Maths

You can take GCSE or IGCSE Maths as the GCSE does not involve controlled assessment, no matter which board you choose.  GCSE was the easier option in the past but won't be now - IGCSE covers more topics than the old GCSE. However, from Summer 2017, the New GCSEs graded 1-9 will be examined in maths and English, and these are significantly harder than the old GCSEs. There are currently two sets of past papers available for the new 1-9 GCSE (June 2018) as well as several commercially produced sets and specimen sets produced by the exam boards. IGCSE maths is still available but the Edexcel specification will be changing from summer 2018 exams.

There is very little difference between the exam boards for maths, so choose whichever you can find a convenient exam centre for. The most popular (and perhaps the most straightforward to find exam centres and resources for) is Linear GCSE maths, but all options are discussed below.

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For exams in Winter 2017, IGCSE maths is probably the better bet because the new GCSE will not have past papers to practise on. (There are also OFQUAL rules as to who can sit GCSE exams in November - this does NOT APPLY to IGCSE - where there are no age limits)

November 2017 - you can take CIE IGCSE Maths 0500. No changes to syllabus.

January 2018 - The current Edexcel IGCSE specification 4MA0 is last available in January 2018 and this sitting is available to first-time candidates as well as re-sitters.

For exams in 2018 and after, CIE IGCSE maths will still have the old specification,but Edexcel IGCSE maths will have changed slightly (not too much)- now called 4MA1. The new GCSE will have some past papers available so will be more viable.

How do the old and new GCSE maths compare for difficulty? - new research (2015) on how current and new specs compare to foreign exams and IGCSE .

Further and Additional Maths is a stepping-stone in between GCSE and AS-level; that now has its own page.

A-Level and AS-Level Maths has its own page.

We have a page full of maths resources - useful, mostly free, maths sites, YouTube channels, and some paid-for resources like online courses. Please see Maths Resources .

Maths Decisions

There are many options, but for those who just want to get a GCSE-level maths qualification with minimal hassle, the most popular choice is probably either GCSE Linear Maths, such as Edexcel 1MA1 or edexcel IGCSE (4MA1 from June 2018)

• Which qualification?  GCSE or IGCSE? A-level?
• Which tier?  Foundation or Higher?

• Which exam board?  Edexcel or AQA?

• Which specification?  
• A-level maths from home?

GCSE or IGCSE Maths?

GCSE maths is changing from the summer 2017 exams.

From summer 2017 , GCSE maths will be the new syllabus graded 9-1. There won't be any past papers, just a set of specimen papers, which are examples of what the exam board intends to produce.

With the changeover to 1-9 GCSEs, many home educators are opting to sit IGCSE maths, since there are several years' worth of past papers available for practice and GCSE will not have that resource. GCSE Maths has, in the past, been considered the easiest way to get the qualification, but the consensus is that IGCSE is better preparation for A level as it includes calculus and some other topics which aren't in GCSE.  On the other hand, able students who have taken GCSE maths can cover this material later, or may do an Additional Maths qualification between GCSE and A-level. Many independent schools have switched to IGCSE. Some state schools put their top maths set in for GCSE maths in Year 10 and then IGCSE maths in Year 11.

In IGCSE maths, a calculator is allowed in both papers.  For GCSE maths, there is at least one non-calculator paper in each specification. However, the non-calculator questions will be designed to be manageable without a calculator, so you don't need to expect terrifying questions.

GCSE is available in the summer only (unless you are a resit candidate or are over 16), whereas IGCSE is available in the winter and summer sittings to external candidates, regardless of whether they've taken the exam before.

Foundation or Higher Tier?

When entering the exam you have to choose whether the candidate is taking Foundation Tier or Higher Tier papers. The papers have different codes.  You choose one or the other - these courses are not intended for you to work through Foundation and then go on to Higher Tier. To do this would involve a lot of repetition and unnecessary work.

Foundation Tier is intended for students who struggle with maths, or who simply need a maths qualification to satisfy a requirement, and do not want to study maths or sciences at higher level.  The highest grade you can obtain at this tier is a C.  Although the mark necessary to pass this paper is higher than for the Higher Tier papers, the paper is designed to be accessible and to cover fewer topics, and so to be less offputting for students. This means it may well be easier to gain, say, 75% on the Foundation tier than to get 30% on the Higher tier (numbers pulled out of a hat!).

Higher Tier is for students who want the chance to get a grade B or higher, or who might wish to study maths or sciences at a later date. It requires a lower mark to pass but the subject material is harder, so you cannot directly compare the marks.  If the student wishes to have any chance of studying maths at a higher level in future, they must take the Higher tier. They may also need to obtain a Grade B or above if they wish to study sciences or Computing at most colleges.

Although you can retake the exam at Higher Tier after passing at Foundation level, in order to obtain a higher grade, generally students go straight for the most appropriate tier.

Edexcel produce a document to help you decide which tier to enter?

Some home-ed families take both tiers.  However, you can't usually do this in the same exam season, because Foundation and Higher tier maths will be timetabled in the same slot, on the assumption that nobody would do both.  There are ways round this, eg you could enter for Foundation IGCSE maths and Higher GCSE maths, or do IGCSE maths in the winter sitting and GCSE in the summer.

Which board? Edexcel, CIE, OCR or AQA?

There is no consensus on which board is easiest or better in any way! There is very little to choose between them, so don't worry too much about this choice. If your choice of exam board is not determined by your exam centre, the best approach is to download some sample papers from each board and see which suits your child, and/or look at the materials available for each syllabus and see which your family prefers.

For GCSE maths, the syllabus is dictated by the government and so there is little difference in topics or difficulty between boards. The number of resources e.g. commercially produced practice books and papers and online resources varies between boards. Currently the board with most available resources is Edexcel.

For IGCSE maths, there are some style and content differences between Edexcel and CIE.

Which specification for GCSE Maths?

This relates to GCSE maths. For IGCSE maths specifications, see below.

GCSE sittings are controlled by the government and are only available to all in the summer. The November sitting is restricted to students who were aged 16+ on 31 August before the exams.

Edexcel GCSE Maths

Edexcel GCSE Maths (2015) main page - exams from summer 2017

Specification code 1MA1

Exams from June 2017

This exam is graded 9-1 and has Higher and Foundation tiers.

Foundation tier (grades 1 – 5) and a Higher tier (grades 4 – 9 but grade 3 allowed). Students must take three question papers at the same tier. All question papers must be taken in the same exam season

3 papers, each 1 hour 30 minutes. Paper 1 is non-calculator, while papers 2 and 3 are calculator papers.

Resources for Edexcel GCSE Maths - in order of progression.

AQA GCSE Maths

AQA 9-1 GCSE Maths (2015) page - exams from Summer 2017.  

• Exams from: June 2017
• Specification code: 8300

GCSE Mathematics has a Foundation tier (grades 1 – 5) and a Higher tier (grades 4 – 9). Students must take three question papers at the same tier. All question papers must be taken in the same exam season

3 papers, each 1 hour 30 minutes. Paper 1 is non-calculator, while papers 2 and 3 are calculator papers.

Summary of the specification from AQA. 

OCR GCSE Maths

OCR 1-9 GCSE Maths - exams from summer 2017

EDUQAS 1-9 GCSE Maths

EDUQAS 1-9 GCSE Maths - exams from summer 2017

IGCSE Maths Specifications

The term "Certificate" is still to be found on some old IGCSE/Edexcel Certificate past papers- but the option to enter the "certificate" versions ( which did apply to UK schools) no longer exists.  

Edexcel International GCSE Maths

Edexcel offer IGCSE Maths A and B.  Specification A is the one most commonly taken in the UK.  Specification B is considered more difficult.

Edexcel IGCSE maths is changing for exams from summer 2018, but the changes planned are minor and mainly it's a move to the 9-1 grading system. The last sitting of the current specification, graded A*-G, will be January 2018. Although this is described as a 'resit opportunity', Edexcel have confirmed that first-time candidates can take the exam at this time, but there will be no opportunity to resit it after that.

Guide to Edexcel International GCSE Maths from 2016 - useful guide comparing the Maths A, Maths B, and Further Pure specifications and confirming when first and last exams will be held.

Edexcel's IGCSE Maths A 4MA0

There will be some small changes to the specification for exams from 2018.The new spec is called 4MA1. Edexcel's website offers the following overview:

"Mathematics A

• A move from the current A*–G to the new 9–1 grading structure
• Some minor additions to the content assessed at each tier to reflect this new 9–1 grading structure
• A small increase in the Number & Algebra assessment objective weighting at the expense of Statistics
• A few more questions on problem-solving and mathematical reasoning
• A revised formulae sheet at each tier.

Beyond the above, we are not changing how we assess the International GCSE Mathematics Specification A, which will continue to have two tiers of entry and two × two-hour calculator papers."

[Edexcel Certificate IGCSE maths KMA0 -no longer available.

The Maths B IGCSE page states:

The International GCSE from 2009 Mathematics B (4MB0) specification is based on the legacy O level Mathematics Syllabus B (7361) specification

Resources for Edexcel IGCSE Maths

Edexcel provide lots of resources for teachers. They have a collection of Mapping Documents which compare the old specification IGCSE to the new specification, and comparing the new GCSE to the new IGCSE. You can find all these on Edexcel International GCSE Maths from 2016 - Teaching and Learning Materials.

Edexcel GCSE Maths A Student Book A bit short on content compared to the usual standard.

IGCSE Mathematics for Edexcel by Alan Smith An independent textbook which many home educators consider more thorough than Edexcel's own book. Answers are on the included CD-Rom, but you can also access this backup copy of the Answers for Alan Smith IGCSE Mathematics for Edexcel

"We found the book much more thorough than Edexcel's own textbook, unusually, with clear explanations and lots of practice questions."

Another view:

"We have just bought the Alan Smith book as it was so highly recommended but I can't see anything that sets it above the Collins or Oxford editions. It does seem to have a lot of 'white paper' i.e. empty space on the page as though it is formatted for a different size paper.   There are a lot of number problems and, compared to the other books, not many word problems.  The explanations appear no more detailed than the other books.   We'll be sending it back."

CIE IGCSE Maths

[CIE IGCSE Maths 0580]

This is graded A*-G and there have been no announcements that it will change soon, so it is unlikely to change before 2019 at the earliest. 

This syllabus is approved for use in England, Wales and Northern Ireland as a Cambridge InternationalLevel 1/Level 2 Certificate (QN: 500/5655/4).  In many centres, UK candidates are automatically entered for the Certificate version rather than the IGCSE.  The only difference is the code for entries and the title which appears on the certificate.   

Maths Resources

We have a page full of maths resources - useful, mostly free, maths sites, YouTube channels, and some paid-for resources like online courses. Please see Maths Resources .   

Textbooks for GCSE / IGCSE Maths

Choose your textbook according to whether it is GCSE/IGCSE and the board eg search for 'edexcel gcse maths 2015 Student Book' or 'cie igcse maths Student Book' on Amazon. Note that a 'Student book' is a complete textbook offering full explanation and enough practice to be a complete course, whereas a 'Revision guide' is intended merely to supplement a course taught elsewhere.  High street shops normally only stock Revision Guides, but you can order Student Books online.  Check whether full answers are available for Student Books, as some publishers only make these available in their hugely expensive Teacher's Guides, while others make all answers freely available online or in a free CD-ROM.  Edexcel will always provide answers to their own textbooks; experience on the HE Exams group has been that other publishers may also provide them if you explain your predicament.

Edexcel GCSE Maths A Student Book A bit short on content compared to the usual standard.

IGCSE Mathematics for Edexcel by Alan Smith An independent textbook which many home educators consider more thorough than Edexcel's own book. Answers are on the included CD-Rom, but you can also access this backup copy of the Answers for Alan Smith IGCSE Mathematics for Edexcel

"We found the book much more thorough than Edexcel's own textbook, unusually, with clear explanations and lots of practice questions."

Another view:

"We have just bought the Alan Smith book as it was so highly recommended but I can't see anything that sets it above the Collins or Oxford editions. It does seem to have a lot of 'white paper' i.e. empty space on the page as though it is formatted for a different size paper.   There are a lot of number problems and, compared to the other books, not many word problems.  The explanations appear no more detailed than the other books.   We'll be sending it back."

Collins CIE IGCSE Maths Student Book Complete textbook for the course, but note that book only includes answers to practice questions; for the exam-style revision questions, the answers are in the teacher's guide which has to be bought separately at around £100! It may be possible to obtain them from the publisher but we have no information on whether they will provide it at present.

Collins CIE IGCSE Maths Revision Workbook
"The Revision book has 120 pages of very readable revision at the front of the book and then 200 pages of 'workbook' at the back, with space to work the answers etc.    The answers to the problems are in the back of the book.   This book presumes you have either finished the course or have the textbook.  I doubt it could be used as a stand-alone book for teaching the course, although if you are also using Stuckonhomework or Conquer Maths it may be enough."

Collins Edexcel GCSE Maths A Revision Workbook  Edexcel *workbook* for GCSE A (note GCSE, not IGCSE).

What next after GCSE maths?

Additional Maths / Further Maths / FSMQ - see separate page on Further and Additional Maths, and other ways to make use of the time between GCSE and A-level maths.

Other Maths Activities

UKMT Individual Challenges and mentoring materials. The UKMT material is good because it's fresh and a different approach from standard 'textbook' maths.  See above for links.

The Problem Solver's Handbook, from UKMT

The Art of Problem Solving books, also from UKMT - these would probably be good for the proofs you're after, and it's an international approach so may work well with what your son has already used.

Project Euler - maths problems combined with programming problems - https://projecteuler.net/

"Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems."

Vedic Maths - DS1 enjoyed learning lots of shortcuts with this approach.  I wouldn't get too carried away with stories of its heritage because that part is probably made up - they are maths tricks, but useful ones and apparently very efficient.  See http://blogannath.blogspot.co.uk/2009/06/introduction-to-vedic-mathematics.html?m=1

The following books were recommended by a maths whizz on the HE-Exams list as being good material for mathsy teens, and the sort of thing which might be good to discuss at interviews:

• James Gleick's book on chaos

• Euclid's Elements

• Principia

• Ian Stewart's Cabinet of Mathematical Curiosities

• C J Bradley's Introduction to Number Theory

• Surely You're Joking Mr Feynman

• The Man Who Loved Only Numbers

• The Man Who Knew Infinity (Ramanujan)