MA16010 After Exam 3 Practice Questions If ytrolling/After_Exam_3_Practice_Quest… · MA16010...

MA16010 After Exam 3 Practice Questions

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If dydt

= −3y and y(1) = 5, find y(10).

1.A© y(10) = e−30

B© y(10) = 5e−30

C© y(10) = e−27

D© y(10) = 5e−29

E© y(10) = 5e−27

F© y(10) = e−29

Given that the radioactive isotope Plutonium-240 has a half-life of 6563 years, what is its decay rate, k?

2.A© − 16563

B© ln 26563

C© − 26563

D© ln 1

2

6563

E© −6563

F© − 12

Evaluate

∫ 2

0

(3x2 − 2x+ 7ex) dx.

3.A© 7e2 + 13

B© 7e2 − 3

C© 7e2 − 8

D© 7e2 + 4

E© 7e2 + 11

F© 7e2 − 1


Find the Left Riemann Sum that approximates the area under the curve of y = e4x on the interval [0, 2] with 8rectangles.

4.A©8∑

i=0

14e

i

2

B©7∑

i=1

14e

2i

C©8∑

i=1

14ei

D©9∑

i=1

14ei

E©9∑

i=0

14ei

F©7∑

i=0

14ei

If∫ b

a2f(x) dx = 1 and

∫ c

a− 1

2f(x) dx = 1, where a, b and c are some constants, find∫ c

bf(x) dx.

5.A© − 32

B© 0

C© − 52

D© 32

E© 52

F© 1

Compute the signed area of the region bounded by y = 8− 2x2 and y = 0 for 0 < x < 3.

6.A© 6

B© 403

C© −18

D© −12

E© 463

F© 12


Evaluate the definite integral∫ 1

0x2−x3

2√xdx.

7.A© 435

B© 215

C© 415

D© 1235

E© 235

F© 45

The rate of change of a certain population of bacteria is modeled by P ′(t) = 2√t (10t+ 3), where t is in hours. What

is the increase in the bacteria population between t = 4 and t = 9 hours?

8.A© 1764

B© 386

C© 2052

D© 558

E© 852

F© 172

Evaluate∫ π

3

0(sec2 t+ sin t) dt.

9.A©√

33 −

12

B©√

34

C©√

32

D©√

32 + 1

2

E©√

3− 12

F©√

3 + 12


Approximate the area of the shaded region by using the Trapezoidal Rule with n = 3.

10.A© 18

B© 28

C© 24

D© 14

E© 42

F© 21

Given dydt

= 12y and y(0) = 2, find y(4).

11.A© y(4) = e2

B© y(4) = e4

C© y(4) = 2e2

D© y(4) = 2e4

E© y(4) = 2e1

2

F© y(4) = 4e1

2


If we deposit $1000 into a savings account which compounds interests continually, at an annual rate of 5%, how manyyears will it take for the money to double?

12.A© ln 2 years

B© 5 ln 2 years

C© 2 ln 2 years

D© ln 22 years

E© ln 25 years

F© 20 ln 2 years

Use the Left Riemann Sum to approximate∫ 3

1x3 dx with four rectangles.

13.A© 14

B© 54

C© 20

D© 28

E© 10

F© 27

Compute∫ 1

−π(3x+ π) dx.

14.A© 32 + 2π − π2

2

B© 32 + π + π2

2

C© 32 + 2π + π2

2

D© 32 + π − π2

2

E© 32 (1− π2)

F© 32 (1 + π2)


Find the area of the region bounded by x = 0, x = 10, y = 0, and y = x3 + 5.

15.A© 300

B© 1850

C© 2200

D© 2550

E© 1050

F© 600

Compute∫ ln(10)

0

ex dx

16.A© e10 − 1

B© 11

C© 9

D© 11− e

E© 9− e

F© eln(10)


Evaluate the integral

∫ 12

−6

f(x)dx using geometric formulas.

17.A© 60

B© 42

C© 30

D© 54

E© 36

F© 48

You have just placed $800 into a bank account that accumulates interest with continuous compounding. If 20 yearsfrom now you will have $1200, how much money will you have in your bank account 30 years from now? Round youranswer to the nearest cent.

18.A© $600.00

B© $1469.69

C© $1342.23

D© $1546.63

E© $1400.00

F© $1537.32


Suppose that the half life of some radioactive isotope is 50,000 years. If you start out with 2,500 grams of thisradioactive isotope, how much will be left after 65,000 years? Round your answer to the nearest whole number.

19.A© 1005 grams

B© 920 grams

C© 983 grams

D© 1015 grams

E© 994 grams

F© 1028 grams

Suppose that the half-life of some radioactive material is 2 years. If you start with 1, 024, 000 pounds of this radioactivematerial, how long will it be until there are only 1, 000 pounds left? Round your answer until the nearest year.

20.A© 15 years

B© 100 years

C© 40years

D© 10 years

E© 20 years

F© 60 years

Evaluate the following integral∫ 4

1

x+ x2

√xdx.

21.A© 26815

B© 25615

C© 8

D© 38

E© 26

F© 34


Let f(x) and g(x) be functions with antiderivatives F (x) and G(x) respectively.

Given that F (3) = 3, G(3) = 5, F (6) = 1, and G(6) = 6, evaluate the following integral

∫ 6

3

(3f(x)− 4g(x)) dx

22.A© −9

B© −50

C© 20

D© 11

E© −32

F© −10

Given that∫ 8

1f(x) dx = 3,

∫ 4

0f(x) dx = −7, and

∫ 8

0f(x) dx = 10, find

∫ 4

1

f(x) dx.

23.A© 0

B© 6

C© 10

D© −20

E© −14

F© −8

Consider the function f(x) = 6x + 2. Thomas approximates the area under the curve of f(x) on the interval of [1,2] using the Right Riemann Sum with three rectangles. Don calculates the exact value of the area under the curve

on the interval of [1, 2] by evaluating the definite integral∫ 2

1f(x)dx. Let T be Thomas’s estimate and D be Don’s

calculated value. What is 5T −D?

24.A© 50

B© 49

C© 39

D© 51

E© −1

F© 1


The growth rate of a population is given by P ′(t) = 2et + t3 − 7 where t is months after January 1, 2000. By howmuch did the population increase from March 1, 2000 to November 1, 2000? Round your anwer to the nearest integer.

25.A© 9253

B© 584611

C© 5894

D© 268812

E© 46478

F© 33648

The velocity function, in meters per second, of a particle moving is given by

v(t) = 5t− 2,

where t is time in seconds. Find the displacement of the particle from t = 0 seconds to t = 6 seconds.

26.A© 88 meters

B© 109 meters

C© 28 meters

D© 78 meters

E© 102 meters

F© 45 meters

A faucet is turned on and water begins to flow into a tank at a rate of

r(t) = 10√t

cubic feet per hour, where t is in hours. How many hours later will there be 1603 cubic feet of water in the tank?

27.A© 3

B© 2

C© 16√

2

D© 4

E© 6

F© 8


Which of the following gives the correct expression for the approximation of

∫ 3

1

ln(x2 + 3) dx

using the Trapezoidal Rule with n = 4 trapezoids?

28.A© 14 (ln 4 + ln 21

4 + ln 7 + ln 374 + ln 12)

B© 12 (ln 4 + ln 9

2 + ln 5 + ln 112 + ln 6)

C© 14 (ln 4 + ln 9

2 + ln 5 + ln 112 + ln 6)

D© 12 (ln 4 + 2 ln 21

4 + 2 ln 7 + 2 ln 374 + ln 12)

E© 14 (ln 4 + 2 ln 21

4 + 2 ln 7 + 2 ln 374 + ln 12)

F© 14 (ln 4 + 2 ln 9

2 + 2 ln 5 + 2 ln 112 + ln 6)

Given that dydt

= 60y and y(0) = 120, find y(t).

29.A© y(t) = ln(60t+ 120)

B© y(t) = e60t + 120− e

C© y(t) = 60t+ 120

D© y(t) = e60t + 120

E© y(t) = 120e60t

F© y(t) = 120et + 60t

Evaluate5∑

i=2

i(i+ 1)

2.

30.A© 34

B© 9

C© 47

D© 72

E© 58

F© 28


The half-life of carbon-14 is about 5715 years. Explorers found a mummy containing only 70% of the amount of thisisotope that is normally found in living human beings. How old is this mummy? Round your answer to the nearestinteger.

31.A© 2536 years old

B© 2823 years old

C© 3202 years old

D© 2941 years old

E© 853 years old

F© 1245 years old

Joe has invested $50, 000 in a fund which pays him 8% a year, continuously compounded. He estimates that he canretire with $200, 000. How long will that take?

32.A© 19.42 years

B© 15.21 years

C© 13.65 years

D© 25.96 years

E© 30.26 years

F© 17.33 years

The population of a city has been growing at a rate that is proportional to the population itself. According to censusdata, the population was 150 thousand in 2000, and 170 thousand in 2010. Let t = 0 correspond to 2000. Assumingthat trend continues, how many people will be in this city by the year 2020 when the next census will take place?Round your answer to the nearest integer.

33.A© 261, 325 people

B© 195, 223 people

C© 182, 365 people

D© 192, 667 people

E© 178, 389 people

F© 201, 624 people


Write a definite integral that describes the shaded area.

34.A©∫ 1

−2− 1

2x dx

B©∫ 1

−2− 1

3x dx

C©∫ 6

−3− 1

3x dx

D©∫ 6

−3− 1

2x dx

E©∫ 1

−2−3x dx

F©∫ 6

−3−3x dx


Use the right Riemann sum with n = 200 to approximate the area under f(x) = x2e2x over the interval [0, 100].

35.A© R200 = 18

200∑

i=1

i2ei

B© R200 = 18

199∑

i=0

i3ei

C© R200 = 14

199∑

i=0

i2ei

D© R200 = 18

199∑

i=0

i2ei

E© R200 = 18

200∑

i=1

i3ei

F© R200 = 14

200∑

i=1

i2ei

Compute the signed area of the region bounded by the curves y = 2 + sin x, y = 0, x = 0 and x = 2π.

36.A© 4π − 2

B© 0

C© 3π2

D© 8π

E© 8π − 2

F© 4π

Compute the definite integral

∫ π

3

π

6

(2 sec2 θ + 3θ) dθ.

37.A© 52√

327 + π2

8

B© 3√

33 + π2

4

C© 4√

33 + π2

4

D© 3√

33 + π2

2

E© 52√

327 + π2

2

F© 4√

33 + π2

8


Evaluate

∫ 8

1

(2x−3√x

3) dx.

38.A© 15

B© 2516

C© 25681

D© 1535

E© 1383

F© 2374

Evaluate

∫ π

2

π

4

cscx(2 cscx+ 3 cotx) dx.

39.A© 3√

5− 3

B© 2√

2− 3

C© 3√

2− 1

D© 2√

5− 1

E© 3√

25 − 4

F© 2√

3− 1

Find the signed area enclosed by the region bounded by the curves of

y =x+ 4√x√x, y = 0, x = 0 and x = 16.

40.A© 2120

B© 1603

C© 240

D© 803

E© 120

F© 1565


The growth rate of the population of a country is given by P ′(t) = 3√t (2651t + 2210), where t is in years and t = 0

corresponds to 2010. How much did the population grow from 2010 to 2013? Round your answer to the nearestinteger.

41.A© 19, 030 people

B© 21, 919 people

C© 23, 223 people

D© 17, 925 people

E© 42, 555 people

F© 35, 774 people

A car is travelling at 60 mph. The acceleration of the car t seconds after the driver steps on the brake, before thecar comes to a full stop, is a(t) = −(t − 3)2 mph per second. How fast is the car traveling 3 seconds of the brake isapplied?

42.A© 49 mph

B© 35 mph

C© 46 mph

D© 39 mph

E© 51 mph

F© 55 mph

Given dydt

= −4y and y(3) = 42, find y(5).

43.A© 42e14

B© 42e12

C© 42e−36

D© 42e−8

E© 42e32

F© 42e−20


Robot A and Robot B start moving at the same time and their velocity functions are vA(t) = t + 2 feet per minuteand vB(t) = 2t feet per minute respectively. Choose the correct statement below.

44.A© The two robots will never have the same displacement after they start moving.

B© The two robots have the same displacement 1 minute after they start moving.

C© The two robots have the same displacement 2 minutes after they start moving.

D© The two robots have the same displacement 4 minutes after they start moving.

E© The two robots have the same displacement half a minute after they start moving.

F© The two robots have the same displacement 3 minutes after they start moving.

Evaluate the sum3∑

i=0

(−i2 + 2i+ 1).

45.A© 30

B© −30

C© −2

D© 2

E© −27

F© 27

Use the left Riemann sum with 120 rectangles to estimate the signed area under y = 2 cos(3x) on the interval [0, 2π].Give the answer in sigma notation.

46.A©120∑

i=0

π30 cos( 1

60πi)

B©119∑

i=0

π30 cos( 1

20πi)

C©119∑

i=0

π60 cos( 1

60πi)

D©120∑

i=0

π60 cos( 1

20πi)

E©119∑

i=0

π30 cos( 1

60πi)

F©120∑

i=1

π30 cos( 1

20πi)


Given∫ −2

−52f(x) dx = 6 and

∫ −2

0f(x) dx = 1, compute

∫ 0

−53f(x) dx.

47.A© 7

B© 5

C© 21

D© 18

E© 6

F© 15

Use the left Riemann sum with n = 5 to approximate the area under the graph of the curve f(x) = x ln x over theinterval [1, 11]. Give your answer with two decimal digits of accuracy.

48.A© 44.74

B© 26.38

C© 71.12

D© 94.21

E© 89.48

F© 142.23

Consider f(x) = (x+ 1)2. Ethan approximates the area under f(x) on the interval [0, 2] using the right Riemann sumwith 2 rectangles. Vincent approximates the area under f(x) on the interval [0, 2] using the Trapezoidal Rule with 2trapezoids. Let E be Ethan’s estimate and V be Vincent’s estimate. What is E − V ?

49.A© 14

B© 9

C© 4

D© 5

E© 13

F© 8


Write a definite integral that describes the shaded area.

50.A©∫ 8

−2(4x+ 2) dx

B©∫ 4

0( 2

3x) dx

C©∫ 8

−2( 1

4x+ 2) dx

D©∫ 4

0( 2

3x+ 2) dx

E©∫ 4

0(x+ 2) dx

F©∫ 8

−2( 1

3x+ 2) dx


Find the value of the following definite integral:

∫ 2

−2

(4x3 − 2x) dx

51.A© −12

B© 12

C© 20

D© 26

E© −26

F© 0

Given∫ 2

0f(x) dx = 3,

∫ 2

8f(x) dx = 10 and

∫ 8

−3f(x) dx = 25. Which of the following statements is/are TRUE?

(I)∫ 8

0f(x) dx = 13

(II)∫ 2

−3f(x) dx = 35

(III)∫ 2

06f(x) dx = 9

52.A© I Only

B© I and III only

C© II and III only

D© I and II only

E© III only

F© II Only


The velocity function , in meters per second, of a particle moving along a straight line is given by

v(t) = 5t− 3

where t is time in seconds. The particle begins moving at t = 0. Find the time t at which the particle’s displacementis 0 after the particle begins to move.

53.A© 2

5seconds

B© 1

5second

C© 3

5seconds

D© 4

5seconds

E© 1 second

F© 6

5seconds

Find the area of the region bounded by the graphs of the following equations: y =(

1√x

+√x)2, y = 0, x = 1 and

x = e.

54.A© 72 + 2e+ 1

2e2

B© 12e

2 + 12

C© 2√e+ 2

3

√e3 − 8

3

D© 2e+ 12e

2 − 32

E©√e3

3 + 1

3√e3

+√e+ 1√

e− 8

3

F© 72 − 2e− 1

2e2


Find the value of R100−L100, which is the difference of the Right Riemann sum and the Left Riemann sum using 100rectangles to estimate the (signed) area under the function f(x) = 7x on [0, 10].

55.A© 7

B© 10

C© 8

D© 9

E© 6

F© 5

Givendy

dt= 6y and y(0) = 10, find y(2).

56.A© e12

B© 10e2

C© 10e6

D© e2

E© e6

F© 10e12

Use the Trapezoidal Rule to approximate the integral∫ 4

1e(x

2−1) dx with 3 trapezoids.

57.A© T3 = 12 + e3 + e8 + 1

2e15

B© T3 = e3 + e8 + 12e

15

C© T3 = 12 + 2e3 + 2e8 + 2e15

D© T3 = 1 + e3 + e8 + e15

E© T3 = 14 + 1

2e3 + 1

2e8 + 1

4e15

F© T3 = e3 + e8 + e15


George deposits $100 into an account paying 4% interest continuously compounded. Rounded to the nearest year,when will he have $400 in the account?

58.A© 30 years

B© 25 years

C© 35 years

D© 50 years

E© 40 years

F© 45 years

The population, P , of a species of wolves in a forest is decreasing at a rate proportional to the population itself. IfP = 3000 when t = 1 and P = 2500 when t = 2, what is the population when t = 5? Round your answer to thenearest whole number.

59.A© 1522

B© 1563

C© 1447

D© 1651

E© 1480

F© 1689

Radioactive plutonium has a half-life of 24110 years. What percent of a given amount remains after 1000 years?(Round your answer to two decimal places.)

60.A© 91.33%

B© 97.17%

C© 95.67%

D© 85.40%

E© 89.84%

F© 92.97%

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MA16010 After Exam 3 Practice Questions If ytrolling/After_Exam_3_Practice_Quest… · MA16010...

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Transcript of MA16010 After Exam 3 Practice Questions If ytrolling/After_Exam_3_Practice_Quest… · MA16010...