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Worksheets

Luis Canicon - Math

Total questions: 100

Worksheet time: 50mins

Name
Class
Date
1.

A balloon is rising vertically 150m from an observer. At exactly 1 min, the angle of elevation is 29 deg 28 min. How fast is the balloon rising at that instant?

a)

104 m/min

b)

102 m/min

c)

106 m/min

d)

108 m/min

2.

Find the length of vector (2,4,4)

a)

5

b)

6

c)

4

d)

8

3.

A triangular fish pen has sides 30cm, 50cm and 60cm. Find the acute angle opposite to the shortest side.

a)

90 deg

b)

45 deg

c)

30 deg

d)

60 deg

4.

A support wire is anchored 12 ft up from the base of a flagpole and the horizontal distance of the base of a flagpole from the other end of the wire is 16ft. Find the length of the supporting wire.

a)

34 ft

b)

36 ft

c)

20 ft

d)

22 ft

5.

In how many ways can 5 people be lined to get on a bus, if a certain 2 persons refuse to follow each other?

a)

36

b)

48

c)

96

d)

72

6.

A balloon is rising vertically 150 m from an observer. At exactly 1 min, the angle of elevation is 29 deg 28 min. how fast is the balloon rising at that instant?

a)

104 m/min

b)

102 m/min

c)

106 m/min

d)

108 m/min

7.

Simplify 1/(csc x + cot x) + 1/(csc x - cot x)

a)

2cosx

b)

2secx

c)

2cscx

d)

2sinx

8.

How many positive real roots are there in x^4 - 4x^+7x^2 - 6x - 18 = 0?

a)

1 or 0

b)

1 or 2

c)

3 or 0

d)

3 or 1

9.

Using the parametric equations of the hypocycloid of four cups x = acos3 theta y = asin3 theta find the area enclosed by it.

a)

3 pi a^2

b)

3/8 pi a^2

c)

4 pi a^2

d)

3/4 pi a^2

10.

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

a)

y = 3x - 2

b)

y = -3x + 2

c)

y = 3x + 2

d)

y = -3x - 2

11.

Find the length of vector (2,4,4)

a)

5

b)

6

c)

4

d)

8

12.

In triangle ABC where AC = 4 and angle ABC = 90 degrees, an altitude t is drawn from C to the hypotenuse. If t = 1, what is the area of the triangle ABC?

a)

1.82

b)

1.78

c)

2.07

d)

2.36

13.

Determine all the values of 1^(sqrt. of 2).

a)

sin(sqrt. of 2kpi) + icos(sqr. of 2kpi)

b)

cos(sqrt. of 2kpi) + isin(sqrt of 2kpi)

c)

sin(2 sqrt. of 2kpi) + icos(2 sqrt of 2kpi)

d)

cos(2sqrt. of 2kpi) + isin(2 sqrt. of 2kpi)

14.

When two lines are perpendicular, the slope of one is;

a)

Equal to the negative of other

b)

Equal to the other

c)

Equal to the negative reciprocal of the other

d)

Equal to the reciprocal of the other

15.

Find the term involving x squared in the expansion of (x^3 + k/x)^10

a)

210ksq.xsq.

b)

32 ksq.xsq.

c)

92 ksq.xsq.

d)

120 k^7 xsq.

16.

If cos z = 2, find cos 3z

a)

7

b)

17

c)

26

d)

37

17.

Using the parametric equations of the hypocycloid of four cups x = acos3 theta y = asin3 theta find the area enclosed by it.

a)

3 pi a^2

b)

3/8 pi a^2

c)

4 pi a^2

d)

3/4 pi a^2

18.

A class of 40 took examinations in algebra and trigonometry. If 30 passed algebra, 36 passed trigonometry, and 2 failed in both subjects, the number of students who passed the two subjects is:

a)

28

b)

30

c)

25

d)

23

19.

From past experience, it is known 90% of one year old children can distinguish their mother's voice of a similar sounding female. A random sample one year's ole are given this voice recognize test. Find the probability that all 20 children will recognize their mother's voice.

a)

0.122

b)

0.500

c)

1.200

d)

0.222

20.

Find the are bounded by r = 2/(1 + cos theta) and cos theta = 0

a)

2/3

b)

5/3

c)

8/3

d)

1/3

21.

A support wire is anchored 12ft up from the base of a flagpole and the horizontal distance of the base of a flagpole from the other end of the wire is 16ft. Find the length of the supporting wire.

a)

34ft

b)

36ft

c)

20ft

d)

22ft

22.

Evaluate log(2 - 5i)

a)

0.7 - 0.5i

b)

-0.7 + 0.5i

c)

0.7 + 0.5i

d)

-0.7 - 0.5i

23.

Using the parametric equations of the hypocycloid of four cups x = acos3 theta y = asin3 theta find the area enclosed by it.

a)

3 pi a^2

b)

3/8 pi a^2

c)

4 pi a^2

d)

3/4 pi a^2

24.

Find the term involving x squared in the expansion of (x^3 + k/x)^10

a)

210ksq.xsq.

b)

32 ksq.xsq.

c)

92 ksq.xsq.

d)

120 k^7 xsq.

25.

A triangular fish pen has sides 30cm, 5cm and 60cm. Find the acute angle opposite to the shortest side.

a)

90deg

b)

45deg

c)

30deg

d)

60deg

26.

Displacement A is 2m north, displacement B is 3m south. FInd the magnitude and direction of B-A.

a)

1S

b)

1N

c)

5S

d)

5N

27.

You are given n = 5 measurement 0. 5, 1, 1, 3. Find the mode.

a)

2

b)

3

c)

1

d)

1.5

28.

What is the vector which is orthogonal both to 9i + 9j and 9i + 9k?

a)

81i + 81j - 81k

b)

81i - 81j - 81k

c)

81i + 81j + 81k

d)

81i + 81j + 81k

29.

An arrow is shot straight upward from the ground with an initial velocity of 160 ft/s. It experience both the deceleration of gravity and deceleration (v squared)/800 due to air resistance. How high in the air does it go?

a)

314.11 ft

b)

289.31 ft

c)

277.26 ft

d)

254.84 ft

30.

Find the perimeter of a rectangular pentagon inscribed in a circle with a circumference of 100 cm

a)

93.55 cm

b)

125.68 cm

c)

115.63 cm

d)

89.56 cm

31.

Find k so that the line 4x - y + 3 = 0 is tangent to the curve x^2 - y + k = 0

a)

4

b)

11

c)

0

d)

7

32.

Find k so that the line 4x - y + 3 = 0 is tangent to the curve x^2 - y + k = 0

a)

4

b)

11

c)

0

d)

7

33.

A class of 40 took examination in algebra and trigonometry. If 30 passed algebra, 36 passed trigonometry, and 2 failed in both subjects, the number of students who passed the two subjects is:

a)

28

b)

30

c)

25

d)

23

34.

What is the sum of the interior angles of a 15 - sided regular polygon

a)

2560

b)

2340

c)

2480

d)

2620

35.

The top of a 32m ladder leans on a vertical wall. The foot of the ladder is being pushed toward the wall at the rate of 2in/min. At what distance from the bottom of the wall is the top of the ladder moving at the rate of 3in/min?

a)

15.10m

b)

15.50m

c)

17.75m

d)

2.43m

36.

What is the vector which is orthogonal both to 9i + 9j and 9i + 9k?

a)

81i + 81j - 81k

b)

81i - 81j - 81k

c)

81i + 81j + 81k

d)

81i + 81j + 81k

37.

Calculate the eccentricity of an ellipse whose major axis and latus rectum has lengths of 10 and 32/5, respectively

a)

0.4

b)

0.5

c)

0.8

d)

0.6

38.

A trough filled with water is 2m long and has a cross section in the shape of isosceles trapezoid 30 cm wide at the bottom, 60 cm wide at the top and a height of 50 cm. If the trough leaks water at a rate of 2000cu.cm/min, how fast is the water level rising when the water is 20cm deep?

a)

-5/21

b)

-7/20

c)

-4/26

d)

-8/21

39.

A trough filled with water is 2m long and has a cross section in the shape of isosceles trapezoid 30 cm wide at the bottom, 60 cm wide at the top and a height of 50 cm. If the trough leaks water at a rate of 2000cu.cm/min, how fast is the water level rising when the water is 20cm deep?

a)

-5/21

b)

-7/20

c)

-4/26

d)

-8/21

40.

Find the solution of y^2 + 10y = 0.

a)

y = C1cos(sqrt.of 10x) + C2sin(sqrt of 10x)

b)

y = C1cos(sqrt. of 5x) + C2sin(sqrt. of 5x)

c)

y = Ccos(sqrt. of 10x)

d)

y = Csin(sqrt. of 10x)

41.

The top of a 32m ladder leans on a vertical wall. The foot of the ladder is being pushed toward the wall at the rate of 2in/min. At what distance from the bottom of the wall is the top of the ladder moving at the rate of 3in/min?

a)

15.10m

b)

15.50m

c)

17.75m

d)

2.43m

42.

Determine the divergence of the vector V = i(x^2) + j(-xy) + k(xyz) at the point (3, 2, 1)

a)

13.00

b)

9.00

c)

11.00

d)

7.00

43.

When two lines are perpendicular, the slope of one is;

a)

Equal to the negative of other

b)

Equal to the other

c)

Equal to the negative reciprocal of the other

d)

Equal to the reciprocal of the other

44.

Determine the complex number equivalent to tanh(i pi/3) where pi = 3.1416

a)

0.8660 angle - 90deg

b)

1.7321 ang 90 deg

c)

1.4142 angle 180deg

d)

0.70717 angle 0deg

45.

What is the value of x if logx1296 = 4?

a)

4

b)

5

c)

6

d)

3

46.

A student already finished 70% of his homework in 42 minutes. How many minutes does he still have to work?

a)

18

b)

16

c)

20

d)

24

47.

The 3 sides of a triangle are: a = 12cm, b = 10cm, c = 8cm. What is the sum of the 3 heights each perpendicular to the 3 sides?

a)

23.25cm

b)

22.03cm

c)

24.47cm

d)

25.70cm

48.

Find apporximately the difference between areas of two spheres whose radii are 4 feet and 4.05 feet.

a)

1.4pi sq.ft.

b)

1.6pi sq.ft.

c)

1.2pi sq.ft.

d)

1.8pi sq.ft.

49.

Find the area of the region inside the triangle with the vertices (1,1), (3,2) and (2,4).

a)

5/2

b)

3/2

c)

1/2

d)

7/2

50.

The area enclosed is revolved about the line x=3, what is the volume generated?

a)

370.3

b)

360.1

c)

355.3

d)

365.1

51.

Evaluate the Laplace transform of t^2 cosh kt

a)

6s(s² + 2k²)/(s2 – k2)3

b)

6s(s2 -2k2)/(s2 – k2)3

c)

6s(s2 +3k2)/(s2 – k2)3

d)

6s(s2 – 3k2)/(s2 – k2)3

52.

You are given n = 5 measurements 0,5,1,1,3. Find the mode.

a)

2

b)

3

c)

1

d)

1.5

53.

A 400-gal tank initially contains 100 gal of brine combining 50 lb of salt. Brine containing 1 lb of salt per gallon enters the tank at the rate of 5 gal/s, and the well mixed brine in the tank flows out at the rate of 3 gal/s. How much salt will the tank contain when it is full of brine?

a)

393.75 lb

b)

389.65 lb

c)

426.35 lb

d)

435.85 lb

54.

In a certain family, the sum of the parents ages is twice the sum of their children ages now. Five years ago, the sum of the parents age was four times the sum of the childrens ages during that time.In Fifteen years, the sum of the parents age will be equal to the sum of their children ages. How many children are there in the family?

a)

8

b)

7

c)

5

d)

6

55.

Using the parametric equations of the hypocycloid of four cusps x= a cos3 theta y = a sin3 theta find the area enclosed by it.

a)

3 pi a2

b)

3/8 pi a2

c)

4 pi a2

d)

3/4 pi a2

56.

A conic section whose eccentricity is equal to one(1) is known as.

a)

a parabola

b)

an ellipse

c)

a circle

d)

a hyperbola

57.

You are given n = 5 measurements 0,5,1,1,3. Find the mode.

a)

2

b)

3

c)

1

d)

1.5

58.

Suppose that a crossbow bolt is shot straight upward with initial velocity 288 ft/s. if its deceleration due to air resistance is (0.04v), then its height x(t) satisfies the initial value problem x = -32 –(0.04)x, x(0) = 0, x(0) = 288. Find the time required for it to reach the maximum height.

a)

7.9 s

b)

7.2 s

c)

7.0 s

d)

7.7 s

59.

Determine the complex number equivalent to tanh (I pi/3) where pi = 3.1416

a)

0.8660 angle – 90 deg

b)

1.7321 angle 90 deg

c)

1.4142 angle 180 deg

d)

0.70717 angle 0 deg

60.

In a certain family, the sum of the parents ages is twice the sum of their children ages now. Five years ago, the sum of the parents age was four times the sum of the childrens ages during that time. In fifteen years, the sum of the parents age will be equal to the sum of their childrens ages. How many children are there in the family?

a)

8

b)

7

c)

5

d)

6

61.

Simplify 1/(csc x + cot x) + 1/(csc x – cot x).

a)

2cosx

b)

2secx

c)

2cscx

d)

2sinx

62.

A parabolic arch 18 m high has a horizontal beam 64 m long placed across the arch 8 m from the top. Find the width at the bottom.

a)

109 m

b)

96 m

c)

82 m

d)

76 m

63.

In certain family, the sum of the parents ages is twice the sum of their children ages now. Five years ago, the sum of the parents age was four times the sum of the childrens ages during that time. In fifteen years, the sum of the parents age will be equal to the sum of their childrens ages. How many children are there in the family?

a)

8

b)

7

c)

5

d)

6

64.

Determine the divergence of the vector. V = i(x2) + j(- xy) + k(xyz) at the point (3,2,1)

a)

13.00

b)

9.00

c)

11.00

d)

7.00

65.

You are given n = 5 measurements 2,1,1,3,5. What is the sample variance?

a)

1.496

b)

2.24

c)

2.8

d)

2.24

66.

The longest diagonal of a cube is 15 cm. Find the volume of the cube.

a)

625.85 cu. cm.

b)

647.52 cu. cm.

c)

1193.24 cu. cm.

d)

1193.24 cu. cm.

67.

When two lines are perpendicular, the slope of one is;

a)

equal to the negative of the other

b)

equal to the other

c)

equal to the negative reciprocal of the other

d)

equal to the reciprocal of the other

68.

A cardboard 20 in x 20 in is to be formed into a box by cutting four equal squares and folding the edges. Find the volume of the largest box.

a)

592 cu. in.

b)

529 cu. in.

c)

698 cu. in.

d)

689 cu. in.

69.

Determine the complex number equivalent to tanh (I pi/3) where pi = 3.1416

a)

0.8660 angle – 90 deg

b)

1.7321 angle 90 deg

c)

1.4142 angle 180 deg

d)

0.70717 angle 0 deg

70.

The mean duration of television commercials on a given network is 75 seconds, with a standard deviation of 20 seconds. Asumme that duration time are approximately normally distributed. What is the approximate probability that a commercial will last less than 35 seconds.

a)

0.055

b)

0.025

c)

0.045

d)

0.035

71.

In certain family, the sum of the parents ages is twice the sum of their children ages now. Five years ago, the sum of the parents age was four times the sum of the childrens ages during that time. In fifteen years, the sum of the parents age will be equal to the sum of their childrens ages. How many children are there in the family?

a)

8

b)

7

c)

5

d)

6

72.

The are enclosed by the ellipse 4x2 + 9y2 = 36 is revolved about the line x = 3, what is the volume generated?

a)

370.3

b)

360.1

c)

355.3

d)

365.1

73.

A triangular fish pen has sides 30 cm, 50 cm and 60 cm. Find the acute angle opposite to the shortest side.

a)

90 deg

b)

45 deg

c)

30 deg

d)

60 deg

74.

A stell ball at 120 deg C colls in 20 minutes to 80 deg C in a room at 25 deg C. Find the temperature of the ball after half an hour.

a)

40.96 deg C

b)

45.96 deg C

c)

66.85 deg C

d)

55.96 deg C

75.

A line is perpendicular to the y-axis has a slope equal to:

a)

one

b)

infinity

c)

zero

d)

inderterminate

76.

You are given n = 5 measurements 0,5,1,1,3. Find the mode.

a)

2

b)

3

c)

1

d)

1.5

77.

A water tank has the shape obtained by revolving the curve y = x raised to (4/3) around the y – axis. A plug at the bottom is removed at 12 noon when the depth of water in the tank is 12 ft. at 1 PM, the depth of the water is 6 ft. When will the tank be empty?

a)

1:26 PM

b)

1:15 PM

c)

1:38 PM

d)

1:20 PM

78.

The magnitude of vector product of two vector is sqrt. Of 3 times their scalar product. The angle between the vector is

a)

pi/4

b)

pi/2

c)

pi/6

d)

pi/3

79.

Find the term involving x squared in the expansion of (x^3 +k/x)^10

a)

210 k sq. x sq.

b)

32 k sq. x sq.

c)

92 k sq. x sq.

d)

210 k^7 x sq.

80.

The longest diagonal of a cube is 15 cm. Find the volume of the cube.

a)

625.85 cu. cm.

b)

647.52 cu. cm.

c)

1193.24 cu. cm.

d)

1295.36 cu. cm.

81.

A class of 40 took examination in Algebra and Trigonometry. If 30 passed Algebra, 36 passed Trigonometry, and 2 failed in both subjects, the number of students who passed the two subjects is:

a)

28

b)

30

c)

25

d)

23

82.

The are enclosed by the ellipse 4x2 + 9y2 = 36 is revolved about the line x = 3, what is the volume generated?

a)

370.3

b)

360.1

c)

355.3

d)

365.1

83.

Using power series expansion about 0, find cosx by differentiating from sinx

a)

1 - (x2/2!) + (x4/4!) – (x6/6!) + ?

b)

x - (x2/2!) + (x4/4!) – (x6/6!) + ?

c)

– (x3/3!) + (x5/5!) – (x7/7!) + ?

d)

x – (x3/3!) + (x5/5!) – (x7/7!) + ?

84.

Find the area of the lemniscate r2 = a2 cos 2 theta

a)

s2

b)

a

c)

2a

d)

a3

85.

N engineers and N nurses, if two engineers are replaced by nurses, 51% of the engineers and nurses are nurses. Find N.

a)

100

b)

110

c)

50

d)

200

86.

There is avector v = 7j, another vbector u starts from the origin with a magnitude of 5 rotates in the xy plane. Find the maximum magnitude of u x v .

a)

24

b)

70

c)

12

d)

35

87.

4 lbs of nuts and raisins is 2/3 nuts. How much in lbs are raisins?

a)

2.6

b)

1.3

c)

3.9

d)

0.065

88.

Evaluate lim(z squared + 1)/(z raised to the 6 + 1) as z approaches to i.

a)

sq. rt. Of 2(1 + i)/2

b)

(-4/3) – 4i

c)

1/3

d)

-12 +6i

89.

The mean duration of television commercials on a given network is 75 seconds, with a standard deviation of 20 seconds. Asumme that duration time are approximately normally distributed. What is the approximate probability that a commercial will last less than 35 seconds.

a)

0.055

b)

0.025

c)

0.045

d)

0.035

90.

You are given n = 5 measurements 2,1,1,3,5. What is the sample variance?

a)

1.496

b)

2.24

c)

2.8

d)

2.4

91.

Determine the complex number equivalent to tanh (I pi/3) where pi = 3.1416

a)

0.8660 angle – 90 deg

b)

1.7321 angle 90 deg

c)

1.4142 angle 180 deg

d)

0.70717 angle 0 deg

92.

What is the unit vector which is orthogonal both to 9i + 9j and 9i + 9k?

a)

(i / sqrt3) + (j / sqrt 3) + (k / sqrt3)

b)

(i / 3) + (j / 3) + (k / 3)

c)

(i / sqrt3) – (j / sqrt 3) – (k / sqrt 3)

d)

(i/3) – (j/3) – (k/3)

93.

Using power series expansion about 0, find cosx by differentiating from sinx

a)

1 - (x2/2!) + (x4/4!) – (x6/6!) + ?

b)

x - (x2/2!) + (x4/4!) – (x6/6!) + ?

c)

– (x3/3!) + (x5/5!) – (x7/7!) + ?

d)

x – (x3/3!) + (x5/5!) – (x7/7!) + ?

94.

Simplify 1/(csc x + cot x) + 1/(csc x – cot x).

a)

2cosx

b)

2secx

c)

2cscx

d)

2sinx

95.

What is the sum of the interior angles of a 15-sided regular polygon?

a)

2560

b)

2340

c)

2480

d)

2620

96.

You are given n = 5 measurements 0,5,1,1,3. Find the mode.

a)

2

b)

3

c)

1

d)

1.5

97.

What is the area of the largest rectangle that can be inscribed in a semicircle of radius 10?

a)

1000

b)

50

c)

10

d)

100

98.

Find the height of a tree if the angle of elevation of itrs top changes from 20 deg to 40 deg as the observer advances 23 meters toward the base.

a)

14.78 m

b)

13.78 m

c)

15.78 m

d)

16.78 m

99.

A parabolic arch 18 m high has a horizontal beam 64 m long placed across the arch 8 m from the top. Find the width at the bottom.

a)

109 m

b)

96 m

c)

82 m

d)

76 m

100.

A conic section whose eccentricity is equal to one (1) is known as:

a)

a parabola

b)

an ellipse

c)

a circle

d)

a hyperbola