Advanced level mathematics

Last updated

Advanced Level (A-Level) Mathematics is a qualification of further education taken in the United Kingdom (and occasionally other countries as well). In the UK, A-Level exams are traditionally taken by 17-18 year-olds after a two-year course at a sixth form or college. Advanced Level Further Mathematics is often taken by students who wish to study a mathematics-based degree at university, or related degree courses such as physics or computer science.

Contents

Like other A-level subjects, mathematics has been assessed in a modular system since the introduction of Curriculum 2000, whereby each candidate must take six modules, with the best achieved score in each of these modules (after any retake) contributing to the final grade. [1] Most students will complete three modules in one year, which will create an AS-level qualification in their own right and will complete the A-level course the following year—with three more modules.

The system in which mathematics is assessed is changing for students starting courses in 2017 (as part of the A-level reforms first introduced in 2015), where the reformed specifications have reverted to a linear structure with exams taken only at the end of the course in a single sitting.

In addition, while schools could choose freely between taking Statistics, Mechanics or Discrete Mathematics (also known as Decision Mathematics) modules with the ability to specialise in one branch of applied Mathematics in the older modular specification, in the new specifications, both Mechanics and Statistics were made compulsory, with Discrete Mathematics being made exclusive as an option to students pursuing a Further Mathematics course. The first assessment opportunity for the new specification is 2018 and 2019 for A-levels in Mathematics and Further Mathematics, respectively.

2000s specification

Prior to the 2017 reform, the basic A-Level course consisted of six modules, four pure modules (C1, C2, C3, and C4) and two applied modules in Statistics, Mechanics and/or Decision Mathematics. The C1 through C4 modules are referred to by A-level textbooks as "Core" modules, encompassing the major topics of mathematics such as logarithms, differentiation/integration and geometric/arithmetic progressions.

The two chosen modules for the final two parts of the A-Level are determined either by a student's personal choices, or the course choice of their school/college, though it commonly took the form of S1 (Statistics) and M1 (Mechanics).

Further mathematics

Students that were studying for (or had completed) an A-level in Mathematics had the opportunity to study an A-level in Further Mathematics, which required taking a further 6 modules to give a second qualification. The grades of the two A-levels will be independent of each other,[ citation needed ] with Further Mathematics requiring students to take a minimum of two Further Pure modules, one of which must be FP1, and the other either FP2 or FP3, which are simply extensions of the four Core modules from the normal Maths A-Level. Four more modules need to be taken; those available vary with different specifications. [2]

Not all schools are able to offer Further Mathematics, due to a low student number (meaning that the course is not financially viable) or a lack of suitably experienced teachers. To fulfil the demand, extra tutoring is available, with providers such as the Further Mathematics Support Programme. [3]

Some students had the opportunity to take a third maths qualification, "Additional Further Mathematics", which added more modules from those not used for Mathematics or Further Mathematics. Schools that offer this qualification usually only took this to AS-level, taking three modules, although some students went further, taking the extra six modules to gain another full A-Level qualification. Additional Further Mathematics is offered by Edexcel only, and a Pure Mathematics A-level is available for students who—on the Edexcel exam board—take the modules C1, C2, C3, C4, FP1 and either FP2 or FP3. No comparable qualification has been available since the 2017 reforms.

Results and statistics

Each module carried a maximum of 100 UMS points towards the total grade, and each module is also given a separate grade depending on its score. The number of points required for different grades were defined as follows:

GradeModule (Out of 100)AS level (Out of 300)A level (Out of 600)
A*--480 (With 180/200 from C3 + C4)
A80240480
B70210420
C60180360
D50150300
E40120240

The proportion of candidates acquiring these grades in 2007 are below:[ citation needed ]

Mathematics

MaleFemaleCombined
Entries60093
Grade A42.6%45.5%43.7%
Grade B20.8%22.2%21.4%
Grade C15.8%15.1%15.6%
Grade D10.9%10.0%10.4%
Grade E6.4%5.0%5.9%
Grade U3.5%2.2%3.0%

Further mathematics

MaleFemaleCombined
Entries7972
Grade A57.1%56.2%56.8%
Grade B19.4%20.2%20.3%
Grade C11.6%10.9%11.4%
Grade D6.6%6.2%6.5%
Grade E3.6%3.0%3.4%
Grade U1.7%1.5%1.6%

2017 specification

A new specification was introduced in 2017 for first examination in summer 2019. Under this specification, there are three papers which must all be taken in the same year. There are three overarching themes - “Argument, language and proof”, “Problem solving” and “Modelling” throughout the assessment. [4]

Each board structures the three papers as follows:

AQA

[5]

Edexcel

[6]

OCR

[7]

Grading

It was suggested by the Department for Education that the high proportion of candidates who obtain grade A makes it difficult for universities to distinguish between the most able candidates. As a result, the 2010 exam session introduced the grade A*—which serves to distinguish between the better candidates. [8]

Prior to the 2017 reforms, the A* grade in maths was awarded to candidates who achieve an A (480/600) in their overall A Level, as well as achieving a combined score of 180/200 in modules Core 3 and Core 4. For the reformed specification, the A* is given by a more traditional grade boundary based on the raw mark achieved by the candidate over their papers.

The A* grade in further maths was awarded slightly differently. The same minimum score of 480/600 was required across all six modules. However, a 90% average (or a score of 270/300) had to be obtained across the candidate's best 'A2' modules. [9] A2 modules included any modules other than those with a '1' (FP1, S1, M1 and D1 are not A2 modules, whereas FP2, FP3, FP4 (from AQA only), S2, S3, S4, M2, M3 and D2 are).

List of Subjects

```List of subjects in A Level Mathematics```

1. Core Mathematics:

Covers foundational topics like algebra, calculus, trigonometry, and coordinate geometry.


2. Further Mathematics:

Expands upon Core Mathematics with additional areas such as complex numbers, matrices, differential equations, and numerical methods.


3. Pure Mathematics:

Explores advanced topics in algebra, calculus, and mathematical proofs.


4. Applied Mathematics:

Focuses on practical applications of mathematical concepts to solve real-world problems in various fields.


5. Mechanics:

Focuses on the study of motion, forces, and vectors, particularly relevant for physics or engineering interests.


6. Statistics:

Involves collecting, analysing, and interpreting data, including topics like probability, hypothesis testing, regression analysis, and sampling.


7. Discrete Mathematics:

Deals with separate and distinct mathematical structures, including topics such as combinatorics, graph theory, and algorithms.


8. Decision Mathematics:

Applies mathematical techniques to solve real-world problems related to optimisation, networks, and decision-making.


9. Financial Mathematics:

Applies mathematical concepts to analyse financial markets, investments, and risk management.

Related Research Articles

<span class="mw-page-title-main">General Certificate of Secondary Education</span> British public examinations, generally taken aged 15-16

The General Certificate of Secondary Education (GCSE) is an academic qualification in a range of particular subjects, taken in England, Wales, and Northern Ireland, having been introduced in September 1986, and its first exams sat in 1988. State schools in Scotland use the Scottish Qualifications Certificate instead. However, private schools in Scotland often choose to follow the GCSE system in England.

In the Scottish secondary education system, the Higher is one of the national school-leaving certificate exams and university entrance qualifications of the Scottish Qualifications Certificate (SQC) offered by the Scottish Qualifications Authority. It superseded the old Higher Grade on the Scottish Certificate of Education (SCE). Both are normally referred to simply as "Highers".

<span class="mw-page-title-main">AQA</span> British examination board and registered charity

AQA Education, trading as AQA, is an awarding body in England, Wales and Northern Ireland. It compiles specifications and holds examinations in various subjects at GCSE, AS and A Level and offers vocational qualifications. AQA is a registered charity and independent of the government. However, its qualifications and exam syllabi are regulated by the Government of the United Kingdom, which is the regulator for the public examinations system in England and Wales.

<span class="mw-page-title-main">Edexcel</span> British multinational education and examination body owned by Pearson

Edexcel is a British multinational education and examination body formed in 1996 and wholly owned by Pearson plc since 2005. It is the only privately owned examination board in the United Kingdom. Its name is a portmanteau term combining the words education and excellence.

The Advanced Extension Awards are a type of school-leaving qualification in England, Wales and Northern Ireland, usually taken in the final year of schooling, and designed to allow students to "demonstrate their knowledge, understanding and skills to the full". Currently, it is only available for Mathematics and offered by the exam board Edexcel.

Sixth Term Examination Papers in Mathematics, often referred to as STEP, are university admissions tests for undergraduate courses with significant mathematical content - most notably for Mathematics at the University of Cambridge. Starting from 2024, STEP is administered by OCR, although in previous years it was administered by OCR's parent company CAAT.

<span class="mw-page-title-main">International General Certificate of Secondary Education</span> English language based academic qualification

The International General Certificate of Secondary Education (IGCSE) is an English language based secondary qualification similar to the GCSE and is recognised in the United Kingdom as being equivalent to the GCSE for the purposes of recognising prior attainment. It was developed by Cambridge Assessment International Education. The examination boards Edexcel, Learning Resource Network (LRN), and Oxford AQA also offer their own versions of International GCSEs. Students normally begin studying the syllabus at the beginning of Year 10 and take the test at the end of Year 11. However, in some international schools, students can begin studying the syllabus at the beginning of Year 9 and take the test at the end of Year 10.

Further Mathematics is the title given to a number of advanced secondary mathematics courses. The term "Higher and Further Mathematics", and the term "Advanced Level Mathematics", may also refer to any of several advanced mathematics courses at many institutions.

Curriculum 2000 was a reform of A Level examinations in the United Kingdom. It was introduced in September 2000. An A Level under this reform consists of four or six units studied over two years. Normally, two or three units are assessed at the end of the first year, and make up a stand-alone Advanced Subsidiary qualification. Another two or three modules are assessed at the end of the second year, which make up the A2 Level. A2 units do not form a qualification in their own right; the satisfactory completion of the AS and A2 units in the same subject is required to constitute a complete A Level qualification.

In England, Wales, Northern Ireland and the Isle of Man, the Diploma in Digital Applications (DiDA) was an optional information and communication technology (ICT) course, usually studied by Key Stage 4 or equivalent school students. DiDA was introduced in 2005 as a creation of the Edexcel examination board. DiDA was notable for its time in that it consisted entirely of coursework, completed on-computer; all work relating to the DiDA course was created, stored, assessed and moderated digitally. In the late 2000s it was generally taught as a replacement for GCSE ICT, and the GNVQ which had been withdrawn in 2007. DiDA faced controversy in its lifetime, particularly after the Wolf report found that it was primarily being taught by schools because it was the equivalent of studying four GCSEs at once, which had a major impact on league table scores. From 2012 a revised DiDA and CiDA were taught by a smaller number of centres, with the original qualification removed from league table consideration in 2014. The revised version was ultimately discontinued in 2020. At the scheme's launch, 200,000 students were enrolled on the qualification; this had declined to 6,000 on the revised version in 2016 and to 1,400 students by the time of the final report in 2020.

Free-standing Mathematics Qualifications (FSMQ) are a suite of mathematical qualifications available at levels 1 to 3 in the National Qualifications Framework – Foundation, Intermediate and Advanced.

A Uniform Mark Scale, or UMS, is a way of standardising the marking of papers across different examination boards, allowing someone to compare two marks marked by two different examination boards. Grades are then calculated using grade boundaries set at particular UMS scores.

<span class="mw-page-title-main">A-level</span> British educational certification

The A-level is a subject-based qualification conferred as part of the General Certificate of Education, as well as a school leaving qualification offered by the educational bodies in the United Kingdom and the educational authorities of British Crown dependencies to students completing secondary or pre-university education. They were introduced in England and Wales in 1951 to replace the Higher School Certificate. The A-level permits students to have potential access to a chosen university they applied to with UCAS points. They could be accepted into it should they meet the requirements of the university.

<span class="mw-page-title-main">GCE Ordinary Level</span> British educational certification

The O-Level is a subject-based qualification conferred as part of the General Certificate of Education. It began in the United Kingdom and has been adopted, often with modifications, in several other countries.

Examination boards in the United Kingdom are the examination boards responsible for setting and awarding secondary education level qualifications, such as GCSEs, Standard Grades, A Levels, Highers and vocational qualifications, to students in the United Kingdom.

The General Certificate of Education (GCE) Advanced Level, or A Level, is a main school leaving qualification in England, Wales, Northern Ireland, the Channel Islands and the Isle of Man. It is available as an alternative qualification in other countries.

The Business and Technology Education Council (BTEC) is a provider of secondary school leaving qualifications and further education qualifications in England, Wales and Northern Ireland. While the T in BTEC stood for Technical, according to the DfE (2016) it now stands for Technology. BTECs originated in 1984 and were awarded by Edexcel from 1996. Their origins lie in the Business Education Council, formed in 1974 to "rationalise and improve the relevance of sub-degree vocational education". They are the responsibility of the Minister of State for Skills, Apprenticeships and Higher Education in the Department for Education.

Additional Mathematics is a qualification in mathematics, commonly taken by students in high-school. It features a range of problems set out in a different format and wider content to the standard Mathematics at the same level.

Extended Project Qualification (EPQ) is a qualification taken by some students in England and Wales, which is equivalent to 50% of an A-Level. Graded A*–E and worth up to 28 UCAS tariff points, it is part of level three of the national qualifications framework.

<span class="mw-page-title-main">Science education in England</span> Overview of science education in England

Science education in England is generally regulated at all levels for assessments that are England's, from 'primary' to 'tertiary' (university). Below university level, science education is the responsibility of three bodies: the Department for Education, Ofqual and the QAA, but at university level, science education is regulated by various professional bodies, and the Bologna Process via the QAA. The QAA also regulates science education for some qualifications that are not university degrees via various qualification boards, but not content for GCSEs, and GCE AS and A levels. Ofqual on the other hand regulates science education for GCSEs and AS/A levels, as well as all other qualifications, except those covered by the QAA, also via qualification boards.

References

  1. ↑ "A level retake courses at CIFE colleges". CIFE. Retrieved 2020-01-22.
  2. ↑ "The Further Mathematics Support Programme". furthermaths.org.uk. Retrieved 2020-01-22.
  3. ↑ "Supporting and Promoting Advanced and Further Mathematics". The Further Mathematics Support Programme. Archived from the original on 11 June 2011. Retrieved 25 May 2011.
  4. ↑ STEM Learning https://www.stem.org.uk/cpd/ondemand/75722/teaching-level-mathematics-proof-problem-solving-and-modelling
  5. ↑ "AQA: Specification at a glance". aqa.org.uk. Archived from the original on 2016-07-21. Retrieved 2020-01-22.
  6. ↑ "Pearson Edexcel AS and A level Mathematics (2017) | Pearson qualifications". qualifications.pearson.com. Retrieved 2020-01-22.
  7. ↑ "OCR - AS and A Level - Mathematics A - H230, H240 (from 2017) - Specification at a glance". www.ocr.org.uk. Archived from the original on 2019-06-03. Retrieved 2020-01-22.
  8. ↑ "OCR: A Level A* frequently asked questions" (PDF). ocr.org.uk. Archived (PDF) from the original on 2013-02-23. Retrieved 2020-01-21.
  9. ↑ "Understanding A level marks and grades | Pearson qualifications". qualifications.pearson.com. Retrieved 2020-01-22.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.