Free Printable 2413 trig and ROC

1.

What is the derivative of cot(x)?

a)

sec²(x)

b)

-sec²(x)

c)

csc²(x)

d)

-csc²(x)

2.

What is the derivative of csc(x)?

a)

csc(x)cot(x)

b)

-csc(x)cot(x)

c)

-csc²(x)

d)

-cot²(x)

3.

What is the derivative of sin(x)?

a)

-sin(x)

b)

-cos(x)

c)

cos(x)

d)

sin(x)

4.

What is the derivative of cos(x)?

a)

sin(x)

b)

-sin(x)

c)

cos(x)

d)

-cos(x)

5.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

6.

When we "take the derivative" of a function what are we finding?

a)

What's a derivative?

b)

The rate at which our struggles in Calculus are increasing.

c)

The slope of the secant line

d)

The slope of the tangent line

7.

What is the derivative of tan(x)?

a)

-sec²(x)

b)

-csc²(x)

c)

sec²(x)

d)

csc²(x)

8.

What is the derivative of sec(x)?

a)

sec(x)tan(x)

b)

csc(x)cot(x)

c)

-sec(x)tan(x)

d)

-csc(x)cot(x)

9.

Find the derivative.

a)

x⁴cosx - 4x³sinx

b)

x⁴cosx + 4x³sinx

c)

4x³cosx

d)

-4x³cosx

10.

What is the derivative of a constant, C?

a)

C

b)

1

c)

0

11.

Derive y=3x²-4x+2

a)

6x-6

b)

6x-2

c)

4-6x

d)

6x-4

12.

Note: Not finding derivative, just finding what it's equal to...

a)

csc x

b)

sec x

c)

cot x

d)

tan x

13.

Note: Not finding derivative, just finding what it's equal to...

a)

cos x

b)

csc x

c)

sec x

d)

cot x

14.

Note: Not finding derivative, just finding what it's equal to...

a)

csc x

b)

sec x

c)

cot x

d)

tan x

15.

Solve f '(2) for
f(x) = x² + 2x

a)

2x + 2

b)

6

c)

12

d)

2x

16.

Product Rule in relation to derivatives.

a)

uv' - vu'

b)

uv' + vu'

c)

v'u'

d)

uv

17.

cos(π)=

a)

0

b)

1

c)

-1

d)

1/2

18.

sin(7π/4)

a)

1/2

b)

-√2/2

c)

√2/2

d)

-1/2

19.

cos(5π/6)

a)

1/2

b)

-√3/2

c)

√3/2

d)

-1/2

20.

sin(5π/3)

a)

1/2

b)

-√3/2

c)

√3/2

d)

-1/2

21.

sin(π/6)

a)

1/2

b)

√2/2

c)

√3/2

d)

2

22.

cos (11π/6)

a)

1/2

b)

-1/2

c)

-√3/2

d)

√3/2

23.

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

24.

Find the derivative of f(x) = x²sinx

a)

f'(x) = 2xsinx - x²cosx

b)

f'(x) = 2xsinx + x²sinx

c)

f'(x) = 2xsinx + x²cosx

d)

f'(x) = 2xcosx

25.

If a free-falling object is dropped from a height of 100 feet, the height h (in feet) of the object at time t (in seconds) is given by $h=-16t^2\ +100$ . Find the average velocity of the object over interval [1, 2]

a)

-32 f/s

b)

-48 f/s

c)

48 f/s

d)

-16 f/s

26.

If a free-falling object is dropped from a height of 100 feet, the height h (in feet) of the object at time t (in seconds) is given by $h=-16t^2+100$ . Find the velocity of the object when t=1.

a)

-16 f/s

b)

-48 f/s

c)

-32 f/s

d)

48 f/s

27.

A diver jumps from a diving board that is 32 feet high
and initial velocity is 16 feet per second, his position
function is $h=-16t^2+16t+32$ . When does the diver hit the water?

a)

t=1

b)

t=-1

c)

t=2

d)

t=-2

28.

A diver jumps from a diving board that is 32 feet high
and initial velocity is 16 feet per second, his position
function is $h=-16t^2+16t+32$ . What is the diver’s velocity at t=2?

a)

-48 f/s

b)

-32 f/s

c)

48 f/s

d)

-16 f/s

29.

A ball is thrown upward from the top of a 160-foot cliff
with the position function $s=-16t^2+48t+160$ . Find the height of the ball when t=3.

a)

48 feet

b)

100 feet

c)

16 feet

d)

160 feed

30.

A ball is thrown upward from the top of a 160-foot cliff
with the position function s=-16 $t^2$ +48t+160. Find the acceleration of the ball when t=3.

a)

-48 f/ $s^2$

b)

-32 f/s^2

c)

32 f/s^2

d)

48 f/s^2

31.

A ball is propelled straight upward from ground level with an initial velocity of 144 feet per second.

Write the position function of the ball

a)

$-16t^2+144t+100$

b)

$-16t^2+100$

c)

$-16t^2+144t$

d)

$144t^2+16t$

32.

If the position of a particle is represented by x(t) = -t² + 1, what is its instantaneous velocity at t = 1?

a)

-2

b)

2

c)

1

d)

3

33.

The velocity of an object is given as v = 2t + 3t³. What is the acceleration of the object at t = 2 s?

a)

27 m/s

b)

38 m/s

c)

16 m/s

d)

49 m/s

34.

Find the second derivative of
f(x) = x²+ e^x - cosx

a)

f"(x) = 2 + e^x + cosx

b)

f"(x) = 2x + e^x + cosx

c)

f"(x) = 2x + xe^x - cosx

d)

f"(x) = 2x + e^x + sinx

35.

Given the position function, find the velocity at t=7

a)

10

b)

6

c)

11

d)

1

36.

Given the position function, find the acceleration at t=8

a)

-2

b)

1

c)

2

d)

3

2413 trig and ROC

Total questions: 36

Worksheet time: 46mins

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