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Essential mathematics 2

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This module builds on the concepts and techniques in Essential mathematics 1 (MST124) to provide a complete foundation for higher-level mathematics studies. It introduces enjoyable and essential topics, such as proof, differential equations, mechanics and discrete mathematics, and extends your knowledge of calculus and its applications. You’ll also use mathematical software and learn how to typeset mathematics.

What you will study

There are twelve study units in this module.

In the first unit, you’ll revise and consolidate the mathematics taught in Essential mathematics 1 (MST124).

In the remaining study units you’ll cover the following topics.

  • Number theory: you’ll learn about divisibility properties of the integers. These have many practical applications, such as in cryptography.
  • Conics: these are the curves obtained by slicing a cone along a plane. Their applications include modelling the motion of planets and other heavenly bodies.
  • Geometric transformations: these include reflections, rotations and translations, and other similar ways of transforming geometric figures. You’ll use an algebraic approach, involving matrices and vectors.
  • Mathematical language and proof: you’ll look at how mathematical results can be stated clearly, and how they can be proved to be true.
  • Further calculus: you’ll extend your knowledge and skills in calculus.
  • Differential equations: these are equations that involve an unknown function and one or more of its derivatives. They are used extensively in applied mathematics to model a range of situations involving quantities that change.
  • Mechanics: you’ll analyse forces that act on stationary objects, and the motion of moving objects.
  • Eigenvalues and eigenvectors: these are numbers and vectors associated with matrices, which arise in a range of situations in both pure and applied mathematics.
  • Combinatorics: you’ll learn how to solve problems involving the positive integers, such as how many different ways there are to choose objects from a set. You’ll also study some interesting sequences of numbers, such as the Fibonacci sequence.

With a choice of three options of typesetting software, you’ll learn how to typeset mathematics.

You’ll work mainly from the module books, which are available in electronic formats as well as in print. You can view some of the worked examples in the books in an alternative video format, in which tutors work through and discuss the examples. You’ll use specially designed software applications to help you understand the concepts taught, and the same mathematics computer package as used in Essential mathematics 1 (MST124). There are many online interactive practice questions to help you consolidate your learning.

You can find the full content list on the Open mathematics and statistics website.

You will learn

In Essential mathematics 2 (MST125), you’ll further develop your mathematical skills and begin to develop new ones:

  • thinking logically about mathematical problems
  • expressing problems in mathematical language
  • using mathematical techniques to find solutions to problems
  • communicating mathematical ideas clearly and succinctly

Professional recognition

This module can help you to gain membership of the Institute of Mathematics and its Applications (IMA).

Entry requirements

You must have passed, or currently be studying, one of the following modules:

Or be able to provide evidence you have the required mathematical skills.

You can check you’re ready for MST125 and see the topics it covers here.

Talk to an advisor if you’re not sure you’re ready.

Preparatory work

You should aim to be confident and fluent with the concepts covered in the Are you ready? quiz here, and follow the advice in the quiz.

The key topics to revise include:

  • algebraic manipulation and solving equations
  • quadratics and parabolas
  • geometry and trigonometry
  • exponentials and logarithms.

Essential mathematics 1 (MST124) is ideal preparation.

What's included

Module books and website, including access to optional tutorials as well as computer applications, which you need to download.

You will need

We recommend a basic scientific Casio ‘Natural’ calculator such as the fx-83GTX PLUS or fx-85GTX PLUS. The module website includes a calculator guide with references to this series of calculator.

Note that the only type of calculator permitted in the final examination is a scientific calculator that does not offer algebraic manipulation, differentiation or integration, language translation or communication with other devices or with the internet. It should also not be programmable, and not have any retrievable information (such as databanks, dictionaries, mathematical formulas or text) stored in it.

Computing requirements

You’ll need broadband internet access and a desktop or laptop computer with an up-to-date version of Windows (10 or 11) or macOS Ventura or higher.

Any additional software, including any required to complete the online invigilated exam, will be provided or is generally freely available.

To join in spoken conversations in tutorials, we recommend a wired headset (headphones/earphones with a built-in microphone). You’ll need a webcam and microphone for the online invigilated exam.

Our module websites comply with web standards, and any modern browser is suitable for most activities.

Our OU Study mobile app will operate on all current, supported versions of Android and iOS. It’s not available on Kindle.

It’s also possible to access some module materials on a mobile phone, tablet device or Chromebook. However, as you may be asked to install additional software or use certain applications, you’ll also require a desktop or laptop, as described above.

Teaching and assessment

Support from your tutor

Throughout your module studies, you’ll get help and support from your assigned module tutor. They’ll help you by:

  • Marking your assignments (TMAs) and providing detailed feedback for you to improve.
  • Guiding you to additional learning resources.
  • Providing individual guidance, whether that’s for general study skills or specific module content.
  • Facilitating online discussions between your fellow students, in the dedicated module and tutor group forums.

Module tutors also run online tutorials throughout the module. Where possible, recordings of online tutorials will be made available to students. While these tutorials won’t be compulsory for you to complete the module, you’re strongly encouraged to take part.


The assessment details for this module can be found in the facts box.

This module includes a remote exam you will take at home or another suitable location. From the February 2025 start, the exam will be invigilated online by ProctorU, a service based outside the UK and with whom you must agree to additional Terms of Service to study this module. Find out more about online invigilation.

If you have a disability

The OU strives to make all aspects of study accessible to everyone and this Accessibility Statement outlines what studying MST125 involves. You should use this information to inform your study preparations and any discussions with us about how we can meet your needs.

Future availability

Essential mathematics 2 (MST125) starts twice a year – in January/February and October.

This page describes the module that will start in October 2024 and February 2025.

We expect it to start for the last time in October 2029.

Course work includes:

3 Tutor-marked assignments (TMAs)
4 Interactive computer-marked assignments (iCMAs)

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