Description

AP Calculus BC includes all topics in AP Calculus AB, as well as additional topics, such as differential and integral calculus (including parametric, polar, and vector functions) and series. It is equivalent to at least one year of calculus at most colleges and universities. AP Calculus BC is an extension of AP Calculus AB, and each course is challenging and demanding and requires a similar depth of understanding of topics.

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 BC is designed to be the equivalent to both first and second semester college calculus courses. AP Calculus BC applies the content and skills learned in AP Calculus AB to parametrically defined curves, polar curves, and vector-valued functions; develops additional integration techniques and applications; and introduces the topics of sequences and series.

 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. Students who take AP Calculus BC should have basic familiarity with sequences and series, as well as some exposure to parametric and polar equations.

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 témata, která se běžně nevyučují na našich středních školách. Student se tak seznámí s tématy diferenciální rovnice, nekonečné řady a jejich konvergence, nevlastní integrál nebo polární souřadnice. Kurz AP Calculus BC 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. Students will therefore encounter topics such as differential equations, infinite series and their convergence, improper integrals or polar co-ordinates. The AP Calculus BC 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

Course syllabus

Syllabus AP Calculus BC

• Syllabus AP Calculus BC

AP Calculus BC Course and Exam Description

• AP Calculus BC 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):

Price

course fee: 811,- EUR / 19 300,- Kč

Student’s Experience

Díky CTM Online programu jsem měl možnost během středoškolského studia absolvovat online kurzy matematiky zaštítěné CTY při univerzitě Johnse Hopkinse v USA. Ve druháku jsem začal kurzem Honors Pre-Calculus, kde jsem se naučil myslet matematicky a hledat za každým vzorcem jeho původ a pravý význam. Ve třeťáku jsem pak pokračoval kurzem AP Calculus BC, který mi dal velmi solidní základy diferenciálního a integrálního počtu, na kterých jsem mohl s přehledem stavět při studiu na University of Aberdeen, na níž jsem ve studiu matematiky pokračoval. Během studia těchto kurzů jsem začal mít matematiku skutečně rád. Profesor Edward Burger, který připravoval videa do těchto kurzů, je jedním z nejlepších učitelů matematiky v USA. A snad právě díky němu jsem začal mít matematiku opravdu rád a posléze ji i začal studovat na vysoké škole. Ukázal mi, že je to svět zábavy, svět hledání pravdy, svět, kde všechno dává smysl.

Velice důležitou součástí této mé zkušenosti byla paní profesorka Jana Kalová. Byla mojí instruktorkou – pomáhala mi pochopit, co jsem nepobíral, pomáhala mi pravidelně na kurzech pracovat a často mi i psala různé zajímavosti navíc, díky čemuž jsem poznal, že skvělí, milí a nápomocní matematici jsou všude po světě. Během svého středoškolského studia jsem měl přístup k mnoha zdrojům vzdělání - absolvoval jsem různé stáže, psal SOČku, učil se pečlivě do některých předmětů - a všechny byly přínosné, ale CTM Online kurzy rozhodně nejpřínosnější! Doporučil bych je každému a kdykoli!

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Thanks to the CTM Online programme, I had the opportunity to study online Maths courses, made by the CTY Johns Hopkins University, while I was still at the Bishop Grammar School in Žďár nad Sázavou. I started with the Honors Pre-Calculus course and then continued by AP Caculus BC. These courses taught me what is the mathematical thinking and how to think about maths problems. It also helped me to develop a wide foundation on which I was building during my studies at the University of Aberdeen, where are continued my studies of mathematics later on. In AP Calculus BC, the concepts of integration and differentiation were amazingly explained by professor Edward Burger, one of the best teachers of mathematics in the USA. But it was not just professor Burger who showed my what a joy doing maths is.

Professor Jana Kalova, my supervisor in this programme, was helping me to understand what I was not able to grasp yet, to help me keep pace with the course tempo and to motivate me when I felt it is too much work for me. During my high school studies, I was using many sources to learn maths – I was taking part in internships, reading books, watching interesting videos on YouTube – but nothing was as beneficial as doing these CTM Online courses. I am eternally grateful to everyone who gave me this opportunity and I would recommend this courses to anyone anytime.

Daniel Mužátko, student CTM, nyní student University of Aberdeen