Garden Grove Unified School District
AP Calculus AB Syllabus
La Quinta High School - Mr. Hall
Course Overview
Students of calculus will be involved in various learning activities such as lectures, computer labs, group
explorations, problem solving, and homework, to help them develop a conceptual and working knowledge of
calculus. They will show competence in the topics listed below covered by the College Board on the Advanced
Placement Test.
Grading Procedures
Marks are determined from exams (40%), quizzes (30%), homework / labs / activities (10%), and a final exam
(20%). Quizzes and homework collection will be used as warm-up activities. Tests and quizzes have been
designed to correlate with how well a student should perform on the AP examination in May. Over the past
several years nearly every student enrolled in AP calculus has taken the AP Calculus AB examination with pass
rates from 83% to 90%. Any student earning at least a C in the class has a high probability of earning a 3 or
better on the examination.
Instructional Materials
Calculus AP Edition, Briggs, Cochran, Gillett, 2014 by Pearson; Graphing Calculator TI-83, TI-89, or
equivalent; TI Graphing Calculator programs and online applets/CDF’s to demonstrate and explore Calculus
concepts.
Students Evaluation and Activities
Students will be engaged in activities, experiences, and/or projects that include:
• investigating functions, graphs, limits, derivatives and integrals (20 min car ride to investigate position,
velocity and speed).
• comparing functions represented graphically, numerically, analytically, and verbally and make the connections
among these representations.
• communicating mathematics and explaining solutions to problems both verbally as well written and presented
on white boards.
• using graphing calculators to help solve problems, experiment, interpret results, and support conclusions.
using symbolic manipulators such as Wolfram CDF player and Mathematica..
• various physics applications including friction fall, Snell’s law, simple harmonic motion, rectilinear motion
etc.
Additional Calculus Resources & Supplements
Helpful resources, links, and class materials can be found online at:
www.laquintahs.org --> staff & faculty --> Mr. Hall
www.classroom.google.com
Course Planner (outline of topics according to Briggs text, timing will be adjusted)
First Semester
Sections Topics
Ch 1
Functions Review
2.1
The Idea of Limits
2.2
Definitions of Limits
2.3
Techniques of Computing Limits
2.4
Infinite Limits
2.5
Limits at Infinity
2.6
2.7
Continuity
Precise definitions of Limits
3.1
3.2
3.3
3.4
Introducing the Derivative
Working with Derivatives
Rules of Differentiation
The Product and Quotient Rules
3.5
Derivatives of Trigonometric Functions
3.6
3.7
Derivatives as Rates of Change
The Chain Rule
3.8
Implicit Differentiation
3.9
3.10
3.11
Derivatives of Logarithmic and Exponential Functions
Derivatives of Inverse Trigonometric Functions
Related Rates
4.1
4.2
4.3
Maxima and Minima
What Derivatives Tell Us
Graphing Functions
4.4
Optimization Problems
4.5
Linear Approximation and Differentials
4.6
Mean Value Theorem
4.8
Newton’s Method
5.1
Antiderivatives
Second Semester
5.2
5.3
5.4
5.5
5.6
5.7
Approximating Areas under Curves
Definite Integrals
Fundamental Theorem of Calculus
Properties of Integrals and Average Value
Substitution Rule
Numerical Integration
6.1
Velocity and Net Change
8.1
Basic Ideas
8.2
Slope Fields (Euler’s Method - BC)
8.3
Separable Differential Equations
8.4
Exponential Models
6.2
Regions between Curves
6.3
Volume by Slicing, Disc and Washer Methods, Solids with known cross sections
4.7
L’Hopital’s Rule
AP
Several MC and FR AP exam problems from years past
Review
AP Exam Format
1) Multiple Choice: Part A (28 questions in 55 minutes) - calculators not allowed
2) Multiple Choice: Part B (17 questions in 50 minutes) - graphing calculators allowed
3) Free Response: Part A (2 problems in 30 minutes) - graphing calculators required
4) Free Response: Part B (4 problems in 60 minutes) – calculators not allowed
AP Exam Scoring
Multiple choice and free response sections are given equal weight.
Grade descriptions: 5 - Extremely well qualified 4 - Well qualified
3 – Qualified
2 - Possibly qualified
1 - No recommendation
After the AP Exam
Students work on a series of calculus related projects including, but not limited to, the following:
● Creation of tutorials using the Wolfram Language [In previous years students used java and visual basic
to generate a web based calculus tutorial similar to the college board’s APCD.]
● Calculator-based calculus applications
● Group problem solving and reporting
● Additional Integration Techniques (parts, partial fractions)
● Introduction into Multi-Variable Calculus through Dimensional Analogy
Topic Outline for Calculus AB
With the aid of technology, graphs of functions are often easy to produce. The emphasis is on the
interplay between the geometric and analytic information and on the use of calculus both to predict
and to explain the observed local and global behavior of a function. Limits of functions (including onesided limits) • An intuitive understanding of the limiting process. • Calculating limits using algebra. •
Estimating limits from graphs or tables of data. Asymptotic and unbounded behavior • Understanding
asymptotes in terms of graphical behavior.• Describing asymptotic behavior in terms of limits involving
infinity. • Comparing relative magnitudes of functions and their rates of change (for example,
contrasting exponential growth, polynomial growth, and logarithmic growth). Continuity as a property
of functions • An intuitive understanding of continuity. (The function values can be made as close as
desired by taking sufficiently close values of the domain.) • Understanding continuity in terms of limits.
• Geometric understanding of graphs of continuous functions (Intermediate Value Theorem and
Extreme Value Theorem). • Derivatives Concept of the derivative • Derivative presented graphically,
numerically, and analytically. • Derivative interpreted as an instantaneous rate of change. • Derivative
defined as the limit of the difference quotient. • Relationship between differentiability and continuity.
Derivative at a point • Slope of a curve at a point. Examples are emphasized, including points at
which there are vertical tangents and points at which there are no tangents. • Tangent line to a curve
at a point and local linear approximation. • Instantaneous rate of change as the limit of average rate of
change. • Approximate rate of change from graphs and tables of values. Derivative as a function •
Corresponding characteristics of graphs of ƒ and ƒ∙. • Relationship between the increasing and
decreasing behavior of ƒ and the sign of ƒ∙. • The Mean Value Theorem and its geometric
interpretation­. • Equations involving derivatives. Verbal descriptions are translated into equations
involving derivatives and vice versa. Second derivatives • Corresponding characteristics of the
graphs of ƒ, ƒ∙, and ƒ ∙. • Relationship between the concavity of ƒ and the sign of ƒ ∙. • Points of inflection
as places where concavity changes. Applications of derivatives • Analysis of curves, including the
notions of monotonicity and concavity. • Optimization, both absolute (global) and relative (local)
extrema. • Modeling rates of change, including related rates problems­. • Use of implicit differentiation
to find the derivative of an inverse function. • Interpretation of the derivative as a rate of change in
varied applied contexts, including velocity, speed, and acceleration. • Geometric interpretation of
differential equations via slope fields and the relationship between slope fields and solution curves for
differential equations. Computation of derivatives • Knowledge of derivatives of basic functions,
including power, exponential, logarithmic, trigonometric, and inverse trigonometric functions. •
Derivative rules for sums, products, and quotients of functions. • Chain rule and implicit differentiation.
III. Integrals Interpretations and properties of definite integrals • Definite integral as a limit of Riemann
sums. • Definite integral of the rate of change of a quantity over an interval interpreted as the change
of the quantity over the interval• Basic properties of definite integrals (examples include additivity and
linearity). Applications of integrals. Appropriate integrals are used in a variety of applications to model
physical, biological, or economic situations. Although only a sampling of applications can be included
in any specific course, students should be able to adapt their knowledge and techniques to solve
other similar application problems. Whatever applications are chosen, the emphasis is on using the
method of setting up an approximating Riemann sum and representing its limit as a definite integral.
To provide a common foundation, specific applications should include finding the area of a region, the
volume of a solid with known cross sections, the average value of a function, the distance traveled by
a particle along a line, and accumulated change from a rate of change. Fundamental Theorem of
Calculus • Use of the Fundamental Theorem to evaluate definite integrals. • Use of the Fundamental
Theorem to represent a particular antiderivative, and the analytical and graphical analysis of functions
so defined. Techniques of antidif ferentiation • Antiderivatives following directly from derivatives of
basic functions. • Antiderivatives by substitution of variables (including change of limits for definite
integrals). Applications of antidif ferentiation • Finding specific antiderivatives using initial conditions,
including applications to motion along a line. • Solving separable differential equations and using
them in modeling (including the study of the equation y∙ = ky and exponential growth). Numerical
approximations to definite integrals. Use of Riemann sums (using left, right, and midpoint evaluation
points) and trapezoidal sums to approximate definite integrals of functions represented algebraically,
graphically, and by tables of values.