Exam
Name___________________________________
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
Choose the graph that matches the given function.
1)
f(x) =x+ 2
1)
A)
B)
C)
D)
Choose the inequality that matches the graph.
2)
2)
A)
y –x2– 6x – 2
B)
y > – x2– 6x – 2
C)
y < – x2– 6x – 2
D)
y –x2– 6x – 2
Provide an appropriate response.
3)
Which one of the following is a description of the graph of the solution set for the system below?
x2+ y2
36
4x2+ 9y2
36
3)
A)
The area inside the ellipse (defined by the second equation), including the border.
B)
The area inside the ellipse (defined by the second equation) and outside the circle (defined by
the first equation), including both borders.
C)
The area inside the circle (defined by the first equation) and outside the ellipse (defined by the
second equation), including both borders.
D)
None of these
Which system of inequalities matches the given calculator–generated graph?
4)
4)
A)
y < – x2+ 2
y < 5
B)
y > – x2+ 2
y > 5
C)
y > – x2+ 2
y < 5
D)
y < – x2+ 2
y > 5
Provide an appropriate response.
5)
Which one of the following is a description of the graph of the solution set for the system below?
x2+ y2
36
4x2+ 9y2
36
5)
A)
The area inside the ellipse (defined by the second equation), including the border.
B)
The area inside the ellipse (defined by the second equation) and outside the circle (defined by
the first equation), including both borders.
C)
The area inside the circle (defined by the first equation) and outside the ellipse (defined by the
second equation), including both borders.
D)
None of these
Choose the inequality that matches the graph.
6)
6)
A)
y x2+ 4x + 4
B)
y x2+ 4x + 4
C)
y > x2+ 4x + 4
D)
y < x2+ 4x + 4
Choose the equation that matches the graph.
7)
7)
A)
(x + 3)2
9–(y + 5)2
4= 1
B)
(x + 3)2
4+(y + 5)2
9= 1
C)
(x + 3)2
9+(y + 5)2
4= 1
D)
(y + 5)2
4–(x + 3)2
9= 1
8)
8)
A)
(x – 5)2– (y – 6)2=2
B)
(x – 5)2+ (y – 6)2=2
C)
(x – 5)2+ (y – 6)2=4
D)
(x – 5)2– (y – 6)2=4
Choose the graph that matches the given function.
9)
f(x) =x + 3
9)
A)
B)
C)
D)
6
Choose the inequality that matches the graph.
10)
10)
A)
y < – x2– 6x – 3
B)
y > – x2– 6x – 3
C)
y –x2– 6x – 3
D)
y –x2– 6x – 3
Choose the equation that matches the graph.
11)
11)
A)
x2
25 +y2
4= 1
B)
y2
25 –x2
4= 1
C)
x2
4+y2
25 = 1
D)
x2
4–y2
25 = 1
Which system of inequalities matches the given calculator–generated graph?
12)
12)
A)
y > – x2– 1
y < – 4
B)
y < – x2– 1
y < – 4
C)
y > – x2– 1
y > – 4
D)
y < – x2– 1
y > – 4
Choose the equation that matches the graph.
13)
13)
A)
x2
9–y2
36 = 1
B)
y2
36 –x2
9= 1
C)
x2
36 +y2
9= 1
D)
y2
9–x2
36 = 1
Provide an appropriate response.
14)
Which one of the following is a description of the graph of the solution set for the system below?
x2+ y2
36
4x2+ 9y2
36
14)
A)
The area inside the ellipse (defined by the second equation), including the border.
B)
The area outside the circle (defined by the first equation), including the border.
C)
The area outside the ellipse (defined by the second equation), including the border.
D)
None of these
Choose the inequality that matches the graph.
15)
15)
A)
y 1
2x2+ 3x + 6
B)
y >1
2x2+ 3x + 6
C)
y <1
2x2+ 3x + 6
D)
y 1
2x2+ 3x + 6
D
B
16)
16)
A)
y x2+ 4x + 2
B)
y x2+ 4x + 2
C)
y >x2+ 4x + 2
D)
y <x2+ 4x + 2
Choose the equation that matches the graph.
17)
17)
A)
x2
4+y2
16 = 1
B)
x2
4–y2
16 = 1
C)
x2
16 –y2
4= 1
D)
x2
16 +y2
4= 1
Choose the inequality that matches the graph.
18)
18)
A)
y 1
2x2+ 4x + 6
B)
y 1
2x2+ 4x + 6
C)
y >1
2x2+ 4x + 6
D)
y <1
2x2+ 4x + 6
Choose the graph that matches the given function.
19)
f(x) =x – 3
19)
A)
B)
C)
D)
Which system of inequalities matches the given calculator–generated graph?
20)
20)
A)
y < – x2+ 5
y < 2
B)
y > – x2+ 5
y > 2
C)
y > – x2+ 5
y < 2
D)
y < – x2+ 5
y > 2
Choose the graph that matches the given function.
21)
f(x) =x– 1
21)
A)
B)
C)
D)
Which system of inequalities matches the given calculator–generated graph?
22)
22)
A)
y >x2
y < – 2
B)
y <x2
y < – 2
C)
y <x2
y > – 2
D)
y >x2
y > – 2
23)
23)
A)
y >x2– 4
y > 3
B)
y <x2– 4
y < 3
C)
y >x2– 4
y < 3
D)
y <x2– 4
y > 3
Choose the equation that matches the graph.
24)
24)
A)
(x + 7)2+ (y – 7)2=9
B)
(x + 7)2+ (y + 7)2=9
C)
(x – 7)2+ (y – 7)2=9
D)
(x – 7)2+ (y + 7)2=9
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Provide an appropriate response.
25)
A student thinks that the graphs of the equations
x2
9–y2
16 = 1 and y2
16 –x2
9= 1
are identical. Is the student correct? Explain.
25)
Which method should be used to solve the system? Explain your answer, including a description of the first step.
26)
5x2+ 3y2=36
4x2– 7y2=100
26)
Provide an appropriate response.
27)
Explain the differences between an ellipse and a hyperbola. Both definitions emphasize
distance, but how is distance used differently in these two definitions?
27)
28)
Describe the graph of the solution set of the following inequality:
25x2+ 36y2<49
28)
Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of
intersection of the two graphs is as given. Make a sketch satisfying these conditions.
29)
A line and an ellipse; two points
29)
Which method should be used to solve the system? Explain your answer, including a description of the first step.
30)
x2– y2=16
x + 9y =2
30)
Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of
intersection of the two graphs is as given. Make a sketch satisfying these conditions.
31)
A parabola and a hyperbola; one point
31)
Which method should be used to solve the system? Explain your answer, including a description of the first step.
32)
x2+ y2=9
–6x + y =5
32)
33)
x2+ y2=81
8x – 5y =6
33)
Provide an appropriate response.
34)
Describe the graph of the solution set of the following inequality:
x < – y2– 9
34)
Which method should be used to solve the system? Explain your answer, including a description of the first step.
35)
x2– 7y2=9
10x2+ 9y2=100
35)
Suppose that a nonlinear system is composed of equations whose graphs are those described, and the number of points of
intersection of the two graphs is as given. Make a sketch satisfying these conditions.
36)
A circle and an ellipse; two points
36)
Which method should be used to solve the system? Explain your answer, including a description of the first step.
37)
–9x2– 7y2=4
–3x – 3y = – 2
37)
38)
Two parabolas; four points
38)