Learning Outcomes

Definitions and Vocabulary

Non-Positive Exponents

Polynomials - Multiplication and Division

Multiplication of Polynomials

Division of Polynomials

Solving Fractional Equations

Lesson Summary

This module will explain the functions of monomials from the vocabulary associated with this concept. Learn how to carry out addition, subtraction, multiplication, and division of monomials. You will also learn about the laws of exponents detailing the functions of non-positive exponents.

Greatest Common Factor

Trinomials in Factoring

Sum and Difference of Two Perfect Cubes

Problem Solving Applications

In this module, you will learn how to factor various types of polynomials from the factoring techniques that can be applied in solving equations and inequalities. Also, you will learn how to solve problems using factoring applications.

Laws of Exponents and Factoring in Algebra - Course Assessment

Learn about non-positive exponents in algebra and how to factor polynomials from this free online math course.

Laws of Exponents and Factoring in Algebra

This course provides you with a comprehensive guide to the functions of monomial and non-positive exponents. Explore the commonly used vocabulary of monomials along with the relationship between variable expressions with exponents. This course shows you how fractional equations are solved in algebra. Begin today to improve your numeracy and algebra skills!

Factorising Quadratics

Factorising - Difference of Two Squares

Expanding Brackets (Grid Method)

Expanding Brackets (FOIL method)

Expanding Any Two Brackets

Rearranging Simple Formulae

Rearranging Simple Formulae 2 Steps

Rearranging Formulae with Squares and Square Roots

Rearranging Formulae New Subject Appearing Twice

Simplifying Surds

Further Calculations with Surds

Completing The Square

General Completing The Square

Binomial Expansion

Learn about expression and formulae used in the Algebra and Mathematics,

Equations with Linear Functions in The Denominator

Quadratic Equations Using The Formula

Simultaneous Equations Both Negative Signs

Quadratic Equations Non Unitary x Squared

Quadratic Equations Both Brackets The Same Sign

Quadratic Equations Brackets With Different Signs

Quadratic Equations That Have to be Rearranged

Solving Simultaneous Equations Graphically

Simultaneous Equations Negative and Positive Signs

Simultaneous Equations Both Positive

Hidden Quadratics

Use of The Discriminant

Equations With Indices

Learn about solving Quadratic equations and simultaneous equations, along with what hidden quadratics are, the discriminant and how to solve equations with indices.

Logarithmic Equations

Solving Exponential Equations

From Roots to Functions

Non Linear Simultaneous Equations

Factor Theorem

The Remainder Theorem

General Remainder and Factor Theorem

Finding Roots of Cubic Equation

Modulus Equations

Using Graphs to Solve Modulus Equations

Learn more about solving Logarithmic and exponential equations, along with what the factor and remainder theorems are and how they work.

Finding Inequalities from Shaded Regions

Solving Linear Inequalities with Fractions

Solving Quadratic Inequalities – Method 1

Solving Quadratic Inequalities – Method 3

Non-Unitary x^2 - Trial and Error Method

Solving Quadratic Inequalities – Method 2

Non-Unitary x^2 - Algebra Method

Non-unitary x^2 - Graphical Method

Solving Quadratic Inequalities - Special Cases

Rational Inequalities

Modulus Inequalities

Modulus Function On a Graph

Graphical Solution of Modulus Inequalities

Learn about solving and working out quadratic equations with inequalities, demonstrating three different methods to do so, explaining what modulus equations are and how to work them out.

Manipulating Complex Numbers and The Complex Conjugate

The Argand Diagram and Modulus

The Meaning of i

Patterns with Imaginary Numbers

Writing Complex Numbers in Polar Form

Multiplying and Dividing in Polar Form (Proof)

Multiplying and Dividing in Polar Form (Example)

Proof of De Moivre’s Theorem

Complex Numbers When Solving Quadratic Equations

Cubic Equations With Complex Roots

Finding The Cube Roots of 8

Learn about how to work with and use complex numbers, how to convert them to the polar form, multiplying and dividing in the polar form, solving quadratic equations with complex numbers, and complex roots with cubic equations.

Algebra in Mathematics - Assessment

With this online course gain a good understanding of the fundamentals and key aspects of Algebra in mathematics.

Algebra in Mathematics

This free online algebra course offers a comprehensive introduction to algebra and carefully and clearly explains the concepts of algebraic fractions. Have you ever asked yourself why algebra is so complicated? Well, you're not alone. This Algebra in Mathematics course is designed to make studying mathematical symbols much easier for you. Take this free online course today and make your math studies a lot less stressful!

Expressions and Formulas

Solving Equations

Inequalities

Complex Numbers

This first module looks at some basic expressions and formulas. It takes the learner through Inequalities and then moves onto complex numbers. Within each topic are a number of videos which will cover various sub-topics, such as Argand diagrams for complex numbers.

Synthetic Geometry

Coordinate Geometry

Trigonometry

In this module you will learn how to work with and solve synthetic geometry including shapes, coordinate geometry including parallel and perpendicular lines, circles and graphs. You will also learn how to work with trigonometry including sines, cosines and tangents.

Number Systems

Arithmetic

Length - Area - Volume

In this module you will learn how to work with and solve number systems including indices, arithmetic series and geometric series; use arithmetic to work with percentages, simple interest, compund interest and depreciation; and how to calculate the length, area or volume of a shape or segment.

Diploma in Mathematics - First Assessment

You must score 80% or more to pass this assessment.

Counting and Probability

Statistics

In this module you will learn how to work out the probability of simple and compound events, and work with normal distributions and binomial distributions. The topic also introduces you to Bernoulli trials and Bayes' Theorem. You will also learn how to work with statistical methods including sampling methods, correlation and regression, stem and leaf diagrams.

Functions

Calculus - Differentiation

Calculus - Integration

In this module you will learn how to work with functions to plot graphs, including quadratic graphs, cubic graphs and exponential graphs. This topic also review differentiation in detail including the Chain Rule, Product Rule and Quotient Rule. You will also learn about integration, covering areas such as trigonometric functions and exponentials.

Diploma in Mathematics - Second Assessment

Diploma in Mathematics - Assessment

We take you through important mathematical concepts step by step in this free online mathematics diploma course.

Diploma in Mathematics

Enhance and refresh your mathematical knowledge with this diploma course. We cover a wide range of topics, including algebra, statistics, calculus, geometry and trigonometry. We break down these complex ideas and go through them step by step with exercises and examples to prepare you for many professional fields. This course widens your career options as mathematics is essential in a world that is constantly moving forward with new technologies.

Why Duolingo is Worth More Than Coursera and Udemy Combined

10 Best Programming Courses for 2025

Coursera Announces Layoffs, Stock Plunges Despite $100M Milestone

[2025] 150+ Online Courses to Help Your Career

12 Best Data Analysis Courses for 2025: From Data to Insights

Coursera Q1 2022: $120.4M Revenue, $38.3M in Losses, 16K Degree Students

2U Abandons Bootcamp Business, Announces More Layoffs

Medical Education Platforms with 800 Free Certificates & CME Credit

6 Best Cyber Threat Intelligence (CTI) Courses in 2025

Coursera’s New Deal with Google Could Cost the Company Millions

Duolingo Acqui-hires Music Gaming Studio NextBeat for $34.5 Million

6 Best Free OCaml Courses for 2025

6 Best Influencer Marketing Courses for Marketers

8 Best Crochet Courses for 2025: Practical, Enriching, Creative

SEO Content Strategy Demystified: Coursera, MasterClass, and edX

Stanford Medicine Offers Courses with Free Certificate & CME Credit