AP Calculus AB Online

Online Program

course code: FLVS_APCAB
course name: AP Calculus AB Online
course length: 2 semesters
grade: 10 - 13
partner: FLVS - Florida Virtual School Global

Description Structure Syllabus Materials required Price Student’s Experience Print

Description

AP Calculus AB includes techniques and applications of the derivative, the definite integral, and the Fundamental Theorem of Calculus. It is equivalent to at least a semester of calculus at most colleges and universities.

This online course offers a combination of assessment and instruction in an online environment containing but not limited to the areas of functions, functions and limits, differential calculus, and integral calculus. The course applies differential calculus to finding the slope of a curve, solving problems with related rates, calculating motion properties of moving particles, etc. It then applies integral calculus to finding the areas of irregular regions in a plane, volumes of rotation by various methods, and other scientific applications.

The purpose of this course is to provide students with a deep understanding of the concepts of calculus in order to prepare them for the AP exam and for further college and university calculus courses.

AP Calculus AB and AP Calculus BC focus on students’ understanding of calculus concepts and provide experience with methods and applications. Through the use of big ideas of calculus (e.g., modeling change, approximation and limits, and analysis of functions), each course becomes a cohesive whole, rather than a collection of unrelated topics. Both courses require students to use definitions and theorems to build arguments and justify conclusions. The courses feature a multi-representational approach to calculus, with concepts, results, and problems expressed graphically, numerically, analytically, and verbally. Exploring connections among these representations builds understanding of how calculus applies limits to develop important ideas, definitions, formulas, and theorems. A sustained emphasis on clear communication of methods, reasoning, justifications, and conclusions is essential. Teachers and students should regularly use technology to reinforce relationships among functions, to confirm written work, to implement experimentation, and to assist in interpreting results.

AP Calculus AB is designed to be the equivalent of a first semester college calculus course devoted to topics in differential and integral calculus.

RECOMMENDED PREREQUISITES
Before studying calculus, all students should complete the equivalent of four years of secondary mathematics designed for college-bound students: courses that should prepare them with a strong foundation in reasoning with algebraic symbols and working with algebraic structures. Prospective calculus students should take courses in which they study algebra, geometry, trigonometry, analytic geometry, and elementary functions. These functions include linear, polynomial, rational, exponential, logarithmic, trigonometric, inverse trigonometric and piecewise-defined functions. In particular, before studying calculus, students must be familiar with the properties of functions, the composition of functions, the algebra of functions, and the graphs of functions. Students must also understand the language of functions (domain and range, odd and even, periodic, symmetry, zeros, intercepts, and descriptors such as increasing and decreasing). Students should also know how the sine and cosine functions are defined from the unit circle and know the values of the trigonometric functions at the numbers 0,π/6, π/4, π/3, π/2, and their multiples.

Study materials (e-books, Discovery, Education, etc. ...) for FLVS Global courses are INCLUDED in the price of the course.

Calculus je důležitým a nezbytným nástrojem nejen pro matematiky. Bez porozumění funkcím a jejich vlastnostem, diferenciálnímu a integrálnímu počtu se jen těžko studuje také fyzika, některé části chemie, ekonomie, ale také třeba biologie. Calculus je tak skutečně základním stavebním kamenem pro vybudování dalších, nejen matematických disciplín. V našem kurzu provedeme studenta světem funkcí a jejich vlastností, limitami, derivacemi i jejich aplikacemi. V kurzu jsou obsažena také témata, která se běžně nevyučují na našich středních školách, např. diferenciální rovnice. Kurz AP Calculus AB je přípravou na AP Exam. Studenti se seznámí s konceptem AP exam a nacvičí si typové úlohy. Naši absolventi jsou na tuto náročnou zkoušku výborně připraveni.

RNDr. Ing. Jana Kalová, PhD., instruktorka CTM Online kurzů

Calculus is an important and essential tool not just for mathematicians. Without understanding of functions and their properties, derivatives and integrals, it is very difficult to conduct further studies in Physics, certain parts of Chemistry, Economy or even Biology. Calculus is therefore truly the foundation for developing other, not only mathematical disciplines. In this course we will guide the student through the world of functions and their properties, limits, derivatives and their applications. The course also contains topics, which are not commonly parts of the Czech high school curriculum, such as differential equations. The AP Calculus AB course is also a preparation for an AP exam. Students will be introduced to the AP exam concept and they will practice relevant types of questions. Our alumni will become thoroughly prepared for this challenging examination.

RNDr. Ing. Jana Kalová, PhD., CTM Online instructor

Course Structure

Study Scope and Sequence

Semester One

Module 01 - Limits and Continuity

Using Limits to Analyze Instantaneous Change
Estimating Limit Values from Graphs and Tables
Determining Limits Using Algebraic Properties and Manipulation
Selecting Procedures for Determining Limits
Squeeze Theorem and Representations of Limits
Determining Continuity and Exploring Discontinuity
Connecting Limits, Infinity, and Asymptotes
The Intermediate Value Theorem (IVT)

Module 02 - Differentiation: Definition and Fundamental Properties

Average and Instantaneous Rates of Change and the Derivative Definition
Determining Differentiability and Estimating Derivatives
Derivative Rules: Constant, Sum, Difference, Constant Multiple, and Power
The Product Rule and the Quotient Rule
Derivatives of Trigonometric Functions
Derivatives of Exponential and Logarithmic Functions

Module 03 - Differentiation: Composite, Implicit, and Inverse Functions

The Chain Rule
Implicit Differentiation
Differentiating Inverse Functions
Differentiating Inverse Trigonometric Functions
Selecting Procedures for Calculating Derivatives
Calculating Higher-Order Derivatives

Module 04 - Contextual Applications of Differentiation

Interpreting and Applying the Derivative in Motion
Rates of Change in Applied Contexts Other Than Motion
Related Rates
Approximating Values of a Function Using Local Linearity and Linearization
L\'Hospital\'s Rule

Segment Two

Module 05 - Analytical Applications of Differentiation

Mean Value and Extreme Value Theorems
Determining Function Behavior and the First Derivative Test
Using the Candidates Test to Determine Absolute Extrema
Determining Concavity of Functions and the Second Derivative Test
Connecting Graphs of Functions and Their Derivatives
Optimization Problems
Exploring Behaviors of Implicit Relations

Module 06 - Integration and Accumulation of Change

Exploring Accumulations of Change
Riemann Sums and the Definite Integral
Accumulation Functions Involving Area and the Fundamental Theorem of Calculus
Applying Properties of Definite Integrals
Finding Antiderivatives and Indefinite Integrals
Integrating Using Substitution
Integrating Functions Using Long Division and Completing the Square
Selecting Techniques for Antidifferentiation

Module 07 - Differential Equations

Solutions of Differential Equations
Sketching and Reasoning Using Slope Fields
Finding Solutions Using Separation of Variables
Exponential Models with Differential Equations

Module 08 - Applications of Integration

Average Value and Connecting Position, Velocity, and Acceleration Using Integrals
Using Accumulation Functions and Definite Integrals in Applied Contexts
Finding the Area Between Curves
Finding the Area Between Curves That Intersect at More Than Two Points
Volumes with Discs
Volumes with Washers
Volumes with Cross Sections

Course syllabus

AP Calculus AB Course and Exam Description

AP Calculus AB Course and Exam Description

Materials required

For this course you need to secure the following textbook and materials (if lab kit is listed, check first the possibility of using your school lab prior to buying the lab kit):

Description	Number	Type	Source
Graphing Calculator		Tool	NOT included in the price of the course
Study Forge		Software	included in the price of the course

Price

course fee: 811,- EUR / 19 300,- Kč

Student’s Experience

First of all, I would like to thank for the opportunity to take this course. I have learned things that I would never learn in my school. It helped me a lot throughout this year and made it possible to take my AP exam without any trouble. I will definitely remember and revise occasionally what I learned in this course. Overall, I am very happy with this course and I will recommend it to anyone who is thinking about taking AP exams.

Dominik H., 2021

This course introduced me to calculus, even thou I might not be able to pass the final test completely, I at least grasped the overall knowledge of calculus and I am thankful for that. This course has been a ride for me and I make out of the things I learned.

Samuel S., 2021

The course gave me a great insight of the topics, that were discussed. The most important source of information were for me the videos, which had a great quality. It took me a lot of time, but I definitely enjoyed it and I think I now have really strong foundation in math on university level.

Kryštof P., 2021

Course Catalog

Filtres

Online Program