
Free Course

XSIQ

34 Hours

Assessment

Certification

50 Pts
Advanced Mathematics 1

Description

Outcome

Certification

This free online training explores complex numbers and equations, polynomial equations, conics, advanced trigonometry, differentiation, antiderivatives, and vectors in 2 and 3space. This course is both an ideal studyaid for students to improve their skills in their spare time or for anyone interested in exploring the world of mathematics.

Upon completion of this course you will understand nominal, discrete and continuous data in frequency tables. You will know the product rule and you will be able to easily perform calculations of differentiation. You will gain a good knowledge of antiderivatives including Hyperbolic functions, partial fractions, linear substitution, odd and even powers. You will understand the relationship between graphs and their antiderivatives. You will be able to calculate complex numbers using addition, subtraction, multiplication and division. You will be familiar with DeMoivre's Theorom, polar form multiplication and division. This course will teach you how to calculate conics, degrees, radians, inverse circular functions, polynomial equations and much more.

All Alison courses are free to study. To successfully complete a course you must score 80% or higher in each course assessments. Upon successful completion of a course, you can choose to make your achievement formal by purchasing an official Alison Diploma, Certificate or PDF.
Having an official Alison document is a great way to celebrate and share your success. It is: Ideal to include with CVs, job applications and portfolios
 A way to show your ability to learn and achieve high results
Modules List( 17 )

Module
1 Creating a frequency table from data
Creating a frequency table from data This free online course covers types of data such as nominal, discrete and continuous data, and how to create frequency tables from data. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Frequency and graphs  overview

Nominal data

Discrete data

Continuous data

Frequency tables with nominal data

Frequency tables with discrete data

Frequency tables  discrete data and summary statistics

Mean from frequency tables  discrete data

Interpreting column graphs

Family size cumulative frequency


Module
2 Differentiation  Product rule
Differentiation  Product rule This free online course covers the product rule for antiderivatives. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Product Rule

Example 1

Example 2

Example 3


Module
3 Antiderivatives
Antiderivatives This free online course covers topics related to antiderivatives such as standard antiderivative types, hyperbolic functions, and partial fractions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Review of Standard Antiderivatives

Standard Antiderivative Types

Type 2  Hyperbolic Functions

Type 3  Partial Fractions

Example 2

Type 5  Linear Substitution


Module
4 Antiderivatives of circular functions
Antiderivatives of circular functions This free online course covers the topic of the antiderivatives of circular functions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Type 4  Inverse Circular Functions

Examples 1 and 2

Examples 3 and 4

Examples 5 and 6

Type 6  Odd and Even Powers

Odd Powers

Even Powers


Module
5 Antiderivatives and their graphs
Antiderivatives and their graphs This free online course covers the relationship between the graphs of functions and their antiderivatives. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Relationships Between Graphs of Functions and their Antiderivatives

Original and Antiderivative Functions

Graphs of Antiderivatives

Examples 1 and 2

Examples 3 and 4

Examples 5 and 6


Module
6 Complex numbers 1
Complex numbers 1 This free online course covers topics related to complex numbers such as the addition, subtraction, multiplication, and division of complex numbers. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Introduction

Operations with Complex Numbers

Addition and Subraction of Complex Numbers

Multiplication of Complex Numbers by a Constant

Multiplication of Complex Numbers by Another Complex Number

Division and Complex Conjugates

Division of Complex Numbers

Argand Diagram


Module
7 Complex numbers 2
Complex numbers 2 This free online course covers topics related to complex numbers such as the polar form multiplication, and division and the conversion between polar form and cartesian form. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Polar form

Conversion between polar form and cartesian form

DeMoivre's Theorem

Polar form multiplication  example 1

Polar form division  example 1

Polar form multiplication  example 2

Polar form division  example 2


Module
8 Conics (elipses and hyperbolae)
Conics (elipses and hyperbolae) This free online course covers topics graphs of hyperbolae and ellipses and the transformation of hyperbolae. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Graphs of Ellipses

Examples

Graphs of Hyperbolae

Example 1

Example 2

Example 3

Example 4

Transformations of hyperbolae

Translations


Module
9 Degrees and radians
Degrees and radians This free online course covers the conversion of radian and degree measures. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Exact Values

Conversions of Radian and Degree Measures


Module
10 Inverse circular functions
Inverse circular functions This free online course covers derivatives of inverse circular functions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Derivatives of Inverse Circular Functions

Example 2

Example 3


Module
11 Polynomial equations
Polynomial equations This free online course covers solutions to polynomial equations and the Fundamental Theorem of Algebra. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Solution of Polynomial Equations

Example

The Fundamental Theroem of Algebra

Equations

Examples


Module
12 Reciprocal function graphs
Reciprocal function graphs This free online course covers graphs of reciprocal functions. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Graphs of Reciprocal Functions

Example 1

Example 2

Example 3


Module
13 Vectors in 2 and 3 dimensions
Vectors in 2 and 3 dimensions This free online course covers topics related to scalars. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Vector Definition

Symbols Used to Represent Vectors

Magnitude of a Vector

Zero Vector

Subtracting Vectors

Equal vectors

Parallel Vectors

Vectors in Cartesian Form

Position Vectors

The Cartesian Plane

Linear Dependence and Independence

Unit Vector

Multiplying by a Scalar

Linear Dependence and Independence Example


Module
14 Scalar products of vectors
Scalar products of vectors This free online course covers topics such as scalar and vector resolutes, and finding the angle between two vectors. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Scalar and vector resolutes

Scalar resolutes

Vector resolutes

Vector resolute examples

Scalar (or dot) Product

Using the Dot Product in Vector Proofs

Example 1

Finding the Angle Between Two Vectors

Example 2 (midpoints)

Perpendicular Vectors

Inclination to the x or y axis

Example 3 (midpoints)

Example 4 (Colinear points)


Module
15 Symmetry and periodicity
Symmetry and periodicity This free online course covers topics related to symmetry and periodicity. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Use of Symmetric, Periodic and Complementary Relationships of Circular Functions

Symmetry Example 1

Example 2

Example 3

Periodicity

Complementary Relationships

Complementary Relationship Examples


Module
16 Trigonometric identities
Trigonometric identities This free online course covers topics related to reciprocal circular functions, inverse circular functions, and trigonometric identities. The Contents tab displays all the lessons and topics of the course. Each time you click the Contents tab, you will come to this page. A green tick indicates those lessons and topics you have completed, so you can easily see your progress.

Reciprocal Circular Functions

Inverse Circular Functions

Trigonometric Identities


Assessment

Assessment

Advanced Mathematics 1 Assessment
