Free Printable Derivatives Review Game

1.

Find the derivative of
$f\left(x\right)=-\frac{2}{3}x^3-\frac{1}{2}x^2+9x$

a)

$-2x^2-x+9$

b)

$-2x^3-x^2+9x$

c)

$-\frac{2}{12}x^4-\frac{1}{6}x^3+\frac{9}{\ 2}x^2$

d)

$-2x^4-x^3+9x^2$

2.

Which of the following is the derivative of $y=\left(3x^4-7\right)\left(5x^2+1\right)$

a)

$\left(12x^3\right)\left(10x\right)$

b)

$\left(3x^4-7\right)\left(10x\right)+\left(12x^3\right)\left(5x^2+1\right)$

c)

$\left(3x^4-7\right)\left(10x\right)-\left(12x^3\right)\left(5x^2+1\right)$

d)

$\frac{3x^4-7}{10x}+\frac{12x^3}{5x^2+1}$

3.

Find the derivative of
$f\left(x\right)=xe^x$

a)

$f'\left(x\right)=e^x$

b)

$f'\left(x\right)=2xe^x$

c)

$f'\left(x\right)=e^x-xe^x$

d)

$f'\left(x\right)=e^x+xe^x$

4.

Check off all of the words that also mean derivative.

a)

instantaneous rate of change

b)

average rate of change

c)

slope at a point

d)

slope of a secant line

e)

slope of a tangent line

5.

Finding the derivative of
$f\left(x\right)=xe^x$ requires the...

a)

power rule

b)

product rule

c)

quotient rule

d)

chain rule

6.

Given the table of R(t), estimate R'(10).

a)

33

b)

42

c)

9

d)

9/4

e)

9/10

7.

Water flows into a tank for 24 hours. R(t) represents the gallons of water in the tank at t hours. What does R'(t) represent? Check all that apply.

a)

the amount of water in the tank in gallons

b)

the rate of change of the water at t hours

c)

the speed of the water flow at t hours

d)

gallons per hour

8.

Describe how to estimate f'(1) given the table of values for f(x) = 0.5x^3 - 2.

4 lines

9.

Is the above function differentiable for all values of x? Why?

a)

Yes, the slope of the tangent line can be calculated for all values of x.

b)

Yes, the function is continuous for all values of x so the function is differentiable.

c)

No, the function has a sharp turn in the first quadrant so if is not differentiable.

d)

No, the function is discontinuous so it is not differentiable.

10.

In which quadrant of the graph above will there be a value of x that is non-differentiable?

a)

1

b)

2

c)

3

d)

4

11.

Is the above function differentiable at

x = 0? Why?

a)

Yes. The derivative would be equal to zero since there is a vertical tangent.

b)

No. The derivative would not exist at x = 0 since there is a vertical tangent.

c)

No. The derivative does not exist since $\lim_{x\rightarrow0}\ x^{\frac{1}{3}}$ does not exist.

d)

Yes since $\lim_{h\rightarrow0}\ \frac{\left(x+h\right)^{\frac{1}{3}}-x^{\frac{1}{3}}}{h}$ exists.

12.

What is the derivative of xⁿ?

a)

(n-1)xⁿ

b)

nxⁿ⁺¹

c)

(n+1)x^n-1

d)

nx^n-1

13.

What is the derivative of cos(x)?

a)

sin(x)

b)

-sin(x)

c)

cos(x)

d)

-cos(x)

14.

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)

15.

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

16.

You are given a table containing some values of differentiable functions [eval(f,x)], [eval(g,x)] and their derivatives. Use the table data and the rules of differentiation to solve each problem.
If $h\left(x\right)=f\left(x\right).g\left(x\right)$ Find $h'\left(1\right)$

a)

$\frac{3}{2}$

b)

$2$

c)

$\frac{-1}{2}$

d)

$-3$

17.

You are given a table containing some values of differentiable functions [eval(f,x)], [eval(g,x)] and their derivatives. Use the table data and the rules of differentiation to solve each problem.
If $h\left(x\right)=f\left(x\right)-g\left(x\right)$ Find $h'\left(4\right)$

a)

$\frac{3}{2}$

b)

$\frac{-3}{2}$

c)

$\frac{-1}{2}$

d)

$-3$

18.

The three situations where derivatives fail to exist are at corners or cusps, at a vertical tangent, and...

a)

horizontial tangent

b)

discontinuity

c)

curve

d)

intercepts

19.

Find the limit as x approaches 1⁺

a)

1

b)

-1

c)

-3

d)

Infinity

e)

DNE

20.

Let y = 2x³ - 4x + 6. Find y'' (derivative of the derivative)

a)

6x²- 4

b)

12x - 4

c)

12x

d)

6x

21.

Find the derivative of g(x)=(3x-2)/(x²+2)

a)

9x²+2

b)

3(x²+2)/(x²+2)²

c)

(-3x²+4x +6)/(x²+2)²

d)

(-3x²+10)/(x²+2)²

22.

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

23.

Find the derivative f(x) = x²/e^x

a)

f'(x) = (x²e^x - 2xe^x) / (e^x)²

b)

f'(x) = (2xe^x + x²e^x) / (e^x)²

c)

f'(x) = (2xe^x - x²e^x) / (e^x)²

d)

f'(x) = x²e^x + 2xe^x

24.

We've learned power, product, and quotient rules as well as interpreting derivatives and applying derivatives to graphs & tables. How have you felt about these?

a)

I understand these well - I am ready to move on!

b)

I understand some of these well - I need some more practice on a couple topics.

c)

I don't understand any topic well - I feel overwhelmed and need support.

d)

I understand a couple topics well - I need more time to process.

25.

How many languages do you speak?

a)

Just English

b)

2

c)

3

d)

4+

e)

Does math count?

26.

When learning new material I am more

a)

Social (interpersonal): You prefer to learn in groups or with other people.

b)

Solitary (intrapersonal): You prefer to work alone and use self-study.

27.

What type of learner are you?

a)

Visual

b)

Auditory (Listening)

c)

Kinesthetic (Movement)

d)

1:1

28.

Check-in: How engaging / interesting is AP Calculus so far? Be honest!

4 lines

Derivatives Review Game

Total questions: 28

Worksheet time: 51mins

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