Specialist Materials
Purpose
Pure Maths and Statistics for Actuarial Studies (also known as 'Module 0') is a course designed to help students improve their maths and statistics skills in preparation for Subjects CM1, CM2, CS1 and CS2 of the IFoA actuarial exams. The course can be studied in advance of, or alongside, these subjects and is geared specifically towards actuarial students.
To help you decide if you would benefit from this course, we have written an initial assessment. There are 25 questions which are typical of the maths and statistics knowledge required. Your starting point should be to have a go at the assessment, which should take approximately 75 minutes. Compare your answers with the solutions provided. If you scored less than 80% in the assessment, and/or struggled with the questions, and/or would appreciate some relevant reference resources, then the course is for you.
Download the Initial Assessment; download the Initial Assessment Solutions.
Contents and Format
We offer two packages: bronze and gold.
Bronze
The Bronze package provides you with a textbook, which contains easy to follow explanations of topics, several worked examples with solutions, and practice questions with summary solutions at the end of each chapter. The textbook has 16 chapters, covering:
- notation and terminology
- numerical methods
- differentiation and integration techniques
- vectors and matrices
- algebra, including summation of series and binomial expansions
- basic and advanced probability
- measures of location, spread and skewness
- permutations and combinations
- discrete and continuous random variables.
You can order a hardcopy of the textbook, or an eBook copy.
Download a sample of the textbook.
Gold
In addition to the textbook, the Gold package gives access to a course called 'Module 0 Gold' on our Virtual Learning Environment for up to 13 months from the date of purchase. The course offers a variety of easily accessible resources including:
- study guides to help you navigate the material efficiently
- over 75 short videos, recorded by our team of expert tutors, explaining key topics and working through example questions
- introductory and progress tests for each chapter to test your understanding
- full solutions to the textbook questions
- two practice exams and a large bank of additional practice questions to consolidate your learning.
Pricing
Information on the pricing of Pure Maths and Statistics for Actuarial Studies can be found here.
Additional resources
Yes! Whilst it's very comprehensive, there will inevitably be other topics that come up occasionally in the actuarial exams. Below are some PDF files, which you may find helpful.
- Arithmetic and geometric mean inequality
- Complex numbers
- Differential equations
- Differentiating an integral
- Eigenvectors and eigenvalues
- Factorial notation and the gamma function
- Functions of a random variable
- Iteration
- Lagrangian multipliers
- Matrices to solve simultaneous equations
- Multiple integrals
- Normal distribution
- Order notation
- Regression and correlation
- Trapezium rule
The documents are in PDF format, and you will need the latest version of Adobe Acrobat Reader to view them. If you don't have Adobe Acrobat Reader, you can download it here.
Purpose
Our Actuarial Analyst courses, Modules 0 to 5, were originally written for the CAA (Certified Actuarial Analyst) qualification, to equip students with the practical actuarial and modelling techniques needed in a wide variety of financial roles. Although this qualification is now retired, the courses remain useful and relevant for a number of purposes:
- Module 0 (also known as Pure Mathematics and Statistics) is used by many students each year to improve their maths and statistics skills in preparation for Subjects CM1, CM2, CS1 and CS2 of the IFoA actuarial exams. In particular, it is helpful for graduates with a non-mathematical degree.
- Modules 0 and 1 are studied and assessed as part of the Level 4 Actuarial Technician Apprenticeship.
- Modules 0 to 5 are used by employers looking for actuarial training resources for school leavers or for those wanting to focus on the more practical (rather than theoretical) elements of actuarial maths. ActEd are happy to work with employers to produce internal assessments for any of the modules. If this is of interest, please email us.
Contents
| Title | Topics covered | |
|---|---|---|
| Module 0 | Pure Mathematics and Statistics | Notation and terminology, numerical methods, differentiation and integration, vectors and matrices, algebra (including summation of series and binomial expansions), basic and advanced probability, measures of location, spread and skewness, permutations and combinations, discrete and continuous random variables |
| Module 1 | Finance and Financial Mathematics | Ways of raising finance, interest rates, annuities, equations of value, loan schedules, valuing bonds, equities and property, project appraisal, derivatives |
| Module 2 | Statistics and Models | Continuous and discrete distributions, generating functions, sampling, point and interval estimation, hypothesis testing, correlation and regression, stochastic processes and interest rate models, survival models, Markov chains and jump processes |
| Module 3 | Long-Term Actuarial Mathematics | Life tables, assurance and annuity contracts, setting of premiums and reserves, joint life and last survivor functions, competing risks, profit testing, heterogeneity and selection |
| Module 4 | Short-Term Actuarial Mathematics | Loss distributions, reinsurance, compound and individual risk models, ruin and run-off triangles |
| Module 5 | Models and Audit Trails | Spreadsheet modelling: summarising data, descriptive statistics and graphical representation, checks on data, and audit trails: parameters, methods and checks |
Format
We are pleased to offer affordable and comprehensive study packages for the Actuarial Analyst courses. These packages are:
- flexible - offering a choice of resources and the ability to work through the material in your own time and at your own pace
- tailored to your individual needs - they enable you to assess your current level of knowledge and use this to move quickly through the topics with which you are already familiar, leaving you to focus on the topics you need to concentrate on
- interactive - the products contain integrated questions to test yourself, and online tutorials (gold package only) that you can pause to reflect on, and to attempt questions.
We offer two packages: bronze and gold.
| Package includes | |
|---|---|
| Bronze |
A textbook with easy-to-follow explanations of topics, several worked examples with solutions, and practice questions with summary solutions at the end of each chapter. You can order a hardcopy of the textbook, or an eBook copy. Download a sample of the Module 0 textbook. |
| Gold |
The bronze package plus access to an 'Online Classroom' course on our virtual learning environment for up to 13 months from the date of purchase, including:
Download a sample of a teaching video unit. |
Further information on eBooks is available here.
Pricing
Our product range aims to cater for differing needs at affordable prices.
| Bronze | Gold | |
|---|---|---|
| Module 0 | £50 | £100 |
| Module 1-3 | £70 | £210 |
| Module 4 | £50 | £150 |
| Module 5 | £50 | £230 |
Notes
- These prices are for the Actuarial Analyst courses.
- Please be aware that the above prices exclude despatch charges which may also apply.
- Students with a current rate of annual income less than £10,000 pa are eligible for reduced rates with ActEd. Please refer to the reduced-rate prices for details.
- VAT is added for orders of eBooks from within the EU and South Africa. (There is no VAT added to UK eBook orders.) Please email us if you need any further guidance before ordering.
- Students based overseas may incur import tax on delivery of materials. Any VAT, charges and tariffs levied by the customs authorities (and related fees by the courier) are the responsibility of the recipient rather than ActEd.
All prices correct as at 22nd December 2025 but may be subject to change.
Other resources
There is a Worked Example Project that accompanies the bronze and gold packages for Module 5, which can be found here.
If you find an error in the course whilst studying, please email us with details of the problem.
Corrections to the textbooks are as follows: