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Essential mathematics 2

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.

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Module code


  • Credits measure the student workload required for the successful completion of a module or qualification.
  • One credit represents about 10 hours of study over the duration of the course.
  • You are awarded credits after you have successfully completed a module.
  • For example, if you study a 60-credit module and successfully pass it, you will be awarded 60 credits.
Study level
Across the UK, there are two parallel frameworks for higher education qualifications, the Framework for Higher Education Qualifications in England, Northern Ireland and Wales (FHEQ) and the Scottish Credit and Qualifications Framework (SCQF). These define a hierarchy of levels and describe the achievement expected at each level. The information provided shows how OU module levels correspond to these frameworks.
1 7 4
Study method
Distance Learning
Module cost
See Module registration
Entry requirements
See Entry requirements

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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 and 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.

Read the full content list here.

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

Vocational relevance

The practical skills listed in the ‘You will learn’ section are important for any jobs that involve the use of mathematics. In addition, you’ll develop the following skills:

  • typesetting mathematics
  • using a computer algebra system
  • learning independently

Professional recognition

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

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.

Future availability

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

This page describes the module that will start in February 2021.

We expect it to start for the last time in October 2025.


As a student of The Open University, you should be aware of the content of the academic regulations which are available on our Student Policies and Regulations website.

    Course work includes:

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

    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.


    Start End England fee Register
    03 Oct 2020 Jun 2021 £1548.00

    New to OU? Registration closed. Already an OU Student? If you can pay in full by card you can register here until 02/10/20

    30 Jan 2021 Sep 2021 £1548.00

    Registration closes 14/01/21 (places subject to availability)

    This module is expected to start for the last time in October 2025.

    Additional Costs

    Study costs

    There may be extra costs on top of the tuition fee, such as a computer, travel to tutorials, set books and internet access.

    If your income is not more than £25,000 or you are in receipt of a qualifying benefit, you might be eligible for help with some of these costs after your module has started.

    Ways to pay for this module

    Open University Student Budget Account

    The Open University Student Budget Accounts Ltd (OUSBA) offers a convenient 'pay as you go' option to pay your OU fees, which is a secure, quick and easy way to pay. Please note that The Open University works exclusively with OUSBA and is not able to offer you credit facilities from any other provider. All credit is subject to status and proof that you can afford the repayments.

    You pay the OU through OUSBA in one of the following ways:

    • Register now, pay later – OUSBA pays your module fee direct to the OU. You then repay OUSBA interest-free and in full just before your module starts. 0% APR representative. This option could give you the extra time you may need to secure the funding to repay OUSBA.
    • Pay by instalments – OUSBA calculates your monthly fee and number of instalments based on the cost of the module you are studying. APR 5.1% representative.

    Joint loan applications

    If you feel you would be unable to obtain an OUSBA loan on your own due to credit history or affordability issues, OUSBA offers the option to apply for a joint loan application with a third party. For example, your husband, wife, partner, parent, sibling or friend. In such cases, OUSBA will be required to carry out additional affordability checks separately and/or collectively for both joint applicants who will be jointly and severally liable for loan repayments.

    As additional affordability checks are required when processing joint loan applications, unfortunately, an instant decision cannot be given. On average the processing time for a joint loan application is five working days from receipt of the required documentation.

    Read more about Open University Student Budget Accounts (OUSBA).  

    Employer sponsorship

    Studying with The Open University can boost your employability. OU courses are recognised and respected by employers for their excellence and the commitment they take to complete. They also value the skills that students learn and can apply in the workplace.

    More than one in ten OU students are sponsored by their employer, and over 30,000 employers have used the OU to develop staff so far. If the module you’ve chosen is geared towards your job or developing your career, you could approach your employer to see if they will sponsor you by paying some or all of the fees. 

    • Your employer just needs to complete a simple form to confirm how much they will be paying and we will invoice them.
    • You won’t need to get your employer to complete the form until after you’ve chosen your module.  

    Credit/debit card

    You can pay part or all of your tuition fees upfront with a debit or credit card when you register for each module. 

    We accept American Express, Mastercard, Visa and Visa Electron. 

    Mixed payments

    We know that sometimes you may want to combine payment options. For example, you may wish to pay part of your tuition fee with a debit card and pay the remainder in instalments through an Open University Student Budget Account (OUSBA).

    Please note: your permanent address/domicile will affect your fee status and therefore the fees you are charged and any financial support available to you. The fees and funding information provided here is valid for modules starting before 31 July 2021. Fees normally increase annually in line with inflation and the University's strategic approach to fees. 

    This information was provided on 26/09/2020.

    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 an up-to-date version of Windows or macOS.

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

    To join in the spoken conversation in our online rooms we recommend a headset (headphones or earphones with an integrated microphone).

    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.

    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.

    To find out more about what kind of support and adjustments might be available, contact us or visit our Disability support website.