Free Printable BSME SET #8

1.

State the quadrant in which the coordinate (15,-2) lies.

a)

I

b)

IV

c)

II

d)

III

2.

Of what quadrant is A, if sec A is positive and csc A is negative?

a)

III

b)

I

c)

IV

d)

II

3.

The segment from (-1, 4) to (2,-2) is extended three times its own length. The terminal point is

a)

(11,-18)

b)

(11,-24)

c)

(11,-20)

d)

(-11,-20)

4.

The midpoint of the line segment between P1(x,y) and P2(-2,4) is (2,-1). Find the coordinate of

a)

(6,-5)

b)

(5,-6)

c)

(6,-6)

d)

(-6,6)

5.

Find the coordinates of the point P(2, 4) with respect to the translated axis with origin at (1,3).

a)

(1, -1)

b)

(1, 1)

c)

(-1, -1)

d)

(-1, 1)

6.

Find the median through (-2, -5) of the triangle whose vertices are (-6,2), (2,-2), and (-2,-5).

a)

3

b)

4

c)

5

d)

6

7.

Find the centroid of a triangle whose vertices are (2,3), (-4, 6) and (2,-6).

a)

(0,1)

b)

(0,-1)

c)

(1,0)

d)

(-1,0)

8.

Find the area of triangle whose vertices are A (-3,-1), B (5,3) and C (2,-8)

a)

34

b)

36

c)

38

d)

32

9.

Find the distance between the points (4, -2) and (-5, 1).

a)

5

b)

10

c)

7

d)

sqrt(90)

10.

Find the distance between the points (4, 8) and (7, 9).

a)

4.897

b)

8.947

c)

7.149

d)

9.487

11.

Find the distance between A(4, -3) and B(-2, 5).

a)

11

b)

8

c)

9

d)

10

12.

If the distance between the points (8, 7) and (3, y) is 13, what is the value of y?

a)

5

b)

-19

c)

19 or -5

d)

5 or -19

13.

The distance between the points (sin x, cos x) and (cos x, -sin x) is:

a)

1

b)

2

c)

2 sin x cos x

d)

4 sin x cos x

14.

Find the distance from the point (2, 3) to the line 3x+4y+9=0.

a)

5

b)

5.4

c)

5.8

d)

6.2

15.

Find the distance from the point (5, -3) to the line 7x-4y-28=0.

a)

6 units

b)

7 units

c)

5 units

d)

8 units

16.

CE Nov.1998 Select the correct answer.

a)

2.62

b)

2.36

c)

2.48

d)

2.54

17.

How far is the line 3x-4y+15=0 from the origin?

a)

1

b)

2

c)

3

d)

4

18.

Determine the distance from (5,10) to the line x-y=

a)

3.86

b)

3.54

c)

3.68

d)

3.72

19.

The two points on the line 2x+3y+4=0 which are at distance 2 from the line 3x+4y-6=0 are:

a)

(-8,-8) and (-16,-16)

b)

(-44,64) and (-5,2)

c)

(-5.5,1) and (-5,2)

d)

(64,-44) and (4,-4)

20.

The intercept form for algebraic straight-line equation is:

a)

x/a + y/b = 1

b)

y = mx + c

c)

ax + by + c = 0

d)

y - y1 = m(x - x1)

21.

Which of the following is the equation of a straight line?

a)

a/x+y/b=1

b)

y=mx+b

c)

Ax+By+C=0

d)

x/a+y/b=1

22.

Find the slope of the line defined by y-x=5

a)

1

b)

-1/2

c)

1

d)

5+x

23.

The slope of the line 3x+2y+5=0 is:

a)

-2/3

b)

-3/2

c)

3/2

d)

2/3

24.

Find the slope of the line whose parametric equation is y=5-3 and x=2+t.

a)

3

b)

-3

c)

2

d)

-2

25.

Find the slope of the curve whose parametric equations are x=-1 and y=2t.

a)

2

b)

3

c)

1

d)

4

26.

Find the angle that the line 2y-9x-18=0 makes with the x-axis.

a)

74.77°

b)

4.5°

c)

47.77°

d)

77.47°

27.

Which of the following is perpendicular to the line x/3+y/4=1?

a)

x-4y-8=0

b)

4x-3y-6=0

c)

3x-5=0

d)

x+311=0

28.

Find the equation of the bisector of the obtuse angle between the lines 2x+xy=4a4x=7.

a)

4y=1

b)

8x=15

c)

2y=3

d)

8x+4y=6

29.

The equation of the line through (1, 2) and parallel to the line 3x-2y+4=0 is:

a)

3x-2y+1=0

b)

3x-2y-1=0

c)

3x+2y+1=0

d)

3x+2y-1=0

30.

If the points (-3, -5), (x, y), and (3, 4) lie on a straight line, which of the following is correct?

a)

3x+2y-1=0

b)

2x+3y+1=0

c)

2x+3y-1=0

d)

3x-2y-1=0

31.

One line passes through the points (1, 9) and (2, 6), another line passes through (3, 3) and (-1, 5). The acute angle between the two lines is:

a)

30°

b)

45°

c)

60°

d)

135°

32.

The two straight lines 4x-y+3=0 and 8x-2y+6=0

a)

intersects at the origin

b)

are coincident

c)

are parallel

d)

are perpendicular

33.

A line which passes through (5, 6) and (-3, -4) has an equation of

a)

5x+4y+1=0

b)

5x-4y-1=0

c)

5x+-1=0

d)

5x+y-4=0

34.

Find the equation of the line with slope of 2 and y intercept of -3.

a)

y=-3x+2

b)

y=2x-3

c)

y=2/3x+1

d)

y=3x-2

35.

What is the equation of the line that passes through (4,0) and is parallel to the line x-y-2=0?

a)

y+x+4=0

b)

y-x+4=0

c)

y-x-4=0

d)

y+x-4=0

36.

Determine B such that 3x+2y-7=0 is perpendicular to 2x-y+2=0.

a)

2

b)

3

c)

4

d)

5

37.

The equation of a line that intercepts the x-axis at x=4 and the y-axis at y=-6 is:

a)

2x

b)

3x+2y=12

c)

3x-2y=12

d)

2x-3y=12

38.

How far from the y-axis is the center of the curve?

a)

-3.0

b)

2.75

c)

-3.25

d)

2.5

39.

Find the area of the circle whose center is at (2, -5) and tangent to the line 4x+3y-8=0.

a)

6π

b)

9π

c)

3π

d)

12π

40.

Determine the area enclosed by the curve CF. May 1999

a)

15π

b)

225π

c)

12π

d)

144π

41.

Find the shortest distance from the point (1,2) to a point on the circumference of the circle defined by the equation

a)

5.61

b)

5.71

c)

5.81

d)

5.91

42.

Determine the length of the chord common to the circles and CE Nov.1998

a)

13.86

b)

12.82

c)

13.25

d)

12.28

43.

If (3, -2) lies on a circle with center (-1, 1), then the area of the circle is:

a)

5π

b)

25π

c)

4π

d)

3π

44.

The radius of the circle 2x² + 2y² - 3x + 4y - 1 = 0 is: CE Nov.1994

a)

√33/4

b)

√33/3

45.

What is the value of the following?

a)

33/16

b)

33/16

c)

17

d)

17

46.

What is the radius of a circle with the following ME April 1998 equation?

a)

3.46

b)

5

c)

7

d)

6

47.

The diameter of a circle described by C.4

a)

A.16/9

b)

B.4/3

c)

C.4

d)

D.8/3

48.

Find the center of the circle

a)

(3,-2)

b)

(3,2)

c)

(-3,2)

d)

(-3,-2)

49.

Determine the equation of the circle whose center is at (4,5) and tangent to the circle whose equation is -23=0.

a)

$x^2 + y^2 - 8x + 10y - 25 = 0$

b)

$x^2 + y^2 + 8x - 10y + 25 = 0$

c)

$x^2 + y^2 - 8x - 10y + 25 = 0$

d)

$x^2 + y^2 - 8x - 10y - 25 = 0$

50.

The equation of the circle with center at (-2, 3) and which is tangent to the line 20x - y - 42 = 0 is:

a)

$x^2 + y^2 + 4x - 6y - 12 = 0$

b)

$x^2 + y^2 + 4x - 6y = 0$

c)

$x^2 + y^2 + 4x + 6y = 0$

d)

$x^2 + y^2 - 4x - 6y - 12 = 0$

51.

A circle has a diameter whose ends are at (-3,2) and (12,-6). Its Equation is:

a)

$4x^2 + 4y^2 - 36x + 16y + 192 = 0$

b)

$4x^2 + 4y^2 - 36x + 16y - 192 = 0$

c)

$4x^2 + 4y^2 - 36x - 16y - 192 = 0$

d)

$4x^2 + 4y^2 + 36x + 16y - 192 = 0$

52.

Find the equation of the circle with center x + y = 4 and 5x + 2y + 1 = 0 and having a radius of 3.

a)

$x^2 + y^2 + 6x - 16y + 64 = 0$

b)

$x^2 + y^2 + 8x - 14y + 25 = 0$

c)

$x^2 + y^2 + 6x - 14y + 49 = 0$

d)

$x^2 + y^2 + 6x - 14y + 36 = 0$

53.

If (3, 2) lies on the circle with center (-1, 1) then the equation of the circle is:

a)

$x ^ 2 + y ^ 2 + 2x - 2y - 23 = 0$

b)

$x ^ 2 + y ^ 2 + 4x - 2y - 21 = 0$

c)

$x ^ 2 + y ^ 2 + 2x - y - 33 = 0$

d)

$x ^ 2 + y ^ 2 + 4x - 2y - 27 = 0$

54.

Find the equation of k for which the equation $x^2 + y^2 + 4x - 2y - k = 0$ represents a point circle.

a)

5

b)

6

c)

-5

d)

-6

55.

The vertex of the parabola y^2 - 2x + 6y + 3 = 0 is at:

a)

(-3,3)

b)

(3,3)

c)

(-3,3)

d)

(-3,-3)

56.

The length of the latus rectum of the parabola $y^2 = 4px$ is:

a)

4p

b)

2p

c)

p

d)

4p

57.

Given the equation of the parabola: $y^2 - 8x - 4y - 20 = 0$ The length of its latus rectum is:

a)

2

b)

4

c)

6

d)

8

58.

What is the length of the latus rectum of the curve $x^2 = -12y$ ?

a)

12

b)

-3

c)

3

d)

-12

59.

Find the equation of the directrix of the parabola $y^2 = 16x$ .

a)

x = 8

b)

x = 4

c)

x = -8

d)

x = 4

60.

The curve y = $-x^2 + x + 1$ opens:

a)

upward

b)

to the left

c)

to the right

d)

downward

61.

The parabola y = $-x^2 + x + 1$ opens:

a)

to the right

b)

to the left

c)

upward

d)

downward

62.

Find the equation of the axis of symmetry of the function y = $2x^2 - 7x + 5$ .

a)

4x + 7 = 0

b)

x - 2 = 0

c)

4x - 7 = 0

d)

7x + 4 = 0

63.

Find the equation of the locus of the center of the circle which moves so that it is tangent to the y-axis and to the circle of radius one (1) with center at (2, 0).

a)

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

b)

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

c)

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

d)

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

64.

Find the equation of the parabola with vertex at (4, 3) and focus at (4, -1).

a)

$y^2 - 8x + 16y - 32 = 0$

b)

$y^2 + 8x - 16y - 32 = 0$

c)

$x^2 + 8x - 16y + 32 = 0$

d)

$x^2 - 8x + 16y - 32 = 0$

65.

Find the area bounded by the curves x^2 + 8y + 16 = 0, x - 4 = 0, the x-axis, and the y-axis.

a)

10.67 sq. units

b)

10.33 sq. units

c)

9.67 sq. units

d)

8 sq. units

66.

Find the area (in sq. units) bounded by the parabolas $x^2 - 2y = 0$ and $x^2 + 2y - 8 = 0$

a)

11.7

b)

10.7

c)

9.7

d)

4.7

67.

The length of the latus rectum of the curve $\frac{(x - 2)^2}{4} + \frac{(y + 4)^2}{25} = 1$ is:

a)

1.6

b)

2.3

c)

0.80

d)

1.52

68.

Find the length of the latus rectum of the following ellipse: $25x^2 + 9y^2 - 300x - 144y + 1251 = 0$

a)

3.4

b)

3.2

c)

3.6

d)

3.0

69.

If the length of the major and minor axes of an ellipse is 10 cm and 8 cm, respectively, what is the eccentricity of the ellipse?

a)

0.50

b)

0.60

c)

0.70

d)

0.80

70.

The eccentricity of the ellipse $\frac{2}{4} + \frac{y^2}{16} - 1$ is:

a)

0.725

b)

0.256

c)

0.689

d)

0.866

71.

An ellipse has the equation $16x^2 + 9y^2 + 32x - 128 = 0$ . Its eccentricity is:

a)

0.531

b)

0.66

c)

0.824

d)

0.93

72.

The center of the ellipse $4x^2 + y^2 - 16x - 6y - 43 = 0$ is at:

a)

(2,3)

b)

(4,-6)

c)

(1,9)

d)

(-2,-5)

73.

Find the ratio of the major axis to the minor axis of the ellipse: $9x^2 + 4y^2 - 24y - 72x - 144 = 0$

a)

0.67

b)

1.8

c)

1.5

d)

0.75

74.

The area of the ellipse $9x^2 + 25y^2 - 36x - 189 = 0$ is equal to:

a)

15π sq. units

b)

20π sq. units

c)

25π sq. units

d)

30π sq. units

75.

The area of the ellipse is given as A = 3.1416 a b. Find the area of the ellipse $25x^2 + 16y^2 - 100x + 32y = 284$ .

a)

86.2 square units

b)

62.8 square units

c)

68.2 square units

d)

82.6 square units

76.

The semi-major axis of an ellipse is 4 and its semi-minor axis is 3. The distance from the center to the directrix is:

a)

6.532

b)

6.047

c)

0.6614

d)

6.222

77.

Given an ellipse x²/36+ y²/32 1. Determine the distance between foci.

a)

2

b)

3

c)

4

d)

8

78.

How far apart are the directrices of the curve 25x² + 9y²-300x-144y+1251 = 0?

a)

12.5

b)

14.2

c)

13.2

d)

15.2.

79.

The major axis of the elliptical path in which the earth moves around the sun is approximately 186,000,000 miles and the eccentricity of the ellipse is 1/60. Determine the apogee of the earth.

a)

94,550,000 miles

b)

94,335,100 miles

c)

91,450,000 miles

d)

93,000,000 miles

80.

Find the equation of the ellipse whose center is at (-3,-1), vertex focus at (1,-1)

a)

9x² + 36y² - 54x + 50y - 116 = 0

b)

4x² + 25y² + 54x - 50y - 122 = 0

c)

9x² + 25y² + 50x + 50y + 109 = 0

d)

9x² + 25y² + 54x + 50y - 119 = 0

81.

Point p(x, y) moves with a distance from point (0, 1) one-half of distance from line y = 4 the equation of its focus is

a)

A. 4x² + 3y² = 12

b)

B. 2x² - 4y² = 5

c)

C. x² + 2y² = 4

d)

D. 2x² + 5y² = 3

82.

The chords of the ellipse 64x² + 25y² = 1600 having equal slopes of 1/5 are bisected. Determine the equation diameter of the ellipse.

a)

5x - 64y = 0

b)

64x - 5y = 0

c)

5x + 64y = 0

d)

64x + 5y = 0

83.

Find the equation of the upward asymptote of the hyperbola whose equation is (x - 2)² / 9 - (y + 4)² .

a)

A. 3x + 4y - 20 = 0

b)

C. 4x + 3y * 20 = 0

84.

PROBLEM 17-30: The semi-conjugate axis of the hyperbola x²/9 - y²/4 = 1 is:

a)

2

b)

-2

c)

3

d)

-3

85.

What is the equation of the asymptote of the hyperbola x²/9 - y²/4 = 1?

a)

A. 2x - 3y = 0

b)

B. 3x - 2y = 0

c)

C. 2x - y = 0

d)

D. 2x + y = 0

86.

The graph y = (x-1)/(x+2) is not defined at:

a)

0

b)

2

c)

-2

d)

1

87.

The equation x² + Bx + y² + Cy + D = 0 is:

a)

hyperbola

b)

parabola

c)

ellipse

d)

circle

88.

The general second degree equation has the form Ax² + Bxy + Cy² + Dx + Ey + F = 0 and describes an ellipse if

a)

B² - 4AC = 0

b)

B² - 4AC > 0

c)

B² - 4AC = 1

d)

B² - 4AC < 0

89.

Find the equation of the tangent to the circle x² + y² - 34 = 0 through point (-5,2).

a)

3x + 5y - 34 = 0

b)

3x - 5y - 34 = 0

c)

3x + 5y + 34 = 0

d)

3x - 5y + 34 = 0

90.

Find the equation of the tangent to the curve x² + y² + 4x + 16y - 32 = 0 through (4,0).

a)

3x - 4y + 12 = 0

b)

3x - 4y - 12 = 0

c)

3x + 4y + 12 = 0

d)

3x + 4y - 12 = 0

91.

Find the equation of the normal to the curve y² + 2x + 3y = 0 through point (-5,2).

a)

7x + 2y + 39 = 0

b)

7x - 2y + 39 = 0

c)

2x - 7y - 39 = 0

d)

2x + 7y - 39 = 0

92.

Determine the equation of the line tangent to the graph y = 2x² + 1 at the point (1, 3).

a)

y = 4x - 1

b)

y = 2x + 1

c)

y = 2x - 1

d)

y = 4x + 1

93.

Find the equation of the tangent to the curve $x^2 + y^2 = 41$ through (5,4).

a)

5x + 4y = 41

b)

4x - 5y = 41

c)

4x + 5y = 41

d)

5x - 4y = 41

94.

Find the equation of a line normal to the curve $x^2 = 16y$ at (4, 1).

a)

2x - y + 9 = 0

b)

2x - y + 9 = 0

c)

2x + y - 9 = 0

d)

2x + y + 9 = 0

95.

What is the equation of the tangent to the curve $9x^2 + 25y^2 - 225 = 0$ at (0, 3)?

a)

y + 3 = 0

b)

x + 3 = 0

c)

x - 3 = 0

d)

y - 3 = 0

96.

What is the equation of the normal to the curve $x^2 + y^2 = 25$ at (4, 3)?

a)

A. 3x - 4y = 0

b)

B. 5x + 3y = 0

c)

C. 5x - 3y = 0

d)

D. 3x + 4y = 0

97.

The polar form of the equation 3x + 4y - 2 = 0 is:

a)

3cos θ + 4r cos θ = 2

b)

3r cos θ + 4r sin θ = -2

c)

3r cos θ + 4r sin θ = 2

d)

3r sin θ + 4r tan θ = -2

98.

The polar form of the equation $3x^2 + 2y^2 = 8$ is:

a)

$r^2 = 8$

b)

$r = 8/\cos^2\theta + 2$

c)

r = 8

d)

$r^2 = \frac{8}{\cos^2\theta} + 2$

99.

The distance between points (5, 30°) and (-8, -50°) is:

a)

9.84

b)

10.14

c)

6.13

d)

12.14

100.

Convert θ = π / 3 to Cartesian equation.

a)

x = √3 x

b)

y = x

c)

3y = √3 x

d)

y = √3 x

BSME SET #8

Total questions: 100

Worksheet time: 50mins

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