Free Printable Precalculus First Quarter Exam

1.

What is the set of all points equal distant from a fixed line and a fixed point?

a)

parabola

b)

circle

c)

hyperbola

d)

ellipse

2.

What is the set of all points whose difference from two fixed points is constant.

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

3.

Define the set of all points whose sum from two fixed points is constant

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

4.

The conic sections were first identified by _______ in about 350 BC

a)

Menach

b)

Meneachus

c)

Menaechus

d)

Mechus

5.

What the fixed distance from the center of a circle to any point on the circle.

a)

center

b)

vertex

c)

radius

d)

diameter

6.

What kind of conic section is the image ?

a)

ellipse

b)

circle

c)

parabola

d)

hyperbola

7.

Who is the mathematician who gave us the conic sections using just one cone

a)

Apollonius of Perga

b)

Menaechus

c)

Democrates

d)

Zeus

8.

A ____________ is the set of all points (x, y) in a plane that are equidistant from a fixed point, called the center.

a)

locus

b)

circle

c)

conic sections

d)

radius

9.

It is the fixed distance from the center of a circle to any point on the circle.

a)

center

b)

radius

c)

diameter

d)

vertex

10.

(x-5)^2+ (y- 4)^2 = 4

Determine the center and radius given the equation of a circle in standard form.

a)

center (5,4)

radius 4

b)

center (5,4)

radius 2

c)

center (-5,-4)

radius 2

d)

center (-5,4)

radius 2

11.

On the given standard equation what is the radius

(x-2)^2 + (y-3)^2 =(√6)^2

a)

3

b)

√6

c)

36

d)

6

12.

Identify the set of all points (x, y) in a plane that are equidistant from a fixed point, called the center.

a)

locus

b)

circle

c)

conic sections

d)

radius

13.

Write the equation of a circle with center (7, 0) with radius 3.

a)

(x - 7)² + y² = 9

b)

x² + (y -7)² = 9

c)

(x - 7)² + y² = 3

d)

x² + (y -7)² = 3

14.

What are the coordinates of the center and the radius of the circle with equation (x - 4)² + (y - 3)² = 25 ?

a)

Center (4, 3)

Radius = 5 units

b)

Center (4, 3)

Radius = 25 units

c)

Center (-4, -3)

Radius = 25 units

d)

Center (-4, -3)

Radius = 5 units

15.

What is the radius of the circle with this equation of (x - 5)² + (y + 7)² = 8?

a)

4

b)

8

c)

4√2

d)

2√2

16.

What is the radius of the circle given by the equation (x - 7)² + (y + 3)² = 25?

a)

3

b)

5

c)

10

d)

25

17.

What is the radius of the circle with equation x² + y² = 1?

a)

0

b)

0.5

c)

1

d)

2

18.

How do we define a parabola using its focus and directrix?

a)

A parabola is the set of all points that are the same distance from a single point, called the focus of the parabola, and a line, called the directrix of a parabola.

b)

A parabola is the set of all points that have a greater y value than a single point, called the focus of the parabola, and a lesser x value than a single point, called the directrix of the parabola.

c)

A parabola is a circle with a center point called the focus of the parabola, and a line from the center of the circle to the circle called the directrix of the parabola.

d)

A parabola is a square in which the center of the square is called the focus of the parabola, and the length of one side of the square is called the directrix of the parabola.

19.

What is the standard equation of a parabola that opens right and whose vertex is at the origin?

a)

$x^2=4cy$

b)

$x^2=-4cy$

c)

y^2=4cx

d)

$y^2=-4cx$

20.

What is the focus of the parabola

(y-5)^2=12(x-2)

?

a)

$(5,5)$

b)

$(2,5)$

c)

$(0,5)$

d)

$(5,1)$

21.

Each point on the curve of a parabola is ____________ to focus and the directrix.

a)

equilateral

b)

perpendicular

c)

equidistant

d)

tangent

22.

Given the graph below, what is the equation of the parabola?

a)

$(y-4)^2=12(x+2)$

b)

$(y-4)^2=-12(x-2)$

c)

$(y+4)^2=-12(x-2)$

d)

$(y+4)^2=12(x-2)$

23.

What is the standard equation of a parabola with

Focus (1,3) and the directrix is 6 units to the left of the focus?

a)

$(y-3)^2=24(x-7)$

b)

$(y-3)^2=12(x+2)$

c)

$(y-3)^2=-24(x-7)$

d)

$(y-3)^2=-12(x-7)$

24.

Which parabola has a vertex at

(-3,0)

?

a)

$(y+3)^2=8x$

b)

$(x+3)^2=8y$

c)

$(x-3)^2=8y$

d)

$(y-3)^2=8x$

25.

The focus is always inside the parabola.

a)

true

b)

false

26.

All parabolas with a vertical directrix open the left or right.

a)

true

b)

false

27.

Find the standard equation of the given ellipse

a)

b)

c)

d)

28.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

29.

Find the standard equation of the given ellipse

a)

b)

c)

d)

30.

The set of all points in a plane the sum of whose distances from two fixed points is a constant is a/an _____.

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

31.

The midpoint of the line segment connecting the foci is the _____.

a)

co-vertice

b)

major axis

c)

center

d)

minor axis

32.

The midpoint of the line segment connecting the foci is the _____.

a)

co-vertice

b)

major axis

c)

center

d)

minor axis

33.

In a hyperbola, which is the longest segment?

a)

a

b)

b

c)

c

34.

What is the orientation of the hyperbola?

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

a)

vertical

b)

horizontal

35.

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)

$\left(1,1\right)$

36.

Which is the graph of the hyperbola?

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

a)

b)

c)

d)

37.

What is the center of this hyperbola?

a)

(4,-2)

b)

(4,2)

c)

(3,3)

d)

(5,3)

e)

(7.5,3)

38.

What is the Transverse Axis of this Hyperbola?

a)

Vertical

b)

Horizontal

c)

Radical

d)

Mythical

e)

Eccentricity

39.

Is the sequence arithmetic: 78, 785, 7855, 78555, ...

a)

Yes

b)

No

40.

Is the sequence arithmetic: 17, 9, 1, -7, ...

a)

Yes

b)

No

41.

Find the common difference: -18, -23, -28, -33, ...

a)

d = -5

b)

d = 5

c)

d = -3

d)

d = 3

42.

Calculate the final sum/total of the series.

a)

6

b)

21

c)

9

d)

2

43.

The summation is the same as which series?

a)

(4+10) + (4+20) + (4+30) + (4+40) + (4+50) + (4+60) + (4+70) + (4+80) + (4+90) + (4+100) + (4+110)

b)

1+2+3+4+5+6+7+8+9+10+11

c)

4 + 110

d)

4 + 10

44.

What sequence follows the formula a_n=4n+11

a)

4, 15, 26, 37...

b)

15, 19, 23, 27...

c)

15, 26, 37, 48...

d)

11,15, 19, 23...

45.

Calculate the sum.

a)

66

b)

14

c)

704

d)

114

46.

Evaluate the series.

a)

36

b)

85

c)

35

d)

86

47.

Which of these is a solution to the equation
y = 2x-7?

a)

(2,-3)

b)

(0, 7)

48.

Solve.

a)

-1/2

b)

2

c)

7

d)

no solution

49.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

50.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

Precalculus First Quarter Exam

Total questions: 50

Worksheet time: 52mins

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