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1)
A (2, -1)
B (2, 5)
C (6, -1)
A right triangle is formed by the points shown.
Find the length of the hypotenuse, which is line segment BC.
A)
2)
10
B)
400
C)
8
D)
52
D=
(x2 - x1)2 + (y2 - y1)2
What is the length of line segment JK?
A)
106
B)
13
C)
19
D)
67
3)
Triangle 1 is transformed as shown in the diagram, resulting in triangle 3. Describe
the transformations.
A)
dilation, then reflection
B)
rotation, then translation
C)
reflection, then translation
D)
translation, then reflection
4)
A rotation in the origin is shown. The angle of rotation appears to be
A)
30°.
B)
45°.
C)
60°.
D)
90°.
5)
Which transformation is shown here?
6)
A)
dilation
B)
reflection
C)
rotation
D)
translation
The figure on the left has been transformed into the one on the right. Which
transformation does this show?
A)
(x', y') = (y, x)
B)
(x', y') = (x, -y)
C)
(x', y') = (-x, y)
D)
(x', y') = (-y, x)
7)
After rectangle WXYZ is translated 4 units to the left, what are the coordinates
of X’?
A)
(-2, 2)
B)
(0, -3)
C)
(0, 2)
D)
(8, 2)
8)
Rotate trapezoid ABCD 90° clockwise around the origin. What are the coordinates of D’?
A)
(-4, 2)
B)
(4, -2)
C)
(0, 4)
D)
(4, 0)
9)
Which transformation will be equivalent to rotating a figure 90°
counterclockwise?
A)
reflecting over the x-axis and the y-axis.
B)
translating left 3 units and down 5 units.
C)
Reflecting over the x-axis and then reflecting over the line y = x.
D)
Reflecting over the x-axis and then reflecting over the line y = -x.
10)
Which transformation will be equivalent to rotating a figure 270°
counterclockwise?
A)
reflecting over the x-axis and the y-axis
B)
translating left 3 units and down 5 units
C)
Reflecting over the y-axis and then reflecting over the line y = x
D)
Reflecting over the y-axis and then reflecting over the line y = -x
11)
Triangle ABC has been transformed into triangle A'B'C'. The algebraic formula for
this transformation is
A)
(x', y') = (2x, y)
B)
(x', y') = (x, 2y)
C)
(x', y') = (2x, 2y)
D)
(x', y') = (2y, 2x)
12)
Which type of transformation is shown here?
A)
dilation
B)
reflection
C)
refraction
D)
rotation
13)
If triangle MAS ≅ triangle TAR. Which of the statements could be false?
14)
A)
segment MA ≅ segment TA
B)
segment MA ≅ segment SA
C)
∠ ASM ≅ ∠ ART
D)
∠ MAS ≅ ∠ TAR
reflect across the x-axis and then rotate 90° counterclockwise about the origin
Determine which rectangle was transformed to result in rectangle E.
A)
rectangle A
B)
rectangle B
C)
rectangle C
D)
rectangle D
15)
Fill in the missing reason in the proof.
A)
ASA
B)
SAA
C)
SAS
D)
SSS
16)
These two triangles can be shown to be congruent using which
transformation?
A)
reflection over the x-axis
B)
reflection over the y-axis
C)
translation right 4 units
D)
rotation of 180°
17)
How is angle a related to angle d?
18)
A)
vertical angles
B)
alternate interior angles
C)
alternate exterior angles
D)
corresponding angles
A city is planning to start construction of a new street. The new street will be named Elm
street and is represented by the red dashed line in the diagram. Oak street, Maple street, and
Cherry street are parallel to each other. If Elm street is constructed so that it is parallel to Oak,
Maple, and Cherry, what will be the measure of angle 2?
A)
130°
B)
120°
C)
60°
D)
50°
19)
The angles of a triangle are 2x, 3x, and 4x degrees. Find the value of x.
A)
20
B)
30
C)
40
D)
50
20)
If two sides of a triangle are 3 cm and 5 cm in length, which could NOT be the
measure of the third side?
A)
2 cm
B)
3 cm
C)
4 cm
D)
5 cm
21)
Give the MOST specific name for the figure shown.
A)
parallelogram
B)
quadrilateral
C)
rhombus
D)
trapezoid
22)
What is the MOST SPECIFIC name for the figure?
A)
parallelogram
B)
quadrilateral
C)
rhombus
D)
square
23)
On a map of Tennessee, one inch represents 15 miles. If Chattanooga and Nashville
are 11.3 inches apart on the map, how many miles apart are the cities?
A)
26.5
B)
133.5
C)
163.5
D)
169.5
24)
On a map of the United States, one inch represents 400 miles. If New York and
California are six and
3
4
inches apart, how many miles apart are they?
A)
1,800
B)
2,700
C)
5,400
D)
7,200
25)
Damari is constructing an equilateral triangle inscribed in a circle and has gotten
this far. What is his next step?
A)
connect the endpoints of the arc with a line segment
B)
construct a second arc through the center that opens up.
C)
Draw a line segment from the center to the end point of the arc
D)
draw a line segment from the endpoint of the arc to the endpoint of the
segment on the paper.
26)
Alison has started a construction and has this drawn on her paper. What is she
constructing?
A)
a square inscribed in a circle
B)
a hexagon inscribe in a circle
C)
a pentagon inscribed in a circle
D)
an equilateral triangle inscribed in a circle
27)
Triangle ABC was dilated by 50%. If AC = 6, what is A'C'?
28)
A)
3
B)
6
C)
12
D)
15
You are given rectangle ABCD on the grid shown and are told that the figure is to be
dilated from the origin, but you are not told by what factor. Which COULD be the new
coordinates of point D?
A)
(-8, -4)
B)
(-2, -2)
C)
(-2, -4)
D)
(2, 4)
29)
The triangles shown are similar. Which is an appropriate similarity statement for
the triangles?
A)
ΔABC ~ ΔDEF
B)
ΔABC ~ ΔEFD
C)
ΔCBA ~ ΔEFD
D)
ΔBCA ~ ΔDEF
30)
The actual length of side t is 0.045 cm. Use the scale drawing to find the actual
side length of w.
A)
0.06 cm
B)
0.075 cm
C)
0.45 cm
D)
0.75 cm
31)
You are given two triangles and the information that the three pairs of corresponding
angles are congruent. What other information do you need to have to conclude that the
triangles are similar?
A)
No additional information is needed.
B)
That one pair of corresponding sides have the same measure.
C)
That the three pairs of corresponding sides are proportional.
D)
That the three pairs of corresponding sides have the same measure.
32)
Given the picture, what is the length of AC?
A)
4.5
B)
5
C)
7.5
D)
8
33)
Determine the shortest side in ΔDEF.
A)
EF
B)
DE
C)
FE
D)
DF
34)
Based on the diagram, which statement is accurate?
A)
m∠GDE = m∠FDE
B)
m∠GDE < m∠FDE
C)
m∠DEG < m∠DEF
D)
m∠DFE > m∠DGE
35)
Koby can work about 22 math problems in 30 minutes. At this rate, how many
math problems can Koby work in 3 hours?
A)
36
B)
66
C)
120
D)
132
36)
Given that the triangles shown are isosceles, which set shows two similar
triangles?
A)
B)
C)
D)
* Hover over answer image to enlarge
37)
Julian's shadow is 6 feet long. At the same time a 31 foot tall building casts a
shadow that is 28 feet long. What proportion could be used to find Julian's height?
x
6
A)
=
31
28
x
6
B)
=
28
31
6
x
C)
=
31
28
x
28
D)
=
31
6
38)
At 10 am the shadow of a post on a pergola is 12 feet long. At the same time the
shadow of Jimmy, who is 6 feet tall, is 7 feet long. What is the approximate height of the
post?
A)
3 feet
B)
7 feet
C)
10 feet
D)
14 feet
39)
Find the measure of ∠C to the nearest degree.
A)
20°
B)
22°
C)
24°
D)
66°
40)
The hypotenuse and one of the legs of a right triangle form an angle that has a
cosine of
2
2
. What is the measure of the angle?
A)
30 degrees
B)
45 degrees
C)
60 degrees
D)
90 degrees
Let ∠X and ∠Y be complementary. If sin(X) =
41)
3
5
and cos(X) =
4
5
, then what is the value of sin(Y)?
A)
3
5
B)
4
5
C)
5
4
D)
5
3
42)
Which of these is equal to sin(70°)?
A)
cos(110°)
B)
cos(160°)
C)
cos(20°)
D)
cos(70°)
43)
PL = 10
PK = 8
L is a point of tangency. Segments PL and PN have a common point at P. Find
the length KN.
A)
4
B)
4.5
C)
5
D)
5.5
44)
In the diagram, find m∠BAC.
A)
85 degrees
B)
122 degrees
C)
133 degrees
D)
140 degrees
45)
Quadrilateral PQRS is inscribed in a circle, as shown. Which statement is
true?
A)
The measure of ∠P is equal to the measure of arc QRS, and the measure of ∠R is
equal to the measure of arc SPQ, so angles P and R are supplementary.
B)
The measure of ∠P is equal to the measure of arc QRS, and the measure of ∠R is
equal to the measure of arc SPQ, so angles P and R are complementary.
C)
The measure of ∠P is equal to half the measure of arc QRS, and the measure of ∠R is
equal to half the measure of arc SPQ, so angles P and R are supplementary.
D)
The measure of ∠P is equal to half the measure of arc QRS, and the measure of ∠R is
equal to half the measure of arc SPQ, so angles P and R are complementary.
46)
Triangle XYZ is shown. The line(s) bisecting which angle(s) will pass through the center
of a circle inscribed in the triangle?
47)
A)
angle X only
B)
angles X, Y, and Z
C)
angles X and Y only
D)
angles Y and Z only
A circle has an area of 36 in2. What is the area of a sector of the circle that has
a central angle of
π
6
?
A)
3 in2
B)
6 in2
C)
12 in2
D)
196 in2
48)
Define the radius in terms of arc length, s, and the central angle, Θ.
A)
r = Θs
B)
r=s+Θ
C)
r=Θ-s
r=
D)
s
Θ
49)
Which formula is used to find the volume of a pyramid?
A)
Area of its base · height.
B)
1
2
(Area of its base · height)
C)
1
3
(Area of its base · height)
D)
50)
3·(Area of its base · height)
To find the volume of the figure shown, we multiply the area of the base by the height.
Which figure shown here uses the same formula?
A)
B)
C)
D)
51)
This pentagonal prism is cut by the plane shown. The plane is parallel to the base of the
pentagonal prism. What is the shape of the cross-section?
A)
hexagon.
B)
pentagon.
C)
rectangle.
D)
triangle.
52)
A plane intersects a rectangular prism as shown. Describe the cross-section.
A)
circle
B)
rectangle
C)
trapezoid
D)
triangle
53)
Identify the center of the circle whose equation is
(x - 2)2 + (y + 8)2 = 16.
A)
(-2,-8)
B)
(-2,8)
C)
(2,-8)
D)
(2,8)
54)
On a coordinate grid, where is the center of this circle?
x2 + y 2 = 2
A)
(-1, -1)
B)
(0, 0)
C)
(1, 1)
D)
(2, 2)
55)
We can find the length of FG using the Distance Formula:
FG =
(3 - 1)2 + (-1 - 3)2
Which formula also represents the length of FG?
A)
FG = 4 + 2
B)
FG = (4 + 2)2
C)
FG = (4 - 2)2
D)
FG2 = 42 + 22
56)
The points (5, 3), (3, -4), (10, 3), and (8, -4) are the vertices of a polygon. What
type of polygon is formed by these points?
A)
Kite
B)
Parallelogram
C)
Pentagon
D)
Trapezoid
57)
Find the slope of a line parallel to y =
1
2
x + 3.
A)
-2
B)
1
2
C)
1
2
D)
2
58)
line j: y =
2
3
x+
1
2
line k: y =
1
2
x+
2
3
line l: y =
2
3
x+
3
2
line m: y =
3
2
x+
1
2
These four lines have been graphed on the same coordinate grid. Which lines
are parallel to each other?
A)
j and l
B)
j amd m
C)
k and l
D)
k and m
59)
Find the point, M, that divides segment AB into a ratio of 3:2 if A is at (0, 15)
and B is at (20, 0).
A)
(9, 6)
B)
(12, 6)
C)
(12, 9)
D)
(9, 12)
60)
Find the point, M, that divides segment AB into a ratio of 4:7 if A is at (-33, 0)
and B is at (0, 44).
A)
(-22, 15)
B)
(-22, 16)
C)
(-21, 15)
D)
(-21, 16)
61)
What is the area of this rectangle?
62)
A)
8x8 y3
B)
8x8 y2
C)
15x8 y2
D)
15x8 y3
What is the area of a square with a side whose length = x + 5?
A)
2x + 10
B)
4x + 20
C)
x2 - 10x + 25
D)
x2 + 10x + 25
63)
The base of a 6-inch long ice cream cone with a diameter of 2 inches, is cut 0.25 inches
from the base. This cut creates two shapes, one is a cone, and the other one resembles a
cylinder since it was cut so close to the base. What is the BEST estimate for the volume of the
shape that resembles a cylinder?
A)
0.26 cubic inches
B)
0.52 cubic inches
C)
0.79 cubic inches
D)
2.66 cubic inches
64)
Ray is late for work, but would like to drink some coffee before he leaves. The coffee in the
pot is too hot, so Ray puts 20 small ice cubes in a mug before pouring in the coffee. The ice
cubes measure 1 cm per side. The mug is cylindrical, and has a height of 9 cm and a base of 7
cm. What is volume of the coffee that will fill the mug after the ice cubes have been added
(round to the nearest whole number)?
A)
113 cm3.
B)
326 cm3.
C)
346 cm3.
D)
424 cm3.
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