# Advanced Placement Calculus AB by HC120704005715

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```									                 Advanced Placement Calculus AB
Syllabus

Course Description

Calculus AB is primarily concerned with developing the student's
understanding of the concepts of calculus and providing experience
with its methods and applications. The course will consist of a four
pronged approach to calculus. Concepts, results, and problems will be
expressed graphically, numerically, analytically, and using writing in
context. The connections among these representations also are
important are constantly related. Broad concepts and applicable
methods are emphasized. The focus of the course is neither
manipulation nor memorization of a predetermined list of functions,
curves, theorems, or problem types. Although students must deal with
manipulation and computational competence, they are not the sole
purpose of this course. Technology, in the form of a TI-84 calculator,
will be used throughout the course to reinforce the relationships
among the various representations of functions; f(x) to f ’(x) to f ’’(x),
to confirm written work, to encourage experimentation, and to assist
in interpreting results relating to slope, maxima/minima, and area
using tables, rectangular and trapezoidal approximations, and graphs.
Through the use of the calculator, students will become aware of
connections between derivatives, integrals, limits, approximations, and
applications with modeling. As a result, the course becomes a
connected whole rather than a collection of unrelated topics.

Text

Calculus: Graphical, Numerical, Algebraic by Finney, Demana, Waits,

Multiple-Choice & Free-Response Questions in Preparation for the AP
Calculus AB Examination by David Lederman and Lin McMullin, 2004,
D&S Marketing

Technology

All students either have or are supplied with TI-84 calculators. The
students have been using these calculators in Algebra II Honors, Pre-
calculus Honors, and in AP Calculus AB to interprete graphs, determine
limits, identify asymptotes, find maxima and minima points, and to
determine where a function is increasing, decreasing concave up or
down using graphs and tables.

Students will be tested approximately every 2 to 4 weeks. Each test
will consist of questions using a format that is similar to the AP Exam.
These questions will contain multiple choice questions that include
methodology questions, interpretation of graphs using calculators and
derivatives, numerical tables and their relationship to slope of a curve,
and essay questions from past exams that will include justification
using written statements to interpret what is happening
mathematically. Each test will consist of 4 components. Component 1
will be a timed multiple choice test of approximately 9-10 questions.
This component is non-calculator active. Component 2 will be a timed
multiple choice test of 5-6 questions. This component is calculator
active. Component 3 will consist of 1 essay question (show your work)
consisting of multiple parts that must be completed in 15 minutes.
This question will be calculator active. Component 4 will be 1 essay
question to be completed in 15 minutes. Calculators may not be used
on this question. Grading of the test will be completed in the following
manner: Components 1 and 2 will be combined. Students will earn
credit based upon right, wrong, and blank answers using the formula
(# correct - 1/4 # wrong) x 1.2 = points earned. Blank answers will
not count against the student. 2. Components 3 and 4 will be graded
based upon the student's work. Answers only will only earn the answer
point. Components 1 and 2 are worth 18 points and Components 3 and
4 are worth 9 points each for a total of 36 possible points on each test.

Grades are assigned in the following manner:

36 points----------100
31-35 points--------95
25-30 points--------93
19-24 points--------90
13-18 points--------83
7-12 points--------74
1-6 points--------65

Students may earn bonus points weekly on 10 minutes quizzes given
on Tuesday and Thursday. These points will be totaled at the end of
the nine weeks and divided into 5 zones. Zone 1 will earn 0 points.
Zone 2 will earn 1 point. Zone 3 will earn 2 points. Zone 4 will earn 3
points. Zone 5 will earn 4 points which will be added to the nine weeks
average. These quizzes cannot hurt the student’s grade, but they do
consist of questions that are AP formatted with regards to the multiple
choice form.

Each nine weeks average will be computed as a simple average. Each
semester average will be computed as 1st nine weeks times .4 plus
2nd nine weeks times .4 plus the exam grade. This total will then be
divided by 5 to obtain the semester average.

The grading scale for our District is as follows:

A     93-100
B     85-92
C     77-84
D     70-76
F     69 and below

due to AP calculus being considered an honors course.

Topics and Timeline for First Semester

Section     Topic                                             Timeline
1.1 – 1.3   Equations of lines; domain, range, and            1day
zeroes of functions; exponential growth
and decay functions; parametric forms
1.4-1.6     Continuity; vertical and horizontal               1day
Asymptotes (calculator activity)
2.1         Average/instantaneous rate of change;             3 days
Definition of limit; Properties of limits;
Left/Right-hand limits; Sandwich Theorem
(calculator activity-analysis of functions)
2.2         Limits as x approaches form of infinity;          2 days
Limits of infinity; End behaviors
(calculator activity-table analysis of function
Behavior)
2.3         Continuity at a point; Continuous function;       2 days
Combinations/Composition of continuous
Functions; Intermediate Value Theorem
2.4         Average rate of change and slope; Equations       2 days
of tangent lines; Slope of a curve; Normal
lines to a curve; Speed
3.1         Definition of derivative; Notation; Connections   4 days
between graphs of f and f ’; Graph derivatives
from data and tables

Test Review                                             2 days

Test # 1   Covers all topics listed above                          2 days

3.2        Failure of f ’(x) to exist; Differentiability implies    2 days
linearity and continuity; Intermediate Value
Theorem for derivatives; Use calculator to find
derivatives and graph same
3.3        Rules for differentiation: positive integer              3 days
powers; Sums and differences; Products and
quotients; Negative integer powers; Higher
order derivatives
3.4        Instantaneous rate of change; velocity; motion           3 days
along a line; sensitivity to change; Applications
3.5        Derivatives of sine/cosine; Simple harmonic              2 days
motion; Jerk; Derivatives of tangent/cotangent
and Secant/Cosecant

Test Review                                              2 days

Test # 2   Derivatives of above, definition of derivative,     2 days
multiple derivatives, domain of a function,
velocity/acceleration, limits, reflections, zeroes,
equations of tangent/normal lines, parallel/
perpendicular lines, position, speed, jerk

3.6        Derivatives of composition; Repeated use of        5 days
chain rule; Slopes of parametric curves; Chain
rule with powers of functions
3.7        Implicit functions and their derivatives; Tangents 2 days
and normals; implicit derivatives of higher order;
rational powers and their derivatives
3.8        Derivatives of inverse trigonometric functions      2 days
3.9        Derivatives of all forms of exponential functions; 3 days
derivatives of all forms of logarithmic functions

Test Review                                               2 days

Test # 3   Derivatives of any type of function mentioned             2 days
above, zeroes of functions, multiple derivatives,
laws of logarithms, continuity, asymptotes,
equations of tangent/normal lines, derivatives
of composition, definition of derivative, odd/even
functions, vertical/horizontal tangents, slope of
a curve,

4.1        Absolute extreme values; Local extreme values; 2 days
finding extreme functional values
4.2        Mean Value Theorem; interpretation; increasing/ 2 days
decreasing functions
4.3        First derivative test for local extrema; concavity; 3 days
points of inflection; second derivative test for
local extrema; functions from derivatives

Test Review                                          2 days

Test # 4   Asymptotes, increasing/decreasing functions,          2 days
Concavity, maxima/minima, point of inflection,
Odd/even functions, behavior of tangent lines,
Equations of tangent lines, implicit differentiation,
Derivatives, limits, maxima/minima with justification,
Concavity/point of inflection with justification,
Sketch graph using first derivative information,
Use graph of first derivative to find maxima/minima
with written justification, use graph of first derivative to
find inflection points with written justification

4.4        Modeling and optimization Methodology; Business 5 days
and industry; Mathematics; Economics
4.5        Linearization; Newton’s method; Differentials;  5 days
L”Hopital’s Rule
Estimating change with derivatives; Absolute,
relative, and percent of change
4.6        Related rates; solution strategy                5 days

Test Review                                          2 days

Test # 5   Normal/tangent lines, related rates, derivatives, 2 days
Definition of derivative, limits, maxima/minima,
Evaluate derivatives, odd/even and symmetry,
Differentiability, zeroes of a function, Mean Value
Theorem for derivatives
First Semester Exam—covers all topics listed above; Split format: 28
questions-multiple choice without calculator and 17 questions-multiple
choice with calculator.

Topics and Timeline for Second Semester

Section                  Topic                             Timeline

5.1        Distance traveled; Rectangular Approximation       2   days
Left, right, and midpoint rectangular approx-
imation;
5.2        Summation notation; Reimann sums;                  2   days
Notation of integration; Definite integrals and
area; Constant functions; Integrals on calculator;
Discontinuous integrable functions
5.3        Properties of definite integrals; Average value    3   days
of a function; Mean Value Theorem for Definite
Integrals; Connecting Differential and Integral
Calculus
5.4        Forms of Fundamental Theorem of Integral           3   days
Calculus; Area connection; Applications
5.5        Trapezoid and Simpson’s approximations             2   days
6.1        Initial value, anti-derivatives and indefinite     2   days
integrals, properties of indefinite integrals,
slope-fields
6.2        Integration by substitution, change of limit,      2   days
separation of variables for differential equations

Test review                                       2 days

Test # 6   Symbolic differentiation, First Fundamental Th. 2 days
of Integral Calculus, definite integrals, properties of
integrals, definition of derivative, integrals with
absolute value, Fundamental Theorem of Integral
Calculus (alternative version), integration with unknown
limits, max/min, symmetry, inverses, area between
curves, equations of tangent lines, points of inflection
with justification

6.3        Integration by parts, repeated use, solve unknown 2 days
integrals
6.4        Solve exponential change using separation of        3 days
variables
6.5        Exponential and logistics growth models; Partial    2 days
fractions
6.6        Euler’s method                                      2 days

Test review                                         2 days

Test # 7   Definite integrals, derivatives, integrals with      2 days
unknown limits, derivatives and distance using
graphs, tangent or normal lines, functions from
graphs, increasing or decreasing functions,
concavity, Fundamental Theorem of Integral
Calculus, area under curve, definition of derivative
and continuity, Mean Value Theorem for
derivatives, Maxima and minima with analysis,
roots and average value of a function, initial
conditions problem, velocity

7.1        Linear motion, net change from data, work          3 days
7.2        Area between curves, boundaries with               3 days
changing functions, integration with respect
to y
7.3        Volumes of solids: disc, washer, and shell;        6 days
known cross-sections and volume
7.4        Length of smooth curves, vertical tangents,        3 days
corners, and cusps

Test Review                                        2 days

Test # 8   Concavity, indefinite integrals, tangent lines,    2 days
approximation of zeroes, limits from graphs,
definite integrals, relative extrema, derivatives,
initial conditions problems, area using properties
of integrals, area between curves, volume of
known cross-sectional area, integration by
parts, Intermediate Value Theorem, instantaneous
and average velocity, total distance traveled,
area between curves, length of a curve

Review for AP exam Practice problems in exam format. 20-25 days
Students will initially work in groups of 2-3.
Practice problems will be worked in class in an
exam format. Students will consult with each
other or the teacher to address specific difficulties.
After 10 class days, the students will work
individually on practice tests under a time format
that conforms to AP guidelines. After each
specific problems.

Practice AP exam Previous AP multiple-choice exam and last 1 day
year’s essay exam will be given following exam
time and form requirements

Final Review Students will discuss the practice exam or any     5 days
specific topics they feel are necessary to help them
achieve their desired score on the exam

Total days                                                       162 days

AP Exam

Last days of class Review of essay exam and preparation 14 days
for BC calculus

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