Free Printable Analytic Geometry

1.

It refers to the horizontal number line in a rectangular coordinate system.

a)

Origin

b)

X-axis

c)

Y-axis

d)

Quadrants

2.

It refers to the vertical number line in a rectangular coordinate system.

a)

Origin

b)

X-axis

c)

Y-axis

d)

Quadrants

3.

It refers to the intersection of the horizontal and vertical number line in a rectangular coordinate system with coordinates as (0,0).

a)

Origin

b)

X-axis

c)

Y-axis

d)

Quadrants

4.

It refers to the four infinite regions in a rectangular coordinate system.

a)

Origin

b)

X-axis

c)

Y-axis

d)

Quadrants

5.

In what quadrant does point A lies?

a)

Quadrant I

b)

Quadrant II

c)

Quadrant III

d)

Quadrant IV

6.

In what part of the axis does point D lies?

a)

Positive x axis

b)

Positive y axis

c)

Negative x axis

d)

Negative y axis

7.

What is the distance between AB

a)

0

b)

8

c)

9

d)

7

8.

How is AB written in the distance formula?

a)

$d\ =\ \sqrt{\left(5-3\right)^2\ +\ \left(0--2\right)^2}$

b)

$d\ =\ \sqrt{\left(2-5\right)^2\ +\ \left(3\ -0\right)^2}$

c)

$d\ =\ \sqrt{\left(5-3\right)^2\ -\ \left(0--2\right)^2}$

d)

$d\ =\ \sqrt{\left(4-3\right)^2\ -\ \left(2-4\right)^2}$

9.

Find the distance between (-3, -11) and (8, -42).

a)

32.1

b)

32.3

c)

32.7

d)

32.9

10.

Find the distance.

a)

9.7

b)

10.7

c)

11.7

d)

12.7

11.

Find the direct distance between the court house and the town hall.

a)

26

b)

6.8

c)

10

d)

7.2 km

12.

Find the midpoint of the segment with the endpoints:(6, 7) and (6, -5)

a)

(0, -1)

b)

(6, 1)

c)

(1, 6)

d)

(0, 1)

13.

Which of the following is the correct midpoint formula given two endpoints (x₁, y₁) and (x₂, y₂)?

a)

b)

c)

d)

14.

What is the midpoint between (3,-1) and (7,-5)?

a)

(5,-2)

b)

(5,-3)

c)

(10,-6)

d)

(2,-2)

15.

a)

1

b)

2

c)

3

d)

4

16.

a)

1

b)

2

c)

3

d)

4

17.

a)

1

b)

2

c)

3

d)

4

18.

a)

PC = 1400

PS = 700

b)

PC=700

PS=1400

c)

PC=1500

PS=700

d)

PC = 1400

PS=800

19.

Given point B(3, k) divides the line segment which joins points A(-1, 3) and C(4, 5) in the ratio m : n. Find the ratio m : n

a)

1 : 4

b)

4 : 1

c)

7 : 4

d)

4 : 7

20.

The slope, represented by 𝒎, is defined as the ratio of the vertical change between two points to the horizontal change between the same two points.

a)

TRUE

b)

FALSE

21.

The vertical change is referred to as the RUN and the horizontal change as the RISE.

a)

TRUE

b)

FALSE

22.

The hilly roads has a slope of positive.

a)

TRUE

b)

FALSE

23.

The road has a slope of negative.

a)

TRUE

b)

FALSE

24.

What is the slope of the line with the equation

4x-y=-12

?

a)

- 4

b)

4

c)

- 1/4

d)

1/4

25.

What is the slope on the line described by the equation

y=\frac{2}{3}x-6

?

a)

$6$

b)

$-6$

c)

$\frac{2}{3}$

d)

$-\frac{2}{3}$

26.

What is the slope of the line passing through the points (2,-3) and (5,6)?

a)

1

b)

2

c)

3

d)

4

27.

What is the slope of the line?

a)

3/2

b)

-3/2

c)

2/3

d)

-2/3

28.

Find the slope of the line that passes through the points (2, 4) and (6, 12)

a)

1/2

b)

-1/2

c)

2

d)

-2

29.

(TRUE or FALSE). If the graph of an equation is a vertical line, then the slope is UNDEFINED.

a)

True

b)

False

30.

Find the slope of the line.

a)

1/2

b)

-1/2

c)

2/1

d)

-2/1

31.

What is the definition of inclination of a line?

a)

The inclination of a line is the slope of the line.

b)

The inclination of a line is the angle that the line makes with the positive x-axis in a coordinate plane.

c)

The inclination of a line is the length of the line segment between two points on the line.

d)

The inclination of a line is the angle that the line makes with the positive y-axis in a coordinate plane.

32.

Find the inclination of a line with a slope of 2.

a)

90 degrees

b)

30 degrees

c)

45 degrees

d)

63.43 degrees

33.

What is the inclination of a horizontal line?

a)

180 degrees

b)

0 degrees

c)

90 degrees

d)

45 degrees

34.

Calculate the inclination of a line passing through the points (-1, 4) and (3, -2).

a)

0

b)

-3/2

c)

2/3

d)

-5/2

35.

What is the measure of the angle of inclination of the line 2x = 5 - y?

a)

$-63\degree$

b)

$63\degree$

c)

$117\degree$

d)

$-117\degree$

36.

If the line passes through P(9, 4), and V(-11, 4), what is the angle of inclination?

a)

$90\degree$

b)

$0\degree\ or\ 180\degree$

c)

$Between\ 0\degree\ and\ 90\degree$

d)

$Between\ 90\degree\ and\ 180\degree$

37.

The slope of the line passing through (x, 9) and (-5, 2) is undefined. What is the value of x?

a)

$all\ real\ numbers$

b)

$greater\ than\ -5$

c)

$-5$

d)

$5$

38.

The angle from line 1 to line 2 is 45°. If line 1 is y = 2x + 1, what is the slope of line 2?

a)

$1$

b)

$-1$

c)

$3$

d)

$-3$

39.

Calculate the angle formed by the lines 3x + 4y = 8 and 6x - 8y = 16.

a)

45 degrees

b)

90 degrees

c)

30 degrees

d)

180 degrees

40.

What is the measure of ∠ABC?

a)

25°

b)

75°

c)

108°

d)

150°

41.

The angle between two lines: 2x+3y=5 and 3x-2y=7 is

a)

$\theta=90^0$

b)

$\theta=\frac{13}{12}$

c)

$\theta=\frac{1}{2}$

d)

$\theta=1$

42.

What is standard form of a line?

a)

y = mx + b

b)

Ax + By = C

c)

y - y1 = m(x - x1)

d)

y = Ax + By

43.

Which equation is written in STANDARD form?

a)

y = 1/2x + 2

b)

y - 3 = -5(x + 2)

c)

7x + 2y = 9

d)

3x + 2 = y

44.

Put this into standard form:

2x - 9 = 13y

a)

2x - 13y - 9 = 0

b)

2x - 13y = 9

c)

2x = 13y + 9

d)

2x + 13y = 9

45.

Give the x-intercept
3x + 8y = 24

a)

(8, 0)

b)

(0, 8)

c)

(3, 0)

d)

(0, 3)

46.

What is the y-intercept of

2x - 5y = 35?

a)

(0,-7)

b)

(-7,0)

c)

(35/2, 0)

d)

(0,35/2)

47.

Rewrite the equation into Standard form

a)

5x + 8y = 56

b)

-5x + 8y = 56

c)

8x + 5y = 56

d)

5x + y = 7

48.

Name the x- and y-intercepts for the equation: 5x + 3y = 15

a)

(3, 0) and (0, 5)

b)

(0, 3) and (5, 0)

c)

(5, 15) and (15, 3)

d)

(0, -3) and (5, 0)

49.

Write this equation in Standard Form

13 - 6x - y = 0

a)

-6x - y = -13

b)

13 - 6x = y

c)

6x + y = 13

d)

y = -6x + 13

50.

Find the slope of a line that passes through the given points:

(5,1) and (8,3)

a)

$\frac{2}{3}$

b)

$\frac{-2}{3}$

c)

$\frac{3}{-2}$

d)

$\frac{3}{2}$

51.

Write a linear equation in slope intercept form of a line with a slope of 12 and y intercept of 10

a)

y=12x-10

b)

y=10x+12

c)

y=12x+10

d)

x=10x-12

52.

How do we solve for slope given two points

a)

y=mx+b

b)

Y₂-Y₁/X₂-X₁

c)

Y-Y=M(X-X)

d)

X₂-X₁/ Y₂-Y₁

53.

What is point slope form

a)

x-x₁=m(y-y₁)

b)

y=mx+b

c)

y-y₁=m(x-x₁)

d)

y₁-y=m(x₁-x)

54.

What is the equation for the line that passes through the points (4,2) and (0,6)?

a)

y = x + 6

b)

y = -2x + 2

c)

y = -x - 6

d)

y = -x + 6

55.

Write the equation of the line.

a)

y = -2/3x + 4

b)

y = 2/3x + 4

c)

y = 3/2x + 4

d)

y = -3/2x + 4

56.

What does the "b" stand for in y=mx+b?

a)

slope

b)

x-intercept

c)

y-intercept

57.

m= 5

(2, 4)

a)

y - 2= 5(x - 4)

b)

y - 4= 5(x - 2)

c)

y- 5 = 4(x - 2)

d)

y - 2 = 4(x - 5)

58.

Which of these represents point-slope form of a linear equation?

a)

y - y₁ = m(x - x₁)

b)

Ax + By = C

c)

y = mx + b

d)

y=kx

59.

Write the equation in point-slope form of the line that passes through the given point and has the given slope:

(-2, -1); m= -3

a)

y + 1 = -3(x - 2)

b)

y + 1 = -3(x + 2)

c)

y - 1 = 3(x - 1)

d)

y + 2 = -3(x + 1)

60.

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

a)

Ellipse

b)

Circle

c)

Hyperbola

d)

Parabola

61.

What type of conic section is

2x^2+2y^2-4x-16y-9=0

?

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

62.

What type of conic section is

x^2-x+3y+6=0

?

a)

Hyperbola

b)

Circle

c)

Ellipse

d)

Parabola

63.

When the cutting plane intersects the two cones parallel to their vertical axes and perpendicular to their bases, then the conic section is a __________.

a)

Parabola

b)

Hyperbola

c)

Circle

d)

Ellipse

64.

There are figures that formed by intersecting two inverted cones and a plane.

a)

Cross Sections

b)

Circles

c)

Conic Sections

d)

Parabolas

65.

Conics are special curves and are classified into four types. EXCEPT?

a)

Ellipse

b)

Parabola

c)

Circle

d)

Cone

e)

Hyperbola

66.

Which equation shows an ellipse?

a)

y^2+x-3y-15=0

b)

$4x^2+4y^2-16y+81=0$

c)

$2x^2-4y^2+18x+120y-159=0$

d)

$16x^2+11y^2+54x-61y-121=0$

67.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

68.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

69.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

70.

What is the center of the ellipse?

a)

(0, 0)

b)

(1, 5)

c)

(1, 0)

d)

(0, 1)

71.

What are the vertices of the ellipse?

Write the equation in standard form:

a)

(0, 0)

b)

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

c)

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

d)

(3, 1)

72.

Write the equation of the circle with a radius of 3 and a center of (4, 2).

a)

( x - 4)² + (y - 2)² = 3

b)

( x - 2)² + (y - 2)² = 3²

c)

( x - 4)² + (y - 2)² = 3²

d)

( x + 4)² + (y + 2)² = 3²

73.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

74.

What is the equation of the circle shown in the graph?

a)

(x-3)²+ (y+4)² = 9

b)

(x-3)²+ (y+4)² = 3

c)

(x+3)²+ (y-4)² = 9

d)

(x+3)²+ (y-4)² = 3

75.

What is the vertex of the parabola: $x=7\left(y-6\right)^2-2$

a)

(6, -2)

b)

(-6, -2)

c)

(-2, 6)

d)

(-2, -6)

76.

Name the center of the ellipse and the a and b values: $\frac{x^2}{100}+\frac{\left(y+2\right)^2}{25}=1$

a)

Center: (0, -2)

a = 100

b = 25

b)

Center: (0, 2)

a = 10

b = 5

c)

Center: (0, -2)

a=10

b=5

d)

Center: (0, 2)

a=100

b=25

77.

What is the standard form of the equation of a circle with center C (4,3) and radius r = 6?

a)

(x + 4)² + (y - 3)² = 36

b)

(x - 4)² + (y + 3)² = 36

c)

(x + 4)² + (y + 3)² = 36

d)

(x - 4)² + (y - 3)² = 36

78.

What is the standard form of equation of a parabola if the opening is upward or downward?

a)

y = a(x - h)² + k

b)

x = a(y - k)² + h

c)

y = a(x + h)² + k

d)

x = a(y + k)² + h

79.

What is the standard form of equation of a parabola if the opening is right or left?

a)

y = a(x - h)² + k

b)

x = a(y - k)² + h

c)

y = a(x + h)² + k

d)

x = a(y + k)² + h

80.

What is the coordinate of the vertex given the equation y = 3(x - 2)² - 4?

a)

(2,-4)

b)

(-2,4)

c)

(2,4)

d)

(-2,-4)

81.

What is the standard form of equation of a horizontal ellipse?

a)

$\frac{(x-h)^2}{a^2}\ +\frac{(y-k)^2}{b^2}=1$

b)

$\frac{(x-h)^2}{a^2}\ -\frac{(y-k)^2}{b^2}=1$

c)

$\frac{(x-h)^2}{b^2}\ +\frac{(y-k)^2}{a^2}=1$

d)

$\frac{(x-h)^2}{b^2}\ -\frac{(y-k)^2}{a^2}=1$

82.

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

a)

(3,2)

b)

(-3, -2)

c)

(-2, -3)

d)

(2, 3)

83.

In the equation (x+2)²+(y-3)²=4, the radius of the circle is...

a)

4

b)

2

c)

3

d)

16

84.

What is the focus of this parabola?

a)

(1/2,0)

b)

(0,1/2)

c)

(2,0)

d)

(0,2)

85.

What is the equation of this parabola?

a)

x²= -3y

b)

y² = 12x

c)

x² = -12y

d)

y² = 3x

86.

What is the equation of this parabola?

a)

x²= 4y

b)

y² = x

c)

x² = -y

d)

y² = -16x

87.

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)

88.

Find the standard equation of the given ellipse

a)

b)

c)

d)

89.

Find the standard equation of the given ellipse

a)

b)

c)

d)

90.

What are the vertices of the ellipse?

a)

(-5,3)

b)

(-5,0) and (-5,6)

c)

(3,-5)

d)

(-10, 3) and (0,3)

91.

Which of the following is the graph of $\frac{\left(x+3\right)^2}{4}+\frac{\left(y+1\right)^2}{9}=1$

a)

b)

c)

d)

92.

What is the center of the hyperbola?

a)

(0, 4)

b)

(4, 0)

c)

(-4, 0)

d)

(0, -4)

93.

Is the hyperbola vertical or horizontal?

a)

Vertical

b)

Horizontal

94.

What is the center of this hyperbola?

a)

Center $\left(-1,\ 4\right)$

b)

Center $\left(1,\ 4\right)$

c)

Center $\left(-1,\ -4\right)$

d)

Center $\left(1,\ -4\right)$

95.

What are the foci of the hyperbola with the equation $\frac{y^2}{12}-\frac{x^2}{5}=1$ .

a)

(0, ±√17)

b)

(±√17, 0)

c)

(0, ±√7)

d)

(±√7, 0)

96.

What are the coordinates of the Vertices?

a)

(0 , 5) ; (0 , -5)

b)

(0 , 9) ; (0 , -9)

c)

(5 , 0) ; (-5 , 0)

d)

(9 , 0) ; (-9 , 0)

97.

What are the asymptotes of the hyperbola in the picture?

a)

y = x and y = –x

b)

y = 2x and y = –2x

c)

y = ¹/₂x and y = –¹/₂x

d)

y = 2x and y = 4x

98.

Identify the asymptotes of the equation:
. $\frac{\left(y-1\right)^2}{64}-\frac{\left(x+9\right)^2}{36}=1$

a)

$y=\frac{4}{3}x\ +\ 13\ \ ;\ y=-\frac{4}{3}x\ -\ 11$

b)

$y=\frac{4}{3}x\ +\ \frac{23}{3}\ ;\ y=-\frac{4}{3}x\ +\ \frac{31}{3}$

c)

$y=\frac{3}{4}x\ +\ \frac{31}{4}\ ;\ y=-\frac{3}{4}x\ -\ \frac{23}{4}$

d)

$y=\frac{4}{3}x\ -\ \frac{23}{3}\ ;\ \ y=-\frac{4}{3}x\ -\ \frac{31}{3}$

99.

Find the standard form of the hyperbola given
$4x^2-y^2+72x+20y+160=0$ .

a)

$\frac{\left(x+9\right)^2}{16}-\left(y-10\right)^2=1$

b)

$\frac{\left(x+9\right)^2}{64}-\frac{\left(y-10\right)^2}{16}=1$

c)

$\frac{\left(y-10\right)^2}{16}-\frac{\left(x+9\right)^2}{64}=1$

d)

$\frac{\left(x+9\right)^2}{16}-\frac{\left(y-10\right)^2}{64}=1$

100.

A hyperbola centered at (-3, 2) with a horizontal tranverse axis has asymptotes y = ± ¾x. Which of the following could be the equation of the hyperbola in standard form?

a)

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

b)

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

c)

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

d)

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

Analytic Geometry - Final Exam

Total questions: 100

Worksheet time: 7hrs 32mins

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