticket. Jen said she spent $5.75 on
each matinee and $9 on each regular show. Is Jen
correct? Justify your answer. Use your system of
equations to algebraically determine both the actual
cost of each matinee ticket and the actual cost of
each regular ticket.
75 The functions
f(x)
and
g(x)
are graphed on the set
of axes below.
What is the solution to the equation
f(x) = g(x)
?
1) 1 and 5
2)
−
5
and 0
3)
−
3
and 5
4) 0 and 4
ID: A
Algebra I Regents at Random Worksheets
Answer Section
1 ANS: 4 PTS: 2 REF: 062401ai NAT: F.IF.B.4
TOP: Graphing Quadratic Functions KEY: key features
2 ANS: 4
2 54 + 26= 296 + 26= 66+ 26= 86
PTS: 2 REF: 082415ai NAT: N.RN.B.3 TOP: Operations with Radicals
KEY: addition
3 ANS: 2 PTS: 2 REF: 062402ai NAT: A.CED.A.3
TOP: Modeling Systems of Linear Inequalities
4 ANS: 3
69,70,70,71,72,74,76,78 ordered. median:
71 + 72
2
= 71.5
PTS: 2 REF: 082409ai NAT: S.ID.A.1 TOP: Box Plots
KEY: represent
5 ANS: 3 PTS: 2 REF: 062408ai NAT: A.SSE.A.1
TOP: Modeling Expressions
6 ANS: 3 PTS: 2 REF: 062407ai NAT: F.LE.A.1
TOP: Families of Functions
7 ANS:
; No, because
2 > 3(2) − 4
is false.
PTS: 4 REF: 082432ai NAT: A.REI.D.12 TOP: Graphing Systems of Linear Inequalities
8 ANS:
x
2
+ 10x = 30
x
2
+ 10x + 25 = 30 + 25
(x + 5)
2
= 55
x + 5 = ± 55
x = −5± 55
PTS: 2 REF: 062429ai NAT: A.REI.B.4 TOP: Solving Quadratics
KEY: completing the square
ID: A
9 ANS: 1 PTS: 2 REF: fall2301ai NAT: N.RN.B.3
TOP: Operations with Radicals KEY: addition
10 ANS: 1 PTS: 2 REF: 062421ai NAT: F.LE.B.5
TOP: Modeling Linear Functions
11 ANS:
x =
−3± (3)
2
− 4(1)(−6)
2(1)
=
−3± 33
2
PTS: 4 REF: 082429ai NAT: A.REI.B.4 TOP: Solving Quadratics
KEY: quadratic formula
12 ANS:
f
1
2
=
30
1
2
2
1
2
+ 2
=
30
4
5
2
=
15
2
×
2
5
= 3
PTS: 2 REF: 082426ai NAT: F.IF.A.2 TOP: Functional Notation
13 ANS: 3 PTS: 2 REF: 082411ai NAT: F.BF.B.3
TOP: Transformations with Functions
14 ANS:
Play Video Games Do Not Play Video Games Total
Social Media
85 40 125
No Social Media
15 10 25
Total
100 50 150
PTS: 2 REF: 062428ai NAT: S.ID.B.5 TOP: Frequency Tables
KEY: two-way
15 ANS:
For every value of x, there is a unique value of y.
PTS: 2 REF: 082427ai NAT: F.IF.A.1 TOP: Defining Functions
16 ANS: 2
mean:
3(0) + 3(1) + 4(2) + 5(3) + 2(4) + 2(5) + 1(6)
3 + 3 + 4+ 5 + 2 + 2+ 1
=
50
20
= 2.5
, mode: 3, median:
2+ 3
2
= 2.5
PTS: 2 REF: 062416ai NAT: S.ID.A.1 TOP: Dot Plots
ID: A
17 ANS:
5x − 10 ≤ 3x + 20
2x ≤ 30
x ≤ 15
PTS: 2 REF: 062425ai NAT: A.REI.B.3 TOP: Solving Linear Inequalities
18 ANS:
20x
3
− 45x = 5x(4x
2
− 9) = 5x(2x + 3)(2x − 3)
PTS: 2 REF: 062430ai NAT: A.SSE.A.2
TOP: Factoring the Difference of Perfect Squares
19 ANS: 2
6 − ax = ax − 2
8 = 2ax
8
2a
= x
4
a
= x
PTS: 2 REF: 082420ai NAT: A.CED.A.4 TOP: Transforming Formulas
20 ANS: 2
4(x − 5)
3
= 12
4x − 20 = 36
4x = 56
x = 14
PTS: 2 REF: 062406ai NAT: A.REI.B.3 TOP: Solving Linear Equations
21 ANS: 1
55 − 0
5.5 − 0
= 10
PTS: 2 REF: 062418ai NAT: F.IF.B.6 TOP: Rate of Change
ID: A
22 ANS:
PTS: 2 REF: 082425ai NAT: F.IF.C.7 TOP: Graphing Quadratic Functions
23 ANS: 2
25r
2
= 625
r
2
= 25
r = ±5
PTS: 2 REF: 062412ai NAT: F.IF.A.3 TOP: Sequences
KEY: difference or ratio
24 ANS: 4
(4a
2
− a + 3)(a − 5) = 4a
3
− 20a
2
− a
2
+ 5a + 3a − 15 = 4a
3
− 21a
2
+ 8a − 15
PTS: 2 REF: 082417ai NAT: A.APR.A.1 TOP: Operations with Polynomials
KEY: multiplication
25 ANS:
y = −37.57x + 215.67
,
−0.98
, strong
PTS: 4 REF: 062432ai NAT: S.ID.B.6 TOP: Regression
KEY: linear with correlation coefficient
26 ANS:
PTS: 4 REF: 062431ai NAT: A.REI.C.7 TOP: Quadratic-Linear Systems
ID: A
27 ANS:
0.05(x − 3) = 0.35x − 7.5
x − 3 = 7x − 150
147 = 6x
24.5 = x
PTS: 2 REF: 082428ai NAT: A.REI.B.3 TOP: Solving Linear Equations
28 ANS: 2
3x − ax = 12
x(3 − a) = 12
x =
12
3 − a
PTS: 2 REF: 062422ai NAT: A.CED.A.4 TOP: Transforming Formulas
29 ANS:
x
2
+ 4x − 1 = 2x + 7
x
2
+ 2x − 8 = 0
(x + 4)(x − 2) = 0
x = −4,2
y = 2(−4) + 7 = −1
y = 2(2) + 7 = 11
(-4,-1), (2,11)
PTS: 4 REF: 082434ai NAT: A.REI.C.7 TOP: Quadratic-Linear Systems
30 ANS: 4
3(x
2
− 2x + 3) − (4x
2
+ 3x − 1)
3x
2
− 6x + 9 − 4x
2
− 3x + 1
−x
2
− 9x + 10
PTS: 2 REF: 082403ai NAT: A.APR.A.1 TOP: Operations with Polynomials
KEY: subtraction
31 ANS:
y = 15.13x − 959.63
,
0.99
, strong
PTS: 4 REF: 082431ai NAT: S.ID.B.6 TOP: Regression
KEY: linear with correlation coefficient
32 ANS: 3
425 − 50
350 − 100
= 1.5
PTS: 2 REF: 082410ai NAT: F.IF.B.6 TOP: Rate of Change
33 ANS: 2 PTS: 2 REF: 062409ai NAT: A.APR.B.3
TOP: Zeros of Polynomials
34 ANS: 1 PTS: 2 REF: 082412ai NAT: F.LE.B.5
TOP: Modeling Linear Functions
ID: A
35 ANS:
4x + 2y = 15.5
3x + 5y = 18.1
5(4x + 2y = 15.5)
2(3x + 5y = 18.1)
Courtney is incorrect because of the following calculations:
20x + 10y = 77.5
6x + 10y = 36.2
14x = 41.3
x = 2.95
4(2.95) + 2y = 15.5
11.8 + 2y = 15.5
2y = 3.7
y = 1.85
PTS: 6 REF: 062435ai NAT: A.CED.A.3 TOP: Modeling Linear Systems
36 ANS:
(−1,1)
is a solution as it is in the overlap area.
PTS: 4 REF: 062434ai NAT: A.REI.D.12 TOP: Graphing Systems of Linear Inequalities
37 ANS: 4
2m − 4 ≤ 3(2m + 4)
2m − 4 ≤ 6m + 12
−16 ≤ 4m
−4 ≤ m
PTS: 2 REF: 082413ai NAT: A.REI.B.3 TOP: Solving Linear Inequalities
38 ANS:
x
2
+ 5x − 17 = x − 5
x
2
+ 4x − 12 = 0
(x + 6)(x − 2) = 0
x = −6,2
−6− y = 5
y = −11
2 − y = 5
y = −3
(−6,−11),(2,−3)
PTS: 4 REF: fall2305ai NAT: A.REI.C.7 TOP: Quadratic-Linear Systems
ID: A
39 ANS: 3
x
2
− 5x − 14 = x + 2
x
2
− 6x − 16 = 0
(x − 8)(x + 2) = 0
x = 8,−2
PTS: 2 REF: 082416ai NAT: A.REI.D.11 TOP: Quadratic-Linear Systems
40 ANS: 4 PTS: 2 REF: 062417ai NAT: F.BF.B.3
TOP: Transformations with Functions
41 ANS: 2 PTS: 2 REF: 082404ai NAT: A.CED.A.1
TOP: Modeling Linear Equations
42 ANS:
3
26
⋅
6
6
=
36
12
PTS: 2 REF: fall2303ai NAT: N.RN.B.3 TOP: Operations with Radicals
KEY: division
43 ANS: 3
5−−1
−1− 2
=
6
−3
= −2
5 = −2(−1) + b
3 = b
PTS: 2 REF: 062410ai NAT: F.IF.B.4 TOP: Graphing Linear Functions
44 ANS: 1 PTS: 2 REF: 082405ai NAT: A.SSE.A.1
TOP: Modeling Expressions
45 ANS: 1
a(8) = 2
8
+ 25 = 281
b(8) = 10(8) + 75 = 155
c(8) = 400(8) + 80 ≈ 137
d(8) = 2(8 + 1)
2
− 10(8) + 50 = 132
PTS: 2 REF: 062411ai NAT: F.LE.A.3 TOP: Families of Functions
46 ANS:
5x
3
− 80x = 5x(x
2
− 16) = 5x(x + 4)(x − 4)
PTS: 2 REF: 082430ai NAT: A.SSE.A.2
TOP: Factoring the Difference of Perfect Squares
47 ANS: 2 PTS: 2 REF: 062415ai NAT: F.BF.A.1
TOP: Sequences KEY: explicit
48 ANS: 1 PTS: 2 REF: 082402ai NAT: F.LE.A.1
TOP: Families of Functions
49 ANS: 2
All four functions have a real domain. f has a real range. h has a positive real range. m has a nonnegative real
range.
PTS: 2 REF: 062424ai NAT: F.IF.A.2 TOP: Domain and Range
ID: A
50 ANS: 4
m =
7− 3
2−−1
=
4
3
PTS: 2 REF: fall2302ai NAT: A.REI.D.10 TOP: Writing Linear Equations
KEY: other forms
51 ANS:
t =
−64
2(−16)
= 2
h(2) = −16(2)
2
+ 64(2) + 80 = −64 + 128 + 80 = 144
(2,144). At 2 seconds, the object is 144 feet
above the ground.
0 = −16t
2
+ 64t + 80
0 = t
2
− 4t − 5
0 = (t − 5)(t + 1)
t = 5
PTS: 4 REF: 082433ai NAT: F.IF.B.4 TOP: Graphing Quadratic Functions
KEY: key features
52 ANS: 3 PTS: 2 REF: 062423ai NAT: N.Q.A.1
TOP: Conversions
53 ANS: 4 PTS: 2 REF: 082419ai NAT: F.IF.A.3
TOP: Sequences KEY: difference or ratio
54 ANS: 4 PTS: 2 REF: 082406ai NAT: A.REI.A.1
TOP: Identifying Properties
55 ANS: 2
5
a + 2b
= 5
a
• 5
2b
= 5
a
• 25
b
PTS: 2 REF: 082422ai NAT: A.APR.A.1 TOP: Multiplication of Powers
56 ANS: 3
−2− 4
3− 1
=
−6
2
= −3
PTS: 2 REF: 082423ai NAT: F.IF.A.3 TOP: Sequences
KEY: difference or ratio
57 ANS: 2
110 − 60 = 50
PTS: 2 REF: 062413ai NAT: S.ID.A.1 TOP: Box Plots
KEY: interpret
58 ANS:
x may be any value other than
−2,−1,0
, so that for any value of x, there is a unique y.
PTS: 2 REF: 062427ai NAT: F.IF.A.1 TOP: Defining Functions
59 ANS: 1
1)
−7
; 2)
−4
; 3)
x =
−6
2(1)
= −3
,
c(−3) = (−3)
2
+ 6(−3) + 3 = −6
; 4)
−5
PTS: 2 REF: 062414ai NAT: F.IF.C.9 TOP: Comparing Quadratic Functions
ID: A
60 ANS: 4 PTS: 2 REF: 082424ai NAT: N.Q.A.1
TOP: Conversions
61 ANS:
x =
−(−10) ± (−10)
2
− 4(3)(5)
2(3)
=
10 ± 40
6
=
10 ± 2 10
6
=
5 ± 10
3
PTS: 4 REF: 062433ai NAT: A.REI.B.4 TOP: Solving Quadratics
KEY: quadratic formula
62 ANS: 3 PTS: 2 REF: 082421ai NAT: A.APR.B.3
TOP: Zeros of Polynomials
63 ANS:
g(−3) = (−3)
3
+ 2(−3)
2
− (−3) = −27 + 18 + 3 = −6
PTS: 2 REF: 062426ai NAT: F.IF.A.2 TOP: Functional Notation
64 ANS: 3
68
68 + 79
≈ 0.46
PTS: 2 REF: 082414ai NAT: S.ID.B.5 TOP: Frequency Tables
KEY: two-way
65 ANS: 4 PTS: 2 REF: 082401ai NAT: A.SSE.A.2
TOP: Factoring Polynomials
66 ANS: 4 PTS: 2 REF: 082407ai NAT: N.RN.B.3
TOP: Operations with Radicals KEY: classify
67 ANS: 4
−2x
2
+ 4x − 2+ 3x
2
+ 3x − 5 = x
2
+ 7x − 7
PTS: 2 REF: 062404ai NAT: A.APR.A.1 TOP: Operations with Polynomials
KEY: addition
68 ANS: 1 PTS: 2 REF: 062403ai NAT: A.APR.A.1
TOP: Multiplication of Powers
69 ANS: 1 PTS: 2 REF: 082418ai NAT: A.REI.D.10
TOP: Writing Linear Equations KEY: other forms
70 ANS: 1 PTS: 2 REF: 062405ai NAT: N.RN.B.3
TOP: Operations with Radicals KEY: classify
71 ANS:
x
2
+ 6x + 9 = 41 + 9
(x + 3)
2
= 50
x + 3 = ± 50
x = −3± 52
PTS: 4 REF: fall2304ai NAT: A.REI.B.4 TOP: Solving Quadratics
KEY: completing the square
ID: A
72 ANS: 4
2x
2
+ 7x − 10x − 35 − x − 5 = 2x
2
− 4x − 40
PTS: 2 REF: 062419ai NAT: A.APR.A.1 TOP: Operations with Polynomials
KEY: multiplication
73 ANS: 2
x
2
+ 6x = 18
x
2
+ 6x + 9 = 18 + 9
(x + 3)
2
= 27
PTS: 2 REF: 082408ai NAT: A.REI.B.4 TOP: Solving Quadratics
KEY: completing the square
74 ANS:
2m + 3r = 38.5
6m + r = 47.5
Jen is not correct because the prices are
6m + 9r = 115.5
6m + r = 47.5
8r = 68
r = 8.50
2m + 3(8.5) = 38.5
2m + 25.5 = 38.5
2m = 13
m = 6.50
PTS: 6 REF: 082435ai NAT: A.CED.A.3 TOP: Modeling Linear Systems
75 ANS: 1 PTS: 2 REF: 062420ai NAT: A.REI.D.11
TOP: Quadratic-Linear Systems
