Free Printable Flashcard Quiz Part 1

1.

Fill in the blank: sin(π/2) = ____

a)

0

b)

1

c)

-1

d)

1/2

2.

Fill in the blank: sin(3π/2) = ___

a)

-1

b)

0

c)

1

d)

√3/2

3.

Fill in the blank: cos(π/2) = ______

a)

0

b)

1

c)

-1

d)

√2/2

4.

Fill in the blank: cos(3π/2) = ______

a)

0

b)

1

c)

-1

d)

√3/2

5.

Fill in the blank: tan θ (in terms of sine and/or cosine) = ______

a)

cos θ / sin θ

b)

sin θ / cos θ

c)

1 / (sin θ × cos θ)

d)

sin θ × cos θ

6.

Fill in the blank: sec θ (in terms of sine and/or cosine) = ______

a)

1 / cos θ

b)

cos θ / sin θ

c)

sin θ

d)

1 / sin θ

7.

Which function is pictured in the graph?

a)

Graph of y = cos x

b)

Graph of y = sin x

c)

Graph of y = sec x

d)

Graph of y = tan x

8.

Which function is pictured in the graph?

a)

Graph of y = cos x

b)

Graph of y = tan x

c)

Graph of y = sec x

d)

Graph of y = sin x

9.

Which function is pictured in the graph?

a)

Graph of y = tan x

b)

Graph of y = sec x

c)

Graph of y = cos x

d)

Graph of y = sin x

10.

Pick the equation graphed.

a)

Graph of y = ln(x)

b)

Graph of y = |x|

c)

Graph of y = $\frac{1}{x}$

d)

Graph of y = sqrt(x)

e)

Graph of y = $\sqrt{1-x^2}$

11.

Pick the equation graphed.

a)

Graph of y = ln(x)

b)

Graph of y = |x|

c)

Graph of y = $\sqrt[]{x}$

d)

Graph of y = $\frac{1}{x}$

e)

Graph of y = $\sqrt{1-x^2}$

12.

Pick the equation graphed.

a)

Graph of y = |x|

b)

Graph of y = $\frac{1}{x}$

c)

Graph of y = $\sqrt{1-x^2}$

d)

Graph of y = ln(x)

e)

Graph of y = $\sqrt[]{x}$

13.

Pick the equation graphed.

a)

Graph of y = |x|

b)

Graph of y = ln(x)

c)

Graph of y = $\sqrt[]{x}$

d)

Graph of y = $e^x$

e)

Graph of y = $\sqrt{1-x^2}$

14.

Pick the equation graphed.

a)

Graph of y = |x|

b)

Graph of y = $e^x$

c)

Graph of y = $\sqrt[]{x}$

d)

Graph of y = ln(x)

e)

Graph of y = $\sqrt{1-x^2}$

15.

An even function is symmetric with respect to the ____

a)

y-axis

b)

x-axis

c)

z-axis

d)

origin

16.

An odd function is symmetric with respect to the ____

a)

y-axis

b)

x-axis

c)

z-axis

d)

origin

17.

Fill in the blank: The formula for the circumference of a circle is C = ____.

a)

2πr

b)

πr²

c)

πd

d)

r²

18.

Fill in the blank: The formula for the volume of a cylinder is _______.

a)

V = 2πrh

b)

V = $4/3\pi r^3$

c)

$V = \pi r^2 h$

d)

V = $\pi r^2/3$

19.

Fill in the blank: The formula for the volume of a cone is _______.

a)

V = $(1/3)\pi r^2 h$

b)

$V = \pi r^2 h$

c)

V = $(4/3)\pi r^3$

d)

V = $(1/2)\pi r^2 h$

20.

Fill in the blank: The formula for the volume of a sphere is _______.

a)

V = $(1/3)\pi r^2 h$

b)

V = $(4/3)\pi r^3$

c)

$V = \pi r^2 h$

d)

$V = 2\pi r^2$

21.

Fill in the blank: The formula for the surface area of a sphere is _______.

a)

$A = 4\pi r^2$

b)

$2\pi r^2$

c)

$A = 4\pi r^3$

d)

A = $\pi r^2$

22.

Fill in the blank: The point-slope form of a linear equation is _______.

a)

y = mx + b

b)

y - y₁ = m(x - x₁)

c)

x - x₁ = m(y - y₁)

d)

y = m(x + x₁)

23.

a)

0

b)

1

c)

DNE

d)

$\infty$

24.

a)

0

b)

1

c)

DNE

d)

$\infty$

25.

The line through a point on a curve with slope equal to the slope of the curve at that point.

a)

Normal Line

b)

Tangent Line

c)

Secant Line

26.

The line connecting two point on a curve.

a)

Tangent Line

b)

Secant Line

c)

Normal Line

27.

The line perpendicular to the tangent line at the point of tangency.

a)

Tangent Line

b)

Secant Line

c)

Normal Line

28.

f(x) is continuous at x = c when

II. $\lim_{x\rightarrow c}f\left(x\right)$ exists

I. $f\left(c\right)$ exists

III. $\lim_{x\rightarrow c}f\left(x\right)=f\left(c\right)$

a)

I. and II.

b)

II. and III.

c)

All the above

29.

Fill in the blank: The limit definition of the derivative of f(x) is f'(x) = _________.

a)

lim_{Δx→0} (f(x+Δx) - f(x)) / Δx

b)

lim_{Δx→∞} (f(x+Δx) - f(x)) / Δx

c)

lim_{Δx→0} (f(x) - f(x+Δx)) / Δx

d)

lim_{Δx→0} (f(x+Δx) + f(x)) / Δx

30.

Fill in the blank: The alternate definition of the derivative of f at x = c is f'(c) = _________.

a)

lim_{x→c} (f(x) - f(c)) / (x - c)

b)

lim_{h→0} (f(x+h) - f(x)) / h

c)

lim_{x→0} (f(x) - f(0)) / (x - 0)

d)

lim_{x→c} (f(c) - f(x)) / (c - x)

31.

What does f'(x) tell you about a function?

a)

slope of tangent line

b)

instantaneous rate of change

c)

slope of curve at a point

d)

All the above

32.

Fill in the blank: The definition of average rate of change is _________.

a)

Δy/Δx = (f(b) - f(a)) / (b - a)

b)

Δx/Δy = (f(a) - f(b)) / (a - b)

c)

Δy/Δx = (f(a) + f(b)) / (b - a)

d)

Δy/Δx = (f(b) + f(a)) / (b + a)

33.

Power rule for derivatives: $\frac{d}{dx}(x^n) =$ _______

a)

$nx^{n-1}$

b)

$n x^{n}$

c)

$x^{n-1}$

d)

$n x^{n+1}$

34.

Product rule for derivatives: $\frac{d}{dx}(f(x)g(x)) =$ _______

a)

f(x)g(x)

b)

f'(x)g(x) + g'(x)f(x)

c)

f(x)g'(x) - f'(x)g(x)

d)

f'(x)g'(x)

35.

Quotient rule for derivatives: $\frac{d}{dx}\left(\frac{f(x)}{g(x)}\right) =$ _______

a)

$\frac{f(x)g'(x) - g(x)f'(x)}{(g(x))^2}$

b)

$\frac{g(x)f'(x) - f(x)g'(x)}{(g(x))^2}$

c)

$\frac{f'(x)g'(x)}{g(x)}$

d)

$\frac{f'(x)}{g'(x)}$

36.

Chain rule for derivatives: $\frac{d}{dx}(f(g(x))) =$ _______

a)

$f'(g(x)) \cdot g(x)$

b)

$f'(g(x)) \cdot g'(x)$

c)

$f(g(x)) \cdot g'(x)$

d)

$f'(x) \cdot g'(x)$

37.

Fill in the blank: The derivative of cos(x) with respect to x is _______.

a)

-sin(x)

b)

sin(x)

c)

cos(x)

d)

-cos(x)

38.

Fill in the blank: The derivative of sin(x) with respect to x is _______.

a)

-sin(x)

b)

sin(x)

c)

cos(x)

d)

-cos(x)

39.

Fill in the blank: The derivative of tan(x) with respect to x is _______.

a)

$sec^2(x)$

b)

sin(x)

c)

tan(x)

d)

$cos^2(x)$

40.

Fill in the blank: The derivative of cot(x) with respect to x is _______.

a)

$sec^2(x)$

b)

$-csc^2(x)$

c)

tan(x)

d)

$csc^2(x)$

41.

Fill in the blank: The derivative of sec(x) with respect to x is _______.

a)

sec(x) tan(x)

b)

sec(x) cot(x)

c)

sec(x) sin(x)

d)

sec(x) + tan(x)

42.

Fill in the blank: The derivative of csc(x) with respect to x is _______.

a)

-csc(x) cot(x)

b)

csc(x) tan(x)

c)

sec(x) cot(x)

d)

-sec(x) tan(x)

43.

Fill in the blank: The derivative of arcsin(x) with respect to x is _____.

a)

$\frac{1}{\sqrt{1 + x^2}}$

b)

$\frac{1}{\sqrt{1 - x^2}}$

c)

$arcsin(x) * sqrt(1 - x^2)$

d)

$x / \sqrt{1 - x^2}$

44.

Fill in the blank: The derivative of arccos(x) with respect to x is _____.

a)

$\frac{1}{\sqrt{1 - x^2}}$

b)

$-1 / \sqrt{1 - x^2}$

c)

$\frac{1}{1 + x^2}$

d)

$-1 / (1 + x^2)$

45.

Fill in the blank: The derivative of arctan(x) with respect to x is _____.

a)

$\frac{1}{1 - x^2}$

b)

$\frac{1}{1 + x^2}$

c)

arctan(x)

d)

$2x / (1 + x^2)$

46.

Fill in the blank: The derivative of arccot(x) with respect to x is _____.

a)

$\frac{1}{1 + x^2}$

b)

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

c)

$2x / (1 + x^2)$

d)

arctan(x)

47.

Fill in the blank: The derivative of arcsec(x) with respect to x is _____

a)

$\frac{x}{\sqrt{x^2 - 1}}$

b)

$\frac{1}{x^2 + 1}$

c)

$\frac{1}{(|x| \sqrt{x^2 - 1})}$

d)

$\frac{1}{\sqrt{1 - x^2}}$

48.

The derivative of arccsc(x) with respect to x is

a)

$-\frac{1}{|x|\sqrt{x^2-1}}$

b)

$\frac{1}{|x|\sqrt{x^2-1}}$

c)

$-\frac{1}{x\sqrt{x^2+1}}$

d)

$\frac{1}{x\sqrt{x^2-1}}$

49.

Fill in the blank: Derivative of natural log: $\frac{d}{dx} (\ln x) = \underline{\hspace{2cm}}$

a)

$\frac{1}{x}$

b)

x

c)

\ln x

d)

$e^x$

50.

Fill in the blank: Derivative of log base $a$ : $\frac{d}{dx} (\log_a x) = \underline{\hspace{2cm}}$

a)

$\frac{1}{x a}$

b)

$\frac{1}{x \ln a}$

c)

$\ln a \cdot x$

d)

$\frac{a}{x}$

51.

Fill in the blank: Derivative of natural exponential function: $\frac{d}{dx} (e^x) = \underline{\hspace{2cm}}$

a)

$x e^x$

b)

$e^x$

c)

$x^e$

d)

$e^{x+1}$

52.

Fill in the blank: Derivative of exponential function of any base: $\frac{d}{dx} (a^x) = \underline{\hspace{2cm}}$

a)

$a^x \ln x$

b)

$a^x \ln a$

c)

$x^a \ln a$

d)

$a^x$

53.

Derivative of an inverse function: What is $\frac{d}{dx} (f^{-1}(x)) =$ ?

a)

$\frac{1}{f'(f^{-1}(x))}$

b)

$ f'(x) $

c)

$f^{-1}(x)$

d)

$\frac{1}{f'(x)}$

54.

Rolle’s Theorem: If f is continuous on [a, b], differentiable on (a, b), and…

a)

…f(a) = f(b), then there exists c ∈ (a, b) such that f'(c) = 0.

b)

…f(a) ≠ f(b), then there exists c ∈ (a, b) such that f'(c) = 0.

c)

…f(a) = f(b), then there exists c ∈ (a, b) such that f'(c) ≠ 0.

d)

…f(a) = f(b), then there exists c ∈ (a, b) such that f(c) = 0.

55.

Mean Value Theorem for Derivatives: If f is continuous on [a, b] and differentiable on (a, b), then… (complete the statement)

a)

f'(c) = 0 for all c in (a, b)

b)

f'(c) = (f(a) + f(b)) / 2

c)

f'(c) = f(b) - f(a)

d)

there exists at least one c in (a, b) such that f'(c) = (f(b) - f(a)) / (b - a).

56.

Extreme Value Theorem: If $f$ is continuous on a closed interval, then… (complete the statement)

a)

…f must have both an absolute maximum and an absolute minimum on the interval.

b)

…f must be differentiable everywhere on the interval.

c)

…f must be increasing on the interval.

d)

…f must have a local maximum at the endpoints of the interval.

57.

Intermediate Value Theorem: If $f$ is continuous on [a, b], then… (complete the statement)

a)

…f must be differentiable on [a, b].

b)

…f must have a maximum at either a or b.

c)

…f must take on every y-value between f(a) and f(b).

d)

…f must be constant on [a, b].

58.

If a function is differentiable at a point, then _________.

a)

it must be continuous at that point. (Differentiability implies continuity.)

b)

it must be discontinuous at that point.

c)

it must be non-differentiable at that point.

d)

it must have a jump at that point.

59.

List four ways in which a function can fail to be differentiable at a point.

a)

Oscillation, Periodicity, Symmetry, Translation

b)

Discontinuity, Corner, Cusp, Vertical tangent line

c)

Continuous everywhere, Smooth curve, No inflection, Horizontal tangent

d)

Constant function, Linear function, Quadratic function, Cubic function

60.

A critical number (also known as a critical point or critical value) of f(x) is _________.

a)

a value of x where f(x) is always increasing.

b)

a value of x where f(x) is undefined for all x.

c)

a value of x where f''(x) = 0 always.

d)

a value of x in the domain of f at which either f'(x) = 0 or f'(x) does not exist.

61.

If f'(x) > 0, then _________

a)

f(x) is increasing.

b)

f(x) is decreasing.

c)

f(x) is constant.

d)

f(x) has a maximum.

62.

If f'(x) < 0, then _________.

a)

f(x) is decreasing.

b)

f(x) is increasing.

c)

f(x) is constant.

d)

f(x) has a maximum.

63.

If f'(x) = 0, then _________.

a)

f(x) is always increasing.

b)

f(x) has a vertical tangent.

c)

f(x) has a horizontal tangent.

d)

f(x) is always decreasing.

64.

Definition: f(x) is concave up when _________.

a)

f'(x) is increasing.

b)

f'(x) is constant.

c)

f(x) is decreasing.

d)

f''(x) is negative.

65.

Definition: f(x) is concave down when _________.

a)

f'(x) is decreasing.

b)

f'(x) is constant.

c)

f'(x) is increasing.

d)

f(x) is linear.

66.

f''(x) > 0 means that f(x) is __________.

a)

concave up (like a cup)

b)

concave down (like a frown)

c)

increasing everywhere

d)

decreasing everywhere

67.

f''(x) < 0 means that f(x) is __________.

a)

concave down (like a frown)

b)

concave up (like a cup)

c)

increasing everywhere

d)

a linear function

68.

Definition: A point of inflection is a point on the curve where _________.

a)

concavity changes.

b)

the slope is always zero.

c)

the function is undefined.

d)

the curve has a maximum value.

69.

To find a point of inflection, _________.

a)

look for where f'' changes signs, or, equivalently, where f' changes direction.

b)

look for where f' is zero and f'' is positive.

c)

look for where f is increasing and f' is negative.

d)

look for where f'' is always positive.

70.

To find extreme values of a function, look for where _________.

a)

the function is increasing

b)

the second derivative is positive

c)

the function is continuous

d)

the derivative is zero or undefined

71.

By the First Derivative Test, when the derivative changes from positive to negative

a)

there is a maximum

b)

there is a minimum

c)

there is a zero

d)

the function is undefined

72.

By the First Derivative Test, when the derivative changes from negative to positive

a)

there is a maximum

b)

there is a minimum

c)

there is a zero

d)

the function is undefined

73.

The Second Derivative Test: If f'(x) = 0 and ________, then f has a maximum; if ________, then f has a minimum.

a)

f''(x) < 0; f''(x) > 0

b)

f''(x) > 0; f''(x) < 0

c)

f''(x) = 0; f''(x) > 0

d)

f''(x) > 0; f''(x) = 0

74.

Position function s(t) = ________, the antiderivative of velocity.

a)

∫v(t)dt

b)

v(t) + C

c)

d/dt v(t)

d)

v(t) - C

75.

Velocity function v(t) = s'(t), the derivative of position, as well as ________, antiderivative of acceleration.

a)

∫a(t)dt

b)

a(t) + C

c)

s(t) - v(t)

d)

d/dt a(t)

76.

Acceleration function a(t) = v'(t), the derivative of velocity, as well as ________, the second derivative of position.

a)

s''(t)

b)

s'(t)

c)

v(t)

d)

a'(t)

77.

A particle is moving to the left when ________.

a)

v(t) < 0

b)

v(t) > 0

c)

a(t) < 0

d)

s(t) > 0

Flashcard Quiz Part 1

Total questions: 77

Worksheet time: 39mins

Similar Resources on Wayground