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Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Match the equation to its graph.
1)
x =(y + 1)2+ 4
1)
A)
B)
C)
D)
2)
y2
16 -x2
9= 1
2)
A)
B)
C)
D)
3)
x2
16 -y2
9= 1
3)
A)
B)
C)
D)
4)
x = - (y + 2)2- 2
4)
A)
B)
C)
D)
Graph the ellipse.
5)
9x2+14y2=126
5)
4
A)
B)
C)
D)
Sketch the ellipse for the equation.
6)
(x - 3)2
25 +y2
16 = 1
6)
5
A)
B)
C)
D)
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
7)
(x + 2)2
9+(y - 2)2
4= 1
7)
6
A)
ellipse
B)
hyperbola
C)
circle
D)
parabola
The equation of a horizontal parabola is given. Determine how the parabola opens and find the parabola's vertex.
8)
x =(y + 3)2+ 6
8)
A)
opens to right; (6, -3)
B)
opens to left; (-3, 6)
C)
opens to right; (6, 3)
D)
opens to right; (-3, 6)
Find the coordinates of the vertex for the horizontal parabola defined by the given equation.
9)
x = - (y - 8)2- 10
9)
A)
(-10, 8)
B)
(8, -10)
C)
(-10, -8)
D)
(-8, -10)
Solve the system by the substitution method.
10)
-6x - y = - 1
y =x2- 6
10)
A)
{(-7, 55), (1, 7)}
B)
{(7, 43), (-1, -5)}
C)
{(-7, 43), (1, -5)}
D)
{(7, 43), (1, -5)}
Give the coordinates for the vertex for the parabola.
11)
x =y2- 10y + 29
11)
A)
(29, 0)
B)
(0, -5)
C)
(4, 5)
D)
(5, 4)
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
12)
36y2=9x2+324
12)
A)
hyperbola
B)
parabola
8
C)
circle
D)
ellipse
Give the center and radius of the circle.
13)
x2+ y2- 12x - 8y + 16 = 0
13)
A)
center: (4, 6); r =6
B)
center: (-4, -6); r =36
C)
center: (6, 4); r =6
D)
center: (-6, -4); r =36
Write the standard form of the equation of the circle with the given center and radius.
14)
Center (-4, -9), r =3
14)
A)
(x - 9)2+ (y - 4)2=9
B)
(x - 4)2+ (y - 9)2=3
C)
(x + 9)2+ (y + 4)2=9
D)
(x + 4)2+ (y + 9)2=3
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
9
15)
x =(y + 1)2- 3
15)
A)
parabola
B)
ellipse
C)
hyperbola
D)
circle
10
Solve the system by the addition method.
16)
x2-y2=16
4x2+16y2=64
16)
A)
{(0, 4), (0, -4)}
B)
{(0, 2), (0, -2)}
C)
{(2, 0), (-2, 0)}
D)
{(4, 0), (-4, 0)}
Solve the problem.
17)
Find the dimensions of a rectangle whose perimeter is 36 feet and whose area is 72 square feet.
17)
A)
5 ft by 13 ft
B)
7 ft by 11 ft
C)
5 ft by 11 ft
D)
6 ft by 12 ft
Find the distance between the pair of points. Round to the nearest thousandth.
18)
(-5.6, -9.4) and (-4.4, -7.5)
18)
A)
5.05 units
B)
19.637 units
C)
4.904 units
D)
2.247 units
Solve the system by the substitution method.
19)
xy =42
x + y =13
19)
A)
{(-7, 6), (-6, 7)}
B)
{(-7, -6), (-6, -7)}
C)
{(7, -6), (6, -7)}
D)
{(7, 6), (6, 7)}
Solve the system.
20)
5x2- 4y2= - 19
5x2+ 2y2=77
20)
A)
{(3, 4), (-3, 4), (3, -4), (-3, -4)}
B)
{(-3, -4), (-4, -3)}
C)
{(3, -4), (3, 4)}
D)
{(3, 4), (4, 3), (-3, -4), (-4, -3)}
Sketch the ellipse for the equation.
11
21)
x2
16 +(y - 5)2
4= 1
21)
A)
B)
C)
D)
Solve the problem.
22)
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 9 feet. Two
trucks plan to use this road. They are both 10 feet wide. Truck 1 has an overall height of 8 feet and
Truck 2 has an overall height of 7 feet. Draw a rough sketch of the situation and determine which
of the trucks can pass under the bridge.
22)
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.
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
23)
x =3+(y +8)2
23)
A)
parabola
B)
circle
13
C)
ellipse
D)
hyperbola
Use vertices and asymptotes to graph the hyperbola.
24)
16x2-y2=64
24)
A)
B)
14
C)
D)
Graph the ellipse.
25)
8x2+16y2=128
25)
A)
B)
15
C)
D)
Find the distance between the pair of points. Give an exact answer.
26)
(0, 0) and (-2, 6)
26)
A)
210 units
B)
4 units
C)
40 units
D)
6 units
Find the midpoint of the line segment with the given end points.
27)
(3 5, -7 5) and (8 5, -2 5)
27)
A)
5 5
2, 5 5
2
B)
11 5
2, -9 5
2
C)
(11 5, -9 5)
D)
-5 5
2, -5 5
2
Sketch the ellipse for the equation.
16
28)
(x + 2)2
16 +(y - 2)2
4= 1
28)
A)
B)
C)
D)
Solve the system by the addition method.
29)
x2- 2y2= 2
3x2+ 2y2= 14
29)
A)
{(-1, 2), (1, -2)}
B)
{(2, 1), (2, -1), (-2, 1), (-2, -1)}
C)
{(1, 2), (-1, 2), (1, -2), (-1, -2)}
D)
{(2, 1), (-2, -1)}
Solve the system.
30)
x2+y2=113
x + y =15
30)
A)
{(-8, 7), (-7, 8)}
B)
{(8, 7), (7, 8)}
C)
{(-8, -7), (-7, -8)}
D)
{(8, -7), (7, -8)}
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
31)
4x2=16 -4y
31)
A)
ellipse
B)
hyperbola
18
C)
circle
D)
parabola
Find the vertices of the hyperbola with the given equation.
32)
y2
1-x2
9= 1
32)
A)
(0, -3), (0, 3)
B)
(0, -1), (0, 1)
C)
(-3, 0), (3, 0)
D)
(-1, 0), (1, 0)
33)
9y2=4x2+36
33)
A)
(0, -3), (0, 3)
B)
(-3, 0), (3, 0)
C)
(-2, 0), (2, 0)
D)
(0, -2), (0, 2)
Give the center and radius of the circle described by the equation and graph the equation.
34)
(x +3)2+(y -2)2=4
34)
19
A)
center (-3, 2), r =2
B)
center (3, 2), r =2
C)
center (3, -2), r =2
D)
center (-3, -2), r =2
Indicate whether the graph of the equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.
35)
x2=16 +(y +7)2
35)
20
