Quiz about Calculator Techniques

Question 1

In a class of 60 students, 43 like calculus, 38 like geometry, how many students like both subjects?

Accepted Answer

21

Answer

20

Answer

22

Answer

23

Question 2

In which interval will the following power series converge?

$$\sum_{n=1}^{\infty}\frac{x^n}{\left(n^2+1\right)}$$

Accepted Answer

$$\left[-1,\ 1\right]$$

Answer

$$\left(-\frac{4}{3},\ \frac{4}{3}\right)$$

Answer

$$\left(-4,\ 1\right]$$

Answer

$$\left[0,\ 2\right]$$

Question 3

Given the following functions:

$$f\left(x\right)\ =\ 5x^2-4x+10$$

$$g\left(x\right)\ =\ 3x^3+18x^2-5x+7$$

Find f(g(5)).

Accepted Answer

3253027

Answer

5302732

Answer

4350278

Answer

6534297

Question 4

Given the ff functions:
f(x) = 2x+3

g(x) = 3x+2

Evaluate: f(g(x))

Accepted Answer

6x + 7

Answer

6x + 11

Answer

11x + 6

Answer

7x + 6

Question 5

Find f^-1 (x)
$$f\left(x\right)\ =\ \frac{2x+5}{4}$$

Accepted Answer

$$f^{-1}\left(x\right)\ =\ \frac{4x-5}{4}$$

Answer

$$f^{-1}\left(x\right)\ =\ \frac{4x+5}{4}$$

Answer

$$f^{-1}\left(x\right)\ =\ \frac{2x-5}{4}$$

Answer

$$f^{-1}\left(x\right)\ =\ \frac{2x+5}{4}$$

Question 6

A class of students took examination in Math, Elecs and Comms. 50 passed Math, 48 passed Elecs and 42 passed Comms. 28 passed Math and Elecs, 20 passed Elecs and Comms, while 22 passed Math and Comms. If 15 passed all subjects how many students were there?

Accepted Answer

85

Answer

80

Answer

90

Answer

95

Question 7

Find $$f^{-1}\left(5\right)$$

$$f\left(x\right)\ =\ \frac{2x+5}{4}$$

Accepted Answer

7.5

Answer

2.5

Answer

5.5

Answer

9.5

Question 8

How many distinct elements/arrangements can be formed using all the letters of STATISTICS?

Accepted Answer

50400

Answer

30400

Answer

40500

Answer

60500

Question 9

In each of 4 races, the democrats have 60% chance of winning. Assuming that the races are independent of each other, what is the probability that the democrat won at least 2 races?

Accepted Answer

0.8208

Answer

0.7208

Answer

0.9208

Answer

0.6208

Question 10

Vehicles pass through a junction on a busy road at an average rate of 300 per hour. Find the probability that at most 5 cars passes in a given minute.

Accepted Answer

0.6

Answer

0.3

Answer

0.4

Answer

0.5

Question 11

Given the values: 74 85 94 100 115 and 130.

Find population standard deviation and variance.

Accepted Answer

18.53, 343.55

Answer

343.55, 18.53

Answer

18.53, 340.55

Answer

340.55, 18.53

Question 12

The annual salaries of employees in a company are approximately normally distributed with a mean of 2.5 million pesos and a standard deviation of 1 million pesos. What percent of people earn from between 2.25 and 3.25?

Accepted Answer

0.273

Answer

0.753

Answer

0.573

Answer

0.373

Question 13

Graduates from a certain business school plan to take an admission test. The scores of this test are roughly normally distributed with a mean of 530 and a standard deviation of 110. Which is the lowest score that belongs to the top 10

Accepted Answer

681

Answer

780

Answer

781

Answer

651

Question 14

What is the distance between (4,7) and (2,2)?

Accepted Answer

5.39

Answer

6.39

Answer

7.39

Answer

8.39

Question 15

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

Accepted Answer

4x + 3y = 7

Answer

4x + 7y = 3

Answer

3x + 4y = 7

Answer

7x + 4y = 3

Question 16

Find the equation of the line that passes through the point (-2 6) with a slope of 3.

Accepted Answer

y = 12 + 3x

Answer

y = 12 - 3x

Answer

y = 16 + 3x

Answer

y = 16 - 3x

Question 17

Find the midpoint of the line that passes through the point (-1, 2) and (3, -6)

Accepted Answer

(1, -2)

Answer

(2, -2)

Answer

(-1, -2)

Answer

(-1, -2)

Question 18

Find the equation of the line passing through the points (1, -2, 0) (3, 1, 4) and (0, -1, 2)

Accepted Answer

2x - 8y + 5z = 18

Answer

2x + 8y + 5z = 18

Answer

2x - 8y - 5z = 18

Answer

2x + 8y -5z = 18

Question 19

In a cartesian coordinate, the vertices of a triangle are the ff. points (13, 14) (16, 30) and (50, 10) What is the area?

Accepted Answer

302

Answer

202

Answer

402

Answer

502

Question 20

In a cartesian coordinate the vertices of a polygon are (4,1) (3,6) (-5,1) (-3,1) and (-3, -3). Find the area of the polygon.

Accepted Answer

36.5

Answer

38.5

Answer

40.5

Answer

42.5

Question 21

Find the coordinates of the centroid of the triangle formed by the ff. sets of 3 points: (7, 5) (-2, -5) (4, 6)

Accepted Answer

(3, 2)

Answer

(2, 3)

Answer

(3, 3)

Answer

(2, 2)

Question 22

Find the coordinates of the incenter of the triangle formed by following sets of 3 pts: (0,0) (0,14) (12, -5)

Accepted Answer

(4 -6)

Answer

(4,2)

Answer

(6, -4)

Answer

(2, -4)

Question 23

Find the indicated limit $$\lim_{x,y\rightarrow1,1}\left(\frac{2x^2-xy\ -y^2}{x^2-y^2}\right)$$

Accepted Answer

1.5

Answer

2.5

Answer

3.5

Answer

4.5

Question 24

Find the indicated limit:

$$\lim_{x\rightarrow0}\ \frac{\cos\left(x\right)-1}{x^2}$$

Accepted Answer

-1/2

Answer

-1

Answer

1/2

Answer

0

Question 25

Find the limit.

$$\lim_{x\rightarrow+\infty}\ \frac{\sqrt[]{x^4+1}}{2x^2-5}$$

Accepted Answer

does not exist

Answer

1/2

Answer

-1/2

Answer

0

Question 26

Find the indicated limit:

$$\lim_{\left(x,\ y\right)\rightarrow\left(0,0\right)}\left(\frac{3xy}{x^2+y^2}\right)$$

Accepted Answer

limit does not exist

Answer

3/2

Answer

2/3

Answer

-1

Question 27

Differentiate: $$y=\cot^{-1}\left(3x\right)$$

Accepted Answer

$$y$$

Question 28

Find the y'' of $$y\ =\ \cot^{-1}\left(3x\right)$$

Accepted Answer

$$\frac{54x}{\left(1+9x^2\right)^2}$$

Answer

$$-\frac{6x}{\left(1+2x^2\right)^2}$$

Answer

$$\frac{6x}{\left(1+2x^2\right)^2}$$

Answer

$$-\frac{54x}{\left(1+9x^2\right)^2}$$

Question 29

Find y''' of $$y\ =\cot^{-1}\left(3x\right)$$

Accepted Answer

$$\frac{54-972x^2-13122x^4}{\left(1+9x^2\right)^4}$$

Answer

$$\frac{54+972x^2+13122x^4}{\left(1-9x^2\right)^4}$$

Answer

$$\frac{54+972x^2-13122x^4}{\left(1-9x^2\right)^4}$$

Answer

$$\frac{54-972x^2+13122x^4}{\left(1+9x^2\right)^4}$$

Question 30

Find the radius of curvature at x = pi/3 on $$y\ =\ 2\log\left(\sin\left(\frac{x}{2}\right)\right)$$

Accepted Answer

2.26

Answer

0.26

Answer

1.26

Answer

3.26

Question 31

Find the equation of the normal line to $$y\ =\ \ x^3-2x^2+\ x-3$$ at point (2, -1)

Accepted Answer

y = 5x - 11

Answer

y = 5x + 11

Answer

y = 11x - 5

Answer

y = 11x + 5

Question 32

Find the first order partial derivative of the given function with respect to y

$$z\ =\ \sqrt[]{x^2+\ln\left(5x-3y^2\right)}$$

Accepted Answer

$$-\frac{\frac{3y}{5x-3y^2}}{\sqrt[]{x^2+\ln\left(5x-3y^2\right)}}$$

Answer

$$\frac{\frac{3y}{5x-3y^2}}{\sqrt[]{x^2+\ln\left(5x-3y^2\right)}}$$

Answer

$$-\frac{\frac{6y}{5x-3y^2}}{\sqrt[]{x^2+\ln\left(5x-3y^2\right)}}$$

Answer

$$\frac{\frac{6y}{5x-3y^2}}{\sqrt[]{x^2+\ln\left(5x-3y^2\right)}}$$

Question 33

Differentiate

$$10x^4-16xy^2+10y^3-48$$

Accepted Answer

$$\frac{9y^3-20x^3}{3\left(5y^2-6xy\right)}$$

Answer

$$\frac{20y^3-9x^3}{3\left(5y^2-6xy\right)}$$

Answer

$$\frac{20y^3-9x^3}{3\left(5y^2+6xy\right)}$$

Answer

$$\frac{9y^3+20x^3}{3\left(5y^2-6xy\right)}$$

Question 34

Find the 2nd derivative of the function

$$x+y\ =\ e^{\left(x-y\right)}$$

Accepted Answer

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

Answer

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

Answer

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

Answer

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

Question 35

Find the slope of the curve $$x^2+\ y^2-6x\ +10y\ +5\ =\ 0$$ at point (1,0)

Accepted Answer

2/5

Answer

1/5

Answer

3/5

Answer

4/5

Question 36

In which interval is the function below increasing?

$$f\left(x\right)\ =\ x^4-8x^2$$

Accepted Answer

$$-2<x<0$$

Answer

$$-\ \infty

Answer

$$0<x<2$$

Answer

$$-2<x<+\infty$$

Question 37

A sheet of metal is 12 x 10 is to be used to make an open box. Squares of equal sides x are cutout of each corner. If the sides are folded to make a box, What is the maximum volume possible?

Accepted Answer

96.77

Answer

86.77

Answer

106.77

Answer

206.77

Question 38

Determine the interval in which the concavity is upward

$$f$$

Accepted Answer

$$\left[\frac{3pi}{4},\frac{7pi}{4}\right]$$

Answer

$$\left[0,\frac{3pi}{4}\right]$$

Answer

$$\left[\frac{3pi}{4},\ pi\right)$$

Answer

$$\left(\frac{7pi}{4},\ 2pi\right)$$

Question 39

The radius of a sphere is measured to be 5m. If the measurement is correct to within 0.05m. Estimate the propagated error and percent error in the volume of the sphere.

Accepted Answer

$$\pm15.708;\ \pm3.00\%$$

Answer

$$\pm30.708;\ \pm3.00\%$$

Answer

$$\pm25.708;\ \pm3.00\%$$

Answer

$$\pm35.708;\ \pm3.00\%$$

Question 40

Two poles, one 8 meters tall and another one 20 meters tall are 30 meters apart. A length of wire is attached to the top of each pole. Each wire is staked to the ground somewhere between the poles. How far from the shorter pole should the stake be to minimized the length of the wire used?

Accepted Answer

60/7

Answer

50/7

Answer

40/7

Answer

30/7

Question 41

A billboard 85 ft wide is perpendicular to a straight road and is 40 ft from the road. Find the point on the road at which the angle subtended by the billboard is a maximum.

Accepted Answer

$$50\sqrt[]{2}$$

Answer

$$30\sqrt[]{2}$$

Answer

$$45.5$$

Answer

$$66.7$$

Question 42

Three thousand feet from a radio tower, a man views a plane, which is flying away from him and towards the tower at an elevation of 4000ft. If the plane flies at a rate 600 ft/s at what rate does the distance between the man and the plane increase as the plane passes over the radio tower?

Accepted Answer

360 ft/s

Answer

380 ft/s

Answer

400 ft/s

Answer

450 ft/s

Question 43

What is the maximum volume of right circular cylinder of radius r and height h, which is inscribed in a right circular cone of radius 5 and height 20m?

Accepted Answer

232.71 cu in.

Answer

262.31 cu in.

Answer

162.56 cu in.

Answer

301.87 cu in.

Question 44

Evaluate: $$\int_0^2xydy$$

x = t³; y = 7t²

Accepted Answer

1792

Answer

1592

Answer

1692

Answer

1892

Question 45

Gas escapes from a spherical balloon at a rate of 2 cm³/min. Find the rate at which the surface area is decreasing in cm²/min when the radius is 8 cm.

Accepted Answer

-0.5 cm²/min

Answer

-0.25 cm²/min

Answer

-1.5 cm²/min

Answer

-1.0 cm²/min

Question 46

Water is draining from the bottom of a cone shaped funnel at the rate of 0.03 ft³/s. The height of the funnel is 2ft and the radius at the top of the funnel is 1 ft. At what rate is the height of the water in the funnel changing when the height of the water is 0.5 ft?

Accepted Answer

-0.153

Answer

-0.035

Answer

-0.432

Answer

-0.092

Question 47

Evaluate:
$$\int_{ }^{ }\left(\frac{\cos^3\left(x\right)}{1-\sin\left(x\right)}\right)$$

Accepted Answer

$$\sin\left(x\right)+\frac{1}{2}\sin^2\left(x\right)+C$$

Answer

$$\cos\left(x\right)+\frac{1}{2}\cos^2\left(x\right)+C$$

Answer

$$\sin\left(x\right)-\frac{1}{2}\sin^2\left(x\right)+C$$

Answer

$$\sin\left(x\right)+\frac{1}{2}\cos^2\left(x\right)+C$$

Question 48

Evaluate:

$$\int_0^4\int_0^3\left(3xy^2+x^2y\right)dydx$$

Accepted Answer

312

Answer

412

Answer

512

Answer

612

Question 49

Determine the orthogonal trajectories of the family of sinusoids:

$$y=C\sin x$$

Accepted Answer

$$\cos\left(x\right)=C_1e^{\frac{y^2}{2}}$$

Answer

$$\sin\left(y\right)=C_1e^{\frac{x^2}{2}}$$

Answer

$$\cos\left(x\right)=C_1e^{y^2}$$

Answer

$$\sin\left(x\right)=C_1e^{y^2}$$

Question 50

Find the area between $$y\ =\ -x^3+x^2+16x$$ and the $$y\ =\ 4x$$

Accepted Answer

937/12

Answer

907/12

Answer

957/12

Answer

967/12

Question 51

Evaluate

$$\int_e^{e^2}\left(\frac{1}{x\ln\left(x\right)}dx\right)$$

Accepted Answer

ln(2)

Answer

ln(3)

Answer

ln(e)

Answer

e

Question 52

Given the differential equation: $$y$$ ; y(0) = 3

Find the value of y(2).

Accepted Answer

121.72

Answer

110.56

Answer

150.98

Answer

98.99

Question 53

Evaluate:

$$\int_0^{\frac{pi}{2}}\sin^5\beta\cos^5\beta$$

Accepted Answer

1/60

Answer

1/20

Answer

1/30

Answer

1/50

Question 54

Solve for the D.E.

$$y$$

Accepted Answer

$$y=C_1+C_2e^x+C_3e^{-x}+\frac{1}{30}\cos\left(3x\right)$$

Answer

$$y=C_1+C_2e^{-2x}+C_3xe^{-x}+\frac{2}{30}\sin\left(3x\right)$$

Answer

$$y=C_1e^{-x}+C_2xe^{-x}+C_3x^2e^{-x}+\frac{1}{30}\sin\left(3x\right)$$

Answer

$$y=C_1+C_2e^{-x}+C_3xe^{-x}+\frac{2}{15}\cos\left(3x\right)$$

Question 55

Find the area bounded by $$r^2=\cos heta$$

Accepted Answer

2

Answer

1

Answer

4

Answer

3

Question 56

Evaluate: $$\int_0^1\left(\frac{1}{\sqrt[]{y}}\right)$$

Accepted Answer

2

Answer

1

Answer

3

Answer

5

Question 57

Find the general solution of the equation:

$$y$$

Accepted Answer

$$y=C_1xe^{3x}+C_2e^{3x}$$

Answer

$$y=C_1e^{-3x}+C_2e^{3x}$$

Answer

$$y=C_1xe^{3x}+C_2x^2e^{3x}$$

Answer

$$y=C_1e^{-3x}+C_2e^{-3x}$$

Question 58

Find the area between $$y\ =\ x^{3\ }+\ 3x^{2\ }-4x$$ and the x-axis.

Accepted Answer

131/4

Answer

125/4

Answer

103/4

Answer

151/4

Question 59

Solve for the general solution of the D.E.

$$e^xdy+\left(ye^x+2x\right)dx=0$$

Accepted Answer

$$ye^x+x^2=c$$

Answer

$$xe^y+x^2=c$$

Answer

$$xe^y+y^2=c$$

Answer

$$ye^y+x^2=c$$

Question 60

Derive the DE for the family of plane curves defined by:

$$y^2=2cx$$

Accepted Answer

$$y-2xy$$

Answer

$$2y-x^2y$$

Answer

$$x-2yy$$

Answer

$$x^2-xy$$

Question 61

Bismith-210 has a half-life of 5.0 days. Suppose that a sample originally has a mass of 800 mg. When will its mass be reduced to 1 mg.

Accepted Answer

48.2

Answer

56.2

Answer

62.2

Answer

38.2

Question 62

Form the D.E representing the family of parabolas with equation:

$$y\ =\ C_1\left(x-C_2\right)^2$$

Accepted Answer

$$2yy$$

Answer

$$yy$$

Answer

$$xyy$$

Answer

$$y^2y$$

Question 63

Solve for the DE of the following:

$$y\ =\ C_1e^{-2x}+C_2xe^{-2x}+C_3e^{5x}$$

Accepted Answer

$$y$$

Answer

$$2y$$

Answer

$$3y$$

Answer

$$5y$$

Question 64

Solve for the given D.E

$$y$$ ; y(1) = -2

Accepted Answer

$$y=-\sqrt[]{x^2\ln\left(x^2\right)+4x^2}$$

Answer

$$y=-2\sqrt[]{2x^2\ln\left(x^2\right)+4x^2}$$

Answer

$$y=-2\sqrt[]{3x^2\ln\left(x^2\right)-4x^2}$$

Answer

$$y=-\frac{1}{2}\sqrt[]{x^2\ln\left(x^2\right)+4x^2}$$

Calculator Techniques

118 questions

In a class of 60 students, 43 like calculus, 38 like geometry, how many students like both subjects?

Given the ff functions:
f(x) = 2x+3
g(x) = 3x+2
Evaluate: f(g(x))

A class of students took examination in Math, Elecs and Comms. 50 passed Math, 48 passed Elecs and 42 passed Comms. 28 passed Math and Elecs, 20 passed Elecs and Comms, while 22 passed Math and Comms. If 15 passed all subjects how many students were there?

How many distinct elements/arrangements can be formed using all the letters of STATISTICS?

In each of 4 races, the democrats have 60% chance of winning. Assuming that the races are independent of each other, what is the probability that the democrat won at least 2 races?

Vehicles pass through a junction on a busy road at an average rate of 300 per hour. Find the probability that at most 5 cars passes in a given minute.

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Calculator Techniques

118 questions

In a class of 60 students, 43 like calculus, 38 like geometry, how many students like both subjects?

Given the ff functions: f(x) = 2x+3g(x) = 3x+2Evaluate: f(g(x))

A class of students took examination in Math, Elecs and Comms. 50 passed Math, 48 passed Elecs and 42 passed Comms. 28 passed Math and Elecs, 20 passed Elecs and Comms, while 22 passed Math and Comms. If 15 passed all subjects how many students were there?

How many distinct elements/arrangements can be formed using all the letters of STATISTICS?

In each of 4 races, the democrats have 60% chance of winning. Assuming that the races are independent of each other, what is the probability that the democrat won at least 2 races?

Vehicles pass through a junction on a busy road at an average rate of 300 per hour. Find the probability that at most 5 cars passes in a given minute.

Create a free account and access millions of resources

Similar Resources on Wayground

Popular Resources on Wayground

Discover more resources for Mathematics

Given the ff functions:
f(x) = 2x+3
g(x) = 3x+2
Evaluate: f(g(x))