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Essential mathematics 1

This key introductory module provides a broad and enjoyable foundation for university-level mathematics, but you do require some prior knowledge. It teaches you the essential ideas and techniques that underpin university-level study in mathematics and mathematical subjects such as physics, engineering and economics. You’ll study a range of fundamental topics – including calculus, vectors, matrices and complex numbers – and use mathematical software to solve problems. You’ll also develop your skills in communicating results and defining problems. This is not a module for beginners. Our MathsChoices website ( contains quizzes, sample material and advice to help you decide if this is the right module for you.

Modules count towards OU qualifications

OU qualifications are modular in structure; the credits from this undergraduate-level module could count towards a certificate of higher education, diploma of higher education, foundation degree or honours degree.

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Module code
Study level
1 7 4
Study method
Distance Learning
Module cost
See Module registration
Entry requirements
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What you will study

There are twelve study units in this module.

In the first two, you’ll revise and extend the basic mathematical knowledge and skills in basic algebra and graphs that should mainly be familiar to you. This revision material should help you identify and fill any gaps in your previous knowledge, and develop your basic mathematical skills to the level that you’ll need in the rest of the module. Much of the material in these two units will be available online, so you can make a start on your revision even before the module begins, if you wish. The first two units also teach you about communicating mathematics, and introduce you to the mathematical software that you’ll use in the module.

In the remaining study units you’ll cover these topics:

  • Functions: these provide a means of representing situations where one quantity depends on another. For example, the distance travelled by a car depends on the time that it has been travelling. You need to know about functions before you can study calculus.
  • Trigonometry: you’ll revise the relationships between the angles and side lengths of triangles, and the definitions of the trigonometric functions sine, cosine and tangent for angles of any size. You’ll learn many useful properties of these functions, which are used to model a wide range of cyclical phenomena, such as rotating objects, and waves.
  • Vectors: these are quantities that have both a size and a direction. You’ll learn about the mathematics of vectors, and how to use them to model a variety of physical quantities, such as speed in a particular direction.
  • Calculus: this is one of the most important and widely applicable topics in mathematics. It is concerned with quantities that change continuously, such as the distance travelled by, and the speed of, a moving object. You’ll be introduced to differentiation and integration, and learn how to use calculus to model a range of different situations and to solve problems from areas such as physics and economics. 
  • Matrices: these are arrays of numbers, which can be manipulated mathematically in various ways. They’re used extensively in both pure mathematics and mathematical applications.
  • Sequences: you’ll learn how to work with some commonly occurring types of number sequences, such as those in which each number is obtained by multiplying the previous number by a constant.
  • Complex numbers: these form an intriguing set of numbers that includes all the usual numbers, and also many `imaginary’ numbers, such as the square root of minus one. They have many uses in applied mathematics, as well as being the basis of some fascinating pure mathematics.

You’ll work mainly from the module books, which are available in various electronic formats as well as in print. You can view many of the worked examples in the books in an alternative video format, in which tutors work through and discuss the examples. You’ll also use specially-designed software applications to help you understand the concepts taught, and you’ll learn to use a mathematics computer package to solve problems. 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.

Samples of the study material, including example assessment questions, are available at our MathsChoices website.

You will learn

Successful study of this module should begin to develop your skills in:

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

Essential mathematics 1 is designed to be taken either as your first university-level mathematics module or following on from Discovering mathematics (MU123).

Essential mathematics 2 (MST125) is designed to follow on from Essential mathematics 1. Normally, you should have completed this module first. However, if you have plenty of study time and a high level of confidence and fluency with algebraic manipulation you could study both modules in one year.

Alternatively, if you are considering progressing to Mathematical methods (MST224), normally you should have also completed this module.

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 our Student Registration & Enquiry Service 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

The details given here are for the module that starts in October 2014 and February 2015. We expect it to be available twice a year.


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

Course work includes:

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


This is a key introductory OU level 1 module. OU level 1 modules provide core subject knowledge and study skills needed for both higher education and distance learning, to help you progress to modules at level 2.

Although many of these topics are revised, consolidated and extended in the module, we recommend that you have some previous knowledge of:

  • arithmetic of whole numbers, decimals and fractions (including negative numbers, powers and roots)
  • algebraic manipulation, such as multiplying out brackets, factorising simple expressions, solving linear and quadratic equations, manipulating algebraic fractions and manipulating powers of variables
  • percentages, ratio and proportion.
  • coordinates of points in the plane, and the equations of straight lines and parabolas.
  • geometry of plane figures, such as the sizes of angles, alternate and corresponding angles, the areas of shapes, similar and congruent shapes, and the properties of triangles, rectangles and circles
  • geometry of solid figures, such as volumes and other properties of cuboids and cylinders
  • simple inequalities
  • trigonometric ratios – sine, cosine and tangent
  • logarithms and the rules for manipulating them.

A mathematical A-level, or a high grade in GCSE mathematics (or the equivalent), would normally provide this. If you are not familiar with the majority of the topics listed above, we recommend that you study our OU level 1 module Discovering mathematics (MU123) before this module.

If you have any doubt about the level of study, or about choosing the most suitable mathematics module with which to start, please contact our Student Registration & Enquiry Service. or look at our MathsChoices website. The MathsChoices website also contains a self-assessment quiz to help you decide if Essential mathematics 1 is the right module for you.

Preparatory work

The first two units of the module help you to revise, consolidate and extend the basic mathematical knowledge and skills that are required in the rest of the module. Much of the material in these first two units will be available online before the module begins, and it would be a good idea to start working through it as soon as you can, to make sure that you’re as well prepared as possible for the main work in the module. Working through this material will also help you confirm whether this is a suitable module for you: if you find that most of it is unfamiliar to you, we recommend that you consider taking Discovering mathematics (MU123) first.

If you wish to do some extra preparation before starting on the study material, then we suggest that you work through a GCSE Mathematics Higher Level, or equivalent, text book, which may be available online or in a local library. You could also use a book or website to familiarise yourself with the first core module (C1 – the first pure maths module) of AS-Level Mathematics, or equivalent. This will contain some topics which you are not expected to have studied before you start this module but, if you can do some work on those as well, it may help you to get a head start with your studies. The MathsChoices website contains further suggestions for help on topics you may need to practice, for example algebra and trigonometry. 


Start End England fee Register
04 Oct 2014 Jun 2015 £1316.00

Registration closes 11/09/14 (places subject to availability)


You may need to apply for some payment or funding options earlier. Please check the Fees and Funding information or contact us for information.

31 Jan 2015 Sep 2015 £1316.00

Registration closes 08/01/15 (places subject to availability)


You may need to apply for some payment or funding options earlier. Please check the Fees and Funding information or contact us for information.

This module is expected to start for the last time in October 2021.

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 annual fees and spreads them out over up to a year, enabling you to pay your fees monthly and walk away with a qualification without any further debt. APR 5.1% representative.

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

Employer sponsorship

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

More than one in 10 OU students are sponsored by their employer, and over 30,000 employers have used the OU to develop staff so far. If the qualification 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 modules.  

For more information about employer sponsorship speak to an adviser or request a call back.

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, Maestro (UK only), Mastercard, Visa/Delta and Visa Electron. 

Gift vouchers

You can pay for part or all of your tuition fees with OU gift vouchers. Vouchers are currently available in the following denominations, £10, £20, £50 and £100. 

Mixed payments

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

For more information about combining payment options, speak to an adviser or request a call back.

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 based upon current details for  year 1 August 2014 to 31 July 2015.
This information was provided on 29/07/2014.

What's included

Module books and website, including access to computer applications and to optional online tutorials.

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 programmable calculators are not permitted in the final examination, nor are calculators that can perform algebraic manipulation, differentiation or integration.

Computing requirements

You will need a computer with internet access to study this module as it includes online activities, for use with a web browser. There is also software to download and install on your computer.

  • If you have purchased a new desktop or laptop computer since 2008 you should have no problems completing the online activities.
  • If you’ve got a netbook, tablet or other mobile computing device you may have difficulties with some software, check our Technical requirements section.
  • If you use an Apple Mac you will need OS X 10.7 or later.

You can also visit the Technical requirements section for further computing information (including details of the support we provide).

If you have a disability

By its nature mathematics is a visual subject, and this module will contain considerable amounts of mathematical notation and graphs, and other forms of diagram. If you have a visual impairment or limited manual dexterity you may experience difficulties with some of the activities and assessment questions which involve the interactive use of ICT or which have a high graphical content.

It is important to note that use of the online activities and resources, which include on-screen dynamically-changing graphs and mathematical notation, will be an integral part of your study. You will need to spend considerable amounts of time using a personal computer, and some of your assignments will be interactive and online.

Written transcripts of any audio components and Adobe Portable Document Format (PDF) versions of printed material are available. Some Adobe PDF components may not be available or fully accessible using a screen reader (and mathematical notation may be particularly difficult to read in this way). Other alternative formats of the study materials may be available in the future. 

If you have particular study requirements please tell us as soon as possible, as some of our support services may take several weeks to arrange. Find out more about our services for disabled students.