AP Calculus BC Syllabus 2022-2023 by Dr. Li Ma

AP Calculus BC Syllabus 2022-2023 by Dr. Li Ma

The AP Calculus BC syllabus for the 2022-2023 school year outlines the curriculum designed by Dr. Li Ma. This course is equivalent to two semesters of college-level calculus and prepares students for the AP Calculus BC exam. Key topics include limits, differentiation, integration, and applications of calculus. The syllabus also details assessment methods, including major and minor assessments, and provides resources for technology use in learning calculus concepts. Students will engage in problem-solving and real-world applications throughout the course.

Key Points

  • Covers major calculus topics including limits, differentiation, and integration.
  • Prepares students for the AP Calculus BC exam scheduled for May 8, 2023.
  • Includes Personal Progress Checks to monitor student understanding and progress.
  • Utilizes technology such as TI-84 calculators and Chromebooks for enhanced learning.
  • Emphasizes problem-solving and real-world applications of calculus concepts.
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Advanced Placement (AP) Calculus BC Syllabus
2022-2023 School Year
Instructor: Dr. Li Ma
li.ma@hcbe.net
(478) 218-7537 x64626 Room 2403
Prerequisite:
Algebra 1, Geometry,
Algebra 2 (which includes analytic geometry and logarithms),
Pre-Calculus (which includes trigonometry)
Major Text: Calculus of a Single Variable (advanced) 8th edition
by Larson, Hostetler and Edwards, 2006, Houghton Mifflin Company
Overview
AP® Calculus BC satisfies all the requirements designed by the College Board and is equivalent to two
semesters of college level calculus. This course syllabus is aligned to the AP Calculus AB and BC Course and
Exam Description (CED) released by the College Board in 2019. Students enrolled in this course have completed
precalculus and have chosen to take BC Calculus (in lieu of AB Calculus, which our school also offers). Students
are required to take AP Calculus BC Exam in May. If students cannot afford to pay for the exam, the school will
pay for the exam.
The course is designed around the three “Big Ideas” of calculus, including:
Big Idea #1: Change
Big Idea #2: Limits
Big Idea #3: Analysis of Functions
The College Board’s CED is broken down into 10 units, and my course follows the sequencing/pacing of these 10
units. The three big ideas of calculus are included in the units as reflected in the CED.
UNIT 1: Limits and Continuity (~3 weeks)
UNIT 2: Differentiation: Definition and Fundamental Properties (2–3 weeks)
UNIT 3: Differentiation: Composite, Implicit, and Inverse Functions (2–3 weeks)
UNIT 4: Contextual Applications of Differentiation (~2 weeks)
UNIT 5: Analytical Applications of Differentiation (2–3 weeks)
UNIT 6: Integration and Accumulation of Change (~4 weeks)
UNIT 7: Differential Equations (2–3 weeks)
UNIT 8: Applications of Integration (3–4 weeks)
UNIT 9: Parametric Equations, Polar Coordinates, and Vector-Valued Functions (~3 weeks)
UNIT 10: Infinite Sequences and Series (4–5 weeks)
Student Practice
Throughout each unit, Topic Questions will be provided to help students check their understanding. The Topic
Questions are especially useful for confirming understanding of difficult or foundational topics before moving on
to new content or skills that build upon prior topics. Topic Questions can be assigned before, during, or after a
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lesson, and as in-class work or homework. Students will get rationales for each Topic Question that will help
them understand why an answer is correct or incorrect, and their results will reveal misunderstandings to help
them target the content and skills needed for additional practice.
At the end of each unit or at key points within a unit, Personal Progress Checks will be provided in class or as
homework assignments in AP Classroom. Students will get a personal report with feedback on every topic, skill,
and question that they can use to chart their progress, and their results will come with rationales that explain every
question’s answer. One to two class periods are set aside to re-teach skills based on the results of the Personal
Progress Checks.
An extra lab period each week is devoted to an appropriate calculator activity, multistep word problems, Topic
Questions, Personal Progress Checks, and/or free-response questions (FRQ’s) from released AP Calculus BC
Exams. Emphasis is placed on problem solving, using the calculus in new settings, and helping students to see the
connections among the big ideas and the major themes in calculus. FRQs, which emphasize real-world
applications of the calculus, are selected for discussion during this lab period.
The course is also designed around the four Mathematical Practices in AP Calculus outlined in the 2019 CED
including:
Practice #1: Implementing Mathematical Processes
Practice #2: Connecting Representations
Practice #3: Justification
Practice #4: Communication and Notation
Course Objectives
At the end of the course, students should be able to solve a variety of real-world problems using limits,
derivatives, integrals, and series. Students are shown the interrelationships of these four major themes/threads
throughout the course. The course teaches the students how to communicate their mathematical reasoning using
proper mathematical terminology in complete sentences. Students are instructed how to answer problems in the
context of the problem, both verbally and in written sentences/paragraphs, using appropriate measurement units.
Technology
• All students are expected to have a TI-83, 83+, 84, or 84+ for their use in class and for homework assignments.
For students that cannot afford a calculator, our school will loan a TI 84+ calculator to that student for the
course.
• All students in our school system have been issued a Chromebook during high school years.
• The graphing calculator is used every day in class and students are instructed daily on how to use this
technology to help them understand the various calculus concepts and to connect concepts and different
representations
• Students are exposed to numerous calculus applets during the course, and I have a computer and LCD
projector in my classroom.
• Students download a number of calculator programs from my calculator, including programs for Riemann
Sums, Area between two curves, Euler’s Method, and Slope Fields. These programs are designed to help
students visualize the various concepts and to get a deeper understanding of calculus.
• Students are instructed throughout the course of the Four Functionalities allowed on the AP Exam with the
graphing calculator including:
• Plot the graph of a function within an arbitrary viewing window.
• Find the zeros of functions (solve equations numerically).
• Numerically calculate the derivative of a function.
• Numerically calculate the value of a definite integral.
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• I instruct students on the various software packages to illustrate volumes of solids, slope fields, and
accumulation.
• During the course, problems will be represented and solved in four distinct ways: analytically, numerically,
graphically, and verbally. Students will use a graphing calculator to determine the value of various limits, to
determine the value of a derivative at a point, to find the value of a definite integral, to graph a function in
various windows, and to solve a variety of equations, as well as explore concepts such as the limit of a
function at a point.
Assessment
Our school system’s grading policy is follows:
45% - Major Assessments (Unit tests)
20% - Minor Assessments (Quizzes)
15% - Home/Daily Work
20% - Cumulative Assessment (Final exam)
Unit summative assessments are given at the end of each unit, with formative assessments throughout
the unit. Students will be asked to not only ‘solve’ a problem but also write explanations of their process
to certain problems. Most assessments will mimic the AP exam with 50% calculator use and 50% non-
calculator use. Included in these assessments will be AP exam type questions.
Mock Exam: This exam is a full length practice exam that will be given in one sitting during the
school day some time to be determined in the spring.
AP Calculus BC exam: The College Board sponsors this exam, which is used by most colleges to
award credit. This course will prepare you for this exam. Students are responsible for payment of the
AP exam. It is expected that all students take this exam on Monday, May 8
th
, 2023. To learn more
about this exam, visit www.collegeboard.com/ap. Further information will be forthcoming in class.
AP Exam timeline:
8.26.22– Deadline for students to electronically join all AP classes on College Board website
(APcentral.collegeboard.org). *Help line for students and parents 1-888-225-5427
10.28.22 – Deadline for students to register for AP exams on the College Board website.
2.10.22 – Deadline to pay all AP exam fees.
AP Fees
Paid Students:
$97.00 per exam
Free and Reduced lunch students:
First exam regardless of course is paid for by GADOE and is free of charge to the student.
Additional exams for FR students are $54 each.
STEM exams
For students who do not qualify for College Board fee reduction, GADOE will pay for one AP
STEM exam for each student enrolled in an AP STEM course.
Exams ordered after ordering deadline:
$40 fee per exam regardless of free and reduced lunch/STEM status.
Cancel or fail to take AP exam after ordering deadline:
$40 fee per exam regardless of free and reduced lunch/STEM status.
Monitoring your progress: Students are responsible for knowing their progress throughout the course.
There should be no surprises. The school allows access to the Infinite Campus gradebook system
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Faqs of AP Calculus BC Syllabus 2022-2023 by Dr. Li Ma
What are the main topics covered in the AP Calculus BC syllabus?
The AP Calculus BC syllabus covers a range of topics essential for understanding advanced calculus. These include limits and continuity, differentiation techniques, applications of differentiation, integration methods, and differential equations. Additionally, the course explores parametric equations, polar coordinates, and infinite sequences and series. Each unit is designed to build on the previous concepts, ensuring a comprehensive understanding of calculus.
How is student progress assessed in the AP Calculus BC course?
Student progress in the AP Calculus BC course is assessed through a combination of major assessments, minor quizzes, and daily homework. Major assessments account for 45% of the overall grade, while minor assessments contribute 20%. There are also cumulative assessments, including a final exam, which make up 20% of the grade. Personal Progress Checks are provided to help students identify areas for improvement and ensure they are prepared for the AP exam.
What technology is used in the AP Calculus BC course?
The AP Calculus BC course incorporates several technological tools to enhance learning. Students are required to use TI-84 calculators for various calculus applications, including graphing functions and calculating derivatives. Additionally, each student is issued a Chromebook for online assignments and resources. The use of technology is integrated into daily lessons to help students visualize calculus concepts and solve complex problems.
What is the structure of the AP Calculus BC syllabus?
The AP Calculus BC syllabus is structured around ten units, each focusing on different aspects of calculus. The units include limits and continuity, differentiation, integration, and applications of calculus. Each unit is designed to last several weeks, allowing for in-depth exploration of the topics. The syllabus aligns with the College Board's guidelines and prepares students for the AP exam through rigorous coursework and assessments.
What support is available for students who cannot afford the AP exam fee?
For students who cannot afford the AP exam fee, the school offers financial assistance to ensure all students can participate. The school will cover the cost of the AP Calculus BC exam for eligible students. Additionally, students qualifying for free or reduced lunch may have their first exam paid for by the Georgia Department of Education, with reduced fees for subsequent exams.