Right, well not many people seem to understand this, but it's really fairly simple. I thought I'd post this just so people understand it a bit more.
Basically, as you probably know, all A-levels are graded out of 600 UMS, with AS level making up 300 of these, and A2 making up the other 300. There's nearly always (except for rarer A-levels like Polish, Bengali etc.) three modules for AS and three for A2.
When you've sat 6 modules, you can receive the A-level award. You'll get a mark out of 600. If the mark is above 80% (480/600), this is an A, above 70% (420/600) then it's a B, and so on down to 40% (240/600), when it's an E. Anything lower receives a U. From September 2008 an A* grade has been introduced. To get it you need 80%+ in your AS units and 90% in your A2 units. You don't get an A* grade for 90% overall only for your A2 units. You can't get an A* at AS level.
These UMS marks are the same for all A-levels over all years. You will always need 480/600 UMS marks, or 80%, for an A, and 40% to pass with an E. Here are those UMS boundaries for A2 and AS (just half of A2).
A* - 80% for AS and 90% for A2
A - 480/600 - 80%
B - 420/600 - 70%
C - 360/600 - 60%
D - 300/600 - 50%
E - 240/600 - 40%
U - 0/600 - 0% <-- don't get this
This is at least fairly straightforward. These grade boundaries are ALWAYS the same.
As for individual modules, they're weighted to take up a certain proportion of the A-level. Let's look at an example here: AQA Psychology (Specification A). This has six modules (like nearly all A-levels) and they each amount to a specific proportion of the overall A-level (which is not equal). This is the AS-level part:
PYA1 - 16.67% of the A-level - 100 UMS
PYA2 - 16.67% of the A-level - 100 UMS
PYA3 - 16.67% of the A-level - 100 UMS
This is fairly simple. Each module counts for a sixth of the total marks, of which there are 600. So, obviously, each module counts for 100 UMS marks. The A2 is a little more complex:
PYA4 - 15% of the A-level - 90 UMS
PYA5 - 20% of the A-level - 120 UMS
PYA6 - 15% of the A-level - 90 UMS
As you can see, these are proportioned differently. PYA5 is worth 20% (of the total 600 marks), which is 120, whilst the other two are worth 15% of the total 600, which is 90.
So far most people manage to understand. The problem is that none of these modules are marked out of 90, 100, or 120. The marks you get in the exam are not UMS marks, they are raw scores. Let's look at an example, still in AQA Psychology A, from PYA1. This module is out of 100 UMS, but the actual exam is marked out of 62. In order to find out the relationship between what you get on an exam and what actually goes on the certificate as UMS marks, you need to know the grade boundaries for that exam. These are found in different places for different exam boards, I'll put a list at the bottom of this post.
Let's say for example's sake that you get 30/62 in PYA1. This is roughly 48%, and the first mistake most people make is to assume that this is the UMS mark you get. WRONG. 48 UMS would give a fairly high E, but the grade boundaries tell a different story. Here they are:
A - 39/62 (63%) - 80/100 UMS
B - 33/62 (53%) - 70/100 UMS
C - 27/62 (44%) - 60/100 UMS
D - 22/62 (35%) - 50/100 UMS
E - 17/62 (27%) - 40/100 UMS
So if you got 80 UMS marks, which is 80% and therefore always an A, you'd only actually have attained 39/62. Similarly, if you knew you'd got 39/62 you'd be able to see that you had got an A grade and 80 UMS marks.
So far so good (hopefully). However, I mentioned getting 30/62 above. What happens then; that's not on any grade boundaries...
The answer is, logically, that it goes in between. 30/62 is exactly halfway between the B and C grade boundaries of 33/62 and 27/62, therefore the UMS conversion comes out halfway between the UMS boundaries of B and C, which is 65, or a solid C.
Hopefully you can see the pattern here. It's not so convenient if you got something like 32/62, because that's not exactly in the middle of the grade boundary. You know it's a C, because it's below the B and above the C boundaries, so UMS-speaking it's between 60 and 70. You need to:
1. Work out the gap between the C and B grade in raw marks (6 in this case).
2. Work out the gap between the C and B grade in UMS marks (10 in this case).
3. Work out the gap between your mark and the next lowest grade boundary in raw marks (5 in this case).
4. Divide the number worked out in step 3 by the number worked out in step 1. (in this case, 5/6)
5. Multiply this by the number in step 2 and add it to the next lowest grade boundary in UMS this time.
So for this case, we get (5/6) * 10, which is 8.333. Rounding it down to 8, we add it to the next lowest boundary in UMS, which is C (60). We end up with:
32/62 -> 68/100 UMS (C)
This works just the same when the module is out of 90 UMS, 120 UMS, 105 UMS, or whatever else. If you follow the steps above you'll always be able to work out the UMS marks if you have the grade boundaries.
This system doesn't work quite like this for very low marks. If your UMS mark is less than 40% (40/100, 36/90, 48/120 etc.), but more than 30%, then you are awarded an imaginary 'N' grade (which does not show up on the certificate - you still failed!)... The point of this is to make sure the 'exchange rate is the same on either side of the fail point.
This isn't too easy to follow at first. Let's return to our trusty PYA1 boundaries from June 2006, this time focusing only on the worse grades:
D - 22/62 - 50 UMS
E - 17/62 - 40 UMS
What's not shown on the grade boundaries is the N grade, which comes under E for 30 UMS. Just subtract the width from D to E (in this case 5) from the raw score boundary of E (in this case 17) to find the boundary for 30 UMS and your prestigious 'N'early grade:
N - 12/62 - 30 UMS
Of course the next grade boundary is familiar:
U - 0/62 - 0 UMS
What is interesting here is that for only 12 raw marks you gain 30 UMS marks. This means that for each of the marks up to the 30% boundary in ANY paper are usually much easier to gain (I say usually - if the N boundary was very high, like it often is in coursework, then you need to work very hard just to get those first 30 UMS marks, often needing over 50%).
The system is also distorted at the top end of the scale, and I suspect this is where people who care enough to read this will be thinking of. As you might have heard already, in most A-level papers you do not need full raw marks to get full UMS marks. Put simply, you can get questions wrong in your exam and still get full marks, USUALLY. It works like this (we'll use the example of PYA1 again, because it's convenient):
A - 39/62 - 80/100 UMS
B - 33/62 - 70/100 UMS
Yes, there is an equivalent to the N grade here. It is the 'cap', at which no more UMS marks can be gained (you have got full marks and can congratulate yourself on a job well done). It is calculated in the same way as the N grade, but this time you DOUBLE the distance between the raw mark boundaries for A and B (in this case 6), and then ADD them to the A boundary. This results in:
CAP - 51/62 - 100/100 UMS
A - 39/62 - 80/100 UMS
B - 33/62 - 70/100 UMS
This is a good module to illustrate this, because there is quite a significant cap at play here, meaning for June 2006 you only needed 82.2% for completely full marks and a nice 100/100 on the statement of results.
Anyway, I really hope this answers some questions. Feel free to ask more here; most UMS problems are simply solved once you understand the system, and I've been shocked to discover I've had to explain this to just about every A-level teacher I've been taught by!
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GRADE BOUNDARIES FOR DIFFERENT EXAM BOARDS:
AQA:
AQA do a good job of publishing things like this usually. They have charts with all the module grade boundaries for all exams during June 2006 and January 2007 that can be accessed here. In addition, if you go on their section for your particular A-level, and read the examiner's report for the year you're interested in, at the bottom are the grade boundaries for each of the modules for that subject during that year.
OCR:
It's a little more difficult to find OCR's boundaries, and they only have them for June 2006 and January 2007. Go here and click on your subject's mark scheme for the grade boundaries from last January's exams, and go here to do the same for June 2006's.
Edexcel:
Personally, I don't like Edexcel's website at all. They do a good job of making it hard to use... anyway, go here and select your subject from the second column on the left. Then, if necessary, use the same column again to be more specific. You should come to a list of examiners' reports, which, to their credit, do sometimes go back to 2005. The grade boundaries are towards the end of the report.
WJEC:
This one has an odd layout. Go here and click on your subject in the column to the left. Then look to the right at the 'Documents' box and click on '[View full list of documents]'. Find the examiner's reports; the grade boundaries are in there, but they're written at the start of each module's report, so you might have to scan through for them.
CCEA:
Well this is a frankly horrible site. If anyone can find these grade boundaries on there (we need the raw marks -> UMS one, not any of the others), then post a link here.
If no one reads this, then oh well. Seems like it might be useful though.
If you are unsure about the A* grade then read this thread =)
Okay, well I improved AesopRock's spreadsheet a little by making it more flexible. robot1000, it now allows for modules with an equal share (100 UMS).
If I'm feeling motivated (again...), I'll make a spreadsheet which does all that calculating I explained in the first post for you, so you just type in the bounadries and a raw mark and it gives you a UMS mark. Maybe.
(Original post by sunburnt_note)
Secondly, say the 'A' grade boundary is 42/60, and the 'B' boundary is 38/60, that would make the mark needed to get full UMS (120/120) 50/60? And if so - if you got 46/60, would that mean you got 108/120? I'm just curious as to how it all works!
Yes. This is exactly how it works, and you seem to have understood it.
(Original post by sunburnt_note)
Is the 'cap' on the A grade (where you get full marks UMS) always the distance between A and B multiplied by two? Or is that just in most subjects?
This raises an interesting point that I wasn't sure would come up, but I might as well tackle it. The point of the N grade (30%) is to ensure that below the fail mark the 'rate of exchange' from raw to UMS is the same as for the average marks. The cap works in exactly the same way, except that in some instances if we worked it out by 'adding the doubled boundary difference to the A boundary' the cap would be more than 100%, which is obviously wrong. It is always possible to gain 100% in a module, so the top marks are worked out differently in this case. I'll use a real example here to illustrate this (the Statistics 2 module from the OCR (MEI) Maths specification). The grade boundaries here were from the January 2007 exam, and this exam is marked out of 72 raw marks, and worth 100 UMS marks:
A - 58/72 -> 80/100 UMS (80.6%)
B - 50/72 -> 70/100 UMS (69.4%)
C - 43/72 -> 60/100 UMS (59.7%)
D - 36/72 -> 50/100 UMS (50%)
E - 29/72 -> 40/100 UMS (40.3%)
(In this case the boundaries might not look equally spaced, but this is only because of rounding. We can ignore slight differences in spacing.)
The boundary for 90 UMS is worked out simply by adding the difference between A and B to the A boundary, as explained in the first post:
66/72 (91.7%) -> 90/100 UMS
A - 58/72 (80.6%) -> 80/100 UMS
B - 50/72 (69.4%) -> 70/100 UMS
However, if we try to work out the cap (e.g. 100/100 UMS) by doubling the boundary then adding it to A:
58+16 = 74
-> 100/100 UMS = 74/72 (103%)
Plainly, no one can be expected to get 103% in a module, but everyone expects to be (theoretically) able to achieve full UMS marks, and so they can. In cases like this, 100% UMS marks is given by 100% raw marks, so in this module:
100/100 UMS = 72/72
If someone then got, say, 69/72, we would use the different rate of exchange to calculate their UMS, where their raw marks don't actually mean as much as they perhaps should. In this case, 69/72 is halfway between the 90 UMS (66/72) and 100 UMS (72/72) boundaries, so candidate is awarded 95 UMS.
After emailing AQA I discovered the above is wrong. Quite simply, when the cap is over 100%, then the cap becomes 100%. Logical enough.
To answer the question you actually asked: 'Is the 'cap' on the A grade (where you get full marks UMS) always the distance between A and B multiplied by two?'
Yes, in every module in every A-level, except in cases like the one explained above.
Well... I hesitate to reveal the source of my powers, but oh well. XD
The leaflets here have helped me slightly. AQA are by far the best board at making things accessible and online, and these publications were certainly a good starting point.
(Original post by Noizuf)
Sorry Terrafire, but your method is incorrect. You are assuming there are multiple linear relationships (one relationship per grade) between UMS and raw marks, when in fact, the relationship is not linear. What you are doing is linear interpolation, which provides an approximate UMS, but the actual method of calculating UMS is far more complicated than that.
I'm completely sure that this method is correct, because I had it confirmed by the AQA statistics department via e-mail. The relationships is linear, because the ideal situation is that it is just as easy for an A grade candidate to get one extra mark as it is for an E grade candidate to do so. The rate of exchange should remain the same throughout most of the scale (with only extreme values being distorted).
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I notice that there are a few misconceptions still. Thelfo, you ask how the remaining raw marks are crammed into the few UMS left... and Wez, your answer is good but wrong.
The raw marks are NOT 'crammed into the 20% UMS remaining above 80%. Instead, a cap is introduced, say 73/90, above which EVERYONE gets 100% UMS, even though they have not necessarily got full marks in the paper.
Hrm... over the internet it's very difficult to explain this kind of thing. I'm sure given half a minute or so actually having it explained face-to-face would sort out confusion, but my explanation obviously isn't working for some people. :/
I might be repeating myself, but...
You need to distinguish between raw marks and UMS marks! UMS marks are the final marks that go on a certificate, and they're always specific grades for fixed percentages (80% = A, 70% = B, 60% = C, etc.). However, these are different to the raw marks, which are the marks you actually get for each question on the exam paper itself. These are scaled according to the grade boundaries for that particular module on that particular year, in order to convert to UMS.
An A grade does NOT need to be 80% raw marks. An A grade is given when you reach the set boundary for an A grade on that particular paper, which is rarely 80%. If you achieve these raw marks, you will receive 80% of the UMS marks, despite not having achieved 80% in the raw marks.
I don't know how much clearer I can be, but if anyone doesn't understand I can try again.
Using the (very well explained) information from Terrafire, I've made an Excel spreadsheet that converts a UMS mark into the estimated raw mark, using the published grade boundaries.
It uses a simple linear interpolation method and includes the N grade and upper cap that Terrafire explained.
It seems to work okay but there's probably problems with it somewhere. I'm not too great with Excel, so the 'coding'/calculations are pretty sloppy in places and probably quite confusing if you were trying to understand how it works.
Enjoy, and let me know if there's anything that needs correcting/improving.
Terrafire , I've got some UMS conversion tables you might find interesting for Edexcel Maths which give the exact conversions between raw and UMS.
Your program works pretty well from what I can see but some raw marks don't seem to be mapped into UMS marks.I got 85/100 for Core 4 last year for example , which I know from Edexcel online to be 62/75 .The lower E grade boundary was 29 on that paper and the A boundary was 58.It claimed that I'd have had to get 65/75 for 85 UMS .For 84 points , the program says I needs 64/75 , 83 - 62/75 , 82 - 61/75 , 81 - 59/75 (what happened to 60?) and 80 correctly as 58/75.
Apologies, I got the rounding the wrong way round in the previous spreadsheet. You bring up some good points conroe, and the spreadsheet has been fixed - it now agrees that you got 62, which is good! The culprit was a bug in markdr's original where the upper UMS boundary was calculated to be 90% rather than 100%, thus distorting any marks above 80%, if you're interested.
New spreadsheet attached.
P.S. Now that I've properly looked through the formulae, that must have taken you a while, markdr!
Thanks for the help there, terrafire. I'm not 100% sure what you did () but it seems to have worked!
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I've tidied it up a bit and added some validation to stop things going wrong when wrong data is input. Also I've protected it so formulae can't be deleted or changed by accident.
This should be the final version, unless anything else emerges.
Ok, thanks for the feedback guys. I agree it was buggy as hell, but hopefully this update has sorted out some of the issues. I've tested it briefly and it seems to work okay.
(Original post by michaelyus)
Sorry to bring this up again, but:
The converter seems to always have the same mark for 80% UMS and 90% UMS, so 89% UMS is worth more raw marks than 91% UMS...
Thanks - I don't know how this slipped though. Fixed.
(Original post by Worthers)
I'm getting some odd results when the maximum mark changes. For example it says I have the same raw mark when it's out of 72 and out of a 100. Fantastic converter nontheless, I love it!
I don't actually think this is a problem with the spreadsheet. Unless I'm missing something, if you're only changing the maximum mark, your raw score won't change, because the E and A boundaries are staying the same. Even if your mark is above 80%, the cap is calculated from the A and B marks, so still, nothing will change. So if you wanted to see your mark increase, you'd have to move the A and E boundaries up as well as the maximum. I hope this is right anyway, seems to make sense to me.