Programme of Study & Syllabus
Contents
The Syllabus, Examinations and Assessment
How Your Work is Assessed on the Course
The Relationship Between AS and A Level Further Maths - Some Tips
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Welcome to your Wolsey Hall Cambridge A Level Further Mathematics with Statistics course. Please take the time to read carefully through this page as it explains how the course is structured, how to get the most from your studies and how your work will be assessed. At the end of this page, you will find details of the reading you will need to do from your textbook and also how each module links to the CAIE syllabus and the final examinations.
This course will lead you step-by-step through the syllabus by way of video links, resources, assignments and, of course, the textbook, so that by the end, you will be confident and fully prepared for your examinations.
David Hilbert famously said, ‘Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country’. Mathematics represents a universal language which can be followed by anyone, anywhere in the world. It can be abstracted from the context and studied in a pure form and it can also allow us to apply the same mathematics to a diverse set of situations from a range of disciplines such as space travel, ecology, economics and disease prevention.
The Cambridge A Level in Further Mathematics allows you to develop skills which will help you study a range of STEM subjects at a higher level. It strengthens transferable skills such as logical thinking, modelling and analysis. It is also highly valued when applying to university for competitive courses such as Medicine and Engineering.
At A Level, you will be guided through new mathematical material and also more in-depth study of topics that you will have already met in A Level Mathematics. Studying Further Mathematics alongside A Level Mathematics provides additional support and understanding of the core course material as you will study each topic to a greater depth, which will give you a more solid grasp of all mathematical working.
By the end of the course, you will be able to:
- Demonstrate confidence in using mathematical techniques to solve problems in context;
- Understand the use of a range of statistical techniques and how they should be applied to real data;
- Understand the relationship between statistical findings and everyday life, including contemporary social, cultural and political issues;
- Provide innovative solutions by applying a range of diverse mathematical techniques to problem-solving;
- Recognise and appreciate the beauty and structures of the mathematical world;
- Show a deeper understanding of the subjects studied at university by understanding their links with mathematics;
- Demonstrate strong higher order thinking skills such as analysis, critical thinking and problem solving.
The Syllabus, Examinations and Assessment
This Wolsey Hall course is designed to prepare you for the Cambridge A Level Further Mathematics examinations which you will sit at a Cambridge exam centre. It is vitally important that you become familiar with the syllabus which can be found below:
READ - Syllabus 2023-25 (CAIE) Download READ - Syllabus 2023-25 (CAIE)
READ - Syllabus 2026-27 (CAIE) Download READ - Syllabus 2026-27 (CAIE)
The examination code for AS and A Level Further Mathematics is: 9231
In addition to Paper 1 and Paper 3 taken at AS level, to complete your A Level in Further Mathematics you will sit the following two papers:
- Paper 2: Further Pure Mathematics 2 – This paper is worth 30% of your overall A Level grade. Length: 2 hours.
This paper carries 75 marks in total and consists of seven to nine structured questions, all of which are compulsory.
- Paper 4: Further Probability & Statistics – This paper is worth 20% of your overall A Level grade. Length: 1 hour and 30 minutes.
This paper carries 50 marks in total and consists of five to seven structured questions, all of which are compulsory.
All components are externally assessed.
The syllabus is examined in the June and November examination series.
Assessment Objectives
The assessment objectives (AOs) for AS and A Level Further Maths are as follows:
AO1: Knowledge and understanding
- Show understanding of relevant mathematical concepts, terminology and notation;
- Recall accurately and use appropriate mathematical manipulative techniques.
AO2: Application and communication
- Recognise the appropriate mathematical procedure for a given situation;
- Apply appropriate combinations of mathematical skills and techniques in solving problems;
- Present relevant mathematical work, and communicate corresponding conclusions, in a clear and logical way.
Wolsey Hall offers a unique model of offline and online resources to our homeschooling students – a model which we have developed based on our many years’ experience of providing homeschooling courses to students.
Textbook
Each subject specialist team carefully selects the best textbook for you to use as you study. The textbook for your AS Further Mathematics course is:
Cambridge International AS and A Level Further Mathematics Coursebook by Lee Mckelvey and Martin Crozier, (Cambridge University Press, 2018); ISBN: 9781108403375
Throughout the course, we recommend that you complete all of the questions and exercises in the textbook – the table below will highlight which pages you should read for each module.
Resources
In addition to your textbook, we have sourced a range of additional resources to support your learning. The resources are clearly marked out in the module pages and you should make use of these alongside your textbook to ensure that you get the very best out of your course.
You will also find a range of key resources in the General Resources section of the course. These are items which relate to the course as a whole, rather than to specific modules, and as such, you should make regular use of them. For AS Further Mathematics with Statistics, these are:
- Mathematics Notation List (CAIE Support Materials)
- List of formulae and statistical tables (CAIE Support Materials)
- Command Words (CAIE)
- Useful Websites
All the files required for your course are uploaded onto our Learning Management System, Canvas. Once you have read through this page and downloaded the Programme of Study (POS) then you are ready to begin the course.
The course is divided into eleven modules: six pure mathematics modules and five probability and statistics modules. These modules will help you to get the most out of your textbook. Each module is subdivided into topics so that you can study the course in manageable chunks. Each topic is set out as follows:
- Prerequisite Knowledge – This section will include both the references to the relevant sections of the A Level textbooks and links to external sources to ensure that you have all of the background knowledge in order to start this topic.
- Tasks – This section will include references to the Further Maths textbook to read and complete exercises. There may also be links to additional resources to supplement and increase your understanding of the topic.
- Consolidate – At the end of each topic, there may be additional links to resources to further your understanding of the topic. At the end of each module, there is a section where you will find instructions to make revision cards that help to draw together what you have learnt in the module. This should enable you to complete your assignment and move on to the next module.
How Your Work is Assessed on the Course
Your progress will be assessed by completing an assignment at the end of each module. We recommend that you do NOT look at the assignments until you've studied all the topics in the module. This will ensure that you focus on everything you need to know for the exam. If you focus only on what you need to know to do well in the assignment, you will miss important elements in each module that you need to know and understand.
As in (I)GCSE Maths, at A Level, showing your workings is vital. Often marks are awarded for the method used, and sometimes a correct answer alone will not receive full marks. The specimen answers to each assignment will give you an idea of how to show these workings.
The assignments have been designed to help you prepare for your final examination – many of the questions are based on past exam papers. Answering exam-style questions is crucial in developing your exam technique, understanding exactly what the examiner is looking for in each case and ensuring you are confident when you tackle the real exams. We do not expect you to complete your assignments without referring to your notes or textbook, however, we encourage you to rely less on these as you progress.
The assignments allow you to think critically about what you have learned and will enable your tutor to see how well you are progressing. Your tutor will mark your assignments and provide you with detailed feedback. Once you have had your marked assignment returned, you will be able to access the mark scheme and/or a specimen answer (an A-grade piece of work). You should always reflect carefully on your tutor’s feedback and apply it in your future assignments.
You should read the assignment questions carefully and answer them to the best of your ability, providing relevant examples where necessary. If you don’t do well in your first assignment, don’t worry; your tutor is there to provide advice.
We ask that you do not submit multiple assignments at the same time. For you to see a steady improvement in your marks, it is very important that you reflect on your tutor’s feedback before beginning each new assignment, so that you can incorporate their tips for improvement into each new piece of work.
To get the best out of your course, before submitting each new assignment, you must:
- Complete all the reading, notes and activities in the preceding module;
- Read carefully through all of your tutor’s comments on your last assignment;
- Use the mark scheme and/or any exemplar or specimen answers provided to help you plan for the next assignment.
We cannot guarantee that tutors will be able to mark multiple assignments within the 3-5 working day window and your work may be returned to you to complete again in light of more recent feedback.
All assignments are submitted via Canvas – you should consult the Canvas Guide for more information.
The Relationship Between AS and A Level Further Maths - Some Tips
Further Maths at A Level builds directly on, and assumes prior knowledge of many topics from, A Level Maths. You may not have studied all of the relevant topics before, as A Level Maths courses may vary. This is why we have included a prerequisite knowledge section in each topic. Remember to check this section, and your understanding, using the questions in the textbook before starting the new material in each topic.
When you study a Wolsey Hall course, you are never alone. There are lots of people who are willing to help you. Everyone is on your side!
- Tutors: At Wolsey Hall, all our tutors are friendly and knowledgeable. They are subject experts and you should not be shy about asking them questions about your course. You will meet your tutor at the start of your course and you should contact them via Canvas messaging if you have any questions.
- Student Progress Managers: You have already been assigned a Student Progress Manager who can help with your Assignment Schedule.
- Exams Officers: Wolsey Hall’s Exams Officers are here to help students with any queries regarding exam centres.
- Canvas Help Desk: Canvas is a great virtual learning environment, but we understand that sometimes, even the best things can go wrong! If you have any problems with Canvas (e.g. uploading assignments or unable to access resources) you should submit a Canvas Help Ticket.
For information about how to create and submit a Help Ticket, please refer to the Canvas Guide.
We hope you’ll enjoy your course and studying at Wolsey Hall. We wish you the best of luck in your studies and success in your examinations. Please do let us know how you get on when you receive your examination results!
The Wolsey Hall Team