Name _________________________________________ ID Number ____________________________
Unit 3 Evaluation
Advanced Algebra 2 (MTHH 040 057)
This evaluation will cover the lessons in this unit. It is open book, meaning you can use your
textbook, syllabus, and other course materials. To submit the evaluation, follow the directions
provided.
A graphing calculator may be used on this evaluation. You may also use scratch paper to
work out the solutions. Select the response that best completes the statement or answers the
question.
____1. The graph of which equation of a circle contains all the points in this table?
x –3
0
y 0
3 0
3
a. x 2 y 2 4 0
b. x 2 y 2 25
c. x 2 y 2 36
d. 6 x 2 6 y 2 54
____2. The graph of which equation of an ellipse contains all the points in this table?
x
–4
–2
0
2
4
y
0
3
2
3
0
a. x 2 4 y 2 16
b. 4 x 2 16 y 2 144
c. 4 x 2 25 y 2 64
d. 9 x 2 y 2 81
____3. Which point is not on the graph of 4 x 2 y 2 4 ?
a. ( 2, 2 3)
b. (–1, 0)
c. (1, 0)
Unit 3 Evaluation
MTHH 040
d. (2, 2)
____4. Which equation does not represent a line of symmetry for the circle with equation
x 2 y 2 100 ?
a. x = 0
b. y
1
x
2
c. y = x
d. y = x + 1
____5. Which equation represents a line of symmetry for the ellipse with equation x 2 9 y 2 9 ?
a. y = –x
b. y = 0
c. y = x
d. xy = 1
____6. The focus of a parabola is at (–3, 3). The vertex is at (0, 3). What is the equation of the
parabola?
1 2
x
12
1
b. x ( y 3)2
12
1
c. y ( x 3)2
12
1
d. x
( y 3)2
12
a. y 3
____7. What is the distance from P(2, –5) to the line y = –8?
a. –6
b. 3
c. 5
d. 10
____8. Which point is equidistant from F(0, 5) and the line y = –5?
a. (–10, 5)
b. (–5, 0)
c. (0, 1)
d. (10, 10)
____9. Which equation represents a parabola that opens to the left?
a. x 2y 2
b. x 2y 2
Unit 3 Evaluation
MTHH 040
c. y 2 x 2
d. y 2 x 2
____10. Which equation represents a parabola that opens downward?
a. x 2y 2
b. x 2y 2
c. y 2 x 2
d. y 2 x 2
____11. Which equation models a circular fountain with C(24, 22) and radius = 10?
a. ( x 24)2 ( y 22)2 100
b. ( x 22)2 ( y 24)2 100
c. ( x 24)2 ( y 22)2 10
d. ( x 24)2 ( y 22)2 10
____12. What is the radius of the circle with equation ( x 5)2 ( y 3)2 144 ?
a. 3
b. 5
c. 12
d. 144
____13. What is the radius of the circle with equation ( x 2)2 3 ( y 1)2 7 ?
a. 2
b. 7
c. 7
d. 4
____14. Circle A has equation ( x 5)2 y 2 169 . The diameter of circle B is one fourth as long as
the diameter of circle A. What is the radius of circle B?
a. 6.5
b. 13
c. 3.25
d. 26
____15. What is the distance between T(9, –5) and the center of the circle with equation
( x 6)2 ( y 1)2 10 ?
a. 5
b. 10
c. 6
d. 1
Unit 3 Evaluation
MTHH 040
____16. Find the distance between the centers of the circles with equations ( x 5)2 ( y 1)2 16
and ( x 1)2 ( y 9)2 49 .
a. 3
b. 10
c. 7
d. 9
____17. What is the approximate area of the circle whose equation is ( x 1)2 ( y 1)2 1 ?
a. 1
b. 3.14
c. 2
d. 6.28
____18. Which equation represents the ellipse with foci on the x-axis, a major axis 9 units long, a
minor axis 4 units long, and the center at the origin?
x2 y 2
1
4
9
x2
y2
b.
1
20.25 4
x2 y 2
c.
1
9
4
x2
y2
d.
1
4 20.25
a.
____19. The point A(–10, 0) is on the ellipse with equation
x2 y 2
1. What is the sum of the
100 64
distances AF1 AF2 , where F1 and F2 are the foci?
a. 10
b. 12
c. 14
d. 20
____20. What is the length of the major axis of the graph of
x2 y 2
1?
100 64
a. 12
b. 2 41
c. 16
d. 20
Unit 3 Evaluation
MTHH 040
____21. What is the length of the minor axis of the graph of
x2
y2
1?
100 64
a. 12
b. 2 41
c. 16
d. 20
____22. Which hyperbola has ( 6,0) as its x-intercepts?
a. y 2 x 2 36
y 2 x2
1
36 49
x2 y 2
c.
1
25 36
x2 y 2
d.
1
36 4
b.
____23. Which hyperbola does not have (0, 4) as its y-intercepts?
a. y 2 x 2 16
b. 4 y 2 16 x 2 64
x2 y 2
1
25 16
y 2 x2
d.
1
16 9
c.
____24. What are the x-intercepts of
y 2 x2
1?
25 49
a. ( 7,0)
b. ( 5,0)
c. (0, 5)
d. none
____25. How does the translation of an ellipse affect the lengths of its axes?
a. Both increase in length.
b. Both decrease in length.
c. Both stay the same length.
d. One increase, the other decreases.
____26. An ellipse with center (–4, –2) has a horizontal major axis of length 6 and a minor axis
length of 4. Which equation represents the ellipse?
Unit 3 Evaluation
MTHH 040
( x 4)2
4
( x 2)2
b.
9
( x 4)2
c.
9
( x 4)2
d.
4
a.
( y 2)2
9
( y 4)2
4
( y 2)2
4
( y 2)2
9
1
1
1
1
____27. The foci of a hyperbola are (0, –4) and (0, 8). Which additional information would allow you
to write an equation for the hyperbola?
a. location of the center
b. location of one vertex
c. midpoint of transverse axis
d. distance from the center to a focus
____28. Which of the following is an equation of a parabola?
a. 2 x 2 5 y 2 4 x 36 0
b. 2 x 2 5 y 4 x 36 0
c. 2 x 2 2y 2 4 x 12y 36 0
d. 2 x 2 5 y 2 36 0
____29. Which conic section is represented by the equation x 2 y 2 6 x 14y 9 ?
a. circle
b. ellipse
c. parabola
d. hyperbola
____30. Which of these conic sections have more than one focus?
a. circle and ellipse
b. parabola and ellipse
c. circle and parabola
d. ellipse and hyperbola
For questions 31–35, choose the correct vocabulary terms to complete each sentence.
a. radius
b. directrix
c. major axis
d. transverse axis
e. standard form of an equation of a circle
_____ 31. In the definition of a parabola, the fixed line is the ______________.
Unit 3 Evaluation
MTHH 040
_____ 32. The vertices of an ellipse are on its ________________.
_____ 33. ( x h )2 ( y k )2 r 2 is the ____________.
_____ 34. The distance from a point on a circle to its center is the _____________ of the circle.
_____ 35. The vertices of a hyperbola are on its ________________.
Carefully check your answers on this evaluation and make any corrections you feel are
necessary. When you are satisfied that you have answered the questions to the best of your
ability, transfer your answers to an answer sheet. Please refer to the information sheet that
came with your course materials.
Unit 3 Evaluation
MTHH 040
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