**Welcome to Rio Hondo Prep’s AP Calculus AB Course**

This course will cover all the topics included in the *Calculus AB Course Description *as it appears on the AP Central website. The main objectives of this class are to prepare students for the Advanced Placement exam and for subsequent college courses in mathematics. You will probably find this course demanding, but hopefully you will also find it rewarding and even fun. Students will have the opportunity to learn through classroom, laboratory and real life experiences the importance of calculus in our everyday lives.

Larson, Hostetler and Edwards *Calculus: Early Transcendental Functions*: 4^{th} Edition. HoughtonMifflinCollege Publishing, 2007.

You must bring a pencil or pen, your Calculus book (with a book cover) and a TI-83 or better scientific calculator. Failure to bring these materials will result in an immediate demerit! You may bring a laptop, tablet, or iPad to help take notes. This is a PRIVILEGE not a right. Do not work on other class assignments during our class. *If you are using your device for anything other than the topic at hand you will no longer be allowed to use it for the remainder of the year.*

Students will be taught how to use the calculator to help solve problems, experiment, interpret results, and support conclusions. The graphing calculator will be needed for presentations, classwork, homework, and on some but not all tests. It is a requirement for parts of the Advanced Placement exam. We will use the calculator in a variety of ways including:

• Conduct explorations.

• Graph functions within arbitrary windows.

• Solve equations numerically.

• Analyze and interpret results.

• Justify and explain results of graphs and equations.

For a complete list of calculators approved by the College Board please visit: http://www.collegeboard.com/student/testing/ap/calculus_ab/calc.html?calcab

Tests will be given at the end of each chapter, about once every three weeks. Our test day is Thursdays, but may change depending on the schedule that week. You may retake two tests per semester. It will replace the original test score and it must be done before Finals Week.

Grades will be based on your homework, quizzes, tests, labs, projects and final. Here is a breakdown by percentages:

- Classwork & Homework – 15%
- Tests & Quizzes – 60%
- Final - 25%

- A 93-100
- A- 90-92
- B+ 87-89
- B 83-86
- B- 80-82
- C+ 77-79
- C 73-76
- C- 70-72
- D+ 67-69
- D 63-66
- D- 60-62
- F under 60

Students must pass Math Analysis with a B- or higher. If you have not met this requirement you must fill out a petition form from the school office.

##### Chapter 1 - Preparation for Calculus

##### Chapter 2 - Limits and Their Properties

##### Chapter 3 – Differentiation

##### Chapter 4 – Applications of Differentiation

##### Chapter 5 – Integration

##### Chapter 6 – Differential Equations

##### Chapter 7 – Applications of Integration

##### Chapter 8 – Integration Techniques, L’Hopital’s Rule, and Improper Integrals

### About the Exam

The AP Calculus AB Exam is 3 hours and 15 minutes. The 105-minute, 45-question multiple-choice section tests your proficiency on a wide variety of topics. The 90-minute, six-problem free-response section gives you the chance to demonstrate your ability to solve problems using an extended chain of reasoning.

#### Section I: Multiple-Choice

The multiple-choice section of the exam has two parts. For Part A, you’ll have 55 minutes to complete 28 questions without a calculator. For Part B, you’ll have 50 minutes to answer 17 questions using a graphing calculator. For more information, see the calculator policy for the AP Calculus Exams.

Total scores on the multiple-choice section are based on the number of questions answered correctly. Points are not deducted for incorrect answers and no points are awarded for unanswered questions.

#### Section II: Free-Response

The free-response section tests your ability to solve problems using an extended chain of reasoning. Part A of the free-response section (two problems in 30 minutes) requires the use of a graphing calculator. Part B of the free-response section (four problems in 60 minutes) does not allow the use of a calculator. During the second timed portion of the free-response section (Part B), you are permitted to continue work on problems in Part A, but you are not permitted to use a calculator during this time. For more information, see the calculator policy for the AP Calculus Exams.

### Scoring the Exam

The multiple-choice and free-response sections each account for one-half of your final exam grade. Since the exams are designed for full coverage of the subject matter, it is not expected that all students will be able to answer all the questions.

**Course Planner**1^{st}Semester AP Calculus ABPreparation for Calculus – September 2 – September 13

1.1 Graphs and Models

1.2 Linear Models and Rates of Change

1.3 Functions and Their Graphs

1.4 Fitting Models to Data

1.5 Inverse Functions

1.6 Exponential and Logarithmic Functions

Limits and Their Properties – September 15 – October 10 (science camp 9-29 to 10-3)

2.1 A Preview of Calculus

2.2 Finding Limits Graphically and Numerically

2.3 Evaluating Limits Analytically

2.4 Continuity and One-Sided Limits

2.5 Infinite Limits

Differentiation – October 13 – October 31

3.1 The Derivative and the Tangent Line Problem

3.2 Basic Differentiation Rules and Rates of Change

3.3 The Product and Quotient Rules and Higher-Order Derivatives

3.4 The Chain Rule

3.5 Implicit Differentiation

3.6 Derivatives of Inverse Functions

3.7 Related Rates

Applications of Differentiation – November 3 – December 5

4.1 Extrema on an Interval

4.2 Rolle’s Theorem and the Mean Value Theorem

4.3 Increasing and Decreasing Functions and the First Derivative Test

4.4 Concavity and the Second Derivative Test

4.5 Limits at Infinity

4.6 A Summary of Curve Sketching

4.7 Optimization Problems

4.8 Differentials

Integration – December 8 – January 9 (2 weeks off for Christmas Vacation)

5.1 Antiderivatives and Indefinite Integration

5.2 Area

5.3 Riemann Sums and Definite Integrals

5.4 The Fundamental Theorem of Calculus

5.5 Integration by Substitution

5.6 Numerical Integration

5.7 The Natural Logarithmic Function: Integration

5.8 Inverse Trigonometric Functions: Integration

Review for Final – January 12 – 15

RHP Semester 1 Finals Week – January 16 – 23

2^{nd} Semester AP Calculus AB

Differential Equations – January 26 – February 13

6.1 Slope Fields and Euler’s Method

6.2 Differential Equations: Growth and Decay

6.3 Differential Equations: Separation of Variables

Applications of Integration – February 23 – March 13

7.1 Area of a Region between Two Curves

7.2 Volume: The Disk Method

7.3 Volume: The Shell Method

Integration Techniques, L’Hôpital’s Rule, & Improper Integrals – March 16 – March 27

8.1 Basic Integration Rules

8.2 Integration By Parts

8.3 Trigonometric Integrals

8.4 Trigonometric Substitution

8.5 Partial Fractions

8.6 Integration by Tables and Other Integration Techniques

8.7 Indeterminate Forms of L’Hôpital’s Rule

Preparation for AP Exam using Sample Tests from College Board

March 31 – May 2 (Easter Vacation is April 3-10)

Tuesday, May 5, 2014 @ 8:00AM AP Calculus Exam

Projects & Preparation for Rio Hondo Prep Final Exam May 11 – June 3

RHP Finals Week – June 2 – June 10

High School Graduation – June 12

### RHP Math students should read and think critically.

The student should be able to read the text material and examples and be able to extend what they have read to problem solving. They should attack new problems by relating them to previous problems or by researching the text and other materials. Students are often given an assignment to read the text and then answer the *covering the reading problems *without prior instruction. Problems from math contests are woven into courses to encourage creative thinking. Some classes give an SAT *problem of the day*. Also extended response questions are integrated from the Math Diagnostic Testing Project and through Accelerated Math.

##### RHP Math students should communicate clearly and effectively.

Students must show their work. The steps to solve a problem should be organized so that someone else can follow them. They must be able to frame meaningful questions. They should be able to use appropriate mathematical language. We create a classroom environment where students are encouraged to ask questions and explain their thinking. Occasionally we will give an extended response problem and the student’s grade will be based on how well they are able to communicate their reasoning as well as the correctness of the response.

##### Math students should demonstrate personal, moral and social responsibility.

Students will be required to take notes. They must be able to follow directions. Students should always respect the ideas of others. Students should realize there is always more than one way to solve a problem. We expect students to come to class prepared by bringing necessary materials. As a faculty we also will recognize and reward random acts of kindness. Students may also demonstrate this ESLR by tutoring or mentoring a student in a lower level class.

##### Math students should value teamwork through participation.

Students should participate in class discussions and be able to ask and answer well-phrased questions. They should be able to work with other students in the class on a project. They should not let down their team, but actually work towards the solution. Projects will be given during the course of the year where students will be required to work with others on a team project. Students will be graded on how well they are able to contribute to the team and cooperate with the team.

##### Math students should develop skills to be lifelong learners.

Students should be able to take real-life situations and translate them into some type of mathematical model. They should investigate different approaches to the problem and decide on a plan of attack. We look at Star Math results, ACT/SAT scores, Math Diagnostic Test Project results, and Accelerated Math Objectives.