Question 1
A string running from the ground to the top of a fence has an angle of elevation of
45°. The string is 6 feet long. What is the distance between the fence and where the
string is pegged to the ground?
a)
√6
b)
3√3
c)
3√2
d)
3
e)
12
f)
None of these.
Question 2
Suppose that you are headed toward a plateau 40 meters high. If the angle of
elevation to the top of the plateau is 21°, how far are you from the base of the
plateau, in meters?
∘
a)
b)
c)
d)
e)
∘
∘
∘
∘
f)
None of these.
Question 3
In right triangle ABC with m∠C = 90o, m∠B = 54o and AB measures 16 units.
Find the length of AC.
a)
∘
b)
∘
c)
∘
d)
∘
e)
f)
None of these.
Question 4
Find the area of triangle XYZ if  
∘
, z = 9 and x = 6.
a)
b)
c)
d)
e)
f)
None of these.
Question 5
Find the area of triangle GHJ if  
a)
∘
, h = 6 and j = 17.
b)
c)
d)
e)
f)
None of these.
Question 6
Given isosceles triangle ABC with base BC. If each base angle measures 75° and
each leg is 40 inches long, find the area of this triangle.
a)
b)
c)
d)
e)
f)
None of these.
Question 7
Given triangle ABC, the measure of angle A is 60°, the length of BC is
 , and the
length of AC is
 . How many solutions are there for the measure of angle B?
a)
1
b)
2
c)
Cannot be determined.
d)
0
e)
3
f)
None of these.
Question 8
Given triangle ABC, the measure of angle A is 30°, the length of AB is 4, and the
length of AC is
 . What is the length of side BC?
a)
b)
c)
d)
e)
f)
None of these.
Question 9
ABC is a triangle with
∘
,
∘
, and BC = 4 cm. Find AC.
a)
b)
c)
d)
e)
f)
None of these.
Question 10
ABC is a triangle with AB = 12, BC = 9, and AC = 10. Find cos(A).
Note: You are being asked to find the cosine of A, not the measure of angle A. Do
not use a calculator.
a)
b)
c)
d)
e)
f)
None of these.
Question 11
In triangle ABC, the measure of angle A is 60°, the length of BC is  6√3 , and the
length of AC is  6√2 . Find all possible measures for angle B.
a)
45°
b)
30° or 150°
c)
45° or 135°
d)
60°
e)
120°
f)
None of these.
Question 12
Two cyclists leave the corner of State Street and Main Street simultaneously. State
Street and Main Street are not at right angles; the cyclists' paths have an angle of
135° between them. How far apart are the cyclists after they each travel 7 miles?
The answers below are given in miles. Hint: Use the Law of Cosines.
a)
b)
c)
d)
e)
f)
None of these.
Question 13
State the coordinates of the vertex for the given parabola.
2
a)
b)
c)
d)
e)
f)
None of these.
Question 14
State the endpoints of the focal chord for the given parabola.
2
a)
b)
c)
d)
  and  
  and  
  and  
  and  
e)
  and  
f)
None of these.
Question 15
Find the coordinates of the center for the given circle.
2
2
a)
b)
c)
d)
e)
f)
None of these.
Question 16
State the length of the major axis and the coordinates of the vertices for the given
ellipse.
2
a)
Length of major axis: 14; Vertices:
b)
Length of major axis: 6; Vertices:
c)
Length of major axis: 14; Vertices:
d)
Length of major axis: 6; Vertices:
e)
Length of major axis: 10; Vertices:
f)
None of these.
2
and
and
and
and
and
Question 17
State the coordinates of the foci for the given ellipse.
2
and
a)
and
b)
and
c)
and
d)
and
e)
f)
2
None of these.
Question 18
Write the following in standard form for an ellipse.
2
2
2
2
2
2
2
2
2
2
2
a)
b)
c)
d)
e)
f)
None of these.
2
Question 19
State the coordinates of the foci for the following:
2
a)
  and  
b)
  and  
  and  
c)
d)
  and  
e)
  and  
f)
2
None of these.
Question 20
State the equations of the asymptotes for the following:
2
a)
,
b)
,
c)
,
d)
,
e)
,
f)
None of these.
2
Question 21
Describe the graph of the following equation:
2
a)
Two intersecting lines
b)
Point
c)
There is no graph
d)
One line
e)
None of these.
2
Question 22
Graph the following system of equations. How many points of intersection are
there?
2
2
a)
6
b)
0
c)
2
d)
4
e)
1
f)
None of these.
2
2
Question 23
Find the  x-coordinate(s) of the point(s) of intersection for the following equations:
,
a)
b)
,
,
c)
d)
,
e)
,
f)
None of these.
Question 24
Find the x-coordinate(s) of the point(s) of intersection for the following equations:
2
2
2
a)
2
,
,
b)
c)
,
d)
,
e)
,
f)
None of these.
Question 25
Find the point(s) of intersection for the following functions:
2
a)
and
b)
and
c)
and
d)
and
e)
There are no points of intersection.
f)
None of these.