Free Printable Quarterly Examination

1.

Find the derivative of the given equation
f(x) = 7

a)

7

b)

0

c)

7x

d)

14

2.

Find the derivative of the given equation
f(x) = -4x

a)

4

b)

x

c)

-4

d)

0

3.

Find the derivative of the given equation
f(x) = 1 - x²

a)

1 - 2x

b)

-2x

c)

-2

d)

-1

4.

Find the derivative of the given equation
f(x) = x³ + x² + 3

a)

3x² + 2x

b)

3x + 2x

c)

3x + 2x + 3

d)

x³ + x²

5.

find

a)

y = 2 x^-1

b)

y=2 x^-2

c)

y= −2x^-2

d)

y= −2 x^-1

6.

Find the derivative of f(x) = 6x³⁰-2x¹⁵ + 4x³ - 2x + 1

a)

f'(x) = 18x²⁹+ 30x¹⁵ + 12x³

b)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x²

c)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² - 2

d)

f'(x) = 180x²⁹ - 30x¹⁴+ 12x² +1

7.

Find the derivative. f(x) = 1/(3x²) + 4x³

a)

f'(x) = 6x³ + 12x²

b)

f'(x) = 6x + 12x²

c)

f'(x) = -2/(3x³) + 12x²

d)

f'(x) = -6/x² + 12x²

8.

Find the derivative f(x) = xe^x

a)

f'(x) = e^x

b)

f'(x) = xe^x + xe^x

c)

f'(x) = e^x - xe^x

d)

f'(x) = e^x + xe^x

9.

Find the derivative of f(x)=(x³-2x)²

a)

6x⁵ - 12x³+8x

b)

6x⁵ - 16x³+8x

c)

x⁶-4x⁴+4x²

d)

6x⁵ - 16x^3-8x

10.

Differentiate:
f(x) = x⁷ (5 + 8x)³

a)

f '(x) = x² (5 + 8x)⁶ (35 + 80x)

b)

f '(x) = x⁶ (5 + 8x)² (35 + 80x)

c)

f '(x) = 8x⁷ (5 + 8x)² (35 + 80x)

d)

f '(x) = x⁶ (5 + 8x)³ (35 + 80x)

11.

a)

b)

c)

d)

12.

a)

b)

c)

d)

13.

Determine the derivative of: f(x) = x⁴sinx

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

14.

Find the derivative f(x) = tanxcosx

a)

f'(x) = sec²xcosx - tanxsinx

b)

f'(x) = sec²xcosx + tanxsinx

c)

f'(x) = sec²xsinx

d)

f'(x) = sec²xcosx - tanxcosx

15.

What is the derivative of -cos(x)?

a)

sin(x)

b)

-sin(x)

c)

cos(x)

d)

-cos(x)

16.

If f(x) = sin³(2x), then f'(x) =

a)

3cos(2x)

b)

3sin(2x)⋅2

c)

3sin²(2x)cos(2x)

d)

3sin²(2x)cos(2x)⋅2

17.

What is f'(x) if f(x) = cos(5x⁴)?

a)

f'(x) = sin(20x³)

b)

f'(x) = 20x³ sin(5x⁴)

c)

f'(x) = -sin(20x³)

d)

f'(x) = -20x³ sin(5x⁴)

18.

Find g'(x) if g(x) = sin^1/2(4x)

a)

2cos^-1/2(4x)

b)

4cos^1/2(4x)

c)

2sin^-1/2(4x)cos(4x)

d)

1/2sin^-1/2(4x)cos(4x)

19.

Domain of function $\sin^{-1}x\ is$

a)

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

b)

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

c)

$\left(-1,1\right)$

d)

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

20.

Range of function $\tan^{-1}x\ is$

a)

R

b)

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

c)

$R-\left\{\frac{\pi}{2}\right\}$

d)

$\left[-\frac{\pi}{2},\frac{\pi}{2}\right]$

21.

Find f "'(x) when

f(x)=10x⁵ +3x⁴ -5x³ +2x² -10x+6

a)

200x³+36x²-30x+4

b)

600x² +72x -26

c)

600x² +72x -30

d)

600x² +72x -36

22.

Find the second derivative of the following functions with respect to x.
y=3x⁴

a)

36x²

b)

12x³

c)

4x³

d)

12x²

23.

Find the second derivative of the function:
f (x) = 2x - 5x⁶

a)

f ''(x)= 2 - 30x

b)

f ''(x) = 2-30x⁵

c)

f ''(x) = -30x⁵

d)

f ''(x) = -150x⁴

24.

$\frac{d}{dx}\ln\left(x^3\right)$

a)

$\ln\left(x^3\right)$

b)

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

c)

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

d)

$3x$

25.

$\frac{d}{dx}\log_2\left(x^4\right)$

a)

$\frac{4}{x}$

b)

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

c)

$\frac{1}{\ln\left(2\right)}$

d)

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

26.

$\frac{d}{dx}7^x\cdot x^2$

a)

$x\cdot7^x\left(2+x\ln7\right)$

b)

$2x\cdot7^x\ln\left(7\right)$

c)

$14x$

d)

$x\ln\left(7\right)$

27.

$\frac{d}{dx}e^x\left(x-1\right)$

a)

$x^2e^x$

b)

$x^2e^x-e^x$

c)

$xe^x-e^x$

d)

$xe^x$

28.

$\int5x^4dx$

a)

$x^5$

b)

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

c)

$x^5+C$

d)

$20x^3$ + C

29.

$\int\left(x^2-2x\right)dx$

a)

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

b)

$x^{2\ }-2x+C$

c)

$2x-2$

d)

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

30.

$\int6x\left(x+2\right)dx$

a)

$6x^2+12x+C$

b)

$x^{2\ }-2x+C$

c)

$3x^2+6x+C$

d)

$2x^3+6x^2+C$

31.

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

a)

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

b)

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

c)

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

d)

I didn't look at my notes to see how to do this one.

32.

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

a)

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

b)

$\frac{x^{-3}}{-3}+\frac{6x^{-4}}{-4}+C$

c)

$-x^{-1}-3x^{-2}$

d)

$-x-3x^2+C$

33.

$\int\left(5x^2-7x+6\right)dx$

a)

$\frac{5}{3}x-\frac{7}{2}x+6x+C$

b)

$x+x+x+x+x+C$

c)

$x^3-3x^2+6x+C$

d)

$\frac{5}{3}x^3-\frac{7}{2}x^2+6x+C$

34.

Integrate $\int_{ }^{ }\sin x\ dx$

a)

$=\tan x+c$

b)

$=-\cos x+c$

c)

$=-\sec x+c$

d)

$=\operatorname{cosec}\ x\ +c$

35.

∫(cos x + 3x²)dx =

a)

-sin x + x³ + c

b)

sinx + x³ + c

c)

-sin x + 6x

d)

🌞

36.

a)

A

b)

B

c)

C

d)

D

37.

a)

A

b)

B

c)

C

d)

D

38.

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.

39.

What does C represent in an antiderivative?

a)

A variable

b)

A constant

c)

None of these

d)

Unknown

40.

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

a)

= 0

b)

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

c)

$=\ 3x\ +c$

d)

$=4+c$

41.

Integrate $\int_{ }^{ }x^{\frac{1}{3}}dx$

a)

$=\frac{4}{3}x^{\frac{4}{3}}+c$

b)

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

c)

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

d)

$=\frac{3}{4}x^{\frac{4}{3}}+c$

42.

If y = $ax^n$ , then $\int_{ }^{ }y\ dx\ =$

a)

$\frac{ax^{n+1}}{n+1}$

b)

$\frac{ax^{n-1}}{n-1}+\ c$

c)

$\frac{ax^{n+1}}{n}+\ c$

d)

$\frac{ax^{n+1}}{n+1}+\ c$

43.

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)

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

44.

a)

0

b)

-1

c)

infinity

d)

-infinity

45.

There are 3 cases when a limit does not exist. Which statement below is not one of those cases?

a)

When the limit of a graph is a vertical asymptote.

b)

When there is a hole on the graph at L as x approaches a value.

c)

When there are two or more answers for the limit as x approaches a value.

d)

When there is oscillating behavior for the limit.

46.

Find y' if y=e⁴

a)

0

b)

1

c)

e³

d)

4e³

47.

Derivative means the same thing as

a)

slope of the tangent line

b)

slope of the normal line

c)

exponent

d)

potato

48.

What is sin(π)?

a)

0

b)

1

c)

-1

d)

undefined

49.

Find the derivative f(x) = tanxcosx

a)

f'(x) = sec²xcosx - tanxsinx

b)

f'(x) = sec²xcosx + tanxsinx

c)

f'(x) = sec²xsinx

d)

f'(x) = sec²xcosx - tanxcosx

50.

Find y' if

y = 10sin(x) +3cos(x)

a)

10sin(x)cos(x)+ 3cos(x)sin(x)

b)

10cos(x) - 3cos(x)

c)

30cos(x)sin(x)

d)

10cos(x) -3sin(x)

Quarterly Examination

Total questions: 50

Worksheet time: 7hrs 23mins

Similar Resources on Wayground