Name: , ' AP Calculus AB
Unit 6 eview March 2017
Multiple Choice:
1. Ify=ex2,then dzf=? ([19, 513K I O2Xx d-DEX PfLWCT 2; I
.3 dx 11*
- l x 4X x (A K
; e" -= Rx- L? 91%: aea X i
W = 6" cfw_gl'k' )
A) (2x)l(x: 1)e"2"2 3) 2399"2 C) (2 + 2x)ex2 .- I
-x'>
AP Calculus AB
:1;
Final xamReview Multiple Choice N0 CALCULATOR April 2017
The graph of a function, f , which consists of two line segments and a semi-circle is pictured below. Let
2x , "z (:2
G(x) = x2 + I f (t) dt . Use this information to answer quest
,fl.
AP CALCULUS AB Name: g g Q
Unit-6 Day 1 Notes
Derivatives involving the Natural Log y =1nx
We have examined derivatives using the power rule, product rule, quotient rule, and trig. But what about
the derivative of y = In x? Let's see how your calcu
AP CALCULUS AB
Unit 6 Day 5 Notes
Differential Equations
A differential equation is a mathematical equation that relates a function to its derivatives. It may contain
first and/or higher order derivatives. There are whole courses at the college level on
AP CALCULUS AB Name: Q 2 f a?
Unit 6 Day 4 Notes
Derivatives of the Natural Exponential y = e
[ex] = e" and if u is a differentiable function of x, then %[e"] = 3" = u 'e" by the chain rule.
1
dx
dx
, " *titThe-natural exponential function is the only f
AP CALCULUS AB Name: KY7,ch
Unit 7 Day 1 Notes
Average Value Theorem
Given f(x) is a continuous function, either an algebraic formula or a graph, overthe interval [(1,1)].
The average value of the function is the average height of the yvalue of f(x).
AP- CALCULUS AB Name: /- '24)
Unit 6 Day 2 Notes
Sgecial Integration Formulas
Find the followin antiderivatives:
2) I2x x2+3 dx ) ' 4) I3x2 sin(2gc3) dx
The derivative rule we just learned will now produce the following integration rule:
jidx = 1n
.- . 2
AP CALCULUS AB Name: L
Unit 6 Day 7 Notes
Derivative of the Inverse
. . . . . d h
In this section, we are concerned with findmg the derivatlve of the mverse to a function: El: f '(x)].
Remember from algebra, if f (x) and g(x) are inverse function
J
" AP CALCULUS AB Name: l 42
Unit 7 Day 2 Notes
Area Between Two Curves
Consider two continuous functions f and g with f (x) 2 g(x) throughout [(1, b] .
Thearea between the curves y = f (x) and y = g(x) from a to b is defined as A =J. (f (x) g(x) dx.
T
AP CALCULUS AB Name: 5 24
Unit 6 Day 3 Notes
S ecial Inte ation Formulas
There are more. various ways of solving integration problems in Calculus. Let's practice with a few more examples.
Jada; de
"afda + a Srh"(l;,)+c,
:%()Ui-+ 2.Slr\(%;)1.c_.
1 r 3
Name: AP Calculus AB
Unit 5 Review Days 1-3 January 2017
=x%x+n
( 1)13,fhen on which interval(s)' 15 the continuous function f (x )1 increasing?
x _
2. Given f(x) =sin 2x on the open interval (0 E), consider the following statements:
cfw_09 43/1325;
M
AP CALCULUS AB Name: gig
Unit 7 Day 3 Notes
Volume by Disks and Washers
The Disk Formulas:
. b . d
If the slices are perpendicular to the xaxis: V = III R2 dx If the slices are perpendicular to the y-axis: V = 71:]. R2 dy
(Le. the height of the cylinder
AP CALCULUS AB Name: #
Unit '7 Day 4 Notes (Last Concept!)
Volume by Known Cross Sections
If the slices are gergendicular to the x-axis:
Base = f(x) g (x)
Area = [f-(x) g (x)]
Volmm=k'-f[f(x)g(x):r dx
If the slices are gergendicular to the z-a
cfw_-
AP CALCULUS AB Name: #-
Unit 6 Day 6 Notes
Slope Fields
A slope field (also called vector fields or direction fields) are a tool to graphically obtain the solutions to a
rst order differential equation. A slope field is a graphic representation of t
4-
Name: AP Calculus AB
4
Unit ' 'eview March 2017
Multi -le Choice:
1. What is theErEI [of the region in the first quadrant bounded by the graph of y= I23 and the line A: = 2?
'3 i . a? M 07 6X0 - =25 33:de
. y [I (goal ., 0% 0.2 I 3-
(144:.CQJIQ
2.
Name 91 2F)
Calculus: nit 5 Sudoku
Complete the problems on the back side. Enter the numbers into the puzzle corresponding to
answers of the lettered problems. Then, complete the Sudoku puzzle using the following:
You must ll each row, colunrm; and 3 x 3
More Unit 7 Review Name: 63
1. The/Golng bf the solid obtained by revolving the region enclosed by the top half of the ellipse iven by
l 3
y: 9~9x2 ,aboutthexaxisis sza (lla q 2 -01) Gay V; H _3 (tic; BLQX
i [77 o
71: 4 IT '-~ 1
(a) I (b) 71: (c
Name cfw_E ;_
Calculus: Unit 1 Sudoku
Complete the problems on the back side. Enter the numbers into the puzzle corresponding to
answers of the lettered problems. Then, complete the Sudoku puzzle using the following:
You must ll each row, column, and 3 x
Chapter 3: Nature
and Nurture of
Behavior
Genetic Ingredients
Chromosomes
threadlike
structures made of DNA that
contain the genes
Total of 4623 from Mom, 23 from Dad.
DNA (deoxyribonucleic acid)
complex molecule containing the genetic
information that
Chapter 8 pt. 1: Learning
and Classical Conditioning
How Do We Learn?
Learning
is defined as a relatively
permanent change in an organisms
behavior due to experience (nurture).
Most learning is associative
learning: learning that certain
events occur toge
Chapter 16 pt. 3: Personality and
Somatic Disorders
Personality Disorders are a
diagnostic category which
describes inflexible behavior
patterns that impair social
relationships and functioning.
Personality Disorders are
Organized Into 3 Clusters:
1. Clus
Chapter 18 pt. 2: The
Psychology of Persuasion,
Attitudes, and Prosocial
Behavior
Bump or Jump Illustrates:
Social
Trap: a situation in which
the conflicting parties, by each
rationally pursuing their self-interest
gets caught in mutually destructive
beh
Chapter 1: Thinking Critically
With Psychological Science
Lets Make A Deal!
One
Volunteer is
Needed for A
chance to
win
1,334,499
Turkish
dollars!
Lets Make A Deal Shows Us
That:
Human Intuition
is highly limited.
Critically
thinking rarely comes easily
t
Chapter 1 pt. 2: Experimental
Thinking, Statistics, and Ethics
Human Errors in Thinking
Continued
Since
humans are
always trying to
make sense of the
world, we often make
a thinking error by
perceiving order in
random events.
We do this because
random s
Chapter 6: Perception
Another Color Context
Illusion
Pinnas Scintillating Lustre
Illusion
Backmasking Controversy
In the 1980s there was a great
controversy over backmasking:
the insertion of secret messages
into songs when played
backwards.
Lets see if t
Chapter 10 Thinking and
Language: Cognition, Problem
Solving, and Causes of
Irrationality
Chapter 10s Focus: The
Cognitive Perspective
Cognition
refers to mental
activities associated with
processing, interpreting,
understanding, and
communicating informa
Chapter 8 pt. 1: Learning
and Classical Conditioning
How Do We Learn?
Learning
is defined as a relatively
permanent change in an organisms
behavior due to experience (nurture).
Most learning is associative
learning: learning that certain
events occur toge
Chapter 4 pt. 2:
Developmental Psychology
Counterpart to Piaget: Lev
Vygotsky
Like Piaget, Vygotsky
was
also a cognitive psychologist.
Debate between continuity
vs. discontinuity:
Vygotsky represents
continuity school of
thought since he thought
cogniti
Chapter 13 pt. 2: Physiology
of Emotion, Detecting Lies,
and Experiencing Emotion
The Physical Arousal of
Emotion is Controlled by
The Autonomic Nervous
System
It is very difficult to differentiate the
physical arousal associated with many
emotions (hurt