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Pure Math 30
Module 4 Test (A)
____ Reviewed
Multiple Choice
Circle the best answer. One mark each
1. Replacing x with 1 x in any relation has the effect of:
4
A.
vertically stretching the relation by a factor of 1
4
B.
horizontally stretching the relation by a factor of 1
C.
vertically stretching the relation by a factor of 4
D.
horizontally stretching the relation by a factor of 4
4
2. The degenerate form of a parabola is/are:
A.
a line
B.
a line and no graph
C.
a line, no graph, and a line
D.
a line, no graph, and two parallel lines
axis 0o
Terminology review
edge
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angle at the vertex
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3. A plane intersects a double napped cone and is parallel to the axis of the cone (it does
not pass through the vertex). The conic formed is:
A.
a circle
B.
an ellipse
C.
a parabola
D.
a hyperbola
4. A double napped cone has an angle of 50o at the vertex. Which of the following
angles will produce an ellipse?
A.
90o
B.
60o
C.
25o
D.
22.5o
5. Which of the following is a circle?
A.
x2 + 4x + 6y – 17 = 0
B.
x2 – y2 + 4x + 6y – 17 = 0
C.
x2 + 2y2 + 4x + 6y – 17 = 0
D.
x2 + y2 + 4x + 6y – 17 = 0
6. Which of the following is not a circle?
A.
3x2 + 3y2 + 4x + 6y – 17 = 0
B.
 x  y
     9
3  3
C.
 x  y
     9
3  2
D.
x2 + y2 + 4x + 6y – 17 = 0
2
2
2
2
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7. Which of the following circle has its center in quadrant III
A.
x2 + y2 + 2x + 2y – 2 = 0
B.
x2 + y2 – 2x + 2y – 2 = 0
C.
x2 + y2 + 2x – 2y – 2 = 0
D.
x2 + y2 – 2x – 2y – 2 = 0
8. Which of the following is a circle of radius 3 ?
A.
x2  y2  3
B.
 x  2  y

   9
 2  2
C.
y2
 x
1
  
9
3
D.
 x  y  2
  
 9
3  3 
2
2
2
2
2
9. Which of the equations match the circle shown
A.
B.
C.
D.
10.
(x + 2)2 + (y – 3)2 = 1
(x – 2)2 + (y – 3)2 = 1
(x – 2)2 + (y + 3)2 = 1
(x + 2)2 + (y + 3)2 = 1
The x-intercept(s) of the circle x2 + (y – 2)2 = 12 is/are:
A.
2 3
B.
4
C.
2 2
D.
12
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11.
12.
The equation of the circle of radius 2 with a center at (3 , 4) is:
A.
(x – 3)2 + (y – 4)2 = 2
B.
(x + 3)2 + (y + 4)2 = 2
C.
(x – 3)2 + (y – 4)2 = 4
D.
(x + 3)2 + (y + 4)2 = 4
The equations of the ellipses (in order) are:
A.
(x + 2)2 + 2y2 = 1 ; x2 + 2y2 = 1 ; (x – 2)2 + 2y2 = 1 ; x2 + (2(y + 3))2 =
1 ; x2 + (2(y – 3))2 = 1
B.
(x – 2)2 + 2y2 = 1 ; x2 + 2y2 = 1 ; (x + 2)2 + 2y2 = 1 ; x2 + (2(y – 3))2 =
1 ; x2 + (2(y + 3))2 = 1
C.
x2 + (2(y – 3))2 = 1 ; x2 + 2y2 = 1 ; (x + 2)2 + 2y2 = 1 ; (x – 2)2 + 2y2 =
1 ; x2 + (2(y + 3))2 = 1
D.
(x + 2)2 + 2y2 = 1 ; x2 + 2y2 = 1 ; (x – 2)2 + y2 = 1 ; x2 + (2(y – 3)2 = 1
; x2 + (2(y + 3))2 = 1
13.
Which of the following is not the same as the others?
A.
 x  1  y  1

 
 1
 2   3 
B.
( x  1) 2 ( y  1) 2

1
4
9
C.
9x  1  4( y  1) 2  36
D.
x 2  y 2  2 x  2 y  32  0
2
2
2
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The hyperbola  x  1    y  1   1 has a domain:
2
14.
 2 
A.
x 
B.
x  3 ; x  1
C.
x  5 ; x  3
D.
x  1 ; x  3
2
 3 
15.
The equations of the hyperbola (in order) are:
A.
x 2  y 2  1 ; x 2  y 2  1 ; x 2  ( y  2) 2  1 ; x 2  ( y  2) 2  1 ; x 2  ( y  2) 2  1
B.
x 2  y 2  1 ; x 2  ( y  2) 2  1 ; x 2  y 2  1 ; x 2  ( y  2) 2  1 ; x 2  ( y  2) 2  1
C.
x 2  y 2  1 ; x 2  ( y  2) 2  1 ; x 2  y 2  1 ; x 2  ( y  2) 2  1 ; x 2  ( y  2) 2  1
D.
x 2  y 2  1 ; x 2  ( y  2) 2  1 ; x 2  y 2  1 ; x 2  ( y  2) 2  1 ; x 2  ( y  2) 2  1
16.
The vertex of (y + 2) = 3(x – 3)2 is in Quadrant:
A.
I
B.
II
C.
III
D.
IV
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17.
18.
The quadratic relation (y + 1)2 = -3(x – 3) opens:
A.
up
B.
to the left
C.
to the right
D.
down
The parabola y2 + 16x – 2y – 8 = 0 has the x and y-intercepts of:
A.
x = 2 ; y = 4 , –2
B.
x=2 ; y=0, 2
C.
x = 1 ; y = 4 , –2
2
D.
x = 1 ; y = –4 , 2
2
19. The equation of a conic is described by Ax2 + Cy2 + Dx + Ey + F = 0 represents an
ellipse if
A.
B.
C.
D.
AC > 0 , A  C
AC < 0 , A  C
AC = 0
A=C
20. The slopes of the asymptotes of the hyperbola described by 4x2 – 9y2 – 72y – 180 = 0
are
A.
B.
C.
D.
± 4/9
± 9/4
± 2/3
± 3/2
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21. The equation of the axis of symmetry of the parabola described by x – 2 = -4(y + 3)2
is
A.
B.
C.
D.
x = -2
x=2
y = -3
y=3
Written Response
Write your answers in the spaces provided. For full marks, your answers must address all aspects of the
question. Your answers must be presented in a well-organized manner using complete sentences and
correct units.
1. A second-degree equation in two variables represents a conic section. Consider the
following equation:
4x2 – y2 + 16 = 0
a) What kind of conic does this equation likely represent? Explain. (2 marks)
b) Write the equation in standard form. (3 marks)
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c) Sketch the resulting conic. Clearly show all important information. (3 marks)
d) Describe the transformations required to transform the graph of x2 – y2 = -1 , to the
graph obtained in question 2c). (2 marks)
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Pure Math 30 Formula Sheet
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