AP Calculus AB (Elective)

AP Calculus AB is a year-long elective open to juniors and seniors at IPoly. It is not officially a year-long elective, as students may drop out after the first semester. As such, it is actually comprised of Differential Calculus during the first semester and Integral Calculus during the second. Although it is not technically an AP class, as it does not count toward high school math credits, the class is designed to prepare students for the AP Calculus AB test, which they have the option to take at the end of the year. It is the first and only AP class offered at IPoly.

Since the course is two semesters long, students can decide to drop out for second semester, and they will not take the AP Exam at the end of the year.

Mr. Estrada usually has one or two Teacher's Assistants in the class, who he regularly gives "on-the-spot" questions to show students the thought process that goes into solving a problem in Calculus. These students have already taken the class and passed the AP Test. AP Calc TAs also help students on their homework and classwork.

Purpose
To prepare students for the AP Exam and/or higher- and college-level math courses.

General Structure
Assignments have four major categories: classwork/notes, homework/practice, book problems, and challenge problems. Classwork is not collected, and is meant as a follow-along for the day's lesson. Students are usually given time to complete the assignment in class. Homework is similar to the classwork, but will be collected for a grade. Students might be given some time at the end of class, but this is not a general rule for homework. Book problems are a list of around 15 questions per section in the chapter, and is usually due the day of or the day before the chapter test. The list is accessed through Google Classroom. Challenge problems are more like puzzles, and are meant to gauge the student's grasp of the main points in the chapter. Since challenge problems require a certain amount of mathematical creativity, Mr. Estrada readily explains the solution for students who ask after they've tried to solve it on their own. Challenge problems are usually due either the day of or the day after the chapter test.

Differential Calculus
The first AP Calc class is a discussion about how a speedometer actually calculates the speed of the car at a single moment in time, since speed requires some change in time. This discussion introduces the concept of a limit. After two or three weeks of limit practice, Mr. Estrada introduces the definition of a derivative in terms of limits, including a graphical demonstration. Most of the semester is spent looking at different ways to calculate the derivative. The final few weeks is spent exploring the practical applications of the derivative, such as related-rates problems, extreme values, and projected values.

Integral Calculus
The semester begins with the introduction of Riemann Sums and the area under a curve, which is then transformed into the definition of the integral. Students will then learn some of the more basic methods of integration (power rule, logarithmic rule, trig identities, and u-substitution). They will be taught how to find the area under a graph and the area between two graphs, which will then be built up to finding volumes of various objects (either by using known cross-sections or revolution around an axis).

AP Exam
Students have the option to take the AP Exam at the end of the year. The exam can be counted as college credit for Calculus I depending on the student's score. Scoring a 3, 4, or 5 on the exam will automatically qualify a student to take CalPoly's MAT 1150 course (Calculus II) the next semester, though other colleges require a 4 or 5. The AP Exam costs $94, but students that are on the free and reduced lunch program only pay $10. A few weeks before the exam, students prepare by working through all the AP sample exams beginning at 1999 through 2005. Students who plan on taking the exam are excused from all classes the day before the test, and spend the entire school day reviewing. AP scores are usually released by July 1 on the College Board website.