Free Diploma Online Mathematics Classes and Tutorials | Alison

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Diploma in Mathematics

Want to improve your math skills? This course will guide you through math’s most important concepts and principles.

Core Maths Skills
Free Course
This free online Diploma in Mathematics course will teach you a variety of the most important principles in mathematics, from data distributions to binomial expressions. It starts by refreshing your knowledge of triangles, quadrilaterals, polygons, and other geometric shapes then move on to cover algebra, vectors, functions, calculus, and trigonometry. Start this free online course today to get your maths back up to par.
  • Duration

    15-20 Hours
  • Assessment

  • Certification

  • Publisher

  • Accreditation






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The course covers a comprehensive range of key subjects in mathematics. Starting with calculus and geometry, the course guides you through the mathematics behind shapes and design principles. Next, the course moves through functions, vectors, and data distributions. These are highly important principles used in rocket science, the military, and aerospace engineering. The course will then introduce you to algebra and trigonometry, which are core to a future in any mathematics-oriented career.

Next, you’ll learn how to confidently create graphs and make advanced calculations such as straight-line calculations, kinematics, motion, and quadratic functions. Finally, for the gamblers amongst you, you will learn about probability and statistics, including an overview of the relationship between the graphs of functions and their antiderivatives. This section will also show you how to use binomial expansions for problem solving, so the next time you play poker you will have a real edge over your competitors.

By the end of this course, you will have gained math skills that can open up a range of careers, and will be much better prepared for your next math exam. Math skills are in great demand from international employers, and almost every student in the world needs to learn them. Despite this, very few people have strong math skills. With this free course, and less than 5 hours of work, you’ll stand above the crowd. So why wait? Make Math easier, today.


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Introduction to triangles

Angle types

Angle sizes and sums in triangles

Triangles - Similiarity and congruence

Corresponding angles

Introduction to quadrilaterals


Introduction to polygons


Geometrical solids


Univariate data

Univariate data 2

Bivariate data

Summary statistics



Calculating a seasonal index


Regression line

Non-linear data

Residual analysis


Arithmetic sequences

Arithmetic series

Geometric sequences

Geometric series

Difference equations 1

Difference equations 2

Difference equations 3


Straight lines


Power graphs

Trigonometry 1

Trigonometry 2

Pythagoras and bearings

Ratio and proportion

Ratio and proportion gears

Discrete random variables

Normal distribution

Binomial distribution

Hypergeometric distribution

Rules of integration

Integration applications

Rules of differentiation

Applications of differentiation

Factors of polynomials

Straight line graphs

Graphs of ciruclar functions

Inverse functions

Logarithms and index laws

The binomial theorem

Creating a frequency table from data

Differentiation - Product rule


Antiderivatives of circular functions

Antiderivatives and their graphs

Conics (elipses and hyperbolae)

Degrees and radians

Inverse circular functions

Polynomial equations

Reciprocal function graphs

Vectors in 2 and 3 dimensions

Scalar products of vectors

Symmetry and periodicity

Trigonometric identities

Differential equations

Second derivatives



Resolution of forces


Vectors 2

Introduction to Algebra

Using Formulae 1

Using Formulae 2

Algebraic Expressions 1

Algebraic Expressions 2

Algebraic Fractions 1

Algebraic Fractions 2

Algebraic Fractions 3

Terminology for Algebraic Expressions

Binomial Expressions 1

Binomial Expressions 2

Binomial Expressions 3

Completing the Square

Perfect Squares

Quadratic Trinomials

Substitution into Algebraic Expressions

Summary of Factorisation

Summarising data

Frequency and graphs

Graphs of all kinds

Introduction to probability

Odds and probability

Probability and relative frequency


Learning Outcomes

Alison's math course will greatly enhance your skills, giving you a greater understanding of core mathematics components such as geometry, trigonometry, calculus and more as well as expanding your knowledge base in areas such as chance, data distributions, statistics, probability, correlations and regression.

You will learn about using binomial expansions for problem solving and will understand the relationship between the graphs of functions and their anti-derivatives. You will be able to confidently create graphs and make advanced calculations such as straight-line calculations, kinematics, motion, vectors, algebra, binomial expressions, and quadratic functions.


All Alison courses are free to enrol, study and complete. To successfully complete this Diploma course and become an Alison Graduate, you need to achieve 80% or higher in each course assessment. Once you have completed this Diploma course, you have the option to acquire an official Diploma, which is a great way to share your achievement with the world. Your Alison Diploma is:

Ideal for sharing with potential employers - include it in your CV, professional social media profiles and job applications
An indication of your commitment to continuously learn, upskill and achieve high results
An incentive for you to continue empowering yourself through lifelong learning

Alison offers 3 types of Diplomas for completed Diploma courses:

Digital Diploma - a downloadable Diploma in PDF format, immediately available to you when you complete your purchase
Diploma - a physical version of your officially branded and security-marked Diploma, posted to you with FREE shipping
Framed Diploma - a physical version of your officially branded and security-marked Diploma in a stylish frame, posted to you with FREE shipping

All Diplomas are available to purchase through the Alison Shop. For more information on purchasing Alison Diplomas, please visit our FAQs. If you decide not to purchase your Alison Diploma, you can still demonstrate your achievement by sharing your Learner Record or Learner Achievement Verification, both of which are accessible from your Dashboard. For more details on our Diploma pricing, please visit our Pricing Page.


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