Free Printable PRE-CALCULUS REVIEWER

1.

What are the orientation of the graph of the equation

$\frac{x^2}{169}+\frac{y^2}{225}=1?$

a)

Horizontally Oriented Ellipse

b)

Vertically Oriented Ellipse

c)

Horizontally Oriented Hyperbola

d)

Vertically Oriented Hyperbola

2.

What is the center of

$\frac{x^2}{169}+\frac{y^2}{225}=1?$

a)

$\left(0,\ 0\right)$

b)

$\left(169,\ 225\right)$

c)

$\left(13,\ 15\right)$

d)

$\left(26,\ 30\right)$

3.

What are the vertices of

$\frac{x^2}{169}+\frac{y^2}{225}=1?$

a)

$\left(-13,\ 0\right)\ and\ \left(13,\ 0\right)$

b)

$\left(0,\ -13\right)\ and\ \left(0,\ 13\right)$

c)

$\left(-15,\ 0\right)\ and\ \left(15,\ 0\right)$

d)

$\left(0,\ -15\right)\ and\ \left(0,\ 15\right)$

4.

What are the covertices of

$\frac{x^2}{169}+\frac{y^2}{225}=1?$

a)

$\left(-13,\ 0\right)\ and\ \left(13,\ 0\right)$

b)

$\left(0,\ -13\right)\ and\ \left(0,\ 13\right)$

c)

$\left(-15,\ 0\right)\ and\ \left(15,\ 0\right)$

d)

$\left(0,\ -15\right)\ and\ \left(0,\ 15\right)$

5.

What is the length of the minor axis

$\frac{x^2}{169}+\frac{y^2}{225}=1?$

a)

13 units

b)

15 units

c)

26 units

d)

30 units

6.

What is the length of the major axis

$\frac{x^2}{169}+\frac{y^2}{225}=1?$

a)

13 units

b)

15 units

c)

26 units

d)

30 units

7.

Which is a horizontal ellipse?

a)

$\frac{x^2}{4}+\frac{y^2}{9}=1$

b)

$\frac{x^2}{16}+\frac{y^2}{9}=1$

c)

$\frac{x^2}{16}+\frac{y^2}{16}=1$

d)

$x^2+\frac{y^2}{49}=1$

8.

What is the equation of the given graph?

a)

$\frac{x^2}{7}+\frac{y^2}{6}=1$

b)

$\frac{x^2}{14}+\frac{y^2}{12}=1$

c)

$\frac{x^2}{49}+\frac{y^2}{36}=1$

d)

$\frac{x^2}{36}+\frac{y^2}{49}=1$

9.

What is the equation of a vertical ellipse whose center is (0, 0), length of the major axis is 12 and length of the minor axis is 10?

a)

$\frac{x^2}{36}+\frac{y^2}{25}=1$

b)

$\frac{x^2}{25}+\frac{y^2}{36}=1$

c)

$\frac{x^2}{144}+\frac{y^2}{100}=1$

d)

$\frac{x^2}{100}+\frac{y^2}{144}=1$

10.

In an ellipse, the largest value among a, b, or c is (a) .

11.

What are the foci of the given ellipse?
$\frac{x^2}{64}+\frac{y^2}{81}=1$

a)

$\left(-\sqrt{17},\ 0\right),\ \left(\sqrt{17},\ 0\right)$

b)

$\left(0,-\sqrt{17}\right),\ \left(0,\sqrt{17}\right)$

c)

$\left(0,\ -17\right),\left(0,17\right)$

d)

$\left(-17,0\right),\left(17,0\right)$

12.

In an ellipse, what is the length of the minor axis?

a)

a

b)

2a

c)

b

d)

2b

e)

c

13.

In an ellipse, what is the length of the major axis?

a)

a

b)

2a

c)

b

d)

2b

e)

c

14.

In an ellipse, what distance does c represent?

a)

The distance from the center to a vertex

b)

The distance from the center to an endpoint of the minor axis

c)

The distance from the center to a focus

d)

The length of the minor axis

e)

The length of the major axis

15.

In an ellipse, what distance does b represent?

a)

The distance from the center to a vertex

b)

The distance from the center to an endpoint of the minor axis

c)

The distance from the center to a focus

d)

The length of the minor axis

e)

The length of the major axis

16.

In an ellipse, what distance does a represent?

a)

The distance from the center to a vertex

b)

The distance from the center to an endpoint of the minor axis

c)

The distance from the center to a focus

d)

The length of the minor axis

e)

The length of the major axis

17.

What are the endpoints of the minor axis?

a)

(1, 5) and (1, -5)

b)

(0, 0) and (2, 0)

c)

(4, 0) and (6, 0)

d)

(1, 6) and (1, 4)

18.

Write the standard form of the ellipse:

9x² + 4y² +72x +108=0

a)

$\frac{\left(x-4\right)^2}{16}+\frac{y^2}{36}=1$

b)

$\frac{\left(x+4\right)^2}{4}+\frac{y^2}{9}=1$

c)

$\frac{\left(x-4\right)^2}{4}+\frac{y^2}{9}=1$

d)

$\frac{\left(x+4\right)^2}{16}+\frac{y^2}{36}=1$

19.

The segment containing the center and foci.

a)

Major Axis

b)

Minor Axis

c)

Vertices

d)

Co-Vertices

20.

The major axis coincides with?

a)

the x-axis

b)

the y-axis

21.

What are the endpoints of the minor axis?

a)

(1, 5) and (1, -5)

b)

(0, 0) and (2, 0)

c)

(4, 0) and (6, 0)

d)

(1, 6) and (1, 4)

22.

What are the vertices of the ellipse?

a)

(0, 0)

b)

(7, 1) and (-1, 1)

c)

(3, -5) and (3, 7)

d)

(3, 1)

23.

What is the center of the given equation?

a)

(4, 3)

b)

(-4, -3)

c)

(-4, 3)

d)

(4, -3)

24.

What is the center of the shifted ellipse?

a)

(0,0)

b)

(-3,1)

c)

(1,-3)

d)

(3,-1)

25.

What are the foci of the ellipse?

a)

(-5,1) and (-1,1)

b)

(±√3,0)

c)

(0,1) and (-6,1)

d)

(-3+√3,1) and (-3-√3,1)

26.

The sum of the distances from the foci to any point on the ellipse is equivalent the length of the...

a)

Minor axis

b)

Major axis

c)

Covertex

d)

Vertex

27.

The denotation used to indicate the distance from the center of the ellipse to the focus is...

a)

a

b)

b

c)

c

d)

f

28.

The shorter axis of symmetry of an ellipse is called the...

a)

Major axis

b)

Minor axis

c)

Axis of symmetry

d)

Eccentricity

29.

The endpoints of the major axis of an ellipse are called the...

a)

Vertices

b)

Covertices

c)

Foci

d)

Center

30.

The endpoints of the minor axis of an ellipse are called the...

a)

Vertices

b)

Covertices

c)

Foci

d)

Center

31.

The denotation used to indicate the distance from the center of an ellipse to the covertex is...

a)

a

b)

b

c)

c

d)

f

32.

The standard equation of a horizontal ellipse whose center is at (h, k) is...

a)

b)

c)

d)

33.

The standard equation of a vertical ellipse whose center is at (h, k) is...

a)

b)

c)

d)

34.

Which statement is TRUE?

a)

The center is (0,4)

b)

a = 2

c)

b = 3

d)

c = 5

35.

Which of the following is the standard form of an equation of a horizontal ellipse with center at the origin, length of the major axis is 12 and length of the minor axis is 10?

a)

$\frac{x^2}{36}+\frac{y^2}{25}=1$

b)

$\frac{x^2}{25}+\frac{y^2}{36}=1$

c)

$\frac{x^2}{144}+\frac{y^2}{100}=1$

d)

$\frac{x^2}{100}+\frac{y^2}{144}=1$

36.

Find the equation, in standard form, of the ellipse with the center (2,1), length of vertical major axis of 8 units and length of semi minor axis of 3 units.

a)

$\frac{\left(x+2\right)^2}{16}+\frac{\left(y+1\right)^2}{9}=1$

b)

$\frac{\left(x-2\right)^2}{16}+\frac{\left(y-1\right)^2}{9}=1$

c)

$\frac{\left(x-2\right)^2}{9}+\frac{\left(y-1\right)^2}{16}=1$

d)

$\frac{\left(x+2\right)^2}{9}+\frac{\left(y+1\right)^2}{16}=1$

37.

Given the vertices (-2,4) and (-2,-6) and a focus at (-2,3), what is the location of the center?

a)

C(-2,1)

b)

C(-2,-1)

c)

C(-2,-2)

d)

C(-2,2)

38.

Find the equation, in standard form, of the ellipse with a length of semi major axis of 10 units, foci 5 units left and right of the center (-3,4).

a)

$\frac{\left(x+3\right)^2}{100}+\frac{\left(y-4\right)^2}{75}=1$

b)

$\frac{\left(x-3\right)^2}{100}+\frac{\left(y+4\right)^2}{75}=1$

c)

$\frac{\left(x+3\right)^2}{75}+\frac{\left(y-4\right)^2}{100}=1$

d)

$\frac{\left(x-3\right)^2}{75}+\frac{\left(y+4\right)^2}{100}=1$

39.

Find the equation, in standard form, of the ellipse with the center(5,6), length of vertical semi major axis of 10 units and semi minox axis of 4 units.

a)

$\frac{\left(x+5\right)^2}{100}+\frac{\left(y+6\right)^2}{16}=1$

b)

$\frac{\left(x-5\right)^2}{100}+\frac{\left(y-6\right)^2}{16}=1$

c)

$\frac{\left(x-5\right)^2}{16}+\frac{\left(y-6\right)^2}{100}=1$

d)

$\frac{\left(x+5\right)^2}{16}+\frac{\left(y+6\right)^2}{100}=1$

40.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

41.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

42.

What type of conic section is $3x^2-y^2-11x+4=0$ ?

a)

Ellipse

b)

Circle

c)

Hyperbola

d)

Parabola

43.

Find the standard equation of the given ellipse

a)

b)

c)

d)

44.

Find the standard equation of the given ellipse

a)

b)

c)

d)

45.

Determine the equation of the hyperbola.

a)

$\frac{x^2}{4}-y^2=1$

b)

$\frac{x^2}{2}-y^2=1$

c)

$\frac{x^2}{4}+y^2=1$

d)

$\frac{x^2}{2}+y^2=1$

46.

Coordinates of the foci of the hyperbola

\frac{x^2}{9}-\frac{y^2}{16}=1

are

a)

$\left(\pm\ 3,\ 0\right)$

b)

$\left(\pm\ 4,\ 0\right)$

c)

$\left(\pm\ 5,\ 0\right)$

d)

none of these

47.

Equation of hyperbola if length of transverse axis is 8 and foci $\left(\pm\ 5,\ 0\right)$

a)

$\frac{x^2}{16}-\frac{y^2}{9}=1$

b)

$\frac{x^2}{9}-\frac{y^2}{16}=1$

c)

$\frac{y^2}{16}-\frac{x^2}{9}=1$

d)

none of these

48.

Equation of the hyperbola with vertices

\left(0,\ \pm\ 5\right)

and foci

\left(0,\ \pm\ 8\right)

is

a)

$\frac{y^2}{25}-\frac{x^2}{39}=1$

b)

$\frac{x^2}{25}-\frac{y^2}{39}=1$

c)

$\frac{x^2}{25}+\frac{y^2}{39}=1$

d)

none of these

49.

In a hyperbola, which is the longest segment?

a)

a

b)

b

c)

c

50.

Determine the length of the transverse axis

a)

1.5

b)

2

c)

3

d)

4

51.

Determine the value of b

a)

1

b)

2

c)

3

d)

4

52.

What is the orientation of the hyperbola?

\frac{x^2}{4}-\frac{y^2}{25}=1

a)

vertical

b)

horizontal

53.

Which of the following is a vertex?

\frac{\left(y-1\right)^2}{4}-\frac{\left(x+2\right)^2}{9}=1

a)

$\left(0,2\right)$

b)

$\left(3,0\right)$

c)

$\left(-2,\ -1\right)$

d)

$\left(1,1\right)$

54.

What is the distance between the two foci?

\frac{\left(x+4\right)^2}{36}-\frac{\left(y-5\right)^2}{4}=1

a)

$2\sqrt{10}$

b)

$4\sqrt{10}$

c)

$4\sqrt{2}$

d)

$8\sqrt{2}$

55.

What are the vertices of the graph of $\frac{\left(y-1\right)^2}{16}-\frac{\left(x+1\right)^2}{4}=1$

a)

(-1, 5) and (-1, -3)

b)

(1, 3) and (1, -1)

c)

(5, 1) and (-3, 1)

d)

(1, 5) and (1, -3)

56.

Convert

16x^2-9y^2-64x+18y-89=0\

to standard form

a)

$\frac{\left(x-2\right)^2}{9}-\frac{\left(y-1\right)^2}{16}=1$

b)

$\frac{\left(x-2\right)^2}{9}-\frac{\left(y+1\right)^2}{16}=1$

c)

$\frac{\left(y-1\right)^2}{16}-\frac{\left(x-2\right)^2}{9}=1$

d)

$\frac{\left(y+1\right)^2}{16}-\frac{\left(x-2\right)^2}{9}=1$

57.

Convert

16x^2-9y^2-64x+18y-89=0\

to standard form

a)

$\frac{\left(x-2\right)^2}{9}-\frac{\left(y-1\right)^2}{16}=1$

b)

$\frac{\left(x-2\right)^2}{9}-\frac{\left(y+1\right)^2}{16}=1$

c)

$\frac{\left(y-1\right)^2}{16}-\frac{\left(x-2\right)^2}{9}=1$

d)

$\frac{\left(y+1\right)^2}{16}-\frac{\left(x-2\right)^2}{9}=1$

58.

What are the a and b values for the following hyperbola?
$\frac{\left(x-4\right)^2}{25}-\frac{\left(y+2\right)^2}{4}=1$

a)

a=25, b=4

b)

a=5, b=2

c)

a=4, b=-2

d)

a=0, b=0

59.

What is the center of this hyperbola?

a)

(-2,4)

b)

(4,2)

c)

(3,3)

d)

(5,3)

60.

What are the values of a and b:

$\frac{\left(x+1\right)^2}{9}-\frac{\left(y-3\right)^2}{4}=1$

a)

a = 1, b = 2

b)

a = 9, b = 4

c)

a = 3, b = 2

d)

a = 25, b = 10

61.

This is a conic section where the absolute value of the differences in distances from any point on the curve to the two fixed points is constant.

a)

Hyperbola

b)

Parabola

c)

Ellipse

d)

Circle

62.

What do you call the line segment joining two vertices in a hyperbola?

a)

Transverse axis

b)

Conventional axis

c)

Conjugate axis

d)

Rotational axis

63.

Which of the following is the Standard Form of Equation of a Hyperbola if the Major Axis is Horizontal and the center is at the origin?

a)

$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

b)

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

c)

$\frac{y^2}{a^2}-\frac{x^2}{b^2}=1$

d)

$\frac{y^2}{b^2}-\frac{x^2}{a^2}=1$

64.

The horizontal transverse axis measures 8 units and the conjugate axis measures 5 units. If the center of the hyperbola is at (3, -4), what is the equation of the hyperbola?

a)

$\frac{\left(x-3\right)^2}{16}-\frac{4\left(y+4\right)^2}{25}=1$

b)

$\frac{\left(x+3\right)^2}{16}-\frac{4\left(y-4\right)^2}{25}=1$

c)

$\frac{4\left(x-3\right)^2}{25}-\frac{\left(y+4\right)^2}{16}=1$

d)

$\frac{4\left(x+3\right)^2}{25}-\frac{\left(y-4\right)^2}{16}=1$

65.

Find the equation of the hyperbola with vertices at (5, 6) and (5, 0) and foci at (5, 8) and (5, -2).

a)

$\frac{\left(y-3\right)^2}{9}-\frac{\left(x-5\right)^2}{16}=1$

b)

$\frac{\left(y-3\right)^2}{16}-\frac{\left(x-5\right)^2}{9}=1$

c)

$\frac{\left(y-5\right)^2}{9}-\frac{\left(x-3\right)^2}{16}=1$

d)

$\frac{\left(y-5\right)^2}{16}-\frac{\left(x-3\right)^2}{9}=1$

66.

It is a line passing through the center and covertices of the hyperbola.

a)

transverse axis

b)

major axis

c)

minor axis

d)

conjugate axis

67.

Which of the following has a measure of c units?

a)

center to covertex

b)

center to vertex

c)

focus to center

d)

vertex to covertex

68.

Is the hyperbola vertical or horizontal?

a)

Vertical

b)

Horizontal

69.

The lines which comes closer and closer to the hyperbola and passing through the diagonals of the auxiliary rectangle.

a)

Asymptotes

b)

Transverse axis

c)

Conjugate axis

d)

Principal axis

70.

What are the asymptotes of the hyperbola $\frac{\left(x+2\right)^2}{4}-\frac{\left(y-1\right)^2}{36}=1$

a)

$y=3\left(x+2\right)+1$ $y=-3\left(x+2\right)+1$

b)

$y=9\left(x+2\right)+1$ $y=-9\left(x+2\right)+1$

c)

$y=\frac{1}{3}\left(x+2\right)+1$ $y=\frac{1}{3}\left(x+2\right)+1$

d)

$y=3\left(x+2\right)-2$ $y=-3\left(x+2\right)-2$

PRE-CALCULUS REVIEWER

Total questions: 70

Worksheet time: 3hrs 56mins

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