Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the
question.
Match the equation to its graph.
1)
y2
9–x2
4= 1
1)
A)
B)
C)
D)
2)
x = – (y – 2)2– 1
2)
A)
B)
C)
D)
3)
x =(y + 1)2+ 2
3)
A)
B)
C)
D)
3
4)
x2
4–y2
16 = 1
4)
A)
B)
C)
D)
Solve the system by the substitution method.
5)
10x2+4y2=100
y = x +5
5)
A)
(0, –5), –20
7, 15
7
B)
(0, 5), 20
7, 55
7
C)
(0, –5), 20
7, 55
7
D)
(0, 5), –20
7, 15
7
Solve the problem.
6)
6)
The ferris wheel in the figure has a radius of 35 meters. The distance between the top of the ferris
wheel and the ground is 76 meters. The rectangular coordinate system shown has its origin on the
ground directly below the center of the wheel. Use the coordinate system to write the equation of
the circular wheel.
70 m
76 m
A)
x2+y2=352
B)
x2+(y +41)2=352
C)
x2+(y –41)2=702
D)
x2+(y –41)2=352
Solve the system by the addition method.
7)
x2–y2=25
9x2+25y2=225
7)
A)
{(0, 3), (0, –3)}
B)
{(3, 0), (–3, 0)}
C)
{(0, 5), (0, –5)}
D)
{(5, 0), (–5, 0)}
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
8)
9x2=225 –9y2
8)
A)
ellipse
B)
circle
C)
parabola
D)
hyperbola
Solve the system by the addition method.
9)
y =x2+ 10
y = – x2+ 12
9)
A)
{(1, 11), (–1, 11)}
B)
{(11, 1), (11, –1)}
C)
{(1, 11), (1, –11), (–1, 11), (–1, –11)}
D)
{(1, 11), (1, –11)}
10)
x2– 2y2= 2
3x2+ 2y2= 14
10)
A)
{(1, 2), (–1, 2), (1, –2), (–1, –2)}
B)
{(2, 1), (2, –1), (–2, 1), (–2, –1)}
C)
{(2, 1), (–2, –1)}
D)
{(–1, 2), (1, –2)}
Solve the problem.
11)
11)
The arch beneath a bridge is semi–elliptical, a one–way roadway passes under the arch. The
width of the roadway is 30 feet and the height of the arch over the center of the roadway is 12
feet. Two trucks plan to use this road. They are both 10 feet wide. Truck 1 has an overall height of
11 feet and Truck 2 has an overall height of 12 feet. Draw a rough sketch of the situation and
determine which of the trucks can pass under the bridge.
A)
Truck 1 can pass under the bridge, but Truck 2 cannot.
B)
Truck 2 can pass under the bridge, but Truck 1 cannot.
C)
Both Truck 1 and Truck 2 can pass under the bridge.
D)
Neither Truck 1 nor Truck 2 can pass under the bridge.
Graph the ellipse.
6
12)
x2
9+y2
16 = 1
12)
A)
B)
C)
D)
Find the vertices of the hyperbola with the given equation.
13)
121y2–16x2=1936
13)
A)
(0, –4), (0, 4)
B)
(–4, 0), (4, 0)
C)
(–11, 0), (11, 0)
D)
(0, –11), (0, 11)
Graph the ellipse.
14)
x2+4y2=12
14)
A)
B)
C)
D)
Solve the system by the addition method.
15)
x2+y2=25
25x2+4y2=100
15)
A)
{(0, 5), (0, –5)}
B)
{(0, 2), (0, –2)}
C)
{(2, 0), (–2, 0)}
D)
{(5, 0), (–5, 0)}
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic
section.
16)
2x2=14 –2y
16)
A)
parabola
B)
ellipse
9
C)
hyperbola
D)
circle
Sketch the ellipse for the equation.
17)
9(x + 2)2+(y – 2)2=9
17)
A)
B)
10
C)
D)
Find the coordinates of the vertex for the horizontal parabola defined by the given equation.
18)
x = – 4(y + 7)2+ 2
18)
A)
(–2, 7)
B)
(2, –7)
C)
(2, 7)
D)
(–2, –7)
11
Find the standard form of the equation of the ellipse.
19)
19)
A)
x2
8+y2
5= 1
B)
x2
25 +y2
64 = 1
C)
x2
64 +y2
25 = 1
D)
x2
5+y2
8= 1
Indicate whether the graph of the equation is a parabola, circle, ellipse, or hyperbola.
20)
x2=36 –4y2
20)
A)
parabola
B)
circle
C)
ellipse
D)
hyperbola
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola’s axis of symmetry.
21)
x = – (y – 2)2+ 8
21)
12
A)
Axis of symmetry is x = – 2.
B)
Axis of symmetry is y = – 2.
C)
Axis of symmetry is x =2.
D)
Axis of symmetry is y =2.
Give the center and radius of the circle described by the equation and graph the equation.
22)
(x –2)2+(y +1)2=4
22)
13
A)
center (–2, 1), r =2
B)
center (–2, –1), r =2
C)
center (2, 1), r =2
D)
center (2, –1), r =2
Sketch the ellipse for the equation.
23)
16(x – 1)2+4(y + 2)2=64
23)
14
A)
B)
C)
D)
Solve the system by the addition method.
24)
x2– 3y2– 1 = 0
4x2+ 3y2– 19 = 0
24)
A)
{(1, 2), (–1, 2), (1, –2), (–1, –2)}
B)
{(–1, 2), (1, –2)}
C)
{(2, 1), (2, –1), (–2, 1), (–2, –1)}
D)
{(2, 1), (–2, –1)}
Find the vertices of the hyperbola with the given equation.
25)
x2
100 –y2
1= 1
25)
A)
(–10, 0), (10, 0)
B)
(0, –1), (0, 1)
C)
(–1, 0), (1, 0)
D)
(0, –10), (0, 10)
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic
section.
26)
x2
4+y2
4= 1
26)
A)
ellipse
B)
circle
16
C)
hyperbola
D)
parabola
Use vertices and asymptotes to graph the hyperbola.
27)
x2
49 –y2
16 = 1
27)
A)
B)
17
C)
D)
Find the vertices of the hyperbola with the given equation.
28)
y2
121 –x2
1= 1
28)
A)
(0, –11), (0, 11)
B)
(–1, 0), (1, 0)
C)
(–11, 0), (11, 0)
D)
(0, –1), (0, 1)
Solve the problem.
29)
29)
A rectangle has a diagonal of 5 feet and a perimeter of 14 feet. Find the rectangle’s dimensions.
A)
3 ft by 4 ft
B)
4 ft by 6 ft
C)
3 ft by 8 ft
D)
3 ft by 8 ft or 4 ft by 6 ft
Find the standard form of the equation of the ellipse.
30)
30)
A)
x2+y2
25 = 1
B)
x2
5+y2= 1
C)
x2
25 +y2= 1
D)
x2+y2
5= 1
Graph the ellipse.
31)
x2
25 +y2
16 = 1
31)
A)
B)
19
C)
D)
Solve the problem.
32)
32)
The arch beneath a bridge is semi–elliptical, a one–way roadway passes under the arch. The
width of the roadway is 38 feet and the height of the arch over the center of the roadway is 9 feet.
Two trucks plan to use this road. They are both 10 feet wide. Truck 1 has an overall height of
9 feet and Truck 2 has an overall height of 8 feet. Draw a rough sketch of the situation and
determine which of the trucks can pass under the bridge.
A)
Truck 1 can pass under the bridge, but Truck 2 cannot.
B)
Truck 2 can pass under the bridge, but Truck 1 cannot.
C)
Both Truck 1 and Truck 2 can pass under the bridge.
D)
Neither Truck 1 nor Truck 2 can pass under the bridge.
Use the vertex and intercepts to sketch the graph of the equation. Give the equation for the parabola’s axis of symmetry.
33)
x =y2+ 14y + 57
33)
20