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Essential mathematics 2

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Essential mathematics 2 (MST125) builds on the concepts and techniques in Essential mathematics 1 (MST124) to provide a complete foundation for higher-level mathematics studies. You’ll be introduced to a broad range of enjoyable and essential topics, such as proof, differential equations, mechanics and discrete mathematics, as well as extending your knowledge of calculus and its applications. You’ll use mathematical software, and learn how to typeset mathematics. To study this module you should have a sound knowledge of relevant mathematics as provided by Essential mathematics 1 (MST124) in particular basic calculus.

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.

The module includes a large amount of online study material, and requires you to use mathematical software frequently, so you’ll need regular access to a suitable personal computer.

This module builds on many of the mathematical topics covered in Essential mathematics 1 (MST124). If you have plenty of study time (at least 20 hours per week), a high level of fluency with algebraic manipulation, and a good knowledge of basic topics such as linear and quadratic graphs, linear and quadratic equations, trigonometry, indices and logarithms, it may be possible to study the two modules together. We provide a study schedule to ensure that you study each topic in this module only after you have studied the necessary preliminary topics in Essential mathematics 1 (MST124). Further information on this option is available on our MathsChoices website. If you think this option may suitable for you, please contact us to speak to our Mathematics and Statistics Student Support Team for advice before you register. 

If you are considering progressing to Pure mathematics (M208) or Mathematical methods, models or modelling (MST210), normally you should have completed this module. You are more likely to complete these modules successfully if you have acquired your prerequisite knowledge through passing this OU level 1 module.

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).

IMA logo

Entry requirements

You must have passed (or be studying) Essential mathematics 1 (MST124) or, if you're studying engineering, Engineering: maths. modelling, applications (T194).

Essential mathematics 1 (MST124) underpins Essential mathematics 2 (MST125): providing you with a good knowledge of the algebra, functions, trigonometry, vectors, matrices and calculus (differentiation and integration).

If you already have a strong mathematical background (e.g. an A-Level in mathematics), you may be allowed to study Essential mathematics 2 (MST125) without having first studied Essential mathematics 1talk to an adviser.

Our self-assessed quiz can help you determine if you have the appropriate level of mathematical knowledge.

Preparatory work

In Unit 1 of Essential mathematics 2, you’ll consolidate the mathematical knowledge and skills taught in Essential mathematics 1.

It’s a good idea to start working through Unit 1 well before the module starts. This will also help you confirm if Essential mathematics 2 is suitable: if you find a lot of the material is unfamiliar, consider taking Essential mathematics 1 first.

You’ll find more preparation advice at the end of the self-assessed quiz.

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-83GT PLUS or fx-85GT 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

A computing device with a browser and broadband internet access is required for this module.  Any modern browser will be suitable for most computer activities. Functionality may be limited on mobile devices.

Any additional software will be provided, or is generally freely available. However, some activities may have more specific requirements. For this reason, you will need to be able to install and run additional software on a device that meets the requirements below.

A desktop or laptop computer with either:

  • Windows 7 or higher
  • Mac OS 10.7 or higher

The screen of the device must have a resolution of at least 1024 pixels horizontally and 768 pixels vertically.

To participate in our online-discussion area you will need both a microphone and speakers/headphones. 

Our Skills for OU study website has further information including computing skills for study, computer security, acquiring a computer and Microsoft software offers for students. 

Teaching and assessment

Support from your tutor

You will have a tutor who will help you with the study material and mark and comment on your written work, and whom you can ask for advice and guidance. If you are new to the OU, you will find that your tutor is particularly concerned to help you with your study methods. We may also be able to offer group tutorials (online or face-to-face), that you are encouraged, but not obliged, to attend. The locations of face-to-face tutorials will depend on the distribution of students taking the module.

Contact us if you want to know more about study with The Open University before you register.


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

You can choose whether to submit your tutor-marked assignments (TMAs) on paper or online through the eTMA system. You may want to use the eTMA system for some of your assignments but submit on paper for others. This is entirely your choice.

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 February and October. This page describes the module that will start in October 2018 and February 2019. We expect it to start for the last time in October 2021.

Course work includes:

3 Tutor-marked assignments (TMAs)
4 Interactive computer-marked assignments (iCMAs)
No residential school

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