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```Benchmark Questions
Benchmark #1
Which is the graph of f(x) = x2?
A.
B.
C.
D.
MM1A1 b
Benchmark #2
F(x) = 4x + 6; What is f(2)?
A.
B.
C.
D.
10
12
14
16
MM1A1 a
Benchmark #3
In the equation y = 3x2, 3 ________ the
graph from f(x) = x2.
A.
B.
C.
D.
vertically stretches
vertically shrinks
horizontally stretches
reflects
MM1A1c
Benchmark #4
Solve: -6x + 9 = 21
A. -5
B. -2
C. 5
D. 6
MM1A3 d
Benchmark #5
What is the pattern in the following
sequence {3, 4, 5, 6, 7, …}.
a.
b.
c.
d.
n
n+1
n+2
n2
MM1A1 f
Benchmark # 6
What is the intersection point of the
graphs of the equations f(x) = 4x + 1
and g(x) = x + 2?
a. (1, 3)
b. ( 1 1 )
5

,2
5
c. (3, 1)
d. (2, 4)
MM1A1 i
Benchmark #7
Which is the graph of f(x) = |x|?
A.
C.
B.
D.
MM1A1 b
Benchmark #8
What is 5



x
6
?
a. 30

b. 11 
c. 35
d. 30
MM1A2 b
Benchmark #9
Subtract y2 + 4 from 3y2 + 8y.
a.
b.
c.
d.
4y2 + 12y
4y2 + 8y + 4
2y2 + 8y - 4
2y2 + 8y + 4
MM1A2 c
Benchmark #10
Multiply the binomials (x - 3)(x - 3).
a.
b.
c.
d.
x2 - 6x + 9
x2 - 6x -9
x2 - 9
x2 + 9
MM1A2 d
Benchmark #11
Multiply

b.

y 2x
x 3y 2  x 2 y 2
y 2x
and
y2
x4  x3
a.

x3  x2
y2
x
c.



d.
.
x 4 y 2  2x 3y 4
y 2x
x2  x
MM1A2 e
Benchmark #12
Factor the expression x2 + x - 30.
a.
b.
c.
d.
(x - 6)(x + 5)
(x -10)(x + 3)
(x - 2)(x + 15)
(x + 6)(x - 5)
MM1A2 f
Benchmark #13
What is the difference between the
ranges of Set A and Set B?
Set A: {39, 45, 93}
Set B: {1, 6, 25}
A. 54
B. 24
C. 30
D. 78
MM1D2 a
Benchmark #14
Given the following measures of the angles of a
triangle, find the missing angle.
90, 70 and x
a. 10°
b. 20°
c. 30°
d. 40°
MM1G3 a
Benchmark #15
Given the following triangle, which side is
J
the longest?



A. KJ
B. JL
C. KL
D. Both
K
KL
30
°
80°
L
and KJ are the same.
MM1G3 b
Benchmark #16
Given the two triangles, which theorem for
triangles proves they are equivalent?
a.
b.
c.
d.
SSS
HL
SAS
ASA
1
2
MM1G3 c
Benchmark #17
A square is __________ a rectangle.
a. Always
b. Sometimes
c. Never
MM1G3 d
Benchmark #18
Given the two triangles, which theorem for
triangles proves these are equivalent?
a.
b.
c.
d.
AAS
HL
SAS
ASA
MM1G3 c
Benchmark #19
Point Z is the orthocenter of ∆TUV. Which
term accurately describes TY
a.
b.
c.
d.
altitude
angle bisector

median of triangle
perpendicular bisector
MM1G3 e
Benchmark #20
The point of concurrency of the angle
bisectors is the _______________.
a.
b.
c.
d.
centroid
incenter
circumcenter
orthocenter
MM1G3 e
Benchmark #21
Sally is seven years old and goes to the store with her mother
every Saturday morning. Every time they go, she notices
that here mother gives the check out clerk money before
they leave the store. Sally concluded that everyone has to
give money in exchange for things they want to take out of
the store.
This is an example of:
a. Deductive reasoning
b. Inductive reasoning
c. Analytical reasoning
MM1G2 a
Benchmark #22
If I make all passing grades this week, then I
will go to the movies on Saturday. What is
the inverse of this statement?
a. If I don’t make all passing grades this week,
then I won’t go to the movies on Saturday.
b. If I go to the movies on Saturday, then I
make all passing grades this week.
c. If I don’t go to the movies on Saturday, then
I didn’t make all passing grades this week.
d. If I don’t make all passing grades this week,
then I will go to the movies on Saturday.
MM1G2 b
Benchmark #23
Magdalena has 6 hats, 2 scarves, and 5
pairs of mittens. In how many different
ways can she wear a hat, a scarf and
a pair of mittens?
A. 13
B. 14
C. 12
D. 60
MM1D1 a
Benchmark #24
How many permutations can you find using the letters in the
CAT?
a. 3
b. 6
c. 9
d. 12
MM1D1 b
Benchmark #25
If Joe rolls 2 dice, the probability of him
rolling a six and a double (3, 3) is:
a. Mutually exclusive
b. Not mutually exclusive
c. Both A & B
MM1D2 a
Benchmark #26
If Jonathan is rolling dice and spinning a
spinner, these two events are:
a.
b.
c.
d.
independent
dependent
mutually exclusive
not mutually exclusive
MM1D2 b
Benchmark #27
The spinner below is divided into three
equal sections. What is the probability
of spinning a 3 on the spinner if you
the know the arrow landed on an odd
number?
1
A. 1/6
B. 1/3
C.
D.
1/2
2/3
2
3
MM1D2 c
Benchmark #28
There are 24 candy-coated chocolate pieces in a bag. Eight
have defects in the coating that can be seen only with
close inspection. What is the probability of pulling out a
defective piece of candy from the bag?
A. 8
B. 8/23
C. 1/4
D. 1/3
MM1D2 d
Benchmark #29
What is the mean absolute deviation of
the following set of numbers {2, 7, 9,
1, 6, 4}?
A. 1.5
B. 2
C. 2.5
D. 3
MM1D4
Benchmark #30
y = x2 is a(n) _________ function.
A. Odd
B. Even
C. Neither
MM1A1 h
Benchmark #31
The school cafeteria workers are conducting a survey of
students’ likes and dislikes for the foods they serve
at lunch time. Once they tally the data and begin to
order the food they need, which measure of central
tendency will help most to make the food
purchases?
A.
B.
C.
D.
Mean
Mode
Median
Range
MM1D3 a
Benchmark #32
y = x3 - 2 is a(n) _________ function.
A. Odd
B. Even
C. Neither
MM1A1 h
Benchmark #33
What are the solutions to y = x2 + 5x + 6?
A.
B.
C.
D.
x = 3, 2
x = -3, 2
x = 3, -2
x = -3, -2
MM1A1 a
Benchmark #34
x  2  5. What is x?
A. 3
B. 3
C. 6

D. 9
MM1A3 b
Benchmark #35
1
x
= 0. What is x?
A. 0
B.
1
C. 1

D. 2
MM1A3 b
Benchmark #36
According to the chart, what are the
solution(s), (x-intercepts) to the
equation f(x) = x2 + 2x + 1?
f(x)
A. -1
x
-2
B. 1
-1
0
C. -1, 1
0
1
D. 2, 2
1
4
2
9
1
MM1A3 c
Benchmark #37
According to this chart, what are the
solution(s), (x-intercepts) to the
equation f(x) = -9x2 + 9?
x
f(x)
A. 9
-2
-27
B. -1, 1
-1
0
C. -1, 1, 9
0
9
D. -2, 2
1
0
2
-27
MM1A3 c
Benchmark #38
The points (0, 0), (5, 0), (0, 4) form what type of
triangle?
A.
B.
C.
D.
Isosceles
Equilateral
Scalene
Right
MM1G1 e
Benchmark #39
Solve: 3(x - 2) - 1 = 6(x + 5)


A. -4
37
B. 3
C. 4
23
D.
3
Benchmark #40
Solve: -6x + 9 = 21
A. -5
B. -2
C. 4
D. 6


Benchmark #41
What is the distance between (1, 1) and
(6, 6)?
A.
25
B. 5
C.
50
D. 25

Benchmark #42
What is the distance between (0, 0) and
(3, 2)?
A.
B.
C.
D.
13
13
4.12
3.555
Benchmark #43
What is the midpoint of (6, 4) and (3, -4)?
A.
B.
C.
D.
(4.5, 0)
(0, 4.5)
(-4.5, 0)
(0, -4.5)

Benchmark #44
Use the points A = (0, 0), B = (3, 2) and C
= (0, 2) and the Pythagorean Theorem
to find the distance between A and B.
What is the distance?
A. 13
B. 13
C. 5
D. 5
Benchmark #45
Graph the points (-2, 0), (-2, 3), (2, 2), and
(2, 0) to find out what shape they
create. What shape do they create?
A. A square
B. A rectangle
C. A rhombus
D. A trapezoid
Benchmark #46
f(x) = -x + 1; What is f(-4)?
A.
B.
C.
D.
-3
-5
3
5
Benchmark #47
1
Which is the graph of f(x) =
x

?
Benchmark #48
In the equation y=2x - 1_______
the graph from the function f(x)=2x.
A.shifts
B.shrinks
C.stretches
D.reflects
Benchmark #49
What is the general shape of the function
y=x2?
A.Straight line
B.Parabola
C.N Shape
D.V Shape
Benchmark #50
What is the rate of change of
3
f(x)= - x + 2?
4
3
4
A. B. 3
4

C. 2

D. -2

Benchmark #51
What is 12 3 - 3 3 ?
A. 4

B. 3
C. 9
 D. 9


3

3
2
3
Benchmark #52
Add: y2 + 3y + 2 and 2y2 + 4
A.
B.
C.
D.
y2 + 5y + 6
3y2 + 3y+ 6
6y2 + 6
3y2 + 7y + 2
Benchmark #53
Multiply the binomials (x + 2) ( x + 1).
A.
B.
C.
D.
x2 + 2x + 3
x2 + 2x + 2
x2 + 3x + 1
x2 + 3x + 2
Benchmark #54
A.
B.

x 2  5x 19

2
x  x 6
C.
x 2  6x 1
(x  2)(x  3)
D.
x 2  5x 19
x2  x  6


x2
(x  2)( x  3)
x3
x 2

5
and x  3
Benchmark #55
Factor the expression xy + 4x + 2b + 8 by
grouping.
A. x(y + 4) + 2(b + 4)
B. x(y - 4) + 2(b - 4)
C. x(y - 4) + 2b + 8
D. x(y + 4) + 2(b + 8)
Benchmark #56
What is the area of a triangle with height h
= 6 + x and base b = 13 + x?
A.
B.
C.
D.
x2 + 19x + 78
1/2 x2 + 19x + 39
1/2 x2 + 19/2 x + 39
1/2 x2 + 19/2 x + 78
Benchmark #57
What are the factors of b2 -4b - 5?
A.
B.
C.
D.
(b - 5) (b + 1)
(b + 5) (b -1)
(b - 3) (b + 2)
(b - 2) (b - 3)
Benchmark #58
Give the following triangle, find x.
A.
B.
C.
D.
30°
40°
50°
60°
80
°
50º
x
Benchmark #59
Which of the follow can be the measure of
the third side of a triangle if the other
two sides are 7 and 13?
A. 3
B. 4
C. 5
D. 8
Benchmark #60
Given the two triangles, which theorem for
triangles proves these are equivalent?
110° 40°
110° 40°
A. SSS
B.
HL
C. SAS
D.
AAS
Benchmark #61
Given the two triangles, which theorem for
triangles proves these are congruent?
A. SSS
20°
B. HL
C. SAS
D. ASA
20°
Benchmark #62
What is equivalent to
A. 5 11
B. 8 50
 C. 11 5
D. 17 5




45  8 5 ?
Benchmark #63
A rectangle is ___________ a square.
A.
B.
C.
D.
always
sometimes
never
not enough information
Benchmark #64
The ____________is equidistant from the
vertices of a trinagle.
A.
B.
C.
D.
centroid
incenter
circumcenter
orthocenter
Benchmark #65
A(n) ________is the center of an inscribed
circle.
A.
B.
C.
D.
centroid
Incenter
circumcenter
orthocenter
Benchmark #66
Which is equivalent to this expression?
(7x2 + 3xy - 8y2) + (4x2 - 8y2)
A.
B.
C.
D.
11x4 + 3xy - 16y2
11x2 + 3xy -16y2
11x2 - 5xy - 8y2
11x2 + 3xy
Benchmark #67
Which is a factored form of
x2 - 4?
A. (x - 1)(x + 4)
B. (x - 2) (x + 2)
C. (x + 1)(x - 4)
D. (x + 2)(x -2)
Benchmark #68
What is the value of this expression?
(2t2 - t - 28) divided by (t - 4)
A. (t + 4)
B. (t + 7)
C. (2t - 4)
D. (2t + 7)
Benchmark # 69
Which shows the expansion of (x - y)4?
A.
B.
C.
D.
x4 - 4x3y + 6x2y2 - 4xy3 + y4
x4 - 4x3y - 6x2y2 - 4xy3 - y4
x4 - 5x3y - 10x2y2 - 5xy + y4
x4 - 5x3y - 10x2y2 - 5xy3 - y5
Benchmark #70
What is the product of (4a + 7b)(5a + 3b)?
A.
B.
C.
D.
20a2 + 12a + 35b + 21b2
20a2 - 47ab + 21b2
20a2 + 23ab - 21b2
20a2 + 47ab + 21b2
Benchmark #71
The table of values represent part of a
function. Which equation also
represents this function?
A. f(x) = -3x
B. f(x) = x - 1
C. f(x) = 2x - 3
D. f(x) = 3x
x
0
2
4
6
f(x)
-3
1
5
9
Benchmark #72
The five ordered pairs below represent a
function.
{(-1, 4), (-3, 5), (0, 6), (2, 5), (3, 2)}
What is the range for this function?
A. (-3, -1, 0, 2, 3)
B. (-3, -1, 0, 2, 3, 2, 4, 5, 6)
C. (2, 4, 5, 6 )
D. All real number greater than or equal to 2
and less than 6.
Benchmark #73
Solve the equation below for n.
20
1
15


n  2 n  2 (n  2)(n  2)
A. 5
B. 4
C. 3
D. 2

Benchmark #74
What are the solutions for x2 - 3x - 10 = 0
A.
B.
C.
D.
x = -5 and x = -2
x = 5 and x = -2
x = -5 and x = 2
x = 2 and x = 5
Benchmark # 75
4  k k 2

?
What is the value of k in:
8
6
A. 20
B. 13
C. 4
26
D.
7

Benchmark #76
What value of a makes this equation true?
2a  4  2
A. 2
B. 4

C. 9
D. 18
Benchmark #77
What values of x make this equation true?
8  x x  10

x
9
A. x = -9 and x =8
B. x = -8 and x = 9

C. x = -6 and x = 12
D. x = 6 and x = 12
Benchmark #78
All carnivores are meat eaters. Lions eat meat.
Therefore, lions are carnivores. This kind of
thinking is an example of ___________
reasoning.
A. Applied
B. Inductive
C. Qualitative
D. Deductive
Benchmark #79
If the conditional statement is represented
by pq, then the ___________ is
represented by qp.
A. Inverse statement
B. Converse statement
C. Contrapositive statement
D. Conditional statement
Benchmark #80
If a figure is a triangle, then it has three sides.
Which of the following statements is the
contrapositive statement?
A. If a figure is a triangle, then it has three
sides.
B. If a figure is not a triangle, then it does not
have three sides.
C. If a figure has three sides, then it is a
triangle.
D. If a figure does not have three sides, then it
is not a triangle.
Benchmark #81
If Sara has 6 shirts and 3 pairs of pants,
how many different outfits does she
have?
A. 9
B. 12
C. 15
D. 18
Benchmark #82
If Jessica has a bag containing 3 blue
bracelets and 7 green ones, what is
the probability that she draws 1 blue
and then 1 green (without
replacement)?
A
B

2
9
15
34
 C
5
D
7
9
30
Benchmark #83
Greg has test scores of 77, 90, 92, and 77 in
English class. If he gets a 0 on his next
paper, how will it affect the mean, median
and mode of his scores.
A. The mean will go down. The median will go
down. The mode will remain the same.
B. The mean, median and mode will all remain
the same.
C. The mean, median and mode will all go
down.
D. The mean will go down. The median and
mode will remain the same.
Benchmark #84
A spinner is divided into 7 areas numbered 1 - 7.
If the sections containing 3, 4, 6, and 7 are
shaded, what is the probability of landing on a
A. 3/7
B. 5/7
C. 4/7
D. 6/7
Benchmark #85
What is the absolute mean deviation of
the following set of numbers {3, 6, 2,
9, 1, 7, 2}?
A. 2
B. 2.5
C. 2.61
D. 2.75
Benchmark #86
Which fraction represents the statement, “There is a 65%
probability of snow tomorrow?
A. 1/6
B. 6/100
C. 13/20
D. 3/5
Benchmark #87
This spinner is spun three times. What is probability that
the point stops on Blue the first spin, Yellow on the second
spin and Blue on the third spin?
A. 1/2
B. 1/16
C. 3/8
Yellow
Blue
D. 1/4
Red
Benchmark #88
Using a standard deck of playing cards, the 7 of clubs is
drawn and not replaced. What is the probability that a
second card drawn would be a heart?
A. 13/51
B. 12/52
C. 12/51
D. 13/52
Benchmark #89
Using a standard deck of playing cards, the 5 of hearts is
drawn and not replaced. What is the probability that a
second card drawn would be a 9?
A. 9/52
B. 13/51
C. 4/51
D. 9/13
Benchmark #90
What is the number of possible outcomes when a number
cube is rolled and a coin tossed at the same time?
A. 2
B. 4
C. 8
D. 12
Benchmark #91
A number cube is rolled once and the result is recorded.
The same number cube is rolled a second time. What is
the probability that the sum of the rolls is greater than 7?
A. 0/6
B. 15/36
C. 4/12
D. 5/6

Benchmark #92
Which equation is the slope-intercept form of the equation:
2x + 8y = 35
C. 35  8y
A. 8y = 35 - 2x
B.
1
4
x
2
35
8


D.
MM1A1 b
35  2x
8
Benchmark #93
A line passes through the points (6, 4) and (3, 2). What is
the slope of the line?
A.


C.
3
B.
2
2
 D.
3
MM1A1 c

2
3
3
2
Benchmark #94
What is the equation of a line that is parallel to y = 2x + 1 and
passes through the point (3, 2)?
A. y = 2x + 4
B. y = 2x - 4
C. y = 1/2 x + 1
D. y = 4x - 3
MM1A1 g
Benchmark #95
What is the solution set of the inequality 4|x - 6| + 4 ≥ 12?
A. x ≤ 4 or x ≥ 8
B. 4 ≤ x ≤ 8
C. x ≤ -4 or x ≥ 8
D. x ≤ 4 or x ≤ -8
MM1A1 i
Benchmark #96
If the graph of the line y = x is transformed by a dilation of 4,
what would be the equation of the new line?
A. y = 4x
B. y = 1/4x
C. y = x + 4
D. y = x - 4
MM1A1 c
Benchmark #97
When are two lines are parallel?
A. When both lines have a deflection?
B. When both lines have the same x-intercept?
C. When both lines have the same y-intercept?
D. When both lines have the same slope?
MM1A1 g
Benchmark #98
An empty oil tank has a 4000-gallon capacity. If it is filled at a
rate of 40 gallons per minute, how full will the tank be after
18 minutes?
A. 3280
B. 720
C. 1500
D. 2500
MM1A1 g
Benchmark #99
The function f(x) = |x - 7| is an example of what type of
function?
A. Absolute Value Function
B. Linear Function
C. Linear Inequality
D. Inequality Function
MM1A1 b
Benchmark #100
Which expression is equivalent to the difference:
(9x2 + 3x - 4) - (2x2 - 7x + 9)
a. (7x2 - 4x + 5)
b. (7x2 - 4x + 13)
c. 7x2 - 10x - 13
d.
7x2
+ 10x - 13
MM1A 2 c
Benchmark #101
There are fice points in a plane, but no three points are
colinear. How many different straight lines that pass
through two of the points are possible?
A. 2
B. 10
C. 15
D. 20
Benchmark #102
Danny has 3 identical color cubes. Each of the 6 faces on
the color cubes is a different color. He also has two fair
coins.
What is the total number of possible outcomes if Danny rolls
all three cubes OR flips both coins.
A. 22
B. 144
C. 220
D. 864
Benchmark #103
There are 14 students in a mathematics competition. Each
student will earn points during the competition. The
student with the greatest number of points will be the first
palce winnder, and the student with the second greates
number of points will be the secon place winner.
How many different ways can the 14 students finish in first
place and second place?
A. 27
B.
91
C. 182
D.
196
Benchmark #104
A teacher has 9 red crayons, 4 blue crayons, 7 purple
crayons and 5 black crayons in a basket. A student
reaches into the basket and randomly selects a crayon.
What is the probability that the crayon will be either blue
or black?
A. 4/16
B. 9/25
C. 13/25
D. 9/16
Benchmark #105
There are 6 red apples, 4 yellow apples, and 2 green
applies in a bucket. Maria will choose two apples at
random without replacement.
What is the probability that Maria will choose a red apple
and a green apple?
A. 5/121
B. 6/121
C. 1/11
D. 1/12
Benchmark #106
This table shows the probability of each possible sum when
two cubes with faces numbered 1 through 6 are rolled and
the numbers showing on each face are added.
2
3
Sum
2
3
4
5
36
6
7

Prob

1
36
8
9
10 11 12
```
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