Diploma in AP Calculus BC

This is an AP (advanced placement) diploma course that explores methods of integration and other concepts in calculus, especially various theorems. It analyzes implicit differentiation, definite integrals and sigma notation. It also describes various types of finite sequences, divergence tests and series. Create your account and register for free to improve your calculus results.

What You Will Learn In This Free Course

Limits and Application of Limits

To start, this module introduces you to the limits of a function, how to evaluate limits and some applications of limits. This module discusses the sandwich or squeezes theorem as well as the Algebra of continuous functions.

Derivatives and Methods of Differentiation

To start, this module introduces derivatives and notation. This module covers a variety of methods used to differentiate both explicit and implicit functions. Some of the methods are derivatives of trigonometric functions, implicit differentiation, derivatives of inverse trigonometric functions amongst others.

Graph of Functions and Derivatives

To start, this module introduces higher-order derivatives, and the derivatives of inverse trigonometric functions are analyzed. It discusses the logarithmic differentiation technique and how to graph a logarithmic function. Also, this module covers the roles of derivatives regarding increasing and decreasing behaviors. It explores absolute maximum and absolute minimum.

Extrema and Application of Derivatives

To start, this module introduces linear approximation and using the chart method for finding absolute extrema. It states the mean value theorem and Rolle’s theorem. Also, this module identifies problems that can be solved using derivatives. It evaluates concavity and points of inflection.

Definite and Indefinite Integral

To start, this module introduces the concept of anti-differentiation and integration. It analyzes sigma notation and formulas for the sums of sequences. Also, this module will take you through estimating the area under the curve using trapezoids instead. It explores the estimation with Riemann sums

Diploma in AP Calculus BC – First Assessment

In order to pass this assessment, you will need to score 80 per cent or above. Remember, if you do not achieve the required standard after the first attempt, you can re-take the assessment until a successful outcome is achieved.

Methods of Integration

To start, this module introduces the laws concerning definite integrals. It discusses the first and second fundamental theorem of integral calculus. Also, this module analyzes trigonometric substitutions and natural logarithmic functions.

Integrating Techniques and Definite Integrals

To start, this module introduces the techniques used for integrating functions described by the products of two functions. It explores some of the applications of definite integrals as well as how to calculate the total area under a curve. Also, this module explores the methods for finding the volume of solids with known cross-sections.

Finite Sequences

To start, this module introduces the various types of finite sequences. It explores the sequence defined by a recursive formula. Also, this module distinguishes bounds and monotonic sequences. It describes how to represent sequences on a cartesian graph.

Tests for Convergence

To start, this module introduces various methods used to determine whether or not an infinite series converges. It explores the sequence of partial sums and convergence of series. Also, this module analyzes infinite series written in enumerated forms and how to represent them in a closed-form.

First Order Differential Equations

To start, this module introduces how to solve first-order differential equations using integration, separable methods, and numerical methods. This module also analyzes the Maclaurin and Taylor series. It explores how to find the coefficients and the shortcuts for finding series.

Diploma in AP Calculus BC – Second Assessment

In order to pass this assessment, you will need to score 80 per cent or above. Remember, if you do not achieve the required standard after the first attempt, you can re-take the assessment until a successful outcome is achieved.

Course assessment