Download Maths Paper 2 2022
Veola Delzell
This section includes recent GCSE Maths past papers from AQA, Edexcel, Eduqas, OCR, WJEC, CCEA and the CIE IGCSE. This section also includes SQA National 5 maths past papers. If you are not sure which exam board you are studying ask your teacher. Past papers are a fantastic way to prepare for an exam as you can practise the questions in your own time. You can download each of the exam board's papers by clicking the links below.
How much are editing, revising, updating, adding to, etc., part of the "normal" process of process of drafting math papers? Specifically, papers of moderate (10-15 pages) length. I've noticed I tend to do this for several months, and the thought has occurred to me that perhaps I'm being too "fussy" and that I'm wasting time.
I have published over 2300 pages of technical books, and over 1000 pages of technical papers (conference and journal papers), and if there is one thing I am certain (for me, at least) it is this: writing is editing. Far far more time is spent on editing drafts than initial writing. It is inconceivable that I would or even could write any thing technical from beginning to end and not have to edit it many times.
That being said, it is true that a scholar may get caught up in finicky editing rather than more substantive scholarship and thought, so the question arises when to deem a paper "finished." Often a conference publication deadline dictates the point. Occasionally it is the knowledge that a competitor is about to "scoop" you. Sometimes it is the desire to move to a new topic or new paper that dictates the point.
If you keep revising because you think that it is very important that published papers meet certain standards then it is an ethical choice, in a way. You will have to face consequences (publishing less) which may have an impact on your career. But there is nothing wrong in deciding that your contribution to math will come with a few nicely-written papers rather than with a huge pile of drafty ones.
There is also a possibility that you keep revising because you feel unsure about what others may think of you if you submit a less-than-perfect paper. Which is what often leads to obsessive revising, which doesn't sound as positive, does it?
In this case you should confront yourself on this point. There is a chance that after a number of published papers you'll gain some self-confidence and be more relaxed on this point; but there is also the case that at each submission your level of anxiety will increase and this will in time affect your capability of writing good math.
In any case, personally I've found that after 3-4 rounds of revision it is extremely unlikely that my paper will improve. When it happens that I change the wording of a sentence to a new wording and then I realize it's the one I started with I take it as a sign I have to stop revising.
I don't think that you should be asking about what is "normal." You should instead be asking whether your revisions are improving your paper. If your revisions are improving your paper then it's good to make them. On the other hand, there can come a point where your revisions are actually decreasing the quality of the paper. The most common cause of this is that you add things to the paper that don't really belong in the paper and actually clutter it. If you find yourself doing this then you should train yourself to resist the temptation to try to say or do too much in one paper. But if you are improving the paper then it is unproductive to worry whether what you're doing is "normal." Maybe it's not normal, but if what is normal is not good then why be normal?
Unless you have a need to get the paper published asap, I recommend you put it aside for a month or so instead of looking through it repeatedly. When you next read the paper, many of your preconceptions and assumptions will have been forgotten and you will be much more likely to notice things like missing definitions, logical gaps, and sections of proofs that are going to confuse readers.
If you are building your career and have to follow certain steps to do traditional publishing in journals, then you have deadlines forced upon you (unless you have tenure, in which case your paycheck is not so deadline dependent), and that should factor into your process. I am vaguely aware of different styles my advisors used, but they were different people. I imagine both had several papers in the pipe and protocols for when to tweak and when to let go.
I am a 2nd year graduate student in Number Theory. My advisor has sent me papers to read and I have trouble getting through even a paper. Be warned that my problems may be noobish and borderline childish.
4) how much time in general should I spend on a paper I want to understand? After 2 hours of definition chasing, I would simply get frustrated and call it quits and be discouraged. Is this normal or do I just have bad work ethic and should perservere more?
Of course the answers to these questions are highly personal. People tend to read papers in very different ways one from each other. I would say that probably the most important thing to understand is the structure of the arguments, and why they work. This may be a difficult task, because certain authors don't bother too much in making this clear to the reader, and they rather just pile up technicalities on the top of each other without explaining the reason why they're doing so. In a well-written and informative introduction, you should be able to loosely follow the logic behind the proofs, and you should get a very general idea of what is going on in the paper. This is of course not enough if you want to understand everything carefully. Personally, I tend to read the same sections several times, maybe on different days. Thinking about them in the meantime helps "digesting" the math, and usually at some point things become clear.
1) Essentially, yes. Of course it is also your supervisor's responsibility to give you a paper (at the beginning of your PhD) that you don't need billions of new definitions to understand. On your side, you should definitely have a solid grasp of the basic concepts. Then it's part of your work to bridge the gap. With time you'll learn that certain definitions are crucial, and other mostly cosmetics.
2) Usually no. Again, if a paper is well-written then the arguments explained in it, plus the statements of the quoted theorems from other papers, should be enough to understand everything. Certain people hate to use other papers as "black boxes" though, and go through, even if quickly, the other quoted papers.
First, let me reassure you that your problem is a very common one. Reading a mathematics paper, particularly if you are just starting out in the area, can feel like chasing an endless stream of new definitions and references.
As has been suggested in the comments, you could speak to your supervisor about this. Perhaps also your university offers courses in this kind of thing? I know that the university where I did my PhD ran courses on these types of skills such as reading and writing academic papers.
I read the paper with a pen in my hand, ready to be able to annotate the paper. I used to use a physical print out of the paper with a pen and highlighter. Now I use an electronic version on a tablet and annotate it on there. Either way I think it is very helpful to be able to make marks on the paper.
This last stage of deciding how much detail to go into relies to an extent on your own discretion. If there is some lemma in the paper which you do not understand all the details of, maybe it is not so important for your purposes. On the other hand if this lemma is a crucial part of the proof of a theorem which you wish to generalise, then maybe it is a good idea to really understand what is going on here!
If there are definitions/objects in the paper I do not understand, Itry to learn (or at least write on a separate page) the definitionand find some examples of it first. To keep track of definitions andother material I am learning I use electronic flash cards (Anki). However Ido not know anyone else in person who uses them for this.
I have been skimming over the list of references in mathematical papers by well-regarded researches, but I have not found a definitive pattern. In fact, in many publications, neither the author nor the editor seems to actually care.
Bill Barth is right in that this choice is typically made by the journal's style files and/or copy editor, not by the author. However, just in general, my experience is that the first form (capitalize only first word and proper nouns) is more common when referencing papers, while the second form (capitalize all but "little" words) is used when referencing books.
You are right: in math, neither the author nor the editor is likely to really care. Most math papers are prepared with specialized software (TeX or LaTeX, using BibTeX of AMSRefs) which formats the references automatically. So we just trust the software, and focus our attention on more important things.
Please note, some past papers are based on the old test specifications. The style of the questions will remain unaltered, and most of the STEP questions from previous papers can be used for preparation.
Large Print
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A. Bring pencils or pens (blue or black ink) and the PIN that you were given at the registration platform. Nothing else is needed. Supervisors provide clean, white paper. Calculators, computers, references, and drawing tools are not allowed, and cell phones must be turned off and stowed away during the exam.
Without computers, we would need to work out difficult math problems on paper. This is still true in math tests, where the teacher would give students a few pieces of paper so they can work out their problems. Usually, students can ask for more paper, if needed.
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