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Study sets matching "ap calculus"

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Study sets matching "ap calculus"

10 termscreated on December 10, 2016
5.1-5.5 Review of Logarithmic Functions
logarithmic form
a=b^c in logarithmic form
logarithmic function
what is the common logarithm
an alternate way to write an exponential function
c=logba
function with general equation y=logbx b>0 and b CANNOT = 1 w…
logx implies log10x
logarithmic form
an alternate way to write an exponential function
a=b^c in logarithmic form
c=logba
35 termscreated on December 10, 2016
AMSCO AP World History Chapter 15 Vocab
Henry IV
Henry VIII
Anne Boleyn
Charles V, Holy Roman Empire
Sanctioned religious toleration of the Huguenots, French Calv…
A king of England in the early sixteenth century. With the su…
Queen of England from 1533 to 1536 as the second wife of King…
Was ruler of both the Spanish Empire from 1516 and the Holy R…
Henry IV
Sanctioned religious toleration of the Huguenots, French Calv…
Henry VIII
A king of England in the early sixteenth century. With the su…
8 termscreated on December 10, 2016
5.4-5.6 Review of Exponential Functions
exponential function
if b^x = b^y then...
compound interest formula
compounding continuously formula
function with a numeric (constant) base taken to a VARIABLE p…
x=y
A(t) is the amount after time t... P is the amount invested... r is…
A(t) is the amount after time t... P is the amount invested... r is…
exponential function
function with a numeric (constant) base taken to a VARIABLE p…
if b^x = b^y then...
x=y
104 termscreated on December 10, 2016
History Final Boschetti
absolute monarch
alliance
armada
autocratic
A ruler with complete authority over the government and the l…
formal agreement between two or more nations or powers to coo…
huge fleet of ships, such as the Spanish Armada that unsucces…
ruling with unlimited authority
absolute monarch
A ruler with complete authority over the government and the l…
alliance
formal agreement between two or more nations or powers to coo…
9 termscreated on December 10, 2016
5.3 Inverse Functions
one to one function (1-1)
strictly monotonic
are all even degree polynomials monoto…
if there are no horizontal tangents, i…
a function whose inverse is also a function (the horizontal l…
1-1 functions that increase over its entire domain or decreas…
no
yes
one to one function (1-1)
a function whose inverse is also a function (the horizontal l…
strictly monotonic
1-1 functions that increase over its entire domain or decreas…
75 termscreated on December 10, 2016
AP BC Calculus Final T1
Slope
Terminal Velocity
Symmetric Difference
Logistic Growth Equation
average velocity/average rate of change/how fast you're going
When a falling object begins speeding up
Using either side of a point to find it's slope
p' = kP(1 - P/M)... k = natural exponential growth rate if nothi…
Slope
average velocity/average rate of change/how fast you're going
Terminal Velocity
When a falling object begins speeding up
25 termscreated on December 9, 2016
Age of Absolutism Questions
What country was Bach from?
Did Copernicus publish his findings of…
Building roads, canals, high tariffs,…
Descartes had visions about mind, math…
Germany
No
Mercantilism
Thirty Years War
What country was Bach from?
Germany
Did Copernicus publish his findings of…
No
36 termscreated on December 9, 2016
CH 8 AP PSYCH STUDY GUIDE
Symbolic, generative, structured
Phoneme
Morpheme
Semantics
Imagine that a race of aliens comes to earth. These aliens qu…
The smallest unit of sound in a language is a _____
The smallest unit of meaning in a language is a ______
______ is the component of language concerned with understand…
Symbolic, generative, structured
Imagine that a race of aliens comes to earth. These aliens qu…
Phoneme
The smallest unit of sound in a language is a _____
20 termscreated on December 9, 2016
Spanish in the United States
Jaime Escalante was a teacher that hel…
Who played Anita in West Side Story an…
What city has the highest population o…
Who is famous for singing the song "La…
Calculus
Rita Moreno
New York City
Ritchie Valens
Jaime Escalante was a teacher that hel…
Calculus
Who played Anita in West Side Story an…
Rita Moreno
24 termscreated on December 9, 2016
Derivatives
(d/dx)[cu]
(d/dx)[uv]
(d/dx)[c]
(d/dx)[x]
cu'
uv'+vu'
0
1
(d/dx)[cu]
cu'
(d/dx)[uv]
uv'+vu'
63 termscreated on December 9, 2016
AP Euro; The Scientific Revolution and Enlightenment / 18th century: the expansion of Europe and the enlightenment
Events leading to the scientific revol…
scholasticism
Copernicus
Brahe
1. Discovery of the New World 2. Invention of the Printing Pr…
A philosophical and theological system, associated with Thoma…
Developed the first modern theory of a sun-centered universe…
Amassed nearly 20 years worth of astrological data that event…
Events leading to the scientific revol…
1. Discovery of the New World 2. Invention of the Printing Pr…
scholasticism
A philosophical and theological system, associated with Thoma…
17 termscreated on December 9, 2016
AP BC: Polar Graphs
r = a
r = acos(θ)
r = asin(θ)
r = aθ
circle across both axes
circle on x-axis
circle on y-axis
spiral
r = a
circle across both axes
r = acos(θ)
circle on x-axis
6 termscreated on December 9, 2016
derivatives of inverse trig functions
d/dx(arcsinx)
d/dx(arccosx)
d/dx(arctanx)
d/dx(arccotx)
1/√(1-x²)
-(1/√(1-x²))
1/(1+x²)
-(1/(1+x²))
d/dx(arcsinx)
1/√(1-x²)
d/dx(arccosx)
-(1/√(1-x²))
17 termscreated on December 9, 2016
Unit Circle part 4
cos(0°)
cos(30°)
cos(45°)
cos(60°)
1
√3/2
√2/2
1/2
cos(0°)
1
cos(30°)
√3/2
17 termscreated on December 9, 2016
Unit Circle part 3
sin(0°)
sin(30°)
sin(45°)
sin(60°)
0
1/2
√2/2
√3/2
sin(0°)
0
sin(30°)
1/2
17 termscreated on December 9, 2016
Unit Circle Part 2
30°
45°
60°
π/6
π/4
π/3
30°
π/6
17 termscreated on December 9, 2016
Unit Circle part 1
30º
45º
60º
(1,0)
(√3/2, 1/2)
(√2/2, √2/2)
(1/2, √3/2)
(1,0)
30º
(√3/2, 1/2)
11 termscreated on December 9, 2016
Differentiation Formulas
d/dx(c)=
d/dx(kx)=
d/dx[kƒ(x)]=
d/dx[ƒ(x)±g(x)]=
0
k
kƒ'(x)
ƒ'(x)±g'(x)
d/dx(c)=
0
d/dx(kx)=
k
6 termscreated on December 9, 2016
Integration Formulas
∫cos x dx=
∫sin x dx=
∫sec²x dx=
∫sec x tan x dx=
sin x + c
-cos x + c
tan x + c
sec x + c
∫cos x dx=
sin x + c
∫sin x dx=
-cos x + c
75 termscreated on December 8, 2016
AP Calculus Flash Cards
1
0
Squeeze Theorem
f is continuous at x=c if...
1
0
52 termscreated on December 8, 2016
AP Calculus formula list
Definition of a derivative
Definition of continuity
Average rate of change of f(x) on [a, b]
Rolle's theorem
lim as h->0 f(x+h) - f(x)/h
at c if ... 1. f(c) is defined ... 2. lim as x->c exists ... 3. lim as…
f(b) - f(a)/b-a
If f is continuous on [a,b] and differentiable on (a, b) and…
Definition of a derivative
lim as h->0 f(x+h) - f(x)/h
Definition of continuity
at c if ... 1. f(c) is defined ... 2. lim as x->c exists ... 3. lim as…
46 termscreated on December 8, 2016
Calculus BC AP Equations
Average rate of change of f(x) on [a,b]
Rolle's Theorem
Mean Value Theorem
Intermediate Value Theorem
f'(c) = (f(b) - f(a)) / (b-a)
If f is continuous on [a,b] and differentiable on (a,b) and f…
If f is continuous on [a,b] and differentiable on (a,b), then…
If f is continuous on [a,b] and k is any number between f(a)…
Average rate of change of f(x) on [a,b]
f'(c) = (f(b) - f(a)) / (b-a)
Rolle's Theorem
If f is continuous on [a,b] and differentiable on (a,b) and f…
25 termscreated on December 8, 2016
AP Calculus MUST Know
Integral of sin u du
Integral of cos u du
Integral of tan u du
Integral of cot u du
-cos u + c
sin u + c
-ln |cos u| + c... ln |sec u| + c
ln |sin u| + c... -ln |csc u| + c
Integral of sin u du
-cos u + c
Integral of cos u du
sin u + c
61 termscreated on December 8, 2016
AP Calculus Review - Differentiation
Definition of a Derivative f'(x)
Definition of a Derivative at a Point…
If f is differentiable at x=a ...
Rolle's Theorem
then f is continuous at x=a.
Definition of a Derivative f'(x)
Definition of a Derivative at a Point…
12 termscreated on December 8, 2016
Derivatives of Trig Sheisse
d/dx [sin x] =
d/dx [cos x] =
d/dx [tan x] =
d/dx [cot x] =
cos x
- sin x
sec^2 x
- csc^2 x
d/dx [sin x] =
cos x
d/dx [cos x] =
- sin x
83 termscreated on December 8, 2016
Medical Terminology
ante mortem
morsus
.ramus
bacillis
before death
bite
limb
rod shaped bacteria
ante mortem
before death
morsus
bite
11 termscreated on December 8, 2016
Applications of Differentiation
Extreme Value Theorem
Critical number
Rolle's Theorem
Mean Value Theorem
If f is continuous on a closed interval [a, b], then f has bo…
x-values of a function where f' = 0 or f' is not defined. Rel…
If f is continuous on a closed interval [a, b] and differenti…
If f is continuous on a closed interval [a, b] and differenti…
Extreme Value Theorem
If f is continuous on a closed interval [a, b], then f has bo…
Critical number
x-values of a function where f' = 0 or f' is not defined. Rel…
7 termscreated on December 8, 2016
AP Calculus AB Chapter 5.3
First Derivative Test
Definition of Concavity
Concavity Test
Second Derivative Test for Local Extrema
Use to find extrema ... (1) Find first derivative ... (2) Set equal…
The graph of a differentiable function y = f(x) is ... a) concav…
The graph of a twice differentiable function y = f(x) is ... a)…
(1) If f'(c) = 0 and f''(c) < 0, then f has a local maximum a…
First Derivative Test
Use to find extrema ... (1) Find first derivative ... (2) Set equal…
Definition of Concavity
The graph of a differentiable function y = f(x) is ... a) concav…
9 termscreated on December 8, 2016
limits and continuity
lim(f(x)±g(x))=?
lim(f(x)∙g(x))=?
lim (f(x)/g(x))=?
lim as x→0 of sin(x)÷x=?
lim f(x)± lim g(x)
lim f(x)× lim g(x)
lim f(x)÷ lim g(x), if lim g(x)≠0
1
lim(f(x)±g(x))=?
lim f(x)± lim g(x)
lim(f(x)∙g(x))=?
lim f(x)× lim g(x)
156 termscreated on December 8, 2016
ap euro unit 4: the scientific revolution and the enlightenment
**Ptolemy
Geocentric Model
Copernicus
On the Revolution of the Heavenly Sphe…
supported geocentric model, aka Ptolematic Model
the theory that the Earth was the stationary center of the un…
heliocentric model... On the Revolution of the Heavenly Spheres
Copernicus... proposed heliocentric model... published on his death…
**Ptolemy
supported geocentric model, aka Ptolematic Model
Geocentric Model
the theory that the Earth was the stationary center of the un…
14 termscreated on December 8, 2016
AP Calc BC Chapter 5
Trapezoid Riemann Sum
Fundamental Theorem of Calculus 1 (FTC…
Fundamental Theorem of Calculus 2 (FTC…
Fundamental Theorem of Calculus 2 (FTC…
Tn = ∆x[.5f(x1) + f(x2) + ... + f(xn-1) + .5f(xn)]... (Average o…
See part one and use chain rule
Trapezoid Riemann Sum
Tn = ∆x[.5f(x1) + f(x2) + ... + f(xn-1) + .5f(xn)]... (Average o…
Fundamental Theorem of Calculus 1 (FTC…
16 termscreated on December 8, 2016
FINAL
lim x→±∞ (f(x)/g(x)) = 0 if....
lim x→±∞ (f(x)/g(x)) = ∞ if...
lim x→±∞ (f(x)/g(x)) = ratio of coeffi…
Mean Value Theorem
degree of g(x) > degree of f(x)
degree of f(x) > degree of g(x)
degree of f(x) = degree of g(x)
If f is continuous on [a,b] and differentiable on (a,b), then…
lim x→±∞ (f(x)/g(x)) = 0 if....
degree of g(x) > degree of f(x)
lim x→±∞ (f(x)/g(x)) = ∞ if...
degree of f(x) > degree of g(x)
16 termscreated on December 7, 2016
AP Calculus Semester 1 ** SR
right triangles with natural number le…
(f * g)(x) =
if -x for x results in an equivalent e…
if -y for y results in an equivalent e…
3-4-5, 5-12-13, 8-15-17, 7-24-25
f(g(x))
is symmetric about the y axis
is symmetric about the x axis
right triangles with natural number le…
3-4-5, 5-12-13, 8-15-17, 7-24-25
(f * g)(x) =
f(g(x))
69 termscreated on December 7, 2016
AP Calculus Semester 1 * SR
45-45-90 triangle sides
30-60-90 triangle sides
key idea for a function
domain informal
x:x:xroot2
x:xroot3:2x
for every x there is one and only one corresponding y
allowable in
45-45-90 triangle sides
x:x:xroot2
30-60-90 triangle sides
x:xroot3:2x
12 termscreated on December 7, 2016
Limit Properties, Limits Properties and Continuty
Sum/Difference of limits ... [lim f(x) ±…
Scalar multiplication ... [lim a*f(x)]
Product of limits... [lim f(x) * lim g(x)]
Quotient of limits... [lim f(x) ÷ lim g(x…
limit of the sums/difference ... [lim (f(x) ± g(x))]
a*lim f(x)
limit of products... lim [f(x) * g(x)]
Limit of quotients... lim [f(x) ÷ g(x)]
Sum/Difference of limits ... [lim f(x) ±…
limit of the sums/difference ... [lim (f(x) ± g(x))]
Scalar multiplication ... [lim a*f(x)]
a*lim f(x)
7 termscreated on December 7, 2016
Differentiation
definition of derivative
three places where functions are not d…
if f is differentiable at x=c,
Implicit differentiation
f'(x) = lim as h->0 of [f(x+h) - f(x)]/h
1. discontinuities... 2. sharp turn... 3. vertical tangent
then f is continuous at x=c
used when y cannot be written explicitly as a function of x
definition of derivative
f'(x) = lim as h->0 of [f(x+h) - f(x)]/h
three places where functions are not d…
1. discontinuities... 2. sharp turn... 3. vertical tangent
10 termscreated on December 7, 2016
important people (ap world history unit 4a)
aristotle/ ptolemy
copernicus
kepler
galileo
held that the earth was center of the universe (Geocentric th…
stated that the earth rotated on its axis around the sun (hel…
used math to prove planets orbit around sun
improved telescope, established experimentation set forth law…
aristotle/ ptolemy
held that the earth was center of the universe (Geocentric th…
copernicus
stated that the earth rotated on its axis around the sun (hel…
21 termscreated on December 7, 2016
2016 AP Calculus BC Midterm
Rolle's Theorem
Mean Value Theorem
Fundamental Theorem of Calculus
Second Fundamental Theorem of Calculus
Let f be continuous on [a,b] and differentiable on (a,b)... If…
If f is continuous on [a,b] and differentiable on (a,b), then…
Let f(x) be integrable (continuous) on [a,b] and let F(x) be…
Rolle's Theorem
Let f be continuous on [a,b] and differentiable on (a,b)... If…
Mean Value Theorem
If f is continuous on [a,b] and differentiable on (a,b), then…
36 termscreated on December 7, 2016
sociology chapter 13
education
hidden curriculum
schooling in capitalist america
schools
he process through which academic, social, and cultural ideas…
nonacademic and less over socialization functions of schoolin…
"the educational system...is best understood as an institutio…
help to reinforce and maintain inequalities found within the…
education
he process through which academic, social, and cultural ideas…
hidden curriculum
nonacademic and less over socialization functions of schoolin…
20 termscreated on December 7, 2016
AP Calculus BC Formulas
Mean Value Theorem
Derivative of sinx
Derivative of cosx
Derivative of tanx
If f(x) is continuous on interval [a,b] and *differentiable…
cosx
-sinx
sec^2x
Mean Value Theorem
If f(x) is continuous on interval [a,b] and *differentiable…
Derivative of sinx
cosx
11 termscreated on December 7, 2016
AP Calculus Chapter 4 Vocab
Extreme Value Theorem
Critical Number
Rolle's Theorem
Mean Value Theorem
If f is continuous on a closed interval [a,b], then f has bot…
x values of a function where f'=0 or f' is not defined. Relat…
If f is continuous on a closed interval [a,b] and differentia…
If f is continuous on a closed interval [a,b] and differentia…
Extreme Value Theorem
If f is continuous on a closed interval [a,b], then f has bot…
Critical Number
x values of a function where f'=0 or f' is not defined. Relat…
8 termscreated on December 7, 2016
AP calculus AB Chapter 3
Find where f'(x)=0 or undefined, sign…
Find where f'(x)=0 or undefined, sign…
Find where f''(x)=0 or undefined, sign…
Find where f''(x)=0 or undefined, sign…
Increasing intervals
Decreasing intervals
Concave up
Concave down
Find where f'(x)=0 or undefined, sign…
Increasing intervals
Find where f'(x)=0 or undefined, sign…
Decreasing intervals
16 termscreated on December 7, 2016
Derivatives
Sinx
Cosx
Tanx
Secx
Cosx
-Sinx
Sec^2x
SecxTanx
Sinx
Cosx
Cosx
-Sinx
22 termscreated on December 7, 2016
AP Calculus Differentiation Formulas
[k × u]' = where k is a real number, a…
[u ± v]' = where u and v are functions…
[u × v]' = where u and v are functions…
[u/v]' = where u and v are functions o…
k × u'
u' ± v'
(u)(v)' + (u)'(v)
(v)(u)' - (u)(v)' / (v)²
[k × u]' = where k is a real number, a…
k × u'
[u ± v]' = where u and v are functions…
u' ± v'
50 termscreated on December 6, 2016
AP European History Identifiors Chapter 16
'God's Handiwork"
"natural philosophers"
Alchemy and hermetic magic
Ptolemaic Universe
The world around them. Many educated Europeans were intereste…
medieval scientists that preferred refined logical analysis t…
Tradition believed that the world was a living embodiment of…
Universe seen as a series of concentric spheres with a fixed…
'God's Handiwork"
The world around them. Many educated Europeans were intereste…
"natural philosophers"
medieval scientists that preferred refined logical analysis t…
67 termscreated on December 6, 2016
AP Calculus AB Exam
Intermediate Value Theorem
Average Rate of Change
Instantenous Rate of Change
Formal definition of derivative
If f(1)=-4 and f(6)=9, then there must be a x-value between 1…
Slope of secant line between two points, use to estimate inst…
Slope of tangent line at a point, value of derivative at a po…
limit as h approaches 0 of [f(a+h)-f(a)]/h
Intermediate Value Theorem
If f(1)=-4 and f(6)=9, then there must be a x-value between 1…
Average Rate of Change
Slope of secant line between two points, use to estimate inst…
6 termscreated on December 6, 2016
3.1-3.3
Extreme Value Theorum
Rolle's Theorum
Mean Value Theorum
Critical Number
If f is continuous on a closed interval [a,b], then f has an…
Let f be continuous on the closed interval [a,b] and differen…
If f is continuous on the closed [a,b] and differentiable on…
Let f be defined at c. If f'(c)=0 or if f'(x) is not defined…
Extreme Value Theorum
If f is continuous on a closed interval [a,b], then f has an…
Rolle's Theorum
Let f be continuous on the closed interval [a,b] and differen…
7 termscreated on December 6, 2016
Area & Volume
Area between Curves (up and down)
Area between Curves (side to side)
Area between Curves (weave)
Volume
∫ upper - lower... integrate over "x"... - use "x" values as limit…
∫ right - left... integrate over "y"... - use "y" values as limits…
∫ | f(x) - g(x) |... integrate over "x" or "y", depending on ca…
V = ∫ Area of Cross Section
Area between Curves (up and down)
∫ upper - lower... integrate over "x"... - use "x" values as limit…
Area between Curves (side to side)
∫ right - left... integrate over "y"... - use "y" values as limits…
23 termscreated on December 6, 2016
Scientific Revolution
Copernicus
Kepler
Galileo
Newton
-started an idea of heliocentrism... -believed that earth's orbi…
-Three laws of planetary motion, on elliptical orbit, and two…
-Developed a new telescope... -Observed the moon and it's crater…
-(1643-1727)... -invented Calculus... -originated the theory of gra…
Copernicus
-started an idea of heliocentrism... -believed that earth's orbi…
Kepler
-Three laws of planetary motion, on elliptical orbit, and two…
29 termscreated on December 6, 2016
AP European History
Thirty Years War
States that centralized in 17th century
States that didn't centralize in 17th…
Absolute Monarchs of the 17th century
Bourbon kings of France vs surrounding Spanish and Austrian H…
England, France, Austria, Prussia, and Russia.
United netherlands, ottoman empire, poland, Sweden
Louis XIV of France "the sun king", Hohenzollern rulers in Br…
Thirty Years War
Bourbon kings of France vs surrounding Spanish and Austrian H…
States that centralized in 17th century
England, France, Austria, Prussia, and Russia.
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