# Maths

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**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 to be significantly harder than the old GCSEs. We do not yet know how they will compare with IGCSE as there aren't any past papers to work from, only specimen papers. IGCSE maths will still be available after the new GCSEs come in, but the Edexcel specification will be changing from 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.

### **30-second version of this page:** Edit

For exams in 2016, GCSE is the easiest option - any board. Edexcel linear maths GCSE is very popular with home educators but it doesn't really matter which board you choose.

For exams in 2017, IGCSE maths is probably the better bet because the new GCSE will not have past papers. Edexcel IGCSE Maths A is the most popular option.

For exams in 2018 and after, CIE IGCSE maths will still have the old specification, and 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 .

## Maths Decisions Edit

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 GCSE Linear Maths, such as Edexcel 1MA0

- 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? Edit

GCSE maths is changing from the summer 2017 exams. The November 'resit' for GCSE maths is only available to people who've already taken the exam, or are aged over 16.

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? Edit

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? Edit

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

## Which specification for GCSE Maths? Edit

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** Edit

Edexcel GCSE Maths (2015) main page - all the options and news.

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.

### **AQA GCSE Maths** Edit

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.

## IGCSE Maths Specifications Edit

If you choose IGCSE, you may wish to enter for the "Certificate" version of IGCSE, which is approved for UK state schools. This is exactly the same as the IGCSE but has a different code and different title on the certificate. It satisfies the government's funding criteria for sixth form, which means that if you go to a state sixth form college or school, they will be able to instantly know that you have GCSE-level maths. Note that the "Certificate" IGCSEs are usually just referred to as IGCSEs, so all references to IGCSE maths below also apply to the Certificates. However, the "Certificate" title will be less recognisable outside the UK so if you are considering studying abroad, it may make life easier to stick with the standard IGCSE title.

### **Edexcel International GCSE Maths** Edit

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.

There will be some small changes to the specification for exams from 2018. Edexcel's website offers the following overview:

### "Mathematics A Edit

- 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 - the Edexcel Level 1/ Level 2 Certificate Mathematics is the same exam as IGCSE maths A. It uses the same exam paper and textbooks (there are two different codes on the exam paper). This is the version accredited for use in state schools. Last sitting was summer 2016 . It's no longer relevant to home educators.]

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** Edit

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."

### **AQA Certificate Maths** Edit

[AQA Certificate Further Maths] is a challenging "Additional Maths" qualification intended for more able maths candidates. This qualification is approved for use in state schools, and will still be available after the new GCSE specification comes in. However, as it has the "Certificate" title, it may be less recognisable overseas - you may have to provide documentation to demonstrate it is IGCSE level.

### **CIE IGCSE Maths** Edit

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.

## Textbooks for GCSE / IGCSE Maths Edit

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).

## Additional Maths / FSMQ Edit

Many able home-ed students take GCSE maths early, and wonder what the next step might be. You can move on to A-level maths and, as with GCSE, there is no coursework so all A-level maths exams are available to private candidates. However, this might complicate the situation if you intend to apply to university or go to sixth form, because universities sometimes make offers based only on A-levels yet to be taken, and for 3 taken simultaneously. If going to sixth form, they may insist you take three or more A-levels regardless of whether you already have some. In addition, if you want to study maths at university, some leading departments want to know your A-level UMS (percentage mark), so it may make sense to leave it until you're sure you'll do well. In the meantime, you could look at Additional Maths, and the UK Mathematics Trust activities, to broaden and deepen your mathematics education.

Additional Maths is a stepping stone between GCSE / IGCSE and A-level, and is used to stretch able students who have completed their GCSE maths before they start the A-level course. Some schools enter their more able maths students for GCSE in Year 10 (aged approx 15) and then either Additional Maths or IGCSE Maths in Year 11 (aged approx 16).

### **OCR FSMQ** Edit

OCR FSMQ or Free-Standing Maths Qualification, is a variety of 'Additional Maths' requiring just one 2-hour exam, no coursework:

"This course provides candidates with an introduction to the mathematics studied in AS and A Level GCE modules. It is designed for those students who have a thorough knowledge of the content of the Higher Tier of the National Curriculum for Mathematics. They should have achieved, or be expected to achieve, grade A*, A or B at GCSE."

### **Edexcel Further Maths** Edit

"Our International GCSE in Further Pure Mathematics has been designed for students who have a high ability in, or are motivated by, mathematics. It emphasises the importance of a common core of Pure Mathematics at International GCSE level, and has been constructed to broaden knowledge of the pure mathematics topics contained in the International GCSE Mathematics specifications A (higher tier) and B. It is a single-tier qualification assessed via two exams, and is graded A* to D with a ‘safety net’ grade E available."

### **AQA Level 2 Certificate in Further Mathematics** Edit

AQA Further Maths Certificate/IGCSE will still be available after the move to new 9-1 GCSEs.

"Our Level 2 Certificate in Further Mathematics is complementary to our new Mathematics GCSE, so we do intend to continue offering this qualification." [Source: AQA announcement on the AQA Certificate]

## UK Mathematics Trust / Maths Olympiad Edit

The United Kingdom Mathematics Trust run individual maths competitions which are puzzle-solving exercises. It is a different approach to maths from the usual examination style and offers the opportunity for everyone to have fun, while stretching able students. Top scorers win certificates and the opportunity to go through to prestigious further rounds such as the Kangaroo and the Maths Olympiad.

"Q. Can home schooled pupils take the challenges?

A. Challenges must be taken in a school or college. Parents will need to contact their local school to ask if they participate in the Challenges, and make arrangements locally for their child to take part at this school."Some other interesting material on the website was quite difficult to find so is listed here:

The Mentoring scheme has lots of past problems and solutions to stretch kids in maths.

'Teacher Resources' has lots of past questions and answers.

## Other Maths Activities Edit

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)

## What next after GCSE or IGCSE Maths? Edit

**One family's experience:**

DS1 took his maths GCSE aged 12 because he wanted to. He got an A*, then just pottered with maths for a couple of years after GCSE, and instead focussed on other subjects. I felt that physics (which he did aged 13) and Chemistry (aged 14) would provide some decent practice. He started working through the A-level maths books aged 14 and completed 5 of the 6 units for single maths before we changed course - he didn't take any exams, but had done the work. The plan was that he would take single maths A-level in 2013 aged 15, then further maths in 2014, and go to sixth form already having those two A-levels plus possibly one other. Then, in autumn last year, we went round a couple of sixth forms, including a maths specialist grammar school, which DS1 liked.

I had lots of email correspondence with their head of maths, asking if it would be an issue if DS1 arrived there with single A-level maths, thinking that maybe if he didn't finish Further Maths at home, he could do it at sixth form. He replied that it would be better from their point of view if he arrived without any maths A-levels because it could be difficult to timetable further maths for someone who already had single maths - they're not separate subjects of course, and the students taking double maths will all be in the same classes together the rest of the time, so I think it would be difficult to separate out just the further maths lessons. Also, the school would still require students to do a minimum of 4 subjects even if they had already done some A-levels, so if he'd done his best subject at home, he would have to choose other subjects to make up his numbers. This was what made DS1 decide to leave A-level maths until sixth form; he said he definitely wanted to do his best subject at sixth form. I think there are several reasons. First,, just going to sixth form is going to be an upheaval - early mornings etc - so doing subjects he finds harder would add to that. Secondly, it would be a confidence boost to be studying something you know you can do well in.

The Head of Maths said that they were discouraging their own students from doing early entry for A-level, no matter how able, because unis are now looking at UMS scores and not just grades, so it was vital to get a good grade first time round if the student might want to study maths at university. He suggested that it would be better for DS1 to keep his hand in doing the FSMQ (the OCR Additional Maths qualification) and perhaps the AQA additional maths and the UKMT challenges. He recommended the UKMT Mentoring Scheme, which we're on the waiting list for now - but you can access their materials online free (it's just the email mentor we're waiting for). We also had some great suggestions from members of the HE Exams yahoogroup, which are on the wiki page (below).

DS1 did the FSMQ (OCR Additional Maths); he didn't need long to prepare for it as it's intended as a filler for school children who've taken their GCSE maths early and want to go on to A-level maths. Rather than take another maths qualification in his last year of home-ed, he decided to do his own thing, look at maths from different approaches, and learn to play the guitar. This has all been very positive, and clearly didn't put off the school as he has a place for September.

I know someone (at school) whose school puts bright kids in for AS maths early, in yr11 (GCSE year). This has ended up really restricting the child's choice at sixth form because he too has found that most other places can't really accommodate him turning up with one AS-level and he'd have to repeat the material. This is not a problem if you're planning on doing A-levels from home, of course.

## **Further Maths AS and A Level** Edit

The Further Mathematics Support Programme offers live online support courses in AS and A2 Further Mathematics for mature, gap-year students and home-based students for the cost of £150 for each qualification. The courses, which are designed to supplement students’ independent study, include:

-Up to thirty hours of live online support which includes dedicated lectures and revision time (these sessions take place fortnightly, throughout the year). -Access to the Integral extensive and acclaimed online resources. These have specific sections tailored to support self-study and include additional notes, exercises, interactive resources, multiple choice tests, exam-style questions and worked solutions. -A moderated forum specifically for course participants. -Email support. -Sessions are recorded so that you can replay and review the content covered during the course.

Please note that A level Mathematics is a prerequisite for AS level Further Mathematics, or you will need to be studying both A levels at the same time. AS Further Mathematics is normally a prerequisite for A2 Further Mathematics but it is possible to study both AS Further Mathematics and A2 Further Mathematics in one year.

More details: http://furthermaths.org.uk/fmmature

## Resources Edit

In addition to textbooks, these are very useful maths resources:

### **Maths practice exam questions sorted by topic:** Edit

http://www.themathsteacher.com/

http://www.mrbartonmaths.com/gcse.htm

http://www.examsolutions.net/maths-revision/syllabuses/GCSE/period-1/Higher/module.php

GCSE Maths Takeaway - complete the topic takeaway and get your grade!

### **General maths resources:** Edit

**Maths Genie:** free site, recommended for revision.

**Mr Barton Maths** - lots of tutorials and YouTube video lessons explaining how to do problems. Very popular with home educators, and free.

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 .

CIMT Maths - Centre for Innovation in Mathematics teaching - they do a complete curriculum from reception to A level - it's free, online to print out for yourself, or you can order workbooks. Password needed for some sections - available from CIMT or ask on HE-Exams Yahoogroup.

Conquer Maths Online maths tutorial program. In addition to video and animated tutorials, it includes dedicated worksheets, solutions, marking and reports for each topic. You can subscribe monthly or annually. There is a discount for HEs if you contact them for the code or enquire on the HE-Exams group, and it works out at about £12 per month at present with the HE discount.

Khan Academy Free video tutorials on many topics. You can also find many excellent free tutorials on YouTube.

At £49 per yr, great value - covers all GCSE/IGCSE maths topics with hundreds of online video tutorials.

http://mathshub.help/for-individuals/

This is the previous "Stuck on Homework" maths videos, either online or buy the dvd

MathsWatch CD - excellent value at £6, only for PC (not Mac). Not sold direct to the public as it is usually only supplied to schools but home-educators can buy from Fareham and Gosport HE group

CGP Maths Tutor DVD tutorials A new arrival to the market. Only £3 and highly recommended by some HE families.

### **Past Exam Papers** Edit

You can usually find many past exam papers for your chosen specification on the exam board page for that qualification. You'll find a link to each page above. However, we list some here because exam board resources sometimes disappear or move without warning, and also because the most recent past papers are only made available via the schools login if you use the exam board sites.

Edexcel IGCSE Maths A - past papers for Summer 2015, January 2015, and earlier years.

Edexcel GCSE Maths - past papers for Summer 2015, January 2015, and earlier years.