AP Calculus Syllabus

AP Calculus AB is equivalent to a first-semester college calculus course. Topics include functions, limits and continuity, derivatives, and integrals. The course will focus on applying the skills and concepts of calculus to modeling and solving problems across multiple representations. Students are expected to complete all homework problems to the best of their ability. If they need additional support, they can refer to the additional resources listed below in the tutorials and extra help section. The primary objective of this course is for students to engage themselves in a quality college level mathematics course and to prepare them to perform to their level on the AP exam.

This course is a full-year experience building toward mastery assessed using the AP Exam. Therefore, it is important to consider both specific content and skills related to each unit and to build a coherent understanding of the whole.

To get a more detail view of what the course is about, click the following link. This is will take you to the Course and Exam Description that College Board has approved. Everything that is blue is what will be covered in this class.

●Binder or folder (for notes and assignments)

● Pencil (Pen is only allowed in your notes)

● Loose leaf paper

● Graphing calculator (TI-84 will be provided for you in class if you do not have one)

● Headphones that can be used with a Chromebook

● Black Expo Markers

● Composition Notebook

Delta Math: FM4P-C2N5

Khan Academy: HCX5HNAT

Remind: @phsapcal24

Google Classroom: xq4hki7

● Students should be able to work with functions represented in a variety of ways: graphical, numerical, analytical, or verbal. They should understand the connections among these representations.

● Students should understand the meaning of the derivative in terms of a rate of change and local linear approximation and should be able to use derivatives to solve a variety of problems.

● Students should understand the meaning of the definite integral both as a limit of Riemann sums and as the net accumulation of change and should be able to use integrals to solve a variety of problems.

● Students should understand the relationship between the derivative and the definite integral as expressed in both parts of the Fundamental Theorem of Calculus.

● Students should be able to communicate mathematics both orally and in well-written sentences and should be able to explain solutions to problems.

● Students should be able to model a written description of a physical situation with a function, a differential equation, or an integral.

● Students should be able to use technology to help solve problems, experiment, interpret results, and verify conclusions.

● Students should be able to determine the reasonableness of solutions, including sign, size, relative accuracy, and units of measurement.

● Students should develop an appreciation of calculus as a coherent body of knowledge and as a human accomplishment.

● AP students will develop advanced research skills and methods. Curriculum for AP students should allow for the in-depth learning of self-selected topics within the area of study.

● AP students will develop and practice creative thinking and creative problem-solving skills with a variety of complex topics within the area of study.

● AP students will develop and practice critical thinking and logical problem-solving skills in the pertinent academic area.

● AP students will develop an understanding of self and how their unique characteristics may influence interactions with others.

The grading scale is as follows for PHS:

90% – 100% A

80% – 89% B

70% – 79% C

60% – 69% D

0% – 59% F

The grade weighting for PHS will be on the 25%/75% scale: This is a 6 point weighted class. Because of this, there will be no extra credit, no late work accepted, and no bonus points. Grades will not be rounded either. If you have an 89.7%, it will remain an 89.7% which will be a B.

All multiple choice tests and most quizzes will be through DMAC. You must show your work. If you only have the answers, then the highest grade you will receive on that assignment will be a 50%. Unless it specifically says that you do not have to show work, assume you always do.

You will have several assignments, tests and quizzes, 1 mid-term, and 1 final over the course of the SEMESTER. You will also be required to create a Khan Academy account and a Delta Math account. You will only be required to do the quizzes and tests that will be assigned, but you are encouraged to watch the videos and do the practice problems as well. All quizzes in Khan Academy count as a daily grade, and all unit tests in Khan Academy will count as a test grade. You are able to do these as many times as you want to in order to obtain the grade you desire up until the due date. After the due date, your grade will stand with the highest score.

Tests are given in two parts. The first part will be a multiple choice test either with or without a calculator. The second part will be a Free Response Test (FRQ) that will either be with or without a calculator, depending on what the MC portion was. All tests will be closed notes.

Per PHS Math Department policy, there are no make-up tests unless prior arrangements have been made. This is a non-negotiable. If you are not going to be here, you must make prior arrangements. You are not allowed to retake any test or quiz, even if you get below a 70%. The AP exam will be on May 13th this year.

All tests must be finished in the day it was given. Everyone is allowed one full class period to finish their test. If you are allowed extra time, you must make arrangements PRIOR to the test. Once the test has begun, if you have not made any arrangements to use the extra time you are allowed, you will not be able to. Because this class is a weighted class, there will not be any test retakes. The score that you receive on your test will be that.

The test will start at the beginning of your class period and you will have 50 minutes to complete it. If you show up late to class, you will not have extended time. You must be on time.

There will be several assignments given this semester. All assignments will have a due date and are due at the end of your class period on that due date. No late work will be accepted. If you will be out due to a school function, you will need to get your assignment before you leave. If you are allowed extra time, the assignment has to be turned in at the beginning of class the next day.

You may exempt the final exam as long as you do not have more than 2 absences (E-Days do not count) and have at least an 80% for the semester going into the final exam. I must have your final exam form on the Monday of the final exam for that semester.

In the 4th 9 weeks, all students will take a mock AP exam about 2 weeks before the actual AP exam. This test will be the last test that you will take for the 9 weeks, besides the final exam, if you have to take it. This test is worth 3 test grades and will be graded per the following:

MCQ is worth 54 points:

54 - 100%

48 - 53.9 - 95%

45 - 47.9 - 90%

39 - 44.9 - 85%

33 - 38.9 - 80%

27 - 32.9 - 75%

21 - 26.9 - 70%

15 - 20.9 - 65%

0 - 14.9 - 60%

FRQ is worth 54 points:

54 - 100%

48 - 53.9 - 95%

45 - 47.9 - 90%

39 - 44.9 - 85%

33 - 38.9 - 80%

27 - 32.9 - 75%

21 - 26.9 - 70%

15 - 20.9 - 65%

0 - 14.9 - 60%

Overall Score

5 - 100%

4 - 85%

3 - 70%

2 - 65%

1 - 60%

Class attendance is critical for the successful completion of this course. You must be present at least 90% for the semester and maintain at least a 70% in order to get credit for the class for PHS. This means that you cannot be absent more than 8 days a semester. Per Paris ISD attendance policy: A signed parent's note or doctor’s note must be provided to the campus immediately upon return in order for the absence to be considered excused. Notes submitted more than three school days after the absence will NOT be considered, and the absence will remain unexcused. If you are absent it is your responsibility to make arrangements: DO NOT DELAY!

Tutorials are from 7:30 to 8:00 am. If you need additional help, I do not have a last period class. You are more than welcome to come in during that time and get extra help as long as you give me a little bit of notice since I drive a bus. You are also more than welcome to send me a Remind during this time period. If you have a question throughout the day, you can submit your question through Remind. It will be answered that day, as long as it is before 4 pm. Any time after 4 pm, your question may not get answered until the next working day. For example, if you send me a question at 6 pm on a Tuesday, I will answer it the next day. If you send me a question at 10 pm on a Friday, I will not answer it until Monday morning. If you need help during the weekend, I cannot guarantee that I will respond right away, but I will try, especially if it is right before an exam.

Throughout the year, there will be a variety of different classroom activities that will help you learn and solidify your learning of the concept that is being taught. Below are some examples of activities that we will do throughout the year to make sure your learning experience is a good one!

Traditional Homework

In a homework assignment, students will use the product and quotient rule to find the derivative involving the functions listed in the topics above. The assignment will be cumulative involving all the other derivative rules, but an emphasis will be on the product and quotient rule. In part one, students will find the derivative given a symbolic representation of a function. In this part, the derivative of some problems should use algebra first and would not necessarily warrant a quotient rule even though the function is a quotient. In part two, students will use a table of values to find the value of the derivative. Students will have to pull values from the table in order to compute their answer. In the third part, students will use the graphs of functions to find the value of the derivative.

Pair Ups

In a class exercise, students will work in pairs to discuss how they would solve Free-Response Question 3 – Part C from 2007 (Form B). Students will have to pay attention to the fact that they need to find the derivative w'(t) when they are not given a formula that directly relates w and t; the formula given in the stem of the problem is in terms of w and r. This kind of problem should prompt a good discussion on how to find this derivative.

To make things a little less complicated, I will write on the board a pair of equations like y = u3 and u = x 2 + 1 and ask the students to find dy/dx. I don’t expect students to come up with this rule on their own, so I will demonstrate for the students on how we could write a chain rule (a chain of derivatives) to find dy/dx.

Second, I will now denote u = g(x) = x and ask students to find f(g(x)) and ask them how we could take the derivative of f(g(x)) and end up with our answer from before. This will now lead to the derivative of f(g(x)) using f'(g(x))g'(x). After demonstrating a few examples, I will return to FRQ 3 and ask the students now to write a chain rule with the information they just learned. I will emphasize that students should pay attention to the units and use the units as a guide in writing a valid chain rule.

Group Work (3-4 students)

For calculating higher order derivatives, students will work in groups of four. Each group will be given four derivative problems on index cards. For each problem, there will be three specific derivatives to find while the fourth derivative will be a general rule for finding the nth derivative of the original problem. The first three students within each group will find the indicated derivative while the fourth person will find a general rule in terms of n for finding the nth derivative.

Stations

At the end of units, students will sometimes do stations. Each station will have a different purpose. The first time we will do stations will be with related rates. There will be 6 different stations. The first station is a problem to poster station. You will pick a related rate question and explain how to solve it in detail. The second station is the Khan Academy Unit Test. The third station is an error analysis station. The fourth station is a FRQ that contains related rates. The fifth station is a create your own station (these problems could appear on a future test). The last station is a basic skills station. This is designed to reinforce the skills that are needed to be successful for this unit.

Below is the course pacing for the year. This is not set in stone and is used as a guideline of when certain topics will be covered. This can be changed at the discretion of me at any time. Notice will be given if there will be a significant change.

Week 1 Syllabus, Introductions, Create online accounts, Pretest, and Calculator Activity

Week 2 Intro to Limits, Limits Tables and Graphs, Techniques for Limits

Week 3 Continuity, IVT, Squeeze Theorem

Week 4 AROC and Difference Quotient

Week 5 Infinite Limits and Limits at Infinity

Week 6 Test week

Week 7 Defining the Derivative, AROC vs IROC, Differentiability and Continuity

Week 8 Power Rule, Trig Rules, Ln, Log, and e Rules, Product and Quotient Rule

Week 9 Test week

Week 10 Chain Rule, Inverses

Week 11 Implicit Differentiation

Week 12 Test week

Week 13 Estimation and Interpreting Derivatives, Particle Motion Part 1, L'Hospital's Rule

Week 14 Related Rates

Week 15 Test week

Week 16 Semester 1 Review

Week 17 Finals Week

Week 18 Card Sort, 1st Derivative Test

Week 19 MVT

Week 20 2nd Derivative Test

Week 21 Test week

Week 22 Riemann Sums

Week 23 Definite and Indefinite Integrals, U-Substitution

Week 24 Differential Equations, Integrating other Integrals

Week 25 Test week

Week 26 General and Initial Solutions

Week 27 Exponential Models, Slope Fields, Unit 7 Test

Week 28 AP Review

Week 29 AP Review

Week 30 Average Value, Integral Word Problems, Particle Motion Part 2

Week 31 Area Between Curves

Week 32 Cross Sections, Washer Method

Week 33 AP Review

Week 34 Last Unit Test, AP Review

Week 35 AP Review and Super Saturday

Week 36 AP Test Week!!!!!!!!!!!

Week 37 Stand and Deliver

Week 38 Reflections and Wrap Up