Free Printable MATH

1.

Find the equation of the perpendicular bisector of the line passing through points (2, -5) and (-3, 4).

a)

5x-9y=2

b)

3x-4y=1

c)

x+y=4

d)

3x+7y=3

2.

Find the center of the circle that passes through $P(1,1)$ and is tangent to the line $y=2x-3$ at the point $(3,3)$

a)

(1, 5)

b)

(-1, -5)

c)

(1, -5)

d)

(-1, 5)

3.

The lines $3x+4y-10=0$ and $4x-3y-1=0$ are

a)

parallel

b)

coincident

c)

bisecting

d)

perpendicular

4.

The intersection of the medians of a triangle whose vertices are (-6, -8), (3, -5) and (4, -2) are at

a)

(0, 0)

b)

(-1/3, -5)

c)

(-1/3, 5)

d)

(1/3, -5)

5.

Find the length of the latus rectum of the parabola $y^2-8x-4y-20=0$

a)

4

b)

8

c)

12

d)

16

6.

The vertex of a parabola $y^2-4x+6y+13=0\$ is at

a)

(-3, 1)

b)

(1, -3)

c)

(-1, 3)

d)

(3, 1)

7.

Determine the equation of the diameter of the circle $x^2+y^2+2x-4y=4$ that is parallel to the line $3x+5y=4$

a)

$3x+5y=5$

b)

$3x+5y=6$

c)

$3x+5y=7$

d)

$3x+5y=8$

8.

How far from the x-axis is the focus F of the hyperbola $x^2+2y^2+4x+4y+4=0$

a)

2.73

b)

3.18

c)

4.57

d)

1.65

9.

The polar form of $xy=3\left(x+y\right)\$ is

a)

$r=6\csc2\theta\left(\cos\theta+\sin\theta\right)$

b)

$r^2=6\csc^4\theta$

c)

$r=2\sin2\theta$

d)

$r^2=3\cos^3\theta$

10.

A basketball is losing air at the rate of 3 cubic inches per minute. At the moment that the radius equals inches, at what rate is the radius changing?

a)

$-\frac{3}{\left(50\pi\right)\ }\ in\ per\ \min$

b)

$-\frac{3}{\left(100\pi\right)\ }\ in\ per\ \min$

c)

$-\frac{6}{\left(100\pi\right)\ }\ in\ per\ \min$

d)

$-\frac{3}{\left(10\pi\right)\ }\ in\ per\ \min$

11.

The position of a body moving along a linear track is given by $p\left(t\right)=3t^2-5t+7$ feet. Calculate the acceleration at time t = 3 seconds.

a)

$6\ \frac{ft}{s^2}$

b)

$3\ \frac{ft}{s^2}$

c)

$4\ \frac{ft}{s^2}$

d)

$5\ \frac{ft}{s^2}$

12.

The altitude of a certain right circular cone is the same as the radius of the base and is measured as 5 inches with a possible error of 0.02 in. Find the approximate percentage error in the calculated value of the volume.

a)

1.1 %

b)

1.2 %

c)

0.1 %

d)

0.2 %

13.

A weight is attached to one end of a 33-ft rope which passes over a pulley 18 ft above the ground. The other end is attached to a truck at a point 3 ft above the ground. If the truck moves away at a rate of 2 ft/s, how fast is the weight rising when the truck is 8 ft from the spot directly under the pulley?

a)

0.94 ft/s

b)

0.79 ft/s

c)

0.69 ft/s

d)

0.86 ft/s

14.

The shortest distance from (5, 10) to the curve $x^2=12y$ is

a)

4.331

b)

3.474

c)

5.127

d)

6.445

15.

If three sides if a trapezoid are each 6 inches long, how long must the fourth side be if the area is to be a maximum?

a)

10

b)

16

c)

12

d)

18

16.

A man walks along a straight path a speed of 4 ft/s. A searchlight is located on the ground 20 ft from the path and is kept focus on the man. At what rate is the searchlight rotating when the man is 15 ft from the point on the path closest to the seachlight?

a)

0.185 rad/s

b)

0.274 rad/s

c)

0.128 rad/s

d)

0.384 rad/s

17.

Evaluate $\int_{ }^{ }\frac{3-x}{\sqrt[]{16+6x-x^2}}$

a)

$2\sqrt[]{16+6x-x^2}$

b)

$\sqrt[]{16+6x-x^2}+c$

c)

$-\sqrt[]{16+6x-x^2}+c$

d)

$\frac{1}{2}\left(\sqrt[]{16+6x-x^2}+c\right)$

18.

$\int_{ }^{ }x^{2\cos xdx}$

a)

$x^2\sin x+2x\sin x+\sin x+c$

b)

$x^2\sin x-2x\sin x+2\cos x+c$

c)

$x^2\sin x+2x\cos x-2\sin x+c$

d)

$\frac{1}{2}\left(\sqrt[]{16+6x-x^2}+c\right)$

19.

Find the area bounded by $y+x^2=6$ and $y+2x-3=0$

a)

10.667

b)

14.667

c)

11.667

d)

12.667

20.

Given the area in the first quadrant bounded by $x^2=8y$ , the line $y-2=0$ , and the y-axis. What is the volume generated when this area is revolved about the line $y-2=0$ ?

a)

$26.81\ m^3$

b)

$28.92\ m^3$

c)

$29.24\ m^3$

d)

$21.67\ m^3$

21.

Evaluate the indefinite integral $\int_{ }^{ }\frac{3x^2+7x-4}{x^3-4x}$

a)

$\ln x-\frac{3}{4}\ln\left(x-2\right)+\frac{11}{4}\ln\left(x+2\right)$

b)

$\ln x+\frac{3}{4}\ln\left(x+2\right)-\frac{11}{4}\ln\left(x-2\right)$

c)

$\ln x-\frac{3}{4}\ln\left(x+2\right)+\frac{11}{4}\ln\left(x-2\right)$

d)

$\ln x-\frac{3}{4}\ln\left(x+2\right)+\frac{3}{4}\ln\left(x-2\right)$

22.

Calculate the volume of the solid enclosed when the area between the curves $x=\left(y-2\right)^2+1$ and $x=-\left(y-2\right)^2+9$ is rotated about the line $y=-2$

a)

$\frac{256\pi}{2}$

b)

$\frac{512\pi}{5}$

c)

$256\pi$

d)

$\frac{512\pi}{3}$

23.

Determine the area that lies inside $r=3+2\sin\theta$ and outside $r=2$

a)

28.4

b)

24.2

c)

26.4

d)

28.6

24.

A conservative field has a zero

a)

Divergence

b)

Curl

c)

Laplacian

d)

Gradient

25.

Which of the following equals the laplacian of f?

a)

div(grad f)

b)

grad(div f)

c)

div(curl f)

d)

curl(grad f)

26.

If f is a scalar function then _____ is the directional derivative of the function in the direction of $a_{\iota}$

a)

$\nabla f\circ a_{\iota}$

b)

$\nabla f\times a_{\iota}$

c)

$\nabla f\left(a_{\iota}\right)$

d)

$\nabla^2f\left(a_{\iota}\right)_{ }$

27.

If the curl of a vector is zero $\left(\nabla\times A=0\right)$ , then that vector can always be expressed as a gradient of a certain scalar function, commonly known as the _________ of A.

a)

Divergence

b)

Laplacian

c)

potential

d)

circulation

28.

A vector whose divergence is zero is

a)

Solenoidal

b)

Irrotational

c)

potential

d)

conservative

29.

A semiconductor company will hire 7 men and 4 women. In how many ways can the company choose from 9 men and 6 women who qualified for the position?

a)

680

b)

840

c)

480

d)

540

30.

A bag contains 3 red balls, 3 green balls and 5 blue balls. Find the probability of not getting a red ball in the first draw.

a)

1/3

b)

2/3

c)

2/5

d)

3/5

31.

A bag contains 3 white and 5 black balls. If two balls are drawn in succession without replacement, what is the probability that both balls are black?

a)

5/28

b)

5/16

c)

5/32

d)

5/14

32.

A bag contains 3 white balls and 5 red balls. If two balls are drawn at random, find the probability that both are white.

a)

3/28

b)

3/8

c)

2/7

d)

5/15

33.

When an irregular shaped object is placed in a cylindrical vessel of a water whose radius is 8 cm, the water rises 6 m. What is the volume of the rock if it is completely submerged?

a)

$192\pi\ cm^3$

b)

$24\pi\ cm^3$

c)

$384\pi\ cm^3$

d)

$48\pi\ cm^3$

34.

The two bases of trapezoid are 12 inches and 18 inches, respectively. If the angles of the extremities of one base are $65\degree$ and $40\degree$ respectively, find the longer leg in inches.

a)

5.63

b)

6.23

c)

7.21

d)

7.81

35.

Find the 30th term of the arithmetic progression 4, 7, 10, ...

a)

88

b)

91

c)

75

d)

90

36.

Find the sum of the infinite geometric progression 6, -2, -2/3, ...

a)

5/2

b)

9/2

c)

7/2

d)

11/2

37.

How long will it take a 100-mg sample of $^{14}C$ to decay to 90 mg?

a)

870 years

b)

871 years

c)

872 years

d)

873 years

38.

Solve the equation $y'=x^2y$

a)

$y=Ce^{3x}$

b)

$y=Ce^{3x^3}$

c)

$y=Ce^{x^{\frac{1}{3}}}$

d)

$y=Ce^{x^3}$

39.

Find the equation of the curve at every point of which the tangent line has a slope of $x^2$ and which passes through (1, 1)

a)

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

b)

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

c)

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

d)

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

40.

The differential equation $2xyy'=y^2-x^2$ is

a)

linear

b)

separable

c)

homogeneous

d)

exact

41.

A thermometer reading $5\degree C$ , is brought into a room whose temperature is $22\degree C$ . One minute later, the thermometer reading is $12\degree C$ . How long does it take until the reading is practically $22\degree C$ , say, $21.9\degree C$ ?

a)

9.68 minutes

b)

8.96 minutes

c)

9.86 minutes

d)

8.69 minutes

42.

The differential equation $\frac{dy}{dx}=\frac{2x^2+y^2}{2xy}$ can be made exact by using the integrating factor

a)

$x^2$

b)

$\frac{1}{x^2}$

c)

$y^2$

d)

$\frac{1}{y}$

43.

Obtain the differential equation of the family of straight lines whose slopes and y-intercepts are equal.

a)

$\left(x+1\right)dx-ydy=0$

b)

$\left(x+1\right)dx+ydy=0$

c)

$\left(x+1\right)dy+ydx=0$

d)

$\left(x+1\right)dy-ydx=0$

44.

Which of the following is a solution of the differential equation $y''+2y'+y=0?$

a)

$y=e^{-x}+2e^{-x}$

b)

$y=2e^{-x}+e^{-x}$

c)

$y=2e^{-x}+xe^{-x}$

d)

$y=e^{-x}+2xe^{-x}$

45.

Evaluate the given limit: $\lim_{x\rightarrow\infty}x\sin\frac{\pi}{x}$

a)

0

b)

1

c)

$\pi$

d)

$\frac{\pi}{2}$

46.

Evaluate the limit of $\frac{\left(x-2\right)^{\frac{1}{2}}}{\left(x^2-4\right)}$ as x approaches 2

a)

1

b)

0

c)

no limit

d)

indeterminate

47.

Solve for $y=f\left(x\right)$ from the differential equation $xdy+ydx-3x^2dx=0$

a)

$xy=x+C$

b)

$xy=x^3+C$

c)

$xy=x^2+C$

d)

$xy=C$

48.

What is the rationalized value of the complex quotient $\frac{(6+2.5i)}{\left(3+4i\right)}$

a)

$1.1-0.66i$

b)

$28-16.5i$

c)

$-0.32+0.66i$

d)

$0.32-0.66i$

49.

Given the two vectors $3a_{x0}+4a_y+a_z$ and $B=2a_y-5a_z$ , find the angle between A and B.

a)

84.7

b)

85.7

c)

83.7

d)

81.7

50.

Solve the equation $y''-6y'+13y=0$

a)

$y=e^{3x}\left(c_1\cos2x-c_2\sin2x\right)$

b)

$y=e^{3x}\left(c_1\cos2x+c_2\sin2x\right)$

c)

$y=e^{2x}\left(c_1\cos3x+c_2\sin3x\right)$

d)

$y=e^{2x}\left(c_1\cos3x-c_2\sin3x\right)$

51.

Find the curve which satisfies the equation $xy=\left(1+x^2\right)y'$ and passes through the point (0, 1)

a)

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

b)

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

c)

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

d)

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

52.

a)

10

b)

20

c)

30

d)

40

53.

What is the dc value of the signal?

a)

0.50

b)

0.25

c)

1.0

d)

0.75

54.

What is $a_n$ ?

a)

$-\frac{2}{n^2\pi^2}$

b)

$-\frac{1}{n^2\pi^2}$

c)

$-\frac{4}{n^2\pi^2}$

d)

0

55.

What is $b_n$ ?

a)

$-\frac{2}{n\pi}$

b)

$-\frac{1}{n\pi}$

c)

$-\frac{4}{n^2\pi^2}$

d)

0

56.

Find the convolution of $e^{3t}u\left(t\right)\$ and $t^2u\left(t\right)$

a)

$\frac{3}{s^2\left(s-3\right)}$

b)

$\frac{2}{s^2\left(s-3\right)}$

c)

$\frac{3}{s^3\left(s-3\right)}$

d)

$\frac{2}{s^3\left(s-3\right)}$

57.

Find the assumed particular solution of the differential equation $y''+y'-2y=2x-40\cos2x$

a)

$Ae^x+Be^{-2x}$

b)

$Ax+B\cos2x$

c)

$Ax+B+C\cos2x+D\sin2x$

d)

$Ae^x+Be^{-2x}+Cx+D+E\cos2x$

58.

Find the inverse Laplace transform of $\frac{20}{\left(s+3\right)\left(s^2+8s+25\right)}$

a)

$2e^{-3t}-2e^{-4t}\cos3t-\frac{1}{3}e^{-4t}\sin3t$

b)

$2e^{-3t}-2e^{-4t}\cos3t-\frac{4}{3}e^{-4t}\sin3t$

c)

$2e^{-3t}-2e^{-4t}\cos3t-\frac{2}{3}e^{-4t}\sin3t$

d)

$2e^{-3t}+2e^{-4t}\cos3t+\frac{4}{3}e^{-4t}\sin3t$

59.

Which of the following is not a solution of the linear system of equations

$x+y+z=4$

$2x-3y+4z=33$

$3x-2y-2z=2$

a)

2

b)

-3

c)

5

d)

4

60.

a)

$2+j30$

b)

$3-j40$

c)

$2-j30$

d)

$3+j40$

61.

Find the solution of the equation $D^2\left(D^2+4\right)y=0$

a)

$y=Ae^x+Bxe^x+C\cos2x+D\sin2x$

b)

$y=A+Be^x+C\cos2x+D\sin2x$

c)

$y=A+Bx+C\cos2x+D\sin2x$

d)

$y=A+Bx+C\cos4x+D\sin4x$

62.

Given the differential equation 3y''-y'=2x, the complementary solution is

a)

$y=C_1+C_2e^{\frac{1}{2}x}$

b)

$y=C_1+C_2e^{-\frac{1}{2}x}$

c)

$y=C_1e^x+C_2e^{\frac{1}{2}x}$

d)

$y=C_1e^x+C_2e^{-\frac{1}{2}x}$

63.

Which of the following differential equations is nonlinear?

a)

$y'+2y=x^2\ln x$

b)

$\frac{y''-4y'+\left(2xy+y^2\right)}{y}=e^x$

c)

$\left(x^2-4\right)y'+2xy=x^3+1$

d)

$y'=4y\left(0.5-x^2y\right)$

64.

How old is a fossil whose $\frac{^{14}C}{^{12}C}$ ratio is 10 percent of that found in the atmosphere today?

a)

19 000 years

b)

21 000 years

c)

18 000 years

d)

20 000 years

65.

One hour after a bacteria colony starts growing, a scientist determines that there are 9000 bacteria present. After another hour, there are 12 000 bacteria. How many bacteria were present initially?

a)

6700 bacterial

b)

6570 bacterial

c)

6500 bacterial

d)

6750 bacterial

66.

The probability of A's winning a game against B is 1/3. What is the probability that A will win at least two of a total of 3 games?

a)

7/27

b)

8/27

c)

19/278

d)

15/27

67.

How many of the arrangements of the letter of the word "VOLTAGE" begins with a vowel and end with a constant.

a)

1440

b)

1490

c)

1460

d)

1450

68.

How many different teams of 5 players can be chose out of 12 applicants?

a)

730

b)

718

c)

792

d)

719

69.

How many different committees of 5 members can be formed from 8 men and 6 women if each committee is to have exactly 3 men?

a)

830

b)

840

c)

860

d)

820

70.

In how many ways can 2 or more ties can be selected out of 8 ties.

a)

235

b)

240

c)

247

d)

245

71.

Divide $3x^3+x^2+3x+5$ by $x+1$

a)

$3x^2+2x+5$

b)

$3x^2-2x+5$

c)

$3x^2-2x-5$

d)

$3x^2+2x-5$

72.

Which of the following is not a factor of $x^3-7x-6=0$

a)

$\left(x+3\right)$

b)

$\left(x+2\right)$

c)

$\left(x+1\right)$

d)

$\left(x-3\right)$

73.

The hypotenuse of a right triangle is 34 cm. Find the length of one leg if it is 14 cm longer than the other.

a)

16

b)

14

c)

30

d)

28

74.

What is the solution of the equation $50x^2+5\left(x-2\right)^2=-1$ , where $x$ is a real valued variable?

a)

2/11

b)

-0.52 and 0.700

c)

7.55

d)

no solution

75.

A transit set up 40 m from the base of a vertical chimney reads $32\degree30'$ with the crosshairs set on top of the chimney. With the telescope level, the vertical rod at the base of the chimney is 2.1 m. Approximately how tall is the chimney?

a)

15 m

b)

26 m

c)

28 m

d)

38 m

76.

In the probability, what term describes the set of all possible outcomes of an experiment?

a)

set

b)

cumulative distribution

c)

events

d)

sample space

77.

How can the values of a random variable defined over a sample space be described?

a)

always continuous

b)

always numerical horizon

c)

strictly nonzero

d)

defined only over a finite

78.

A man and a boy can dig a trench in 20 days. It would take the boy 9 days longer to dig it alone than it would take the man. How long would it take the boy to dig it alone?

a)

54 days

b)

45 days

c)

35 days

d)

36 days

79.

Two jeepney start at the same point but are going different directions. If jeepney A runs at the rate of 60 km/hr and jeepney B at 50 km/hr and both start at the same time, when will the two jeepney be 550 km apart?

a)

4 hrs

b)

5 hrs

c)

6 hrs

d)

7 hrs

80.

What is the probability of getting a number ''4" thrice in five tosses of a die?

a)

0.0232

b)

0.0322

c)

0.3220

d)

0.2330

81.

Given the functions $f\left(x\right)=x^2-4x$ and $g\left(x\right)=2-\sqrt[]{x+3}$ , determine $\left(f\degree g\right)\left(x\right)$

a)

$x^2+1$

b)

$x^2-1$

c)

$x+1$

d)

$x-1$

82.

Find the sum of the first ten terms of the sequence $a_n=3+5n$

a)

300

b)

310

c)

305

d)

315

83.

Find the term containing $x^3$ in the expansion of $\left(2x+y\right)^5$

a)

$320x^3y^2$

b)

$160x^3y^2$

c)

$80x^3y^2$

d)

$240x^3y^2$

84.

Determine the inverse function of $f\left(x\right)=\frac{x}{\left(1-3x\right)}$

a)

$\frac{1}{\left(3x-1\right)}$

b)

$\frac{x}{\left(3x+1\right)}$

c)

$\frac{x}{\left(3x-1\right)}$

d)

$\frac{3}{\left(3x+1\right)}$

85.

A store sells clothes for men. It has 3 kinds of jackets, 7 kinds of shirts, and 5 kinds of pants. Find the number of ways a person can buy one of each of the three kinds of clothes.

a)

105

b)

110

c)

115

d)

120

86.

Solve for x in the given equation: $x+4x+7x+10x+...+64x=1430$

a)

4

b)

3

c)

2

d)

1

87.

Find the number of ways a coin can be tossed 6 times so that there are exactly 3 heads and no two heads occur in a row

a)

10

b)

8

c)

6

d)

4

88.

Find the number of ways 10 students can be divided into three teams where one team has 4 students, and the other teams have 3 students

a)

210

b)

230

c)

420

d)

540

89.

The diagonal of the floor of a rectangular room is 7.50 m. The shorter side of the room is 4.4 m. What is the area of the room?

a)

$36\ m^2$

b)

$27\ m^2$

c)

$58\ m^2$

d)

$24\ m^2$

90.

One side of a parallelogram is 10 and its diagonals are 16 and 24. Its area is

a)

156.8

b)

185.6

c)

158.7

d)

143.2

91.

A rectangular triangular pyramid has an altitude of 9 m and a volume of $187.06\ m^3$ . What is the base edge in m?

a)

12

b)

19

c)

11

d)

20

92.

Find the volume of a cone to be constructed from a sector having a diameter of 72 cm and a central angle of $210\degree$

a)

12367.2

b)

13232.6

c)

13503.4

d)

14682.5

93.

The two legs of a triangle are 300 and 150 m each respectively. The angle opposite the 150 m side is $26\degree$ . What is the third side?

a)

197.49

b)

218.61

c)

341.78

d)

282.15

94.

Find the volume generated by rotating the region bounded by $y=x,\ x=1$ and $y^2=4x$ about the x-axis

a)

$7\pi\ cubic\ units$

b)

$8\pi\ cubic\ units$

c)

$9\pi\ cubic\ units$

d)

$10\pi\ cubic\ units$

95.

How far from the y-axis is the centroid pf area bounded by the curve $y=x^3$ , the line $x=2$ and the x-axis

a)

1.4

b)

1.5

c)

1.6

d)

1.7

96.

A solid is obtained by rotating the region below $y=\sqrt[]{x}$ , above the x-axis, and between x=2 and x=4 about the x-axis. What is the resulting volume?

a)

$4\pi$

b)

$3\pi$

c)

$6\pi$

d)

$5\pi$

97.

Determine the length of the arc formed by the graph of $y=4x^{\frac{1}{2}}$ from $x=0$ to $x=4$

a)

6.2

b)

7.2

c)

8.2

d)

9.2

98.

Find the centroid of the region bounded by the line y=x and the parabola $y=x^2$

a)

$\left(\frac{1}{2},\frac{2}{5}\right)$

b)

$\left(\frac{1}{3},\frac{3}{5}\right)$

c)

$\left(\frac{2}{5},\ \frac{1}{2}\right)$

d)

$\left(\frac{3}{5},\ \frac{1}{3}\right)$

99.

Which of the following relates the line integral of a given vector to its curl?

a)

Gauss's theorem

b)

Green's theorem

c)

Stoke's theorem

d)

Baye's theorem

100.

Which of the following is not a term in the partial fraction expansion of

$\frac{5x^2-2x-19}{\left(x+3\right)\left(x-1\right)^2}$

a)

$\frac{2}{x+3}$

b)

$\frac{4}{\left(x-1\right)^2}$

c)

$\frac{5}{x+1}$

d)

$\frac{3}{x-1}$

MATH

Total questions: 100

Worksheet time: 50mins

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