Learning Outcomes

Number Systems

Arithmetic Calculations

Working with Shapes

Lesson Summary

In this module, you will learn how to work with and solve number systems including indices, arithmetic series and geometric series. You'll also use arithmetic to work with percentages, simple interest, compound interest and depreciation. Finally, covering how to calculate the length, area or volume of shapes or segments.

Strand 3 Junior Certificate Ordinary Level Numbers and Shapes - Course Assessment

Gain better understanding of working with complex numbers in this free online course.

Strand 3 Junior Certificate Ordinary Level Numbers and Shapes

Numbers and shapes, concepts that are the basic building blocks of arithmetic and algebra. In this course, you will study a variety of topics to prepare you for your Junior Certificate. Cover topics like scientific notation and indices rules. As well as calculating interest, formulas used to calculate the area of different shapes will be taught. Whether you are a student or simply looking to brush up on your maths skills this course is for you.

Higher Order Derivatives

Derivatives of Logarithmic Functions

Derivatives of Exponential Functions

This module analyzes higher-order derivatives and the derivatives of inverse trigonometric functions. It discusses the logarithmic differentiation technique and how to graph a logarithmic function. Also, this module covers roles of derivatives regarding increasing and decreasing behaviours. It explores absolute maximum and absolute minimum.

Using a Chart to Find Extrema

The Second Derivative

Applications of the Derivative

Linear Approximations

This module discusses 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.

Anti - Derivatives

The Definite Integral

Sigma Notation

Three Sigma Laws

This module evaluates the concepts 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

AP Calculus BC: Derivatives, Definite and Indefinite Integrals - Course Assessment

This free online course describes absolute extrema, the different application of derivatives, as well as sigma notation.

AP Calculus BC: Derivatives, Definite and Indefinite Integrals

This introductory college-level course gives you a broad understanding of the terms, formulas and problem-solving in calculus. Calculus is a versatile and valuable tool. It is deeply integrated into every branch of the physical sciences and other career paths. This course teaches you about definite and indefinite integrals, antidifferentiation as well as how to apply derivatives in your daily activities.

Definition of Dyscalculia

Developmental Patterns and Early Identification

Assessment and Diagnosis of Dyscalculia

Instructional Strategies and Intervention

Technology and Digital Tools

Mathematical Apps, Software and Manipulatives

Creating an Inclusive Learning Environment

Overview of Policies Supporting Inclusive Education

In this module, we will explore the neurological, cognitive, and educational aspects of dyscalculia. We will then examine how technology and digital tools can support students with dyscalculia. Moreover, we will discuss strategies for creating an inclusive learning environment that meets diverse learning needs.

Course assessment

Discover the practical skills and knowledge to support children and youth with dyscalculia in this free online course.

Understanding Dyscalculia

This course will help you understand the features of dyscalculia, a specific learning difficulty that affects numerical and mathematical abilities in children. We will explore evidence-based strategies for diagnosing, assessing, and addressing the challenges faced by individuals with this condition. The course is designed to provide detailed knowledge and practical skills to support children and youth with dyscalculia. Start this course today!

Definitions and Vocabulary

Non-Positive Exponents

Polynomials - Multiplication and Division

Multiplication of Polynomials

Division of Polynomials

Solving Fractional Equations

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.

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.

Arrangements and Selections

Expected Value

Probability Of Simple Events

Probability Of Compound Events

Independent Events

Probability Using Tree Diagrams

Probability Trees With And Without Replacement

Reverse Probability - Bayes' Theorem

Bayes' Theorem And Medical Testing

Probability Patterns Of Discrete Variables

Learn about calculating probability in this module, Starting of with defining arrangements and selections, how to calculate an expected value, and the probability of simple events, eventually leading into Bayes Theorem and the probability patterns of discrete variables.

Comparing Distributions

The Binomial Distribution

A Problem Using Binomial Distribution

Bernoulli Trials And The Binomial Formula

The Normal Distribution

Using Excel To Calculate Binomial Probabilities

Using Excel To Find The Mean Of A Binomial Distribution

Further you knowledge on counting and probability in this module.

Probability and Chance in Mathematics - Course Assessment

Take this free maths course to learn how to calculate the likelihood or possibility that an event will occur.

Probability and Chance in Mathematics

This module will be a massive help to anyone studying mathematical probability and chance. It covers topics from calculating the probability of simple events to Bayes’ theorem and binomial distribution. You will also look into how to conduct a Bernoulli trial (or binomial trial), study the use of Excel to calculate binomial probabilities, learn to find the mean of a binomial distribution, and a whole lot more!

Udemy Announces Layoffs Without Saying ‘Layoffs’

2000+ Free Developer and IT Certifications

Coursera Announces Layoffs, Stock Plunges Despite $100M Milestone

6 Best Cyber Threat Intelligence (CTI) Courses in 2025

Udemy Appoints McKinsey Veteran as CEO Amid Growth Challenges

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

New CEO, New Structure: Greg Hart Reshapes Coursera’s Reporting

Duolingo’s 2026 Strategy: The Road to 100 Million DAUs

The Day MOOCs Truly Died: Coursera’s Preview Mode Kills Free Learning

10 Best Go (Golang) Courses for 2025

6 Best Node.js Courses in 2025

White-Labeling in Online Education: Whose Credential Is It Anyway?

12 Best JavaScript Courses for 2025: Create Interactive Websites

Coursera 10-K Highlights: Lower Partner Revenue Share, 1k+ Employees

2U Abandons Bootcamp Business, Announces More Layoffs

Why Duolingo is Worth More Than Coursera and Udemy Combined