Free Printable Calculus Quiz

1.

Using a left reiman sum on an increasing function produces an over or under estimate?

(a)

2.

Using a right reiman sum on an increasing function produces an over or under estimate?

(a)

3.

Using a left reiman sum on an decreasing function produces an over or under estimate?

(a)

4.

Using a right reiman sum on an decreasing function produces an over or under estimate?

(a)

5.

A midpoint reiman sum on a concave down function produces an over or underestimate?

(a)

6.

A midpoint reiman sum on a concave up function produces an over or underestimate?

(a)

7.

a trapezoidal reimann sum on a concave up function produces an overestimate or underestimate?

(a)

8.

If the acceleration and velocity of a moving particle are opposite signs (one is negative and one is positive), is speed increasing or decreasing?

(a)

9.

The absolute value of velocity is called:

a)

speed

b)

acceleration

c)

positive velocity

d)

change of position

10.

How does the sign of the derivative change at the point where a minimum occurs?

a)

positive to negative

b)

negative to positive

c)

not enough information to tell

d)

does not change

11.

What theorem is described here: If f is continuous on the closed interval [a,b] and k is any number between f(a) and f(b) then there is at least one number c in [a, b] such that f(c) = k

a)

MVT

b)

IVT

c)

EVT

d)

FTC

12.

What theorem is described here: If f is continuous on the closed interval [a, b], then f has both a maximum and a minimum on the interval.

a)

MVT

b)

IVT

c)

EVT

d)

FTC

13.

What theorem is described here: The integral on (a, b) of f(x) dx = F(b) - F(a)

a)

Fundamental theorem of calculus (FTC)

b)

Mean Value Theorem (MVT)

c)

Intermediate Value Theorem (IVT)

d)

Extrema Value Theorem (EVT)

14.

The integral from a to b of f'(x) tells us:

(select all)

a)

the change in f(x) from a to b

b)

the area under the curve of f'(x) from a to b

c)

the value of f(b)

d)

the value of f(b) when the integral described is added to the value of f(a) (i.e. the initial value)

15.

a)

cosx

b)

-cosx

c)

-sinx cosx

d)

sinx cosx

16.

a)

sinx

b)

-sinx

c)

-cscx cotx

d)

sec²x

17.

Find the limit of the function as x approaches 2.

a)

1

b)

-1

c)

5

d)

DNE

18.

Find f(2).

a)

1

b)

-1

c)

5

d)

DNE

19.

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

20.

The acceleration function is the first derivative of...

a)

position

b)

velocity

c)

calculus

d)

particle motion

21.

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

a)

7

b)

0

c)

7x

d)

14

22.

If f'(x) = 0 what does that imply about the x value?

a)

It is a critical point, it is a possible max, min, or point of inflection.

b)

That the limit does not exist.

23.

When applying calculus. The second derivative helps find...

a)

the distance traveled by an object.

b)

The velocity of a particle at any given point

c)

acceleration of an object at any given time

24.

Integration is the inverse of differentiation but it applications it can be used to....

a)

find the area under a curve

b)

calculate the force of an object

c)

Find the altitude of an objects perimeter

25.

1 - sin²x =

a)

cos²x

b)

cos²x+1

c)

csc²x

d)

tan²x

26.

sin(-x)=

a)

sin(x)

b)

-sin(x)

c)

cos(x)

d)

-cos(x)

27.

Please select the correct solution

a)

csc² x

b)

cot² x

c)

sin² x

d)

sec² x

28.

Expand the following logarithm:
log₂ 5x.

a)

log₂ 5 - log₂ x

b)

log₂ 5 + log₂ x

c)

2log 5 + 2log x

d)

log5 2 + log_x 2

29.

Condense the following logarithm: lnx + ln4

a)

ln 4x

b)

ln 4/x

c)

log 4 + log x

d)

ln x⁴

30.

Given a function g(x), if g'(x)=0 at a certain value of x, then g(x) has _____________ at x.

a)

an inflection point

b)

a critical point

c)

a minimum

d)

a maximum

31.

What is a point of inflection?

a)

When a function goes from increasing to decreasing

b)

When a function goes from concave up to concave down

32.

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

a)

The function is increasing

b)

The function is decreasing

c)

The function is concave up

d)

The function is concave down

33.

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

a)

The function is increasing

b)

The function is decreasing

c)

The function is concave up

d)

The function is concave down

34.

what is the derivative of y= sin(2x)?

a)

y^/=cos(2x)

b)

y^/=2sin(2x)

c)

y^/=2sin(x)+cos(2x)

d)

y^/=2cos(2x)

35.

What is the speed of the position function f(x)=-3x²-6x-6 at x=2

a)

-18

b)

18

c)

-6

d)

6

36.

What are the conditions that satisfy the mean value theorem, and what does it mean?

a)

Continuous on the open and differentiable on the closed, and then there is at least 2 numbers c and d in the interval (a,b) (that is a < c < b) such that

b)

Discontinuous on the closed and differentiable on the open, then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

c)

Continuous on the closed and differentiable on the open,and then there is at least one number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

d)

Continuous on the open and differentiable on the open, and then there is no number c in the interval (a,b) (that is a < c < b) such that f'(c)=(f(b)- f(a))/ (b-a)

37.

A particle moves along the x-axis with velocity at time x>0 and the function is v(x)=x²+6x+3, is the speed of the particle increasing at x=4?

a)

No because both velocity and acceleration at x=4 is positive

b)

Yes because both velocity and acceleration at x=4 is positive

c)

No because both velocity and acceleration at x=4 is negative

d)

Yes because both velocity and acceleration at x=5 is positive

38.

What type of graph would be the derivative for a cubic function?

a)

Quartic

b)

Cubic

c)

Parabola

d)

Linear

39.

If the tangent line is horizontal at x=c, which of the following must be true?

a)

c is a point of inflection

b)

c must be a maximum

c)

c must be a critical point

d)

c must be a minimum

40.

If x=c is an inflection point, what must be true? (Select all that apply)

a)

f'(c)=0

b)

the concavity changes

c)

f''(c)=0

d)

the function changes from increasing to decreasing

41.

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

a)

True

b)

False

42.

True/False: The velocity of a function is the derivative of the position function.

a)

True

b)

False

43.

True/False: The slope of the tangent line at a point is the same as the instantaneous rate of change of the function at that point.

a)

True

b)

False

44.

Which of the following is NOT a definite integral property?

a)

$\int_a^{a\ }f\left(x\right)\ dx=0$

b)

$\int_a^b\ f\left(x\right)\ dx\ =\ \int_a^c\ f\left(x\right)\ dx\ +\int_c^b\ f\left(x\right)\ dx$

c)

$\int_b^a\ f\left(x\right)\ dx\ =\int_a^b\ f\left(x\right)\ dx$

d)

$\int_a^b\ kf\left(x\right)dx\ =\ k\int_a^b\ f\left(x\right)\ dx$

45.

Which of the following definite integrals describes the area under the curve?

a)

$\int_0^4\ 4-2x\ dx$

b)

$\int_0^2\ 4-2x\ dx$

c)

$\int_2^0\ 4-2x\ dx$

d)

$\int_4^0\ 4-2x\ dx$

46.

$\int_{ }^{ }\sin udu$

a)

cosu + C

b)

-cosu + C

c)

sinu + C

d)

-sinu + C

47.

∫sec²u du

a)

tanu + C

b)

secu + C

c)

secutanu + C

d)

tan²u + C

48.

$\int_{ }\left(\frac{du}{u}\right)\ =\$

a)

$u^0+\ C$

b)

ln|u| + C

c)

$-\frac{1}{u^2}$ + C

d)

u + C

49.

check all the integral that are true statements.

a)

∫du = u + C

b)

∫udu = 1 + C

c)

$\int_{ }\sqrt{u}du=\frac{1}{2}u^{\frac{3}{2}}+C$

d)

$\int_{ }\left(\frac{du}{\sqrt{u}}\right)=\ln\left|u\right|+\ C$

e)

$\int_{ }e^udu=e^u+C$

50.

$\int_{ }2^udu=$

a)

$2^u+C$

b)

$2^u\ln2\ +\ C$

c)

$\frac{2^u}{\ln2}+C$

d)

$\frac{2^{\left(u+1\right)}}{\ln2}+C$

Calculus Quiz

Total questions: 50

Worksheet time: 1hrs 27mins

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