SAMPLE SYLLABUS #1 AP Calculus BC

SAMPLE SYLLABUS #1 AP Calculus BC

AP Calculus BC syllabus outlines the curriculum for students preparing for the AP exam. It details the course structure, including key topics such as limits, differentiation, integration, and applications of calculus. Designed for high school students, this syllabus aligns with the College Board's guidelines and includes a sequence of ten units. Each unit provides opportunities for students to develop mathematical practices and problem-solving skills. The syllabus also emphasizes the use of graphing calculators to enhance understanding of calculus concepts.

Key Points

  • Covers ten units including Limits, Differentiation, and Integration.
  • Aligns with College Board's AP Calculus BC Course and Exam Description.
  • Incorporates real-world applications of calculus concepts.
  • Includes opportunities for students to develop mathematical practices.
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SAMPLE SYLLABUS #1
AP
®
Calculus BC
Curricular Requirements
CR1
CR2
CR3
CR4
CR5
CR6
CR7
CR8
The students and teacher have access to a college-level calculus textbook,
in print or electronic format.
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4
The course is structured to incorporate the big ideas and required content
outlined in each of the units described in the AP Course and Exam Description.
The course provides opportunities for students to develop the skills related to
Mathematical Practice 1: Implementing Mathematical Processes.
See pages:
16, 17
The course provides opportunities for students to develop the skills related to
Mathematical Practice 2: Connecting Representations.
See page:
16
The course provides opportunities for students to develop the skills related to
Mathematical Practice 3: Justification.
See page:
16
The course provides opportunities for students to develop the skills related to
Mathematical Practice 4: Communication and Notation.
See page:
16
Students have access to graphing calculators and opportunities to use them to
solve problems and to explore and interpret calculus concepts.
See pages:
3, 16
The course provides opportunities for students to use calculus to solve real
world problems.
See page:
17
AP-Course Audit Teacher Resources
© 2020 College Board
Advanced Placement
Calculus BC Sample Syllabus #1
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.
CR2
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 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
CR2
The syllabus must include
an outline of course
content by unit title or topic
using any organizational
approach with the
associated big idea(s) to
demonstrate the inclusion
of required course content.
All three big ideas must be
included: Change, Limits,
and Analysis of Functions.
2
AP-Course Audit Teacher Resources
© 2020 College Board
Advanced Placement Calculus BC Sample Syllabus #1
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.
Prerequisites
All students who are taking AP Calculus BC have completed precalculus and have a firm
understanding of:
Functions – their graphs and behaviors
Trigonometry
Logs and Natural Logs
Transformations and Translations
The use of their graphing calculator to solve problems
The value of the Rule of Four to solve problems (analytical/algebraic, numerical,
graphical, verbal/communication)
Transcendental Functions
These and other prerequisite topics/skills are briefly reviewed, as needed, during the year
to help students make valuable connections between the big ideas.
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 calculator to that student for the course.
CR7
All students have access to the computer labs at our school.
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.
CR7
The syllabus includes a
statement that each student
has individual access to
an approved graphing
calculator.
AND
The syllabus must include
a description of at least one
activity in which students
use graphing calculators to:
graph functions
solve equations
perform numerical
differentiation
perform numerical
integration
explore or interpret
calculus concepts
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Faqs of SAMPLE SYLLABUS #1 AP Calculus BC
What topics are covered in the AP Calculus BC syllabus?
The AP Calculus BC syllabus covers a range of topics organized into ten units. These include Limits and Continuity, Differentiation, Integration, and Applications of Integration. Each unit is designed to build upon the previous one, ensuring a comprehensive understanding of calculus concepts. The syllabus also emphasizes the importance of real-world applications, allowing students to see how calculus is used in various contexts.
How does the syllabus support students' mathematical practices?
The syllabus is structured to provide students with opportunities to develop key mathematical practices outlined by the College Board. These practices include implementing mathematical processes, connecting different representations, and communicating mathematical reasoning. By engaging with various topics and using tools like graphing calculators, students enhance their problem-solving skills and deepen their understanding of calculus.
What prerequisites are recommended for students taking AP Calculus BC?
Students enrolling in AP Calculus BC are expected to have completed precalculus with a strong understanding of functions, trigonometry, and logarithms. Familiarity with graphing calculators is also essential, as they are used extensively throughout the course. The syllabus briefly reviews these prerequisite topics to ensure that all students are adequately prepared for the challenges of calculus.
What assessment methods are used in the AP Calculus BC course?
Assessment in the AP Calculus BC course includes a variety of methods such as daily homework, quizzes, labs, projects, and unit tests. The syllabus outlines the use of Personal Progress Checks designed by the College Board to help students identify areas of struggle. Additionally, students take a midyear exam and a full practice exam before the AP exam in May, which is graded using the same guidelines as the actual AP exam.
What is the significance of the graphing calculator in the syllabus?
The graphing calculator plays a crucial role in the AP Calculus BC syllabus, as it is used daily to explore and understand calculus concepts. Students learn to graph functions, solve equations, and perform numerical differentiation and integration using the calculator. This technology not only aids in problem-solving but also helps students visualize complex concepts, making calculus more accessible and engaging.