8631
/www/nrich/html/content/id/8631/
5
0000-00-00T00:00:00
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0">Diary: <a href="https://nrich.maths.org/8745">https://nrich.maths.org/8745</a>
<h3>Ideas</h3>
<ul>
<li>I think it would be useful to assemble a glossary of sorts, with a little historical background on what was meant by Scholarship Paper, Special Paper, etc.</li>
</ul>
<h3>Tags</h3>
<p>The paper tagging system can be found at <a href="https://bm380.user.srcf.net/NRICH/">https://bm380.user.srcf.net/NRICH/</a>. Note the https: it's only accessible via the secure protocol. Authentication is done via Raven, according to a list of approved users, to which I can add on request.</p>
<ul>
<li>The legibility tag is scattered and incomplete. I think the papers have been checked for legibility from 1951-1958, and sporadically apart from that. 1978 onwards should not be a problem.</li>
<li>The standard for the legibility tag is "could someone with a mathematical background and time to think get it right". For example, if an index $x^\bullet$ is unclear but the question refers to an ellipse, I won't tag it because the context tells you it's a 2. If a full equation is given then I'm less likely to tag it because you can just "solve for" the unreadable bit. Also, where there is
ambiguity I don't tag unless the most reasonable guess is wrong.</li>
<li>Tagging syllabuses, I only use the "Scheme of Papers" tag for when it was a whole section to itself. In some syllabuses, it appears at the beginning of each subject and hence ends up on almost every page, so it's not much use to tag it there.</li>
</ul>
Question tagging is here: <a href="https://bm380.user.srcf.net/NRICH/q">https://bm380.user.srcf.net/NRICH/q</a>
<ul>
<li>I started off tagging questions "mechanics", but this is clearly too broad a classification, so I am now tagging them "kinematics" for questions concerning distance, velocity and acceleration only, "dynamics" for questions involving forces causing acceleration, and "statics" for questions involving forces in equilibrium. In addition, I use "elasticity" for questions involving elastic
extension or collision.
<ul>
<li>Not sure these distinctions are necessarily the most useful. But they're easy to establish and certainly better than just 'mechanics"</li>
</ul>
</li>
<li>I'm also using "conics", "circle", "ellipse", "triangle", "projective geometry" as subcategories of "geometry". Generally speaking, I try to assess whether or not specific knowledge of the thing named in the tag is useful to the question. Projective geometry I'm hazy on because I never did it myself.</li>
<li>"written" means I've written up the LaTeX of the question. "answered" means I've written up an answer as well (usually because I had to answer it to work out what it was about).</li>
<li>The "differentiation" tag is a bit sketchy. I often forget it's there. Likewise "trigonometry" - both of these are pretty vague and perhaps too often applicable; sometimes you can't tell they are applicable until you start doing the problem.</li>
<li>I might be overzealous on the "moments" tag. There always seem to be moments involved somewhere.</li>
</ul>
<h3>Scheme of papers</h3>
<h4>1950s</h4>
<ul>
<li>1951: First paper:
<ul>
<li>Mathematics, Paper I</li>
<li>Mathematics, Paper II, containing Section A and Section B, the latter containing a Questions on Statistics subsection.</li>
<li>Mathematics, Scholarship Paper (Paper III)</li>
<li>Further Mathematics, as with Mathematics (right down to the statistics subsection), but Paper II Section A subtitled Calculus.</li>
<li>All papers are three hours long.</li>
</ul>
</li>
<li>1952: Further Mathematics II no longer has a Section A or B, or questions on statistics. Further Mathematics III is no longer the Scholarship Paper: there is now Further Mathematics IV for that. In the answers, FMIII is subtitled (Mechanics).</li>
<li>1954: Mathematics Scholarship Paper moves to new Paper IV. Maths and Further Maths Papers I-III now allocated "Two hours and a half". II loses Section A and B, Questions on Statistics subsection moves to III. Further Mathematics III starts marking some questions as less highly-scoring than others.</li>
<li>1955: Mathematics III subtitles first half of paper "Mechanics" (second half still "Statistics"), likely a formalisation of what was already the case.</li>
<li>1956: Answers no longer subtitle FMIII (Mechanics) but this doesn't appear to reflect a change in practice.</li>
</ul>
<h4>1960s</h4>
<ul>
<li>1961:
<ul>
<li>Mathematics I resp. II are now also titled Pure Mathematics I resp. II, still two hours and a half.</li>
<li>Mathematics III now also titled Applied Mathematics I, becomes three hours long. Retains Mechanics and Statistics sections, gains History of Mathematics section.</li>
<li>Pure III, Pure IV (Scholarship Paper), Applied II, Applied III (Scholarship Paper) appear, all three hours long. Pure III contains a historical question, but doesn't give it its own section.</li>
<li>Further Mathematics no longer exists.</li>
</ul>
</li>
<li>1962: Roman numerals in paper titles switched to digits. Scholarship papers no longer have numbers. Applied Maths Scholarship paper grows a Statistics section.</li>
<li>1963: The Scholarship Papers are relabelled "Special Paper". In the case of Mathematics, also subtitled "Paper O". Applied Maths Special Paper does not subsection its statistics questions.</li>
<li>1966: Maths 3/Applied 1 gets a third title, Stats 1. Still contains Mechanics and History of Maths. New papers Stats 2 and Stats Special appear, three hours long each.</li>
<li>1968: No longer any papers with multiple titles - Maths/Pure/Applied/Stats<br></br>
papers are all distinct now, all three hours long. Papers per subject are now 1/2/Special. Mathematics 2 contains a Section 1 and a Section 2. Applied 1 says use 32 ft/sec${}^2$ for gravity, Applied 2 says use 32ft/sec${}^2$ or 9.81 m/sec${}^2$. Historical questions appear at the end of Maths 1 and Pure 2.</li>
<li>1969: Questions start including mark numbers. Mathematics 2 Section 1 is split into Mechanics and Statistics.</li>
</ul>
<h4>1970s</h4>
<ul>
<li>1970: Mathematics Special Paper doesn't give mark numbers this year. All others do.</li>
<li>1971: Pure Mathematics Special doesn't give mark numbers this year.</li>
<li>1972:
<ul>
<li>Mathematics 1/2/Special now appear in (Syllabus A) and (Syllabus B) form. Syllabus A seems to be the previous years' syllabus (e.g. Paper 2 contains Stats and Mechanics sections).</li>
<li>Further Mathematics reappears, papers 1/2/Special, Special subtitled (Paper O).</li>
<li>Pure, Applied, and Stats seem to be largely unchanged. Pure Mathematics 1 doesn't have mark numbers this year. Applied says take g to be 9.8m s${}^{-2}$ - seems to have completed the transition to metric.</li>
<li>Mathematics B and Further Mathematics both have Sections A and B. Mathematics Section B is divided into:
<ul>
<li>Option a. Vectors and Mechanics</li>
<li>Option b. Probability and Statistics</li>
<li>Option c. Numerical Calculation (this includes Gaussian elimination, approximation methods, and following flow charts)</li>
<li>Option d. Algebraic Structure (includes Boolean algebra, groups, sets)</li>
<li>Option e. Analysis and Differential Equations</li>
</ul>
</li>
<li>Further Mathematics Section B has the following options:
<ul>
<li>Option a. Groups (Paper 1)</li>
<li>Option b. Projective Geometry (Paper 1)</li>
<li>Option c. Set Theory; Relations; Boolean Algebra</li>
<li>Option d. Probability and Statistics (Paper 1)</li>
<li>Option e. Analysis and Differential Equations (Paper 1)</li>
<li>Option f. Mechanics</li>
<li>Option g. Theory of Numbers (e.g. primes and modular arithmetic) (Paper 1)</li>
<li>Option h. Rings, Fields, and Vector Spaces</li>
<li>Option j. Transformation Geometry</li>
<li>Option k. Complex Numbers</li>
<li>Option l. Numerical Calculation</li>
</ul>
</li>
<li>Paper 1 has options a, b, d, e, g. Paper 2 has options c, f, h, j, k, l. The Special paper has all the options.</li>
<li>Maths B and Further inform the candidate that "slide rules may be used".</li>
<li>Many of the Further questions aren't included in the answers.</li>
</ul>
</li>
<li>1973: History questions no longer appear.</li>
<li>1974: Statistics Special Paper doesn't appear, but this is probably an archive problem.</li>
<li>1975: Stats Special doesn't appear, but answers do.</li>
<li>1976: Stats Special is back. Maths B Paper 1 doesn't actually say (Syllabus B) anymore, but since Papers 2 and Special do I'm assuming it's a typo.</li>
<li>1977: All subjects, Papers 1 and 2: "Slide rules may be used, where appropriate. Candidates at home centres only may use silent electronic calculators, unless their use is specifically forbidden in a question". Special Papers: "Slide rules and silent electronic calculators may be used". Stats Special exists but has no answers.</li>
</ul>
<hr></hr>
<ul>
<li>
<p>1982: Applied Mathematics and Stats both disappear. Further Mathematics now appears in (Syllabus A) and (Syllabus B) form - Syllabus B is what was Further Maths in the past. Maths A 1 and Further A 1 are Pure 1 and 2 respectively (Pure 1 header is missing from the questions but present in the answers and some other paperwork).</p>
</li>
<li>1986: There are maths and further papers subtitled Syllabus C. Syllabus B is now missing.</li>
</ul>
<h3>Archive format remarks, by year</h3>
<ul>
<li>1957: Further Mathematics II is inexplicably at the end of the archive book instead of with the others. This is mentioned in the main text (unhelpfully, with a typo in the paper number) but easy to miss, so not sure this doesn't happen anywhere else.
<ul>
<li>I'm tracking papers more carefully now so I don't think this happens anywhere else (up to wherever I've got to, see above).</li>
</ul>
</li>
<li>1975: The Stats Special paper is missing. The answers are still in there, so it's not because there wasn't a paper that year. This suggests that its omission from the 1974 book may have been accidental.</li>
<li>1978: Some of the papers have a smaller typeface. Seems like all papers from this date onwards have the new typeface.</li>
<li>1979: The new mathematics syllabus appears three times, apparently identically, so if there are legibility problems there is redundancy.</li>
<li>1980: In the middle of the maths answers, there are some science answers. We have previously used the science answers to identify the end of the maths answers, so it's possible we've missed some. This happens again in (at least) 1982.
<ul>
<li>Now we've looked more carefully and probably haven't missed anything.</li>
</ul>
</li>
<li>1982 (and perhaps others): Margins are very small, so text close to the spine of the book may appear distorted.</li>
<li>1988: no answers.</li>
</ul>
<h3><strong>Online Materials</strong></h3>
<ul>
<li>OCR GCE AS/A levels in maths - Present specification; marks schemes, examination papers and examiner reports January, June 2007-2011 (<a href="http://www.ocr.org.uk/qualifications/type/gce/maths/maths/documents/">http://www.ocr.org.uk/qualifications/type/gce/maths/maths/documents/</a>).</li>
<li>AQA GCE AS/A levels in maths - Present specification; marks schemes, examination papers and examiner reports January, June 2006-2011(<a href="http://www.aqa.org.uk/qualifications/a-level/maths/mathematics/mathematics-key-materials">http://www.aqa.org.uk/qualifications/a-level/maths/mathematics/mathematics-key-materials</a>).</li>
<li>Edexcel GCE AS/A levels in maths - Present specification; marks schemes, examination papers and examiner reports January 2003, 2005-2012, June 2005-2012 (<a href="http://www.edexcel.com/quals/gce/gce08/maths/Pages/default.aspx">http://www.edexcel.com/quals/gce/gce08/maths/Pages/default.aspx</a>).</li>
<li>International Baccaleaureate (for comparison) - ?</li>
</ul></mdoxml>
<?xml version="1.0" encoding="UTF-8"?>
<mdoxml version="1.0"><br></br>
<strong>Summary of Specifications:<br></br>
<br></br>
C1</strong><br></br>
<br></br></mdoxml>
2
3
0
0
0
0
0
New A-level project
Working notes for the new A-level project