Midterm in Pre Calculus

1. MIDTERM EXAMINATION in
Pre Calculus
Name: _____________________________________________ Date: ______________ Score: _______
Directions: Read each question carefully. Encircle the letter of your answer.
1. What type of conic section is being described by the equation?
𝑦 =
1
2
𝑥2
A. Circle B. Ellipse
C. Hyperbola D. Parabola
2. Which among the graph describes the given equation?
2 2
x y 25 
A. B.
C. D.
For items 3 and 4, use the figure below:
3. Where is the center of the circle located?
A. (1, -2) B. (2, -2) C. (2,2) D. (-2,2)
4. What is the equation of the circle in standard form?
A. 2 2
4 4 4 0x y x y     C. 2 2
4 4 4 0x y x y    
B. 2 2
4 4 4 0x y x y     D. 2 2
4 4 4 0x y x y    
5. Based on the given information, what is the standard form of the circle?
center: (15,5) and radius: 1
A. (x−15)2
+ (y + 5)2
= 1 B. (x + 15)2
+ (y + 5)2
= 1
C. (x−15)2
+ (y + 5)2
= 9 D. (x−15)2
+ (y−5)2
= 1
6. What is the center and radius of the given circle?

2. 2 2
2y y 18x 57 x    
A. center: (−9,1); radius: 5 B. center: (−10,0); radius: 5
C. center: (9,1); radius: 5 D. center: (2,10); radius: 5
7. If both x2
and y2
appear, and their coefficients A and B have different signs, then these
describes a:
A. Parabola B. Ellipse C. Circle D. Hyperbola
8. If both x2
and y2
appear, and their coefficients A and B have the same signs and are equal,
then these describes a:
A. Parabola B. Ellipse C. Circle D. Hyperbola
9. Which among the graph describes the given equation?
𝑥2
+
𝑦2
9
= 1
A. B.
C. D.
For items 10-13, use the figure below.
10. Where is the center of the ellipse located?
A. (-2,0) B. (-1,0) C. (2,0) D. (-1,0)
11. What is the length of the covertex of the ellipse from its center?
A. 2 units B. 3 units C. 4 units D. 5 units
12. How far is the second foci from the first foci?

3. A. 2 units B. 4 units C. 8 units D. 12 units
13. What the general equation of the given ellipse?
A.
 
2 2
1
1
16 9
x y
  C.
 
22
1
1
16 9
yx 
 
B.
 
2 2
1
1
9 16
x y
  D.
 
22
1
1
9 16
yx 
 
14. Where are the foci of the ellipse
2 2
x y
1
144 169
  ?
A. (5,0), (-5,0) B. (0,5), (0, -5) C. (1,7), (1, -3) D. (-1,6), (-1, -4)
15. Given the equations 2
x y and 2
y x , in how many points will the curves intersect?
A. 0 B. 1 C. 2 D. 3
16. From (12), where will the given curves intersect?
A. (0,0) B. (0,0),(1,1) C. (0,0),(1,1),(-1,-1) D. None of these
17. Given the equations 2 2
x y 16  and, in how many points will they intersect?
A. 0 B. 1 C. 2 D. 3
18. From (10), where will they intersect?
A. (4,0) B. (4,0),(0,-4) C. (-4,0),(4,0),(0,-4) D. None of these
19. In how many points can a circle and a line intersect?
A. 0 B. 1 C. 2 D. All of the above
20. Describe the graph of the equation  
2
y 1 4y   .
A. Parabola opening upward C. Parabola opening to the right
B. Parabola opening downward D. Parabola opening to the left
21. Determine the center of the circle given the equation   
2 2
x 2 y 1 1    .
A. (2,-1) B. (-2,-1) C. (-2,-1) D. (2,1)
22. Which of the following is an equation of a hyperbola?
A.
2
2
25
4
x
y  C. 2
3 5 6 0x y x   
B. 2 2
4 3 4 6 0x y x y     D.
2 2
1
4 9
x y
 
23. Which among the graph describes the given equation?
2 2
y y
1
16 16
 
A. C.

4. B. D.
24. What are the vertices of the given hyperbola?
 
2
2
x 4 y
1
9 36

 
A. (-1,0),(-7,0) B. (0,7),(0,1) C. (-4,3),(-4,-3) D. (-4,6),(-4,-6)
25. In the conic
2 2
x y
1
25 100
  , how far are the vertices from each other?
A. 10 B. 15 C. 20 D. 25
26. Which among the graph describes the given equation?
2
y x
A. B.
C. D.
27. Where is the focus of the given parabola 21
y x 6x 20
3
   ?
A.
33
, 7
4
 
  
 
B.
35
8,
4
 
 
 
C.
55
9,
8
 
  
 
D.
25
9,
4
 
  
 
28. Where is the vertex of the given parabola 2
y 3x 48x 198    ?
A. (-8,6) B. (-8,-6) C. (6,8) D. (6,-8)
29. What is the solution of the given system of equations?
2
2y 27x y 17 0
3x y 1 0
    
   

5. A. (1,2) B. (9,1) C. No solution D. (1,2), (-10,4)
30. Which of the following is not a conic section?
A. Parabola B. Circle C. Line D. Ellipse
31. What is the solution of the given system of equations?
2 2
x y 3x 7y 18 0
x y 3 0
    
  
A. (-3,0),(-6,3) B. (-2,-1) C. (-2,-1),(-6,3) D. (-3,0),(-2,-1)
For items 29-31, given the system of nonlinear equations below:
2 2
25
2 3 6
x y
x y
  

  
32. What kind of conic section is 2 2
1x y  ?
A. Circle B. Parabola C. Ellipse D. Hyperbola
33. What is the graph of the equation 2 3 6x y   ?
A. Circle B. Line C. Parabola D. Ellipse
34. Which of the following is a solution to the system?
A. (-3,0) B. (3,4) C. (-4,2) D. (2,3)
For items 35-36, use the figure below.
35. What are the point of intersection of the line and the circle?
A. (1,0) & (0, -1) C. (-1,0) & (0,1)
B. (-1,0) & (0,-1) D. (1,0) & (-1,0)
36. Which of the following are the equations of the line and the circle.
A.
2 2
1
1
x y
y x
  

 
C.
2 2
1
1
x y
x y
  

 
B.
2 2
1
1
x y
x y
  

 
D.
2 2
1
1
x y
y x
  

  

6. For items 37-39, refer to the figure below.
37. Where is the center of the hyperbola located?
A. (0,0) B. (0, -1) C. (0,1) D. (-1,0)
38. What are the asymptotes of the hyperbola?
A. y x  B. 2y x  C. 3y x  D. 4y x 
39. Where are the vertices of the the hyperbola?
A. ( 2, 1),(2, 1)   C. ( 1, 1),(1, 1)  
B. (2, 1),(1, 1)  D. ( 2,1),(2, 1) 
40. What is the general equation of the hyperbola?
A.  
22
1 1x y   C.  
2 2
1 1x y  
B.  
2 2
1 1x y   D.  
22
1 1x y  