
Free Course

XSIQ

34 Hours

Assessment

Certification

Academic  Secondary  Level 3

50 Pts
Advanced Mathematics 1

Description

Outcome

Certification

This Advanced Mathematics 1 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 Theorem, 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
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Nominal data
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Discrete data
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Continuous data
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Frequency tables with nominal data
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Frequency tables with discrete data
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Frequency tables  discrete data and summary statistics
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Mean from frequency tables  discrete data
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Interpreting column graphs
Start Topic

Family size cumulative frequency
Start Topic


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
Start Topic

Example 1
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Example 2
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Example 3
Start Topic


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
Start Topic

Standard Antiderivative Types
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Type 2  Hyperbolic Functions
Start Topic

Type 3  Partial Fractions
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Example 2
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Type 5  Linear Substitution
Start Topic


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
Start Topic

Examples 1 and 2
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Examples 3 and 4
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Examples 5 and 6
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Type 6  Odd and Even Powers
Start Topic

Odd Powers
Start Topic

Even Powers
Start Topic


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
Start Topic

Original and Antiderivative Functions
Start Topic

Graphs of Antiderivatives
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Examples 1 and 2
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Examples 3 and 4
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Examples 5 and 6
Start Topic


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
Start Topic

Operations with Complex Numbers
Start Topic

Addition and Subraction of Complex Numbers
Start Topic

Multiplication of Complex Numbers by a Constant
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Multiplication of Complex Numbers by Another Complex Number
Start Topic

Division and Complex Conjugates
Start Topic

Division of Complex Numbers
Start Topic

Argand Diagram
Start Topic


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
Start Topic

Conversion between polar form and cartesian form
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DeMoivre's Theorem
Start Topic

Polar form multiplication  example 1
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Polar form division  example 1
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Polar form multiplication  example 2
Start Topic

Polar form division  example 2
Start Topic


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
Start Topic

Examples
Start Topic

Graphs of Hyperbolae
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Example 1
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Example 2
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Example 3
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Example 4
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Transformations of hyperbolae
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Translations
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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
Start Topic

Conversions of Radian and Degree Measures
Start Topic


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
Start Topic

Example 2
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Example 3
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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
Start Topic

Example
Start Topic

The Fundamental Theroem of Algebra
Start Topic

Equations
Start Topic

Examples
Start Topic


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
Start Topic

Example 1
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Example 2
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Example 3
Start Topic


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
Start Topic

Symbols Used to Represent Vectors
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Magnitude of a Vector
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Zero Vector
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Subtracting Vectors
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Equal vectors
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Parallel Vectors
Start Topic

Vectors in Cartesian Form
Start Topic

Position Vectors
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The Cartesian Plane
Start Topic

Linear Dependence and Independence
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Unit Vector
Start Topic

Multiplying by a Scalar
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Linear Dependence and Independence Example
Start Topic


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
Start Topic

Scalar resolutes
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Vector resolutes
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Vector resolute examples
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Scalar (or dot) Product
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Using the Dot Product in Vector Proofs
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Example 1
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Finding the Angle Between Two Vectors
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Example 2 (midpoints)
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Perpendicular Vectors
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Inclination to the x or y axis
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Example 3 (midpoints)
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Example 4 (Colinear points)
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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
Start Topic

Symmetry Example 1
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Example 2
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Example 3
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Periodicity
Start Topic

Complementary Relationships
Start Topic

Complementary Relationship Examples
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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
Start Topic

Inverse Circular Functions
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Trigonometric Identities
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Assessment