Here’s how the English science and mathematics education system works, I included some links to syllabuses and exam papers.
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Primary school, age 4-7
Reception
Year 1
Year 2 (Key Stage 1 SATS Exams taken this year)
Only a little science is taught at this level along with Mathematics, English and creative lessons such as art.
Students are assessed in year 2 by external examinations called Key Stage 1 SATS exams. These are taken in English and Mathematics.
here is an examination report from a few years ago:
Click (Pdf) (mathematics starts on page 43)
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Junior school, age 7 to 11
Year 3
Year 4
Year 5
Year 6 (Key stage 2 SATS exams taken this year)
Science and mathematics are both now taught along with many other subjects.
Students are assessed in year 6 by external examinations called Key stage 2 SATS exams. These are taken in English, Mathematics and Science.
Here is an examination report from a few years ago:
Click (Pdf) (mathematics starts on page 41, science on page 70)
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Secondary school, age 11 to 16 (or 18)
Year 7
Year 8
Year 9 (Key stage 3 SATS exams taken this year)
Students are assessed in year 9 by external examinations called Key Stage 3 SATS exams. These are taken in English, Mathematics and Science.
Here are some examination reports in science and mathematics.
Mathematics:
Click (Pdf)
Science:
Click (Pdf)
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Year 10
Year 11 (GCSE exams taken this year)
GCSE’s are the first important examinations taken by English students. Students are normally required to get a certain amount of A* to B/C grades to be able to continue on at school to A-levels or to go to a sixth form college to do their A-levels.
Here is a mathematics specification:
www.aqa.org.uk/qual/pdf/AQA-3301-W-SP-07.pdf[/URL]
Here is an example mathematics exam paper:
[PLAIN]www.aqa.org.uk/qual/gcse/qp-ms/AQA-3301H2-W-QP-Jun04.pdf[/URL]
Here is a Physics specification:
[PLAIN]www.aqa.org.uk/qual/pdf/AQA-3301-W-SP-07.pdf[/URL]
Here is an example Physics exam paper: [PLAIN]www.aqa.org.uk/qual/gcse/qp-ms/AQA-3451H-W-QP-Jun03.pdf[/URL]
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Students may now leave school after year 11 to get a full time job, an apprenticeship, or do a vocational course such as plumbing or hairdressing at a college (in England a college is not the same as university!).
In some parts of the country schools do not offer A-level’s so students may go to a sixth form college to do them instead.
Year 12 (GCE AS exams taken this year)* [optional]
Year 13 (GCE A2 exams taken this year)* [optional]
*A GCE AS and A2 together (in the same subject) make a GCE A level.
A-levels are the normal requirement for entry to English university's. Most students do three subjects to full A-level (some do more). No subjects are compulsory, students choose the subjects they want to do providing they fit into their timetable.
A-levels consist of six modules (3 at AS and 3 at A2).
Here is a Physics specification:
[PLAIN]www.aqa.org.uk/qual/gcse/qp-ms/AQA-3301H2-W-QP-Jun04.pdf[/URL]
Here is an example exam paper: [PLAIN]www.aqa.org.uk/qual/gceasa/qp-ms/AQA-PHB5-W-QP-Jun04.pdf[/URL]
there are also extension papers called AEA’s in physics (these are optional,and are designed for the top 10% of students).
Here is an example exam paper:
[url=www.rewardinglearning.com/development/qualifications/gce/docs/aea/specs/GCE%20Adv%20Ext%20Award%20Physics%20QP%20June02.pdf]Click (Pdf)[/url]
Here is an example of a A-level mathematics specification: [PLAIN]www.aqa.org.uk/qual/pdf/AQA-5361-6361-W-SP-07.pdf[/URL]
Here are some past exam papers:
Core maths: [PLAIN]www.aqa.org.uk/qual/pdf/AQA-5361-6361-W-SP-07.pdf[/URL]
Further pure maths:
[PLAIN]www.aqa.org.uk/qual/gceasa/qp-ms/AQA-MFP1-MFP2-MFP3-MFP4-SQP.pdf[/URL]
Statistics: [PLAIN]www.aqa.org.uk/qual/gceasa/qp-ms/AQA-MS1A-MS1B-MS2A-MS2B-MS03-MS04-W-SQP.pdf[/URL]
Mechanics: [PLAIN]www.aqa.org.uk/qual/gceasa/qp-ms/AQA-MM1A-MM1B-MM2A-MM2B-MM03-MM04-MM05-SQP.pdf[/URL]
There are also AEA extension papers in mathematics (again they are optional,and are designed for the top 10% of students), Here is an example exam:
[url=www.edexcel.org.uk/VirtualContent/25978.pdf]Click (Pdf)[/url]
People applying to cambridge and warwick for mathematics often take STEP mathematics papers. These contain very difficult questions, here’s an example:
[PLAIN]www.maths.cam.ac.uk/undergrad/admissionsinfo/steppaper/02II.pdf[/URL]
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University, age 18+
In science subjects undergraduate students can either take a 3 year BSc degree or a four year MSci degree.