Free Printable MATH MAJOR 217: Midterm 2025

1.

Find the distance between A(-4, 4) and B(6, 9)

a)

11.18

b)

10.12

c)

13.65

d)

-9.6

2.

Find the distance between C (8, -6) and D (-2, 7)

a)

16.40

b)

15.20

c)

19.40

d)

14.90

3.

Find the slope of the line joining the given pairs of points (-12, 7), (2, 3).

a)

-4/12

b)

-2/7

c)

5/7

d)

2/5

4.

If the line joining the points (-8, y) and (-2, -3) has the slope m = -3. Find y.

a)

y = 15

b)

y = 12

c)

y = 18

d)

y = 10

5.

Write the equation of the line with the slope ¾ and passing through (4, -5).

a)

3x - 4y - 32 = 0

b)

3x + 4y + 32 = 0

c)

x + 4y - 8 = 0

d)

3x - y + 8 = 0

6.

Find the equation of the line passing through the point (-5, 3) and having slope 3.

a)

3x + y - 18 = 0

b)

3x - y + 18 = 0

c)

x + 3y + 8 = 0

d)

x - 3y - 8 = 0

7.

Write the equation of the line through (6, 8) and (-4, -7).

a)

3x - 2y - 2 = 0

b)

x - y - 1 = 0

c)

2x - 3y + 2 = 0

d)

2x - 2y - 3 = 0

8.

Determine the equation of the line with slope 3 and y-intercept -6

a)

3x - y - 6 = 0

b)

x - 3 y + 6 = 0

c)

x - y - 3 = 0

d)

x + y + 3 = 0

9.

Find the equation of the line through (0, -5) and (2, 0).

a)

5x - 2y - 10 = 0

b)

2x - 5y + 10 = 0

c)

5x + 2y + 10 = 0

d)

2x + 5y - 10 = 0

10.

Find the intercepts of the line x – 4y = 5

a)

a = 5, b = -5/4

b)

a = 4, b = -4/5

c)

a = -5, b = 5/4

d)

a = -4, b = 4/5

11.

What is the midpoint between (8, -3) and (2, 5)

a)

(5, 1)

b)

(10, 2)

c)

(-5, -1)

d)

(3, 4)

12.

What is the equation of the line that passes through the points

(6, 5) and (4, -3)?

a)

y= 4x- 29

b)

y= 4x - 19

c)

y= 4x + 19

d)

y=-4x -19

13.

What is the equation of a line that is perpendicular to the line y = 3x + 2 and goes through the point (3, -4)?

a)

y = 3x - 2

b)

y = -1/3x - 5

c)

y = 3x - 4

d)

y = -1/3x - 3

14.

Points A(1,3) & B(-3,5) are the endpoints of a chord on a circle with centre not at the origin. What is the equation of the perpendicular bisector of chord AB?

a)

y = 2x + 4

b)

y = 2x + 6

c)

y = -2x + 6

d)

y = 2x - 6

15.

What is the area of triangle ABC which has vertices at A(-3,6), B(5,2) and C(1,-6)?

a)

35 square units

b)

40 square units

c)

50 square units

d)

55 square units

16.

Convert to standard form

x²+y²+8x-2y-8=0

a)

(x+4)²+(y-1)²=25

b)

(x-4)²+(y+1)²=25

c)

(x+4)²+(y-1)²=8

d)

(x-4)²+(y+1)²=8

17.

(x-4)²+(y-3)²=12 has centre in...

a)

(4,3)

b)

(3,4)

c)

(-4,-3)

d)

(-4,3)

18.

(x-4)²+(y-3)²=12 has radius of...

a)

12

b)

$\sqrt{12}$

c)

4

d)

3

19.

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

a)

b)

c)

d)

20.

Find the intercepts of the line x – 4y = 5

a)

a = 5, b = -5/4

b)

a = 4, b = -4/5

c)

a = -5, b = 5/4

d)

a = -4, b = 4/5

21.

Find the graph to this equation $\left(x-3\right)^2+y^2=4$

a)

b)

c)

d)

22.

The focus is at (2,0) and the vertex is at (-4,0). What is the equation of the parabola?

a)

y² = 24(x+4)

b)

(y+4)² = -12x

c)

x² = 16(y+4)

d)

(x+4)² = -20y

23.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

24.

Which type of conic section is this equation?

a)

circle

b)

ellipse

c)

hyperbola

d)

parabola

25.

What type of conic section is

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

?

a)

Hyperbola

b)

Circle

c)

Ellipse

d)

Parabola

26.

What type of conic section is

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

?

a)

Circle

b)

Ellipse

c)

Parabola

d)

Hyperbola

27.

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

a)

Ellipse

b)

Circle

c)

Hyperbola

d)

Parabola

28.

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

29.

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

30.

What is the equation of the circle that passes through (-15, 10) and has a center at (-16, 11)?

a)

$\left(x+16\right)^2+\left(y-11\right)^2=4$

b)

$\left(x+11\right)^2+\left(y-16\right)^2=4$

c)

$\left(x+16\right)^2+\left(y-11\right)^2=2$

d)

$\left(x+13\right)^2+\left(y-17\right)^2=2$

31.

Find the graph to this equation $\left(x-3\right)^2+y^2=4$

a)

b)

c)

d)

32.

(y-4)² = -8(x+1)
What are the coordinates for the focus?

a)

(1,4)

b)

(-1,6)

c)

(-1,2)

d)

(-3,4)

33.

(x+3)² = 4(y+5)
What is the equation of the directrix?

a)

x = 4

b)

x = 2

c)

y = -4

d)

y = -6

34.

What direction does the parabola point?

a)

Up

b)

Down

c)

Left

d)

Right

35.

The focus is at (2,0) and the vertex is at (-4,0). What is the equation of the parabola?

a)

y² = 24(x+4)

b)

(y+4)² = -12x

c)

x² = 16(y+4)

d)

(x+4)² = -20y

36.

Find the standard equation of the given ellipse

a)

b)

c)

d)

37.

Find the standard equation of the given ellipse

a)

b)

c)

d)

38.

A/An ______________ is the set of all points in a plane such that the sum of the distances from two fixed points is constant.

a)

Parabola

b)

Ellipse

c)

Circle

d)

Hyperbola

39.

A/An ________________ is the set of all points in a plane that are the same distance from a fixed point called the focus and a fixed line called the directrix.

a)

Parabola

b)

Ellipse

c)

Circle

d)

Hyperbola

40.

A/An __________________ is the set of all points in a plane such that the absolute value of the difference of distances from two fixed points is constant.

a)

parabola

b)

ellipse

c)

circle

d)

hyperbola

41.

Calculate the slope between the line that passes through

(3, 7) and (7, 2)

a)

$-\frac{5}{4}$

b)

$-\frac{4}{5}$

c)

5

d)

-4

42.

Calculate the slope of the line that passes through the

points (1, -8) and (-3, 0).

a)

4

b)

-1

c)

-2

d)

6

43.

What is the slope of these two points (5,-11) and (25,9)?

a)

$\frac{2}{3}$

b)

$1$

c)

$-1$

d)

$-\frac{3}{2}$

44.

Write the equation in slope-intercept form: 3x + y = 12

a)

y = -3x +12

b)

x = y + 4

c)

x = y + 12

d)

y = 3x -12

45.

Convert the standard form equation into slope-intercept form.
x + y = -1

a)

y = x - 1

b)

y = 27, 239, 430

c)

y = -1x

d)

y = -x - 1

46.

What is the slope of the line passing through the points (2, 3) and (4, 7)?

a)

2

b)

1

c)

4

d)

3

47.

If the slope of a line is 0, the line is:

a)

Vertical

b)

Horizontal

c)

Diagonal

d)

Undefined

48.

Find the slope of a line passing through (5, -2) and (5, 6).

a)

0

b)

Undefined

c)

1

d)

-1

49.

The slope of a vertical line is:

a)

0

b)

Undefined

c)

1

d)

-1

50.

A line has a slope of 5. Which direction does it rise?

a)

Left to right

b)

Right to left

c)

It is flat

d)

It is vertical

51.

The angle of inclination of a horizontal line is:

a)

0 degrees

b)

45 degrees

c)

90 degrees

d)

180 degrees

52.

The angle of inclination of a vertical line is:

a)

0 degrees

b)

90 degrees

c)

45 degrees

d)

180 degrees

53.

The line y = x has an angle of inclination of:

a)

30 degrees

b)

45 degrees

c)

60 degrees

d)

90 degrees

54.

What is the angle of inclination of a line with slope 1?

a)

30 degrees

b)

45 degrees

c)

60 degrees

d)

90 degrees

55.

A line with a positive slope will have an inclination between:

a)

0 degrees and 90 degrees

b)

90 degrees and 180 degrees

c)

180 degrees and 270 degrees

d)

270 degrees and 360 degrees

56.

A line with slope -1 will have an angle of inclination greater than:

a)

0 degrees

b)

90 degrees

c)

180 degrees

d)

270 degrees

57.

Two lines are parallel if their slopes are:

a)

Equal

b)

Negative reciprocals

c)

Both undefined

d)

Different

58.

Two lines are perpendicular if their slopes are:

a)

Equal

b)

Negative reciprocals

c)

Positive reciprocals

d)

Opposites

59.

The line parallel to y = 2x + 3 is:

a)

y = -2x + 1

b)

y = 2x - 4

c)

y = -1/2x + 5

d)

y = 1/2x + 2

60.

The slope of a line perpendicular to y = -3x + 7 is:

a)

-3

b)

3

c)

1/3

d)

-1/3

61.

If a line has a slope of 2, the slope of a perpendicular line is:

a)

-2

b)

1/2

c)

-1/2

d)

2

62.

A vertical line is perpendicular to:

a)

Another vertical line

b)

A horizontal line

c)

A diagonal line

d)

A line with slope 1

63.

The formula to find the angle between two lines with slopes m1 and m2 is:

a)

tan $\phi$ = |(m₂ - m₁) / (1 + m₁m₂)|

b)

sin $\phi$ = |(m₂ - m₁) / (1 + m₁m₂)|

c)

cos $\phi$ = |(m₂ - m₁) / (1 + m₁m₂)|

d)

None of the above

64.

If two lines are perpendicular, their angle of intersection is:

a)

45 degrees

b)

90 degrees

c)

60 degrees

d)

30 degrees

65.

If the slopes of two lines are m1 = 2 and m2 = -1/2, the lines are:

a)

Parallel

b)

Perpendicular

c)

Coinciding

d)

Neither

66.

In the equation 2x + 3y = 6, the slope is:

a)

-2/3

b)

3/2

c)

-3/2

d)

2/3

67.

What is the y-intercept of 4x - 2y = 8?

a)

4

b)

-4

c)

2

d)

-2

68.

What is the slope of 3x + 2y = 6?

a)

-3/2

b)

-2/3

c)

2/3

d)

3/2

69.

Rewrite 6x - y = 12 in slope-intercept form.

a)

y = 6x + 12

b)

y = -6x + 12

c)

y = 6x - 12

d)

y = -6x - 12

70.

In 5x + 7y = 35, the slope is:

a)

-5/7

b)

-7/5

c)

5/7

d)

7/5

71.

The slope of a line parallel to the x-axis is:

a)

0

b)

1

c)

Undefined

d)

-1

72.

The slope of a line parallel to the y-axis is:

a)

0

b)

1

c)

Undefined

d)

-1

73.

The equation y = 5 is a line parallel to:

a)

x-axis

b)

y-axis

c)

Origin

d)

Both axes

74.

The equation x = -3 represents a line parallel to:

a)

x-axis

b)

y-axis

c)

Origin

d)

Diagonal line

75.

Rearrange y = 3x + 5 into standard form.

a)

3x - y = -5

b)

3x + y = -5

c)

-3x + y = -5

d)

3x - y = 5

76.

What is the standard form of the equation of the line through (0,4) with slope -2?

a)

2x + y = 4

b)

2x - y = 4

c)

-2x + y = 4

d)

-2x - y = 4

77.

Solve for y in the equation 5x + 2y = 8.

a)

y = -5/2x + 4

b)

y = -5/2x - 4

c)

y = 5/2x + 4

d)

y = 5/2x - 4

78.

The slope of 4x + 5y = 20 is:

a)

-4/5

b)

5/4

c)

-5/4

d)

4/5

79.

Find the y-intercept of the line 6x + 2y = 12.

a)

6

b)

-6

c)

2

d)

-2

80.

What is the standard form of the line passing through (2, 3) with slope 3?

a)

3x - y = 3

b)

3x + y = 3

c)

-3x + y = 3

d)

-3x - y = 3

MATH MAJOR 217: Midterm 2025

Total questions: 80

Worksheet time: 3hrs 22mins

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