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What is the perimeter of a pentagon whose side lengths are 3, 5, 7, 2, and 13?

(A)
13

(B)
28

(C)
30

(D)
Such a pentagon doesn't have perimeter

A line segment of length 4 is bisected by a line segment of length 12. What is the
perimeter of this figure?

(A)
16

(B)
14

(C)
8

(D)
This figure does not have a perimeter

If a circle is inscribed in an equilateral triangle with side length 6, what is the
circumference of that circle?

(A)
4Π

(B)
2
Π

(C)
Π

(D)
Impossible to calculate

A circle with what radius has the same area as circumference?

(A)
Radius = 1

(B)
Radius = 2

(C)
Radius = 3

(D)
There is no such circle

In parallelogram ABCD, AB has length
2
BC has length 6, and
angle A is 30 degrees. What is the area of parallelogram ABCD?

(A)
12

(B)
6

(C)
18

(D)
24

What is the area of the figure below?

(A)
2

(B)
4

(C)

(D)
2

What is the area of the shaded region?

(A)
72 - 12Π

(B)
72 - 6Π

(C)
90 - 18Π

(D)
54Π

What must be the side length of an equilateral triangle in order for its area to equal its perimeter?

(A)
3

(B)
4

(C)

(D)
1

What is the area of a regular hexagon with side length 6?

(A)
108

(B)
54

(C)
72

(D)
Impossible to calculate

Two parallel chords of length
2
cut a circle into 4 congruent arcs. What is the area of this circle?

(A)
pi

(B)
2Π

(C)
4Π

(D)
8Π

What is the area of a triangle with sides of lengths 5, 6, and 7?

(A)
6

(B)
18

(C)
4

(D)
Impossible to calculate

What is the area of a triangle with side lengths of 9, 40, and 41?

(A)
120

(B)
64

(C)
12

(D)
180

If a circle with area 49 is inscribed in a square, what is the area of that square?

(A)
49

(B)
49Π

(C)
7

(D)
196/Π

What is the surface area of a right pyramid whose base is a square with side length 6, and
whose altitude has length 4?

(A)
108

(B)
32Π

(C)
96

(D)
54

What is the surface area of a sphere with radius 4?

(A)
4Π

(B)
16Π

(C)
32Π

(D)
64Π

The volume of a right circular cone is
180Π
. What is the volume of the right circular
cone that shares a base with the right circular cylinder and whose vertex lies at the center
of the other base of the cylinder?

(A)
90Π

(B)
60Π

(C)
30Π

(D)
Impossible to calculate

The volume of a prism is 240, and its base has area 12. What are the lengths of its lateral
faces?

(A)
10

(B)
20

(C)
12Π

(D)
Impossible to calculate

A prism has a rhombus for a base. The length of the sides of the rhombus is 13, and the
longer diagonal of the rhombus is 24. The altitude of the prism is 12. What is its
volume?

(A)
1440

(B)
1200

(C)
960

(D)
440

A sphere is circumscribed about a cube with edge length
5
. What is
the volume of the sphere

(A)
200Π

(B)
500Π

(C)
500Π/3

(D)
800Π/3

If the lengths of a triangle are 16, 30, and 34, what is its most specific classification?

(A)
Scalene Obtuse

(B)
Isosceles Acute

(C)
Right

(D)
Scalene Right

What do you know about an isosceles triangle if it contains a 60 degree angle?

(A)
It is also right

(B)
It is equilateral

(C)
It is scalene

(D)
Nothing

What are the lengths of the sides of an isosceles right triangle?

(A)
1, 1, and

(B)
Any length as long as all three sides are the same

(C)
x
,
x
, and
x
, where
x
is any real number greater than zero

(D)
Any length at all

A triangle is formed by a diameter of a circle and two chords of that circle. The radius of
the circle has length
x
. One of the sides of the triangle has length
x
. The area of the
triangle is
32
. What are the lengths of the three sides of the triangle?

(A)
3,
4
, 5

(B)
4, 6, 8

(C)
8,
8
, 16

(D)
Impossible to calculate

When two equilateral triangles are joined by one side, what new polygon is formed?

(A)
A square

(B)
A trapezoid

(C)
A rhombus

(D)
Another equilateral triangle

A triangle's base is three, and its area is 6. What kind of triangle is it?

(A)
An isosceles triangle

(B)
A right triangle

(C)
A scalene triangle

(D)
Impossible to tell

An isosceles triangle with base 8 is divided into two triangles by the altitude from its
vertex angle. If the altitude of the isosceles triangle was 7.5, what were the lengths of its
legs?

(A)
8.5

(B)
5

(C)
4

(D)
Impossible to calculate

An isosceles triangle has an angle of 110 degrees. Which angle is it?

(A)
The vertex angle

(B)
One of the base angles

(C)
It could be any angle

(D)
Such an isosceles triangle cannot exist

If triangle ABC is congruent to triangle DEF, which of the following are true?

(A)
Angle A = angle D

(B)
FD = CA

(C)
Angle BCA = angle DFE

(D)
All of the above are true

Which kinds of triangles always have six parts that correspond?

(A)
Isosceles triangles

(B)
Right triangles

(C)
Equilateral triangles

(D)
All triangles have six corresponding parts

The diagonals of square ABCD intersect at point E. Which of the following pairs of
triangles are congruent?

(A)
ABC and CED

(B)
BEC and ADC

(C)
CED and AEB

(D)
DEA and BAD

Triangles ABC and DEF are both right triangles, with their right angle at vertex A and D,
respectively. Which of the followiong statements is true?

(A)
Triangles ABD and DEF are similar

(B)
Angle B = angle E

(C)
Angle B + angle C = angle E + angle F

(D)
The hypotenuses of the triangles are equal

Triangle ABC has side lengths 9, 10, and 11. Triangle DEF has side lengths
x
,
x + 1
, and
x + 2
. If the two triangles are similar, what is the value of
x
?

(A)
18

(B)
9

(C)
Any positive integer

(D)
No value for
x
exists that will make these triangles similar

What kinds of triangles are always similar?

(A)
30-60-90

(B)
Isosceles right

(C)
Equilateral

(D)
All of the above kinds of triangles are always similar

Two right triangles have equal hypotenuses. What is true of these triangles?

(A)
They are congruent

(B)
They are similar

(C)
They are isosceles

(D)
None of the above

Find the value of
x
.

(A)
70 degrees

(B)
55 degrees

(C)
35 degrees

(D)
30 degrees

A circle segment is defined by a chord that cuts an arc of 60 degrees. The radius of the
circle is 6. What is the area of the sector that is bound by the same arc?

(A)
4Π

(B)
6Π

(C)
8Π

(D)
36Π

What is the area of triangle ABC?

(A)
10

(B)
12

(C)
18

(D)
24

An angle has its vertex inside a cirlce. When its sides are extended into lines, they
intercept two arcs, one of 30 degrees, and another of 210 degrees. What is the measure of
the supplement of the original angle?

(A)
30 degrees

(B)
60 degrees

(C)
120 degrees

(D)
Impossible to calculate

An isosceles trapezoid has legs of length
2
and upper base angles with
measure 120 degrees. What is the area of such a trapezoid if its bases sum to 24?

(A)
24

(B)
36Π

(C)
36

(D)
12

In an equilateral triangle, which of the following are true?

(A)
The centroid is the orthocenter

(B)
The orthocenter is the incircle

(C)
The circumcircle is the centroid

(D)
All of the above

What is the measure of angle 1?

(A)
80

(B)
40

(C)
30

(D)
20

Find the value of
x
.

(A)
72.5 degrees

(B)
60 degrees

(C)
40 degrees

(D)
35 degrees

If the circumcircle of a triangle is contained by one of its sides, what kind of triangle is
it?

(A)
Isosceles

(B)
Right

(C)
Equilateral

(D)
Impossible to tell

A regular hexagon has side length 2. A triangle is formed by an apothem, a radius, and
part of a side, that part which lies between the endpoint of the apothem and the vertex to
which the radius is drawn. What are the lengths of the sides of this triangle?

(A)
1, 1, 1

(B)
1, 1,

(C)
1, 2,

(D)
1, 2, 2

If a tangent segment of length
is drawn from a fixed point outside a
circle with radius one, what is the length of the segment with an endpoint at the center of
the circle and at the fixed exterior point?

(A)

(B)
1

(C)
2

(D)
3

What is true of a point that is equidistant from all three vertices of a triangle?

(A)
It is the orthocenter

(B)
It is the center of the cirlce circumscribed about the triangle.

(C)
It lies in the exterior of the triangle.

(D)
It is the incircle of the triangle

What is the measure of angle A?

(A)
140 degrees

(B)
60 degrees

(C)
80 degrees

(D)
50 degrees

What figure results from an isosceles trapezoid whose legs are extended until they
intersect? (Give the most specific term possible)

(A)
An equilateral triangle

(B)
A right triangle

(C)
An isosceles triangle

(D)
A triangle

What is the measure of angle
x
?

(A)
Impossible to tell

(B)
100 degrees

(C)
60 degrees

(D)
80 degrees

Which of the following are determined by three noncolinear points?