Calculus AB
2011-2012
Brief Description of Course
Ardmore High School Course Syllabus Subject: AP Calculus-AB
Unit 1 (Chapter P for review)
2 weeks
The learner will:
*review graphs and models
*review linear models and rates of change
*classify and graph elementary functions
*represent functions numerically, graphically, algebraically, and verbally
*transform functions by shifting, stretching, and reflecting
*analyze the differences in graphs
*fit models to data
*reinforce these concepts through calculator applications/explorations using the TI-83 or TI-84
Unit 2 (Chapter 1)
3 weeks
The learner will:
*pre-view calculus (1.1)
*find limits graphically and numerically (1.2)
*evaluate limits analytically (1.3)
*find continuity at a point and on an open interval (1.4)
*define and apply properties of continuity (1.4)
*find one-sided limits and continuity on a closed interval (1.4)
*apply graphical interpretations of continuity as in the Intermediate Value Theorem and Extreme
Value Theorem (1.4)
*define (and find if it exists) limits at infinity using horizontal asymptotes (section 3.5)
*define infinite limits and apply properties of infinite limits (1.5)
*define and find vertical asymptotes (1.5)
*reinforce these concepts through calculator applications/explorations using the TI-83 or TI-84
Unit 3 (Chapter 2)
4.5 weeks
The learner will:
*define the derivative as the limit of a difference quotient (2.1) *understand and relate the
concepts of
differentiability and continuity (2.1)
*find the derivative by the limit process (2.1)
*use the derivative to find the slope at a point (2.1)
*find the slope of a curve at a point and use it to write an equation of a tangent line if one exists
(2.1)
*define and apply differentiation rules for sums, products, quotients, and compositions involving
elementary functions (power, logorithmic, trigonometric and inverse trigonometric) of single
variable
calculus (2.2 through 2.4)
*interpret the derivative as the instantaneous rate of change (2.2)
*Differentiate implicitly defined functions (2.5)
*find related rates and solve problems involving related rates (2.6)((** at least 5 days))
*reinforce these concepts through calculator applications/explorations using the TI-83 or TI-84
Unit 4 (Chapter 3)
6 weeks
The learner will:
*define the Extreme Value Theorem and find absolute minimum and absolute maximum on a
closed
interval (3.1)
*find the derivative (if it exists) at given indicated extremum of a function (3.1)
*find critical numbers of given functions (3.1)
*locate absolute extrema of a function (if any exists) over indicated intervals(3.1)
*define and apply Rolle’s Theorem and The Mean Value Theorem (3.2)
*define increasing and decreasing functions (3.3)
*apply the first derivative test to find relative extrema (3.3)
*find intervals on which a function is increasing or decreasing using the test for increasing and
decreasing functions(3.3)
*define concavity (3.4)
*use the second derivative test to determine concavity (3.4)
*find points of inflection and relative extrema/discuss concavity (3.4)
*define (and find if it exists) limits at infinity using horizontal asymptotes (section 3.5)
*find corresponding relationships among graphs of f(x), f’(x), and f"(x) (3.6)
*optimize finding both absolute and relative extrema (3.7)
*use the tangent line as a linear approximation (3.9)
*find differentials using differentiation rules (3.9)
*reinforce these concepts through calculator applications/explorations using the TI-83 or TI-84
Unit 5 (Chapter 4)
5 weeks
The learner will:
*use basic properties of definite integrals (4.1)
*understand that integration is antidifferentiation (the basic premise of The Fundamental
Theorem of
Calculus) (4.1)
*find sums and use sigma notation to write a sum (4.2)
*use upper and lower sums to approximate the area of a region (4.2)
*find area by the limit definition (4.2)
*compute Riemann sums using left, right, and midpoint evaluation points (4.3)
*investigate upper and lower Riemann sums (4.3)
*recognize the definite integral as a limit of Riemann sums over equal subdivisions (4.3)
*evaluate definite integrals by the limit definition (4.3)
*use the Fundamental Theorem of Calculus to evaluate definite integrals (4.4)
*find antiderivatives using substitution, change of variables, and the general power rule for
integration(4.5)
*find antiderivatives of even and odd functions (4.5)
*use the Trapezoidal Rule to approximate definite integrals of functions represented
algebraically,
geometrically, and by tables of values (4.6)
*reinforce these concepts through calculator applications/explorations using the TI-83 or TI-84
Unit 6 (Chapter 5)
6 weeks
The learner will:
*define the Natural Logorithmic Functions and ’e’ (5.1)
*understand and apply logarithmic properties and Natural Logarithmic Function properties (5.1)
*graph logarithmic functions and state graph’s domain (5.1)
*find derivatives of logarithmic functions (5.1)
*use the Log Rule for integration (5.2)
*determine integrals involving trigonometric functions (5.2)
*verify inverse functions both algebraically and geometrically (5.3)
*evaluate the derivative of an inverse function (5.3)
*define The Natural Exponential Function (5.4)
*understand and use operations and properties of Exponential Functions (5.4)
*differentiate and integrate exponential functions (5.4)
*differentiate and integrate exponential functions with bases other than ’e’ (5.5)
*use separation of variables to solve differential equations (5.6)
*solve differential equations involving growth and decay (5.6)
*make applications using separation of variables to find general and particular solutions (5.7)
*solve homogeneous differential equaitons (5.7)
*use inverse trigonometric functions and differentiate (5.8)
*use inverse trigonometric functions and integrate (5.9)
*reinforce these concepts through calculator applications/explorations using the TI-83 or TI-84
Unit 7 (Chapter 6 and AP EXAM Review)
5.5 weeks
The learner will:
*find the area of a region between two curves and between two intersecting curves (6.1)
*find the volume using the Disc and Washer methods of solids (6.2)
*reinforce these concepts through calculator applications/explorations using the TI-83 or TI-84
*review several AP practice exams
Textbooks
Title:Calculas
Publisher: Mcdougal Littell/Houghton Mifflin
Published Date: 1998
Author: Roland E. Larson
Second Author: Robert P. Hostetler
Description:
Other Course Materials
Material Type: Graphing Calculator