# AS-Level Further Mathematics Revision Tips

I recently did my y12 A-level mocks and came away with a grade in Further Maths that I am not fully pleased with (was aiming for A*). I'm looking for some revision tips for a sort of 'retake' exam I will take next year. My issue was mainly core pure.

The core pure content I was examined on was just AS content.
I had completed all the AS core pure past papers but found that each time I did a paper I got negligible improvement in my score and always struggled with timing. I don't think I have any problem with theory, I have a very good understanding of the mathematical concepts in further maths. I find my issue is time pressure and figuring out exactly what the question wants me to do.

Everyone found core pure tight for time, but I lost a LOT of marks because of timing and silly mistakes. What can I do to fix this? How do I significantly improve my speed? Are there any resources you would recommend?
First off, knowing the material well and doing exams well are two different set of skills. Now...

> figuring out exactly what the question wants me to do
The wording for pure is relatively straightforward. Do you have an (explicit) example on how a question might trip you up?

> timing
Ask yourself, given infinite time without access to notes, are you confident at getting close to perfect (in fact, try on one past paper - forget time constraint and give yourself 24 hours to do it)? If yes, try redoing the questions - usually questions aren't as different as you think.

> silly mistake
What counts as a "silly mistake" in your opinion?

> resources
There are way too many practice questions floating around, which I'm sure others will recommend, but I don't think you actually need that many. What I find underrated, repeating myself here, is to redo questions.
(edited 4 weeks ago)
I'll give a few examples of silly mistakes I made on the core pure paper:

Example 1:
Was given a cubic equation in terms of x, told has roots alpha(a), beta(b) and gamma(g). Asked to find the value of 3/a + 3/b + 3/g.
In my answer found value 1/a + 1/b + 1/g correctly but forgot to multiply this figure by 3 so lost a mark.

Example 2:
Summation question. Asked to find values of k for which an equation is valid. Used standard results, simplified, then solved everything correctly, but during simplification cancelled out a linear factor (3k+1) from both sides of the equation without explicitly pointing out that -1/3 is a potential value of k. Lost a mark.

Example 3:
Copied down a matrix element incorrectly, leading to an incorrect result for a subsequent matrix multiplication. Lost a mark

Example 4:
Asked to use matrices to solve for a system of simultaneous equations in terms of x, y and z. Asked to give values of x y and z in terms of k. Applied inverse matrix etc. and got correct x, y and z expressions in vector form in terms of k. Did not explicitly state x=..., y=... z=... . Lost a mark.

Example 5:
Asked to give coordinates of the point of intersection between a plane and a line. Gave correct point of intersection in vector form rather than as a coordinate. Lost a mark.

Example 6:
Asked to find shortest distance between two lines. Copied an element in a vector wrong at one point in workings. Lost a mark.
Later found (my) two points where lines are closest. Did not show working for finding distance between points(i.e. 3D pythag). Lost a method mark.

I think you get the point. So many easily avoidable slip-ups because I was rushing through as quickly as possible. Despite this still bottled the last question and didn't even finish it.
Original post by tonyiptony
First off, knowing the material well and doing exams well are two different set of skills. Now...
> figuring out exactly what the question wants me to do
The wording for pure is relatively straightforward. Do you have an (explicit) example on how a question might trip you up?
> timing
Ask yourself, given infinite time without access to notes, are you confident at getting close to perfect (in fact, try on one past paper - forget time constraint and give yourself 24 hours to do it)? If yes, try redoing the questions - usually questions aren't as different as you think.
> silly mistake
What counts as a "silly mistake" in your opinion?
> resources
There are way too many practice questions floating around, which I'm sure others will recommend, but I don't think you actually need that many. What I find underrated, repeating myself here, is to redo questions.

As for your question about 24hrs, yes I think I'd get 95%+ if not 100% (not that that really means anything anyway). As I said I don't think I did poorly because I don't know content or how to do the questions, I did badly because of timing, bad exam technique(i.e. not stating the obvious) and a ridiculous number of slip-ups as outlined above which could be fixed if I had time to go back over the questions at the end (or even if I had more time on each question in the first place).
Original post by tonyiptony
First off, knowing the material well and doing exams well are two different set of skills. Now...
> figuring out exactly what the question wants me to do
The wording for pure is relatively straightforward. Do you have an (explicit) example on how a question might trip you up?
> timing
Ask yourself, given infinite time without access to notes, are you confident at getting close to perfect (in fact, try on one past paper - forget time constraint and give yourself 24 hours to do it)? If yes, try redoing the questions - usually questions aren't as different as you think.
> silly mistake
What counts as a "silly mistake" in your opinion?
> resources
There are way too many practice questions floating around, which I'm sure others will recommend, but I don't think you actually need that many. What I find underrated, repeating myself here, is to redo questions.

As for the point about figuring out what the question wants me to do, I probably shouldn't have mentioned that on this post because this post is mainly about core pure, where this is not usually a problem for me (more of a problem for me on further statistics).

On a slightly related note, I just want to point out how whack mark allocations are for core pure. Like, I have an exam question in front of me where you are asked to multiply two 3x3 matrices (the second including an unknown variable k in some of its elements) and then make an analytical point about the resultant matrix. This is not a 'difficult' question by any metric, but I it does entail 27 multi-term multiplications, 18 additions, and 9 simplifications, PLUS some work afterwords to make a point about the matrix, all without making a simple clerical error somewhere. Why on earth is this question worth only 2 marks??? When I looked at this question initially, I spent about 20 seconds just wondering whether they are expecting me to do some shortcut method to get an answer. And you can't even use your calculator for this question because of the unknown k. I get further maths is supposed to be harder but like...seriously?
Original post by tonyiptony
First off, knowing the material well and doing exams well are two different set of skills. Now...
> figuring out exactly what the question wants me to do
The wording for pure is relatively straightforward. Do you have an (explicit) example on how a question might trip you up?
> timing
Ask yourself, given infinite time without access to notes, are you confident at getting close to perfect (in fact, try on one past paper - forget time constraint and give yourself 24 hours to do it)? If yes, try redoing the questions - usually questions aren't as different as you think.
> silly mistake
What counts as a "silly mistake" in your opinion?
> resources
There are way too many practice questions floating around, which I'm sure others will recommend, but I don't think you actually need that many. What I find underrated, repeating myself here, is to redo questions.

Yeah, I'll try redoing some questions