Advanced Placement Calculus (AB)
Book: Calculus: Early Transcendentals by Anton, Bivens, and Davis (10th edition)
Objectives
Level
CHAPTER 0-FUNCTIONS
Students will be able to identify
the properties of elementary functions
and apply these to analytic geometry
-- Plotting points and lines
--Slope of a line
-- Sketching quadratic and cubic equations
-- Distance between points
-- Describing a line
point / slope form
slope / intercept form
two point form
standard form
-- Absolute value function
algebraically
geometrically
-- Functions and use functional notation
including domain and range
-- Zeros of a function
-- Sums, Differences, products, and quotients of
functions
-- Composite functions
-- Odd and Even functions
-- Inverse functions
-- Set and interval notation
-- Trigonometric and Inverse Trigonometric Functions
-- Radian measure
--Trigonometric identities
Quizzes
Use of Graphing Calculator
Test
L
-- Definition and computation of the limit of an algebraic
expression in one variable
-- Limit notation and calculations
-- Limits of sums, differences, products, and quotients
-- Limits of composite functions
-- Use of limits to analyze horizontal and vertical
asymptotes
-- Definition and determination of continuity at a point c
-- Determination of the domain for which a given
function is continuous
-- Removable and nonremovable discontinuity
Quizzes
Use of Graphing
Calculator
Test
Students will analyze the
Continuity of a function
(Sections 1.5-1.6 )
L
Page 1 of 4
Content Evaluation
R
Time: 0 days (reviewed on an as needed
basis throughout the year)
CHAPTER 1 -LIMITS & CONTINUITY
Students will be able to define and
use the concepts of limits
(Sections 1.1 - 1.3)
Content
Quizzes
Use of Graphing
Calculator
Test
Advanced Placement Calculus (AB)
Book: Calculus: Early Transcendentals by Anton, Bivens, and Davis (10th edition)
Objectives
CHAPTER 2 & 3 THE DERIVATIVE
Students will be able to use the
definition of the derivative and
the rules of differentiation.
Level
L
CHAPTER 3&4-DERIVATIVE APPLICATION
Students will be able to apply the
L
concept of derivatives to
curve sketching and modeling
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Content
Content Evaluation
-- Definition of the derivative of a function as a limit
(Section 2.1 - 2.2)
-- Use of the definition to compute the derivative
of various functions (Section 2.3)
-- Differentiability of a given function
-- Use of the derivative to find the slope of a tangent line
-- Derivatives of sums, differences,
products and quotients
-- Derivatives of a composite function
the “Chain Rule” (Section 2.6)
-- Derivative of an inverse function
(Section 3.3)
-- Recognition of a relation requiring implicit differentiation
(Section 3.1)
-- Computation of derivatives implicitly
-- Definition of “differential” (Section 3.5)
-- Derivatives in differential notation
-- Increment of a function
-- Logarithmic functions and their derivatives (Sections 3.2)
-- Exponential functions and their derivatives (Section 3.3)
-- Trigonometric functions and their derivatives (Section 2.5)
-- Inverse trigonometric functions and their derivatives
(Section 3.3)
-- Use of L’Hopital’s Rule to determine the limit of
an expression of indeterminate form (Sec 3.6)
Quizzes
graded assignments
Test
Use of Graphing
Calculator
-- Equation of Tangent and Normal Lines
-- Linear Approximation (Section 3.5)
-- Related Rates (Section 3.4)
--Average and Instantaneous Rates of Change
-- Curve analysis: including... (Sections 4.1-4.4)
vertical and horizontal asymptotes
intercepts
intervals of increase/decrease/ concavity
Quizzes
Use of Graphing
Calculator
graded assignments
Test
Advanced Placement Calculus (AB)
Book: Calculus: Early Transcendentals by Anton, Bivens, and Davis (10th edition)
Objectives
Level
Content
Content Evaluation
extrema (relative and absolute)
inflection points
points of nondifferentiability
-- Applied Extrema Problems (Section 4.5)
-- Rolle’s Theorem Section (4.8)
-- Mean Value Theorem (for derivatives)
-- The Intermediate Value Theorem
-- Newton’s Method (Section 4.7)
CHAPTER 5-INTEGRATION
Students will be able to use
Techniques of Integration
L
-- Integration of xa(power rule) (Section 5.2)
-- Integration using u substitution (Section 5.3)
-- Integration of Trigonometric Functions
Quizzes
graded assignments
Use of Graphing Calc.
Test
Students will be able to solve problems
using the indefinite integral
L
-- Definition and computation the indefinite integral
-- Initial Value Problems and the constant
of integration (Section 5.2)
-- Integrating separable differential equations (Section 8.2)
-- Rectilinear Motion-Derivative (Sec 4.6)
-- Rectilinear motion-Integral (Sec 5.7)
-- Euler’s method and Slope fields (Sec 8.3)
-- Exponential Growth/Decay (Sec 8.1)
-- Newtons Law of Cooling (Sec 8.1)
Quizzes
graded worksheets
Test
Students will be able to utilize
limits as a means of
determining the area under a curve
L
-- Estimation of the area under a curve using a finite number
of rectangles (left hand/ right hand) (Section 5.4)
-- Using limits, determining the exact area under a curve
(Section 5.5)
-- Estimation of the area using the trapezoidal and midpoint
2.10.11d
Quizzes
graded worksheets
Use of graphing calc.
L
-- The Fundamental Theorem of Calculus
(Section 5.6)
-- Functions defined by integration
--Integrals involving ln(x) and exp(x) (Section 5.10)
Quizzes
graded worksheets
Test
rules
Students will apply the Definite
Integral to analyze functions
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Advanced Placement Calculus (AB)
Book: Calculus: Early Transcendentals by Anton, Bivens, and Davis (10th edition)
Objectives
CHAPTER 6-APPLICATIONS OF
THE DEFINITE INTEGRAL
Students will apply the Definite
Integral to solve Practical Problems
Level
L
Content
-- Area under a curve (or between curves)
(Section 6.1)
-- Volumes of solids (Section 6.2)
of rotation around a horizontal of vertical axis
(Disk/Washer method)
formed by perpendicular slices to a given axis
-- Displacement and distance traveled in a specific
time interval (Section 5.7)
-- Average Value Problems (Section 5.8)
Content Evaluation
Quizzes
graded worksheets
Test
TOPICS TAUGHT AFTER THE AP EXAM
CHAPTER 7-PRINCIPALS OF
INTEGRAL EVALUATION
-- Volumes of solids (Section 6.3)
(Cylindrical Shell Method)
-- Integration by Parts (Section 7.2)
-- Integration by trig. substitution (Section 7.4)
ADDITIONAL ASSESSMENT: AP FREE RESPONSE QUESTIONS
Released AP Free Response Questions (FRQ) are assigned, solved, discussed and tested. Students work collaboratively both in class and out to solve the
problems. Students are then quizzed on selected problems. The quizzes are strictly graded according to the AP 9 point rubric.
ADDITIONAL ASSESSMENT: END OF THE YEAR REVIEW
In the weeks prior to the exam, students are assigned complete Multiple Choice and Free Response exams from previous years.
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