Free Printable Semester 1 Final Review

1.

Which of the following is true?

a)

b)

c)

d)

2.

a)

+ ∞

b)

Undefined

c)

0

d)

Does not exist

3.

Find the limits above.

a)

0

b)

-6

c)

-12

d)

12

4.

a)

+ ∞

b)

4

c)

2

d)

Does not exist

5.

On the interval [-7, 7] where is the function f not continuous?

a)

-2, 2

b)

2

c)

-2

d)

nowhere

6.

Find the value of k, if possible, that makes the function f continuous everywhere.

a)

3

b)

0

c)

2

d)

no such k exists

7.

The derivative of the function, f(x) = e^x

a)

e^x

b)

-e^x

c)

-e^-x

d)

e^-x

8.

The derivative of the function, f(x) = aln(x)

a)

$f'\left(x\right)=a\ln\left(x\right)$

b)

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

c)

$f'\left(x\right)=\frac{a}{x}$

9.

What is dy/dx?

y^3=6x

a)

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

b)

$\frac{3}{y^3}$

c)

$3y^2$

d)

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

10.

What is dy/dx?

xy=1

a)

$\frac{x}{y}$

b)

$-\frac{x}{y}$

c)

$\frac{y}{x}$

d)

$-\frac{y}{x}$

11.

What is dy/dx?

x^2+y^2=1

a)

$-\frac{y}{x}$

b)

$\frac{x}{y}$

c)

$-\frac{x}{y}$

d)

$\frac{y}{x}$

12.

a)

b)

c)

d)

13.

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)

$-3$

14.

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 $h'\left(3\right)$

a)

$0$

b)

$2$

c)

$\frac{5}{6}$

d)

$-3$

15.

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 $h\left(x\right)=\frac{f\left(x\right)}{g\left(x\right)}$ Find $h'\left(4\right)$

a)

$0$

b)

$2$

c)

$\frac{5}{6}$

d)

$-3$

16.

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

17.

A function whose graph is otherwise continuous will fail to have a derivative at a point where the graph has a...

a)

corner, cusp, horizontal tangent, discontinuity

b)

corner, cusp, vertical tangent, continuity

c)

corner, cusp, vertical tangent, discontinuity

d)

corner, curve, vertical tangent, continuity

18.

Which option shows the same expression?

a)

b)

c)

d)

19.

Rachel is standing atop a 13 ft ladder. The ladder is leaning against a vertical wall. The ladder starts sliding away from the wall at a rate of 3 ft/sec. How fast is the ladder sliding down the wall when the tip of the ladder is 5 ft high?

a)

3 ft/sec

b)

-7.2 ft/sec

c)

7.2 ft/sec

d)

12

20.

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)

80pi in/sec

b)

20pi in/sec

c)

60pi in/sec

d)

4opi in/sec

21.

Determine the derivative of f(x) = 6x

a)

6

b)

x

c)

6x

d)

2x²

22.

Differentiate y= 12x^-2

a)

24x^-1

b)

-24x^-3

c)

-24x^-1

d)

6x^-3

23.

Find the derivative of the given equation
f(x) = x⁴ + 4x³- 2x²

a)

x³ + x²- x

b)

4x³ + 12x²+ 4x

c)

4x + 12x - 4x

d)

4x³ + 12x²- 4x

24.

Find the derivative. f(x) = -8x^-3 + 5x - e^x

a)

f'(x) = -24x^-4 + 5 - e^x

b)

f'(x) = 24x^-4 + 5 - e^x

c)

f'(x) = 24x^-2 + 5 - e^x

d)

f'(x) = 24x^-4 + 5 - e^x-1

25.

Find the slope of the tangent line to f(x) = -3x²-6x at x = 1.

a)

m = 0

b)

f'(x) = -6x - 6

c)

f'(x) = 6x

d)

m = -12

26.

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

27.

Calculate the average rate of change from 20 to 40 minutes.

a)

-2 minutes per gallon

b)

-20 minutes per gallon

c)

-2 gallons per minute

d)

-20 gallons per minute

28.

Which of the following means "first derivative"

a)

f'(x)

b)

y'

c)

dy/dx

d)

all of the above

29.

If a function has a derivative that is negative, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

c)

The concavity of the function is up

d)

The concavity of the function is down

30.

At which point(s) will the slopes of the tangent line be zero?

a)

at C only

b)

at points A, C and E only

c)

at point B and D only

d)

at points A and E only

31.

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

32.

What is the limit?

a)

DNE

b)

2/3

c)

1/4

d)

Infinity

33.

If a function has a derivative that is negative, what does that tell you?

a)

The function is increasing

b)

The function is decreasing

c)

The concavity of the function is up

d)

The concavity of the function is down

34.

What is the derivative of cot(x)?

a)

sec²(x)

b)

-sec²(x)

c)

csc²(x)

d)

-csc²(x)

35.

What is the derivative of csc(x)?

a)

csc(x)cot(x)

b)

-csc(x)cot(x)

c)

-csc²(x)

d)

-cot²(x)

36.

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)

37.

What is the derivative of tan(x)?

a)

-sec²(x)

b)

-csc²(x)

c)

sec²(x)

d)

csc²(x)

38.

How do we find areas of concave down?

a)

First Derivative = 0

b)

Second Derivative = 0

c)

Second Derivative < 0

d)

First Derivative > 0

39.

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

40.

The position of an object is given as a function of time by x = 3t² + 5t³- 2t
What is the acceleration of the object at time t = 2 s?

a)

64 m/s/s

b)

60 m/s/s

c)

66 m/s/s

d)

70 m/s/s

41.

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

a)

38 m/s/s

b)

27 m/s/s

c)

16 m/s/s

d)

49 m/s/s

42.

If the position function for a particle is s(t) = -t² - t, what is the instantaneous velocity function for the particle?

a)

v(t) = -2

b)

v(t) = -2t - 1

c)

v(t) = t³

d)

v(t) = -t

43.

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

44.

A construction worker pulls a five meter plank up the side of a building under construction by means of a rope tied to one end of the plank. Assume the opposite end of the plank follows a path perpendicular to the wall of the building and the worker pulls the rope at a rate of .15 meters per second. How fast is the end of the plank sliding along the ground when when it is 2.5 meters from the wall of the building?

a)

a²+b²=c²

b)

d=√(x²+y²)

c)

h=r⋅sinθ

d)

1=sin²θ+cos²θ

45.

A spherical snowball melts so that its radius decreases at a rate of 4 in/sec. At what rate is the volume of the snowball changing when the radius is 4 in?

a)

-262π in³/sec

b)

-247π in³/sec

c)

-256π in³/sec

d)

-263π in³/sec

46.

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

47.

The function shown

a)

is continuous at x = 2

b)

is differentiable at x = 2

c)

has a limit that exists at x = 2

d)

exists at x = 2

48.

The function shown

a)

is continuous at x = 8

b)

is differentiable at x = 8

c)

has a limit that exists at x = 8

d)

exists at x = 8

49.

The function shown

a)

is continuous at x = 0

b)

is differentiable at x = 0

c)

has a limit that exists at x = 0

d)

exists at x = 0

50.

The function shown

a)

is continuous at x = 0

b)

is differentiable at x = 0

c)

has a limit that exists at x = 0

d)

exists at x = 0

Semester 1 Final Review

Total questions: 50

Worksheet time: 2hrs 6mins

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