Free Printable CW2 Revision

1.

What is the 2nd derivative of y = 2x³ - 4x + 6

a)

6x²- 4

b)

12x - 4

c)

12x

d)

6x

2.

What is the derivative of f?

a)

1/(x - 1)^-1

b)

-1/(x - 1)^-2

c)

-1/(x - 1)

d)

-1/(x - 1)²

3.

Given are rules of differentiation except

a)

Quotient Rules

b)

Chain Rules

c)

Break Rules

d)

Product Rules

4.

Given y=2x sin 6x,find dy/dx

a)

dy/dx=2x cos 6x

b)

dy/dx=2x cos 6x + 2 sin 6x

c)

dy/dx=12x cos 6x + 2 sin 6x

d)

dy/dx=36x cos 6x

5.

Differentiate with respect to x:

$x\ln x$

a)

$\ln x+1$

b)

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

c)

$\ln x+x$

d)

$x\ln x+x$

6.

Find second order differentiation for y= 7x-1

a)

0

b)

7

c)

1

d)

7x

7.

Differentiate

y=\left(2x+1\right)\left(3x-2\right)

a)

$12x-1$

b)

$12x+7$

c)

$12x-12$

8.

Find the derivative of:
f(x) = 7(3x+ 4)⁵

a)

35(3x + 4)⁵

b)

35(3x + 4)⁴

c)

105(3x + 4)⁵

d)

105(3x + 4)⁴

9.

Differentiate

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

a)

$-12x^2-2x+12$

b)

$12x^2+2x-12$

c)

$-12x^2-2x-12$

10.

Use the product rule to find the derivative. $f\left(x\right)\ =\ -x^3\left(3x^4-2\right)$

a)

$-3x^2+12x^3$

b)

$-21x^3+6x$

c)

$-21x^6+6x^2$

d)

$-84x^6-6x^2$

11.

Find $\frac{dy}{dx}$ for $y=3x^2\left(5x+1\right)$ by using product rule.

a)

$45x^2-6x$

b)

$45x^2+6x^{-1}$

c)

$45x+6$

d)

$45x^2+6x$

12.

Find $\frac{dy}{dx}$ for $y=\frac{3x+2^{ }}{2x+1}$ by using quotient rule.

a)

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

b)

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

c)

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

d)

$2x+1$

13.

Differentiate with respect to x:

$\frac{e^x}{x-4}$

a)

$\frac{e^x}{x-4}$

b)

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

c)

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

d)

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

14.

Find $\frac{\text{d}y}{\text{d}x}$ of y = ln (6x+1)

a)

$\frac{1}{6x+1}$

b)

$\frac{6}{6x+1}$

c)

$\frac{1}{6x}$

d)

6

15.

Differentiate with respect to x and simplify:

$\frac{\ln x}{2x}$

a)

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

b)

$\frac{2-2\ln x}{2x^2}$

c)

$\frac{1-2\ln x}{4x^2}$

d)

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

16.

$If\ y\ =\ \tan\left(x^4\right)\ then\ \frac{\text{d}y}{\text{d}x}=$

a)

$\tan\left(3x^4\right)\$

b)

$\sec\left(x^4\right)\tan\left(x^4\right)$

c)

$\sec^2\left(x^4\right)$

d)

$\sec^2\left(x^4\right).4x^3$

17.

Differentiate $\sqrt[]{4x-1}$

a)

$2(4x−1)^{-\frac{1}{2}}$

b)

$2(4x−1)^{\frac{1}{2}}$

c)

$4(4x−1)^{-\frac{1}{2}}$

d)

$4(4x−1)^{\frac{1}{2}}$

18.

Differentiate $\frac{1}{2}e^{5x+4}$

a)

$\frac{5x}{2}e^{5x+4}$

b)

$5e^{5x+4}$

c)

$\frac{1}{2}e^{5x+4}$

d)

$\frac{5}{2}e^{5x+4}$

19.

What is an antiderivative?

a)

The opposite of a derivative

b)

The same as a derivative

c)

A second derivative

d)

It always represents velocity.

20.

What does C represent in an antiderivative?

a)

A variable

b)

A constant

c)

None of these

d)

Unknown

21.

∫(4 - 18x)dx

a)

F(x) = -18

b)

F(x) = 4x - 9x²

c)

F(x) = 4x - 9x²+ C

d)

F(x) = (4 - 18x)² /2 + C

22.

Integrate $\int_{ }^{ }3\ dx$

a)

= 0

b)

$=\frac{3}{x}+c$

c)

$=\ 3x\ +c$

d)

$=4+c$

23.

$\int_{ }^{ }\frac{\text{1}}{\text{2x}}dx$

a)

$=\ln2x+c$

b)

$=2\ \ln2x+c$

c)

$=\frac{1}{2}\ln x+c$

d)

$=\frac{1}{\ln2x}+c$

24.

$\int\left(\frac{4}{x}-e_{ }^x\right)dx$

a)

$\frac{4}{x^2}-xe^x+C$

b)

$4\ln\left|x\right|-e^x+C$

c)

$4\ln\left(x\right)-e^x+C$

d)

$4\ln\left|x\right|+e^x+C$

25.

$\int\cos\left(3-4x\right)dx_{ }^{ }$

a)

$\frac{1}{4}\sin\left(3-4x\right)+C$

b)

$4\sin\left(3-4x\right)+C$

c)

$-\frac{1}{4}\sin\left(3-4x\right)+C$

d)

$-4\sin\left(3-4x\right)+C$

26.

$\int_{ }^{ }e^{5x}dx\ =$

a)

$e^{5x}+c$

b)

$5e^{5x}+c$

c)

$\frac{1}{5}e^{5x}+c$

d)

none of these

27.

∫(cos x + 3x²)dx =

a)

-sin x + x³ + c

b)

sinx + x³ + c

c)

-sin x + 6x

d)

cosx+3x

28.

∫ 1/x dx

a)

ln x

b)

ln x + C

c)

-1/x²

d)

-1/x² + C

29.

$\int5x^4dx$

a)

$x^5$

b)

$\frac{5}{4}x^5+C$

c)

$x^5+C$

d)

$20x^3$ + C

30.

$\int\left(6\sqrt{x}-1\right)dx$

a)

$6x^{\frac{3}{2}}+x+C$

b)

$4x^{\frac{3}{2}}-x+C$

c)

$3x^{-\frac{1}{2}}-x+C$

d)

$6x^{-\frac{1}{2}}+C$

31.

∫_₀^²(3x² - 2x)dx ?

a)

8

b)

4

c)

-8

d)

-4

32.

Find the $\int_0^{\pi}4\ Sinx\ dx$

a)

$Cosx+C$

b)

0

c)

$2\pi$

d)

8

33.

Integrate $\int_{ }^{ }\left(x^2+7\right)dx$

a)

$=2x+c$

b)

$=x^3+7x$

c)

$=\frac{1}{2}x^3+7x$

d)

$=\frac{1}{3}x^3+7x+c$

34.

$\int_{ }^{ }\ \frac{1}{x}+\ \frac{1}{x^2}\ dx$

a)

$x^{-1}\ +\ x^{-2}+\ c$

b)

$x^0\ -\ x^{-1}+\ c$

c)

$\ln x+\ x^{-1}+\ c$

d)

$\ln x-\ x^{-1}+\ c$

35.

Integrate $\sqrt{x}$ with respect to x

a)

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

b)

$\frac{1}{2}x^{-\frac{1}{2}}+\ c$

c)

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

d)

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

36.

Which of the following is the indefinite integral of $\frac{x^3}{2}+7$ ?

a)

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

b)

$\frac{3x^2}{2}+7x+c$

c)

$\frac{x^4}{8}+7x+c$

d)

$\frac{x^4}{8}+c$

37.

Which of the following is the indefinite integral of $\frac{3}{x^4}\ \ ?$

a)

$-\frac{1}{x^3}+\ c$

b)

$\frac{3}{5x^5}+\ c$

c)

$-\frac{12}{x^5}+\ c$

d)

$\frac{1}{x^3}+\ c$

38.

$\int_{ }^{ }\sec^2\ 5x\ \ dx\ \ =$

a)

$\tan\ x\ \ +\ c$

b)

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

c)

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

d)

$\frac{1}{5}\tan^2\ 5x\ \ +\ c$

39.

Integrate $\sin\left(\frac{x}{2}\right)$ with respect to x

a)

$\cos\left(\frac{x}{2}\right)\ +\ c$

b)

$-2\cos\left(\frac{x}{2}\right)\ +\ c$

c)

$-\cos\left(\frac{x}{2}\right)\ +\ c$

d)

$-\frac{1}{2}\cos\left(\frac{x}{2}\right)\ +\ c$

40.

Find the integral with respect to x of $\int_{ }^{ }\ \left(e^{3x}\right)^2\ dx\ .$

a)

$\frac{e^{6x}}{6}\ +\ c$

b)

$\frac{e^{9x}}{9}\ +\ c$

c)

$6e^{6x}\ +\ c$

d)

$\left(e^{3x}\right)^2\ +\ c$

41.

Find indefinite integral for $\int_{ }^{ }\frac{1}{e^{5x}}\ dx$

a)

$\frac{1}{5}e^{5x}\ +\ c$

b)

$-5e^{4x}\ +\ c$

c)

$\frac{e^{-5x}}{-5}+\ c$

d)

$\frac{e^{-4x}}{-4}+\ c$

42.

a)

⅝

b)

-⅝

c)

⅜

d)

45/16

43.

∫cos(4x+5)dx

a)

-¼sin(4x + 5) + C

b)

4sin(4x + 5) + C

c)

¼sin(4x + 5) + C

d)

4cos(4x + 5) + C

44.

a)

14

b)

18

c)

16

d)

15

45.

a)

$22\frac{3}{5}$

b)

$22\frac{1}{10}$

c)

$23\frac{1}{10}$

d)

$23\frac{3}{5}$

46.

Find the area of the shaded region.

a)

-7/3

b)

-13/3

c)

13/3

d)

7/3

47.

a)

-8

b)

8

c)

-2

d)

2

48.

a)

6

b)

2

c)

9

d)

3

49.

Find the area of the shaded region.

a)

$-2\frac{1}{3}unit^2$

b)

$-4\frac{1}{3}unit^2$

c)

$4\frac{1}{3}unit^2$

d)

$2\ \frac{1}{3}unit^2$

50.

$\int_{ }^{ }\frac{\text{1}}{\text{2x}}dx$

a)

$=\ln2x+c$

b)

$=2\ \ln2x+c$

c)

$=\frac{1}{2}\ln x+c$

d)

$=\frac{1}{\ln2x}+c$

51.

The acceleration of a particle in m/s² is given in the formula. If the particle was initially at rest 2m from the origin, find the position after 4 seconds.

a)

40 m

b)

42 m

c)

74 m

d)

80 m

52.

Find the area of the region bounded by the curves

y = cos x, y = sin(2x), x = 0, x = π/2

a)

1/4

b)

1/2

c)

0

d)

2

e)

4

53.

The function v(t) = 2t - 6 is the velocity in m/sec of a particle moving along the x-axis, where t is measured in seconds. Find the particle's displacement for 0 ≤ t ≤ 5.

a)

-5 m

b)

5 m

c)

26.333 m

d)

5/3 m

54.

a)

A

b)

B

c)

C

d)

D

55.

Use the indicated substitution to evaluate the integral.

$\int2x\cos(x^2)\ dx\ ,\ \ \ \ u=x^2$

a)

$\sin\left(x^2\right)+C$

b)

$2\sin\left(x^2\right)+C$

c)

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

d)

$4\cos\left(x^2\right)+C$

56.

Use the indicated substitution to evaluate the integral.

$\int x\left(x^2+5\right)^7dx\ ,\ \ \ \ u\ =\ x^2+5$

a)

$\frac{\left(2x+5\right)^8}{8}+c$

b)

$\frac{\left(x^2+5\right)^8}{16}+c$

c)

$\frac{\left(x^2+5\right)^6}{6}+c$

d)

$\frac{\left(2x+5\right)^8}{16}+c$

57.

Use substitution to evaluate the integral

$\int\ \frac{x\ dx}{x^2+1}$

a)

$2\ln\left(x^2+1\right)+C$

b)

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

c)

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

d)

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

58.

Use substitution to evaluate the integral $\int\left(3x^3+5\right)^5\cdot27x^2dx$

a)

$\frac{1}{2}\left(3x^3+5\right)^6+C$

b)

$\frac{2}{5}\left(3x^3+5\right)^5+C$

c)

$\frac{5}{6}\left(3x^3+5\right)^6+C$

d)

$\frac{3}{5}\left(3x^3+5\right)^5+C$

59.

Evaluate the indefinite integral using integration by parts.
$\int3x\ e^{2x}\ dx\$

a)

$-\frac{xe^{2x}}{2}+\frac{e^{2x}}{4}+C$

b)

$\frac{3xe^{2x}}{2}-\frac{3e^{2x}}{4}+C$

c)

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

d)

$-\frac{xe^{2x}}{2}+\frac{\ln e^{2x}}{4}+C$

60.

Determine $\int_{ }^{ }x\ \sin2x\ dx$

a)

$\frac{-x\ \sin2x}{2}+\frac{\cos2x}{4}+c$

b)

$\frac{-x\ \cos2x}{4}+\frac{\sin2x}{2}+c$

c)

$\frac{-x\ \cos2x}{2}+\frac{\sin2x}{4}+c$

d)

$-x\ \sin2x+\cos2x+c$

CW2 Revision

Total questions: 60

Worksheet time: 1hrs 24mins

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