www.ctm-academy.cz
datum: 30.11.2020

Kód kurzu:

FLVS_PRECALC

Název kurzu:

Pre-Calculus Honors Online

Délka kurzu:

2 semesters

Rok školní docházky / Grade:

9 - 13

Partner:

FLVS - Florida Virtual School Global

Detailní popis

Students, as mathematic analysts, will investigate how advanced mathematics concepts can solve problems encountered in operating national parks. The purpose of this course is to study functions and develop skills necessary for the study of calculus. The Pre-calculus course includes analytical geometry and trigonometry. Pre-calculus is an Honors level course.

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

Kurz Pre-Calculus je důkladnou přípravou pro náročnější kurzy Calculus Honors, AP Calculus AB a AP Calculus BC.  Kurz obsahuje témata jako funkce, trigonometrie, řešení rovnic vyšších stupňů, polární souřadnice, komplexní čísla, nekonečné řady nebo limita funkce. Na uvedeném přehledu je vidět, že učivo v kurzu je tvořeno tématy z různých ročníků našich SŠ a obsahuje také témata, s nimiž se typicky studenti na našich středních školách neseznámí. 

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


The Pre-Calculus course is a thorough preparation for the more demanding courses of Calculus Honors, AP Calculus AB and AP Calculus BC. It contains topics such as functions, trigonometry, solving higher-degree equations, polar co-ordinates, complex numbers, infinite series or limits of functions. It can be seen on the above list that the syllabus of the course consists of fields which are usually encountered during various levels of high-school education, but it also contains certain topics which are above the high-school level and are often not met in the standard classes. 

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

Struktura kurzu

Major Topics and Concepts

Segment 1
·         Functions
·         Domain and range
·         Rigid and non-rigid transformations
·         Composition and arithmetic of functions
·         Function inverses
·         Solve and graph quadratic functions
·         Characteristics of a polynomial function
·         Rational Root Theorem, long and synthetic division, Fundamental Theorem of Algebra, 
          and DesCartes Rule
·         Using the Intermediate Value Theorem and the Extreme Value Theorem
·         Complex numbers as solutions to polynomial equations
·         Domain and asymptotes of a rational function
·         Analyze and graph a rational function with and without a calculator
·         Analyze and graph the exponential function
·         Analyze and graph the logarithmic function
·         Properties of logarithms
·         Exponential and logarithmic equations
·         Angles in radians and degrees
·         Define the trigonometric functions using the coordinates of a unit circle and using
          a right triangle
·         Evaluate the trigonometric function values of any angle measure
·         Analyze and graph sine, cosine and tangent functions with and without a calculator
·         Inverse trigonometric values
·         Applications of right-triangle trigonometry
·         Evaluate trigonometric values using identities
·         Prove that a given equation is an identity
·         Solve equations that contain trigonometric functions
·         Applications involving solving trigonometric equations
·         Use argument identities

Segment 2
·         Use the Law of Sines and Law of Cosines to solve a triangle, including the ambiguous
          case
·         Applications of the Law of Sines and Cosines, including navigation
·         Find the area of the triangle including Heron’s formula
·         Vectors in the Plane: vector arithmetic, dot product, angle between two vectors
·         Vectors in Space:  vector arithmetic, dot product, cross product, and angle between
          two vectors
·         Arithmetic of Complex numbers using Vectors and DeMoivre’s Theorem
·         Terms of a sequence, sigma notation
·         Arithmetic sequences and series
·         Geometric sequences and series
·         Proof by Mathematical Induction, including divisibility proofs
·         Analyze and graph equations that produce parabolas, ellipses and hyperbolas
·         Parametric equations and graphs and conversion to rectangular form
·         Parametric motion
·         Domain and range of parametric equations
·         Plotting points in the polar system
·         Convert rectangular coordinates to polar coordinates
·         Convert polar coordinates to rectangular coordinates
·         Convert rectangular equations to polar equations
·         Convert polar equations to rectangular equations
·         Graphing polar equations
·         Evaluating limits numerically
·         Evaluating limits graphically
·         Evaluating limits analytically
·         Evaluating one-sided limits
·         Continuity at a point, Types of discontinuities

Sylabus kurzu

Materiály

K vašemu kurzu potřebujete tyto učebnice a studijní pomůcky (pokud ke kurzu potřebujete laboratorní sadu, zkuste si nejdříve dohodnout možnost využívání školní laboratoře):

DescriptionNumberTypeSource
Demana et al, Precalculus, Numerical, Algebraic 8th Editione-Bookincluded in the price of the course
Graphing CalculatorToolNOT included in the price of the course

Cena

cena kurzu: 13 920,- Kč / 571,- EUR

Zkušenosti studentů

Program bol veľmi nápomocný a pomohol mi sa pripraviť na štúdium technického smeru. Program môžem ďalším študentom len odporučiť.

Martin, 2012