Free Printable Calculus 1st Semester Review

1.

Where is the graph continuous yet NOT differentiable?

a)

x = a, b, c, d

b)

x = b, c, d

c)

x = a, b,

d)

x = b, d

2.

Find h'(3)

a)

-2

b)

0

c)

1

d)

3

3.

What is the limit?

a)

5/2

b)

-2/3

c)

Infinity

d)

17/3

4.

What is the limit?

a)

DNE

b)

Infinity

c)

6

d)

12

5.

a)

1/2

b)

0

c)

Positive Infinity

d)

Negative Infinity

6.

a)

A

b)

B

c)

C

d)

D

7.

a)

[-2,1]

b)

[-2,3]

c)

[3,5]

d)

[0,1.5] and [3,5]

8.

a)

I only

b)

I and II Only

c)

I, II, and III

d)

II Only

9.

Find f'(x)

a)

A

b)

B

c)

C

d)

D

10.

A bug begins to crawl up a vertical wire at time t = 0. The velocity v of the bug at time t, 0 < t < 8, is given by the function whose graph is shown behind this text. At what value of t does the bug change direction?

a)

2

b)

4

c)

6.5

d)

7

11.

a)

A

b)

B

c)

C

d)

D

12.

Find dy/dx

a)

A

b)

B

c)

C

d)

D

13.

If A = 2x³, what is (dA/dt)?

a)

6x²

b)

6x²(dA/dx)

c)

6x²(dx/dt)

d)

6x (dx/dt)

14.

Given a graph of f'', which could be a Point of Inflection?

a)

A

b)

B

c)

C

d)

D

15.

f' is given, which could be f?

a)

A

b)

B

c)

C

16.

What is true about the following?

a)

A

b)

B

c)

C

d)

D

17.

Where is the graph not differentiable?

a)

x = -2, -1, 0, 1

b)

x = -2, -1, 1

c)

x = -2, -1

d)

x = -1,

18.

a)

0 < t < 2

b)

1 < t < 5

c)

2 < t < 6

d)

3 < t < 5

19.

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

20.

a)

Average Rate of Change

b)

Average Value of f

c)

Intermediate Value Theorem

d)

Rolle's Theorem

21.

a)

position

b)

velocity

c)

acceleration

d)

total distance

22.

Which of the following are synonyms for find the derivative?

a)

f'(x)

b)

dy/dx

c)

y'

d)

slope of the tangent line

e)

instantaneous rate of change

23.

Given u(x) = f(x)g(x), f(2) = 3, g(2) = -3, f '(2) = 5, and g'(2) = 1,

then u'(2) = ?

a)

-12

b)

4

c)

5

d)

12

24.

If f has a derivative at x = a, then f is continuous at x = a?

a)

True

b)

False

25.

The function f has positive 1st derivatives and a negative 2nd derivative. Which of the following could be a table of values for f ?

a)

A

b)

B

c)

C

26.

Which is true at a?

a)

f'(a) < f''(a) < f(a)

b)

f'(a) < f(a) < f''(a)

c)

f''(a) < f'(a) < f(a)

d)

f'(a) = f''(a) < f(a)

27.

Where does f(x) have a point of inflection?

a)

x = -3

b)

x = 3,-3

c)

x= -1

d)

x = -1,3

28.

A particle's speed is decreasing if

a)

it's acceleration is positive

b)

it's velocity is positive

c)

it's velocity and acceleration have the same sign

d)

it's velocity and acceleration have different signs

29.

An objects distance from its starting point at time t is given by the equation

s(t) = t³ - 6t² - 4.

What is the speed of the object when its acceleration is 0?

a)

2

b)

-24

c)

12

d)

44

30.

Use the sign chart for f'(x) and the table of f(x). There is ...

a)

a local maximum at (-10,5).

b)

an absolute minimum at (-2,0).

c)

a local minimum at (20,7).

d)

all of the above

31.

If H(x) = f ^-1(x), then H'(3) equals

a)

4

b)

1/4

c)

- 1/4

d)

-4

32.

Find dy/dx at a given point.

a)

5/4

b)

4/5

c)

1

d)

-5

33.

Find the derivative of the inverse

a)

12

b)

1/12

c)

146

d)

1/146

34.

find y'

a)

A

b)

B

c)

C

d)

D

35.

Find the Derivative

a)

A

b)

B

c)

C

d)

D

36.

Evaluate the derivative at

x = π

a)

-1 - 3/(π³)

b)

9/(π⁴)

c)

3/(π⁴)

d)

9

37.

a)

Only the Quotient Rule

b)

The Quotient and Product Rules

c)

The Quotient and Chain Rules

d)

Only the Chain Rule

38.

Chris is sitting on the edge of a dock tossing rocks into the water. As each rock hits the water, small circles appear traveling outward from the point of impact. The radius of the circle is changing at a rate of 5 in/sec. How fast is the area of the outer circle changing when the diameter is 8 in?

a)

80π in/sec

b)

20π in/sec

c)

60π in/sec

d)

40π in/sec

39.

Find all values of c that satisfy the MVT for the function on the given interval

f(x) = -x² + 8x - 17 on [2,6]

a)

c = 2

b)

c = 3

c)

c = 4

d)

c = 6

40.

A hypothetical cube shrinks so that the length of its sides are decreasing at a rate of 4 m/min. At what rate is the volume of the cube changing when the sides are 5 m each?

a)

-296 m³/min

b)

-297 m³/min

c)

-300 m³/min

d)

-307 m³/min

41.

If (a,b) is a local minimum, then what will be true about f''(a)?

a)

It's postive

b)

It's negative

c)

It's zero

d)

Cannot be determined

42.

If f''(x)>0 over the interval (-7,1), then what will be true about f'(x)?

a)

It's constant

b)

It's increasing

c)

It's decreasing

d)

Cannot be determined

43.

a)

Mean value theorem

b)

Instantaneous Rate of Change

c)

Intermediate Value Theorem

d)

Fundamental Theorem of Calculus

44.

Based on the table, use LRAM and 4 sub-intervals to estimate the Area under the curve. (Choose the correct set-up.)

a)

5(3) + 1(4) + 2(5) + 1(7)

b)

5(4) + 1(5) + 2(7) + 1(6)

c)

5(3) + 6(4) + 8(5) + 9(7)

d)

0(3) + 5(4) + 6(5) + 8(7)

45.

True/False: if the limit of a function exists at x=c, then f(c) exists.

a)

True

b)

False

46.

If f(x) is continuous at interval [a,b], and f(a) is positive and f(b) is negative, then f(c)=0, where c is include in [a,b].

a)

True

b)

False

47.

Find the limit as x approaches -3

a)

0

b)

1

c)

-6

d)

DNE

48.

List the horizontal and vertical asymptotes of the function.

a)

x = 3

b)

x = -3

c)

y = -2

d)

y = 2

49.

a)

0

b)

1

c)

-1

d)

DNE

50.

a)

5

b)

infinity

c)

-1

d)

1

51.

Find the value of f so that f(x) is continuous at x = -1

a)

3

b)

-3

c)

1

d)

-1

52.

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

53.

find y'

a)

y = 2 x^-1

b)

y=2 x^-2

c)

y= −2x^-2

d)

y= −2 x^-1

54.

Find the Limit

a)

4x²-3

b)

8x

c)

4x+4h-3

d)

4x

55.

It's the average rate of change of y=3x^2+4x-2 on the interval [-2, 1].

a)

0

b)

1

c)

2

d)

3

56.

a)

A

b)

B

c)

C

d)

D

57.

a)

A

b)

B

c)

C

d)

D

58.

Oil spilling from a ruptured tanker spreads in a circle on the surface of the ocean. The radius of the spill increases at a rate of 5 m/min. How fast is the area of the spill increasing when the radius is 5 m?

a)

50π m²/min

b)

47π m²/min

c)

52π m²/min

d)

40π m²/min

59.

Find $\frac{dy}{dx}$ : $y^2=10x$

a)

$\frac{5}{y}$

b)

$\frac{10}{y}$

c)

$\frac{y^2}{5}$

d)

$\frac{y^2}{10}$

60.

Find the derivative of $x^2+xy+y^3=0$

a)

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

b)

$-\frac{x+3y^2}{2x+y}$

c)

$-\frac{2x+y}{x+3y^2}$

d)

$-\frac{2x}{x+3y^2}$

61.

a)

A

b)

B

c)

C

d)

D

62.

Find $h'\left(-4\right)$

a)

-4

b)

-1/4

c)

1/4

d)

4

63.

What is x-value at which the function below has the same instantaneous rate of change as the average rate of change over the indicated interval?

f(x) = x² - 3x - 28, [-4,7]

a)

1.5

b)

-1.5

c)

0.5

d)

-0.5

64.

In order for the Extreme Value theorem to apply, which of these must be true. Select all that apply.

a)

It must be discontinuous

b)

It must be closed

c)

It must be open

d)

It must be continuous

65.

a)

0

b)

5/3

c)

e^5x

d)

DNE

66.

The following is a description of what theorem?

If a function is differentiable, then the derivative must be equal to the Average Rate of Change somewhere on that interval.

a)

Intermediate Value Theorem

b)

Mean Value Theorem

c)

Exteme Value Theorem

d)

Differentiable Value Theorem

67.

The following is a description of what theorem?

If a function is continuous, then it is guaranteed to get every y value in between the endpoints on an interval.

a)

Intermediate Value Theorem

b)

Mean Value Theorem

c)

Exteme Value Theorem

d)

Differentiable Value Theorem

68.

The following is a description of what theorem?

If you have a closed, continuous interval, there MUST be an absolute max and min.

a)

Intermediate Value Theorem

b)

Mean Value Theorem

c)

Exteme Value Theorem

d)

Differentiable Value Theorem

69.

What is needed to be shown in order to get full credit on a Free Response L'Hopital's Rule Question?

a)

You MUST STATE THE FUNCTION IS CONTINUOUS

b)

You MUST show the limit of the top is equal to 0

c)

You MUST show the limit of the bottom is equal to 0

d)

You MUST use Limit Notation

e)

You MUST state by L’Hopital’s Rule

70.

If asked to find the absolute maximum of a function and then JUSTIFY, what is the best way to justify on a free response question?

a)

A table including end points and critical points, and the values you get when you plug into the function

b)

A table including just critical points and the values you get when you plug into the function

c)

A sign chart including just critical points to determine all of the maxes.

d)

A sign chart including critical points and end points to determine all of the maxes.

71.

The function f is continuous and differentiable on the closed interval [3, 7]. The table above gives selected values of f on this interval. Which of the following statements must be true?

I. The minimum value off on [3, 7] is 12.

II. There exists c, for 3 < c < 7, such that f′(c)=0

III. f′(x)>0 for 5 < x < 7.

a)

I only

b)

II only

c)

III only

d)

I and III only

e)

All

72.

Find the derivative:

$f\left(x\right)=3x\cdot e^x$

a)

$f'\left(x\right)=3e^x$

b)

$f'\left(x\right)=3x\cdot e^x+3e^x$

c)

$f'\left(x\right)=3e^{3x}$

d)

$f'\left(x\right)=3\cos e^x+3e^x$

73.

Given the following derivative, Find all the critical points of the following. Select all that apply: $f'\left(x\right)=x\ln x-4\ln x$

a)

-2

b)

0

c)

1

d)

4

Calculus 1st Semester Review

Total questions: 73

Worksheet time: 2hrs 9mins

Similar Resources on Wayground