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
D
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
D
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)}
D
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)}
A
Sketch the ellipse for the equation.
11
D
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
Explanation:
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)}
B
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
B
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