Course Objectives AP Calculus AB Mr. Geiswhite
Prerequisite: Successful completion of Honors Precalculus and teacher recommendation.
Primary Textbook: Calculus of a Single Variable, AP Edition, Ninth Edition; Larson, Edwards
Supplemental Textbooks: Applied Calculus, Third Edition; HughesHallett, Gleason, Lock, Flath, et al. Calculus, Graphical, Numerical, Algebraic, AP Edition, Fifth Edition; Finney, Demana, Waits, Kennedy, Bressoud Calculus Concepts, Third Edition; Latorre, Kenelly, Fetta Reed, Harris, Carpenter
Course Overview: This advanced placement course consists of a full academic year of work in calculus and related topics comparable to courses in colleges and universities. This course begins with integral calculus and works through topics tested on the AP Calculus AB exam. I will be focusing on you being able to represent data graphically, numerically, algebraically, and in written form. Colleges may grant advanced placement and credit upon completion of the course and the Advanced Placement Examination taken in May. Students are expected to take the AP Calculus examination. (May 15, 2018)
Course Grading:  Pass/Fail Tests: Given at the beginning of the quarter. Worth 10% of your quarter grade. 15 multiple choice questions; you may retake the same test twice.
 Manic Monday: Every other Monday you will have the option of 5 multiple choice AP Problems or 1 Free Response. Each assignment is worth 10 points.
 Homework: I will collect approximately 5 per quarter with notice. I will grade 5 problems worth 3 points each. Due before the late bell rings or it’s worth half credit.
 Quizzes: You will have quizzes throughout the quarter worth approximately 30 points each.
 Tests: You will have a test at the end of each chapter/unit, approximately 3 per quarter. You can do corrections in my room before or after school. You may retake a test within three days of me returning your test.
 Free Response: Free Response questions will be part of each test. Some will be part of the inclass test and some will be homework assignments. FRQs assigned for homework will be due the next day before the late bell or it’s worth half credit.
Topics Covered and General Pacing Guide: This is a guide and days may be added or removed as I see fit throughout the year. My goal is to be finished the first week of April so we will have 34 weeks of AP review. I will have an AP review day on April 21, 2018 where we will take a fulllength AP Calculus Exam.
Chapter P: Preparation for Calculus (2 weeks) We will cover the following topics as needed after the Summer Review Packet Test. Graphs and Models Sketch the graph of an equation Find the intercepts of a graph Test a graph for symmetry with respect to an axis and the origin Find the points of intersection of two graphs Linear Models and Rates of Change Find the slope of a line passing through two points Write the equation of a line with a given point and slope Interpret slope as a ratio or as a rate Sketch the graph of a linear equation in slopeintercept form Write equations of lines that are parallel or perpendicular to a given line Functions and Their Graphs Use function notation to represent and evaluate a function Find the domain and range of a function Sketch the graph of a function Identify different types of transformations of functions Classify functions and recognize combinations of functions Trigonometric Functions, Identities, and Values Evaluate trigonometric values Solve trigonometric equations Simplify trigonometric expressions using identities Sketch the graph of trigonometric functions
Chapter 1: Limits and Their Properties (2 weeks) Finding Limits Graphically and Numerically Estimate a limit using a numerical or graphical approach Learn different ways that a limit can fail to exist Study and use a formal definition of limit Evaluating Limits Analytically Evaluate a limit using properties of limits Develop and use a strategy for finding limits Evaluate a limit using dividing out and rationalizing techniques Evaluate a limit using the Squeeze Theorem Continuity and OneSided Limits Determine continuity at a point and on an open interval Determine onesided limits and continuity on a closed interval Use properties of continuity Understand and use the Intermediate Value Theorem Infinite Limits Determine infinite limits from the left and from the right Find and sketch the vertical asymptotes of the graph of a function
Limits at Infinity Determine (finite) limits at infinity Determine the horizontal asymptotes, if any, of the graph of a function Determine infinite limits at infinity
Chapter 2: Differentiation (4 weeks) The Derivative and the Tangent Line Problem Find the slope of the tangent line to a curve at a point Use the limit definition to find the derivative of a function Understand the relationship between differentiability and continuity Basic Differentiation Rules and Rates of Change Find the derivative of a function using the Constant Rule Find the derivative of a function using the Power Rule Find the derivative of a function using the Constant Multiple Rule Find the derivative of a function using the Sum and Difference Rules Find the derivatives of the sine function and of the cosine function Use derivatives to find rates of change Product and Quotient Rules and HigherOrder Derivatives Find the derivative of a function using the Product Rule Find the derivative of a function using the Quotient Rule Find the derivative of a trigonometric function Find a higherorder derivative of a function The Chain Rule Find the derivative of a composite function using the Chain Rule Find the derivative of a function using the General Power Rule Simplify the derivative of a function using algebra Find the derivative of a trigonometric function using the Chain Rule Implicit Differentiation Distinguish between functions written in implicit form and explicit form Use implicit differentiation to find the derivative of a function Related Rates Find a related rate Use related rates to solve reallife problems
Chapter 3: Applications of Differentiation (5 weeks) Sketching Derivative Graphs Sketch a derivative graph from an original graph Sketch an original graph from a derivative graph Sketch a second Derivative given an original graph Extrema on an Interval Understand the definition of extrema of a function on an interval Understand the definition of relative extrema of a function on an open interval Find extrema on a closed interval Rolle’s Theorem and the Mean Value Theorem Understand and use Rolle’s Theorem Understand and use the Mean Value Theorem Increasing and Decreasing Functions and the First Derivative Test Determine intervals on which a function is increasing or decreasing Apply the First Derivative Test to find relative extrema of a function Concavity and the Second Derivative Test Determine intervals on which a function is concave upward or concave downward Find any points of inflection of the graph of a function Apply the Second Derivative Test to find relative extrema of a function
A Summary of Curve Sketching Analyze and Sketch the graph of a function Optimization Problems Solve applied minimum and maximum problems Differentials Understand the concept of a tangent line approximation Compare the value of the differential, dy, with the actual change in y, Estimate a propagated error using a differential Find the differential of a function using differentiation formulas
Chapter 4: Integrals (4 weeks) Antiderivatives and Indefinite Integration Write the general solution of a differential equation Use indefinite integral notation for antiderivatives Use basic integration rules to find antiderivatives Find a particular solution of a differential equation Area Use sigma notation to write and evaluate a sum Understand the concept of area Approximate the area of a plane region Find the area of a plane region using limits Riemann Sums and Definite Integrals Understand the definition of a Riemann sum Evaluate a definite integral using limits Evaluate a definite integral using properties of definite integrals The Fundamental Theorem of Calculus Evaluate a definite integral using the Fundamental Theorem of Calculus Understand and use the Mean Value Theorem for Integrals Find the average value of a function over a closed interval Understand and use the Second Fundamental Theorem of Calculus Understand and use the Net Change Theorem Integration by Substitution Use pattern recognition to find an indefinite integral Use a change of variables to find an indefinite integral Use the General Power Rule for Integration to find an indefinite integral Use a change of variables to evaluate a definite integral Evaluate a definite integral involving an even or odd function Numerical Integration Approximate a definite integral using the Trapezoidal Rule Approximate a definite integral using Simpson’s Rule Analyze the approximate errors in the Trapezoidal Rule and Simpson’s Rule
Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions (4 weeks) The Natural Logarithmic Function: Differentiation Develop and use properties of the natural logarithmic function Understand the definition of the number e Find derivatives of functions involving the natural logarithmic function
The Natural Logarithmic Function: Integration Use the Log Rule for Integration to integrate a rational function Integrate trigonometric functions Inverse Functions Verify that one function is the inverse function of another function Determine whether a function has an inverse function Find the derivative of an inverse function Exponential Functions: Differentiation and Integration Develop properties of the natural exponential function Differentiate natural exponential functions Integrate natural exponential functions Bases Other Than e and Applications Define exponential functions that have bases other than e Differentiate and integrate exponential functions that have bases other than e Use exponential functions to model compound interest and exponential growth Inverse Trigonometric Functions: Differentiation Develop properties of the six inverse trigonometric functions Differentiate an inverse trigonometric function Review the basic differentiation rules for elementary functions Inverse Trigonometric Functions: Integration Integrate functions whose antiderivatives involve inverse trigonometric functions Use the method of completing the square to integrate a function Review the basic integration rules involving elementary functions.
Chapter 6: Differential Equations (2 weeks) Slope Fields Use initial conditions to find particular solutions of differential equations Use slope fields to approximate solutions of differential equations Differential Equation: Growth and Decay Use separation of variables to solve a simple differential equation Use exponential functions to model growth and decay in applied problems Separation of Variables and the Logistic Equation Recognize and solve differential equations that can be solved by separation of variables Recognize and solve homogeneous differential equations Use differential equations to model and solve applied problems Solve and analyze logistic differential equations
Chapter 7: Application of Integration (3 weeks) Area of a Region Between Two Curves Find the area of a region between two curves using integration Find the area of a region between intersecting curves using integration Describe integration as an accumulation process Volume: The Disk Method Find the volume of a solid of revolution using the disk method Find the volume of a solid of revolution using the washer method Find the volume of a solid with known cross sections
Chapter 8: Integration Techniques and L’Hopital’s Rule Basic Integration Rules Review procedures for fitting an integrand to one of the basic integration rules Integration by Parts Find an antiderivative using integration by parts Use a tabular method to perform integration by parts L’Hopital’s Rule Recognize limits that produce indeterminate forms Apply L’Hopital’s Rule to evaluate a limit
AP Exam Review (34 weeks) Full AP Calculus Exam April 21, 2018
Final Exam Any student who does not take the AP Calculus Exam will be required to take a written final exam. All students who take the AP Calculus Exam will complete a project for their final.
Technology You will need to know how to use a graphing calculator in order to complete some problems on the AP Exam. Every test you take in class will have a calculator and a noncalculator section as well as a Free Response question. The format is similar to the AP Exam so you are familiar with the setup. If you do not have a graphing calculator one will be issued to you for the year. I will be using TISmartView software to demonstrate how to use the graphing calculators.
