AP Calculus AB Syllabus



Boise State University-Rocky Mountain High School

Concurrent Enrollment Program

Math 170: Calculus 1 (4 Credits)

2016-2017 School Year

Mr. Dan Drlik

drlik.daniel@

208-350-4340 x 1127

Course Overview

I cover everything in the Calculus AB topic outline. My main objective is to enable students to appreciate the simplicity and power of calculus and receive a strong foundation in mathematics. I try to improve my students’ critical thinking skills that will allow them to make the necessary connections needed to be successful on the AP exam. Students know they will work much harder than in any previous math class, but as a result, will gain a tremendous amount of knowledge.

Disciplinary Lens

Math 170: Calculus I satisfies four credits of the Foundation Program's Disciplinary Lens-Mathematics (DL-M) requirement. It supports the following University Learning Outcomes, along with a variety of other course-specific goals.

7. Apply knowledge and the methods of reasoning characteristic of mathematics, statistics, and other formal systems to solve complex problems.

Math 170: Calculus I is designed to introduce students to the principles, techniques and applications of derivatives and integrals. This course helps to achieve the goals of the Foundations program by focusing on the following course learning outcomes. After successful completion of this course, you will be able to:

• Recognize and illustrate the geometric relationships between the derivative and integral of a function and the graph of the function, and relate this geometric information to solutions derived through formulas.

• Identify the relevant data contained in problems presented in verbal, tabular and/or graphical formats.

• Present solutions clearly in logical and mathematically correct terms.

• Formulate and implement solution strategies for problems drawn from the sciences and engineering, and draw meaningful conclusions from the resulting answers.

• Recognize that the derivative is a rate of change, and be able to apply this insight to analyze and solve problems.

• Recognize that the integral can be approximated by finite sums, and be able to apply this insight to analyze and solve problems.

Course Planner

Below is the sequence of the AP Calculus AB course.

Limits and Their Properties

❖ A Preview of Calculus

❖ Finding Limits Graphically and Numerically

❖ Evaluating Limits Analytically

❖ Continuity and One-Sided Limits

❖ Infinite Limits

Differentiation

❖ The Derivative and the Tangent Line Problem

❖ Basic Differentiation Rules and Rates of Change

❖ The Product and Quotient Rules and Higher-Order Derivatives

❖ The Chain Rule

❖ Implicit Differentiation

❖ Related Rates

Students will be shown how to use their calculator to evaluate a derivative at a given point. They will then practice using their calculators to answer several AP exam questions.

Applications of Differentiation

❖ Extrema on an Interval

❖ Rolle’s Theorem and the Mean Value Theorem

❖ Increasing and Decreasing Functions and the First Derivative Test

❖ Concavity and the Second Derivative Test

❖ Limits at Infinity

❖ A Summary of Curve Sketching

❖ Optimization Problems

❖ Newton’s Method

Integration

❖ Antiderivatives and Indefinite Integration

❖ Area

❖ Riemann Sums and Definite Integrals

❖ The Fundamental Theorem of Calculus

❖ Integration by Substitution

❖ Numerical Integration

Students will be shown how to use their calculators to evaluate definite integrals. We will discuss various uses of the Fundamental Theorem of Calculus and work several AP exam problems.

Logarithmic, Exponential and other Transcendental Functions

❖ The Natural Logarithmic Function: Differentiation

❖ The Natural Logarithmic Function: Integration

❖ Inverse Functions

❖ Exponential Functions: Differentiation and Integration

❖ Bases other than e and Applications

❖ Inverse Trigonometric Functions: Differentiation

❖ Inverse Trigonometric Functions: Integration

Differential Equations

❖ Slope Fields and Euler’s Method

❖ Differential Equations: Growth and Decay

❖ Separation of Variables and the Logistic Equation

Applications of Integration

❖ Area of a Region Between Two Curves

❖ Volume: The Disk Method

❖ Volume: The Shell Method

❖ Arc Length and Surfaces of Revolution

❖ Work

❖ Fluid Pressure and Fluid Force

Integration Techniques

❖ Integration by Parts

❖ Trigonometric Integrals

❖ Trigonometric Substitution

❖ Partial Fraction Decomposition

❖ L’Hopital’s Rule

❖ Improper Integrals

Preparation for the AP Exam

In preparing for the AP Exam, I will do various activities. One of the activities we work on the most is having my students explain the calculus concepts and justify their solutions. This is done both orally and in written sentences. We will discuss various concepts as a class and I will call on individual students to give reasons or explanations for the answers. They will then be given assignments that they can work on individually or as groups that require them to write their justifications of the answers in complete sentences. This way I know they not only understand how to get the answers but that they can back up those answers with correct justifications.

Primary Textbook and Tools

Larson, Hostetler, Edwards. Calculus of a Single Variable 8th ed. Boston: Houghton Mifflin Company 2006 ISB: 0-618-50304-8

The majority of my students use TI 83 and TI 84, with some TI 89

Calculator Ideas

Throughout the year, we will discuss how to use the graphing calculators to solve various types of problems. This includes: finding roots, sketching functions in certain windows, and approximating the derivative at a point and definite integrals using numerical methods. Students will also be asked to make connections between the graphs of functions and their analysis, and conclusions about the behavior of functions when using a graphing calculator.

Student Assessment

An exam is given after each topic listed above. Most exams have both a non-calculator and calculator section. This ensures that my students have the required calculator skills for the AP exam but at the same time must show proficiency in understanding the concepts without having to rely on the calculator.

Grades

The course grade will be determined by scores earned on homework, quizzes, projects, tests and the final exam. The weights for each are listed below:

Homework ………10% A……….>90%

Quizzes/Projects…20% B……….80-89%

Tests………….......50% C……….70-79%

Final………………20% D……….60-69%

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