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A-Level Maths + A-Level FM in 1 year - How to structure + is it possible?

I am looking to do this as I want to do Economics and finance subjects at university, both of which require maths at least, and the more competitive courses looking like they require Further Maths too. Wondering if it would be possible to learn these specifications within 1 year and what sort of commitment it would require to achieve an A* and A respectively if doing both in 1 year.

I am aware there are textbooks available, so hopefully this will be helpful for my learning. If I choose to do so, I will begin this in early July and will therefore have from there.

I would perhaps need to sit a Mathematical test in applying to highly competitive universities and wonder if this would be possible to achieve a good score on the STEP test with very condensed experience, as I'd need to cram all the AS content I believe from July - Jan to sit this.

If there is a breakdown on the various tests universities such as Oxbridge/Warwick/UCL will accept that would be helpful. What I mean by this is, for example, the STEP versus the AEA tests, what sort of skills it draws on, their format / content , and their dates in the year - to ultimately see which I'd be better off doing or targeting.
Reply 1
Well, it is possible since that's what I do. I self-learned AL Math, AL Physics and AL Further Math in 2023 and finished them in either 2023 May or October with the percentage scores of 97%, 97% and 96%. I'm now taking STEP 2 and 3 and will get at least 1&1 before my application.(I will get at least 80 for my STEP 2 this year according to my prediction)

I cannot agree more with your ideas, since you may notice that, if you want to have an outstanding performance in some competitions and application, you must finish your study of AL Math and AL Further Math as quickly as possible.

What I will suggest is to read through the textbook as soon as possible, and during that time, take notes for sure. After finishing the reading and note-taking, review the note every weekend, and do all questions behind each chapter in the textbooks. It is acceptable if you want to try all the questions mentioned in the textbooks, but there are too many questions and just doing the questions behind each chapter is enough. It's better for you to complete all the afore-mentioned targets before the next semester. After finishing those questions, do all the past papers from 2019 to 2023. Record your time and take notes if you find you have done really bad in particular areas and then focus on those specific kinds of questions.
Reply 2
Speaking of taking STEPs, here's some advice.

1.
Before trying STEPs, be sure that you finish your AL further mathematics really well, means that you not only know how to use the methods to solve questions, but also their underlying meanings.
Even if STEP2 doesn't require you to have knowledge about A2 further mathematics, you need to know more mathematics knowledges so as to broaden your horizon or to make you think like a mathematician.
If you don't like Mechanics or Statistics, then it is okay to skip them when studying further mathematics, but you have to learn Pure Mathematics really well.
PS: TRY SOME TEST PAPERS OF FURTHER MATHEMATICS! YOU NEED PRACTICE INSTEAD OF MERELY KNOWING THE METHOD!
2.
(option) If you have time, try AMC12 or BMO1 and do some of their past papers, because you need to know 'how mathematicians or university mathematics professors think'.
You may find AoPS website and UKMT website useful. There is a great book called ACE THE AMC 10/12(which you can find online, or I can send it to you through email), written by students and covered almost all knowledge about AMC from geometry to number theory, which is useful if you don't have a basic understanding about these fields.
By the way, some entrance examination of famous mathematics summer schools, like SUMaC, ROSS, PROMYS, are really worth trying. There are far better than STEP questions because you are expected to apply what you have learned in class into reality questions. If you like, search them online or email to me.
3.
Use Cambridge website wisely.
There are some STEP modules and a recommended online book about some great STEP questions on the Cambridge website. Print them out and finish all of them! They are the good start points and you can gain a basic understanding of STEP once you finish them. There are also some knowledge notes organised by Cambridge and they are available on the website.
4.
Finally, do all the question papers from 1998 to 2023.
You no longer need to do STEP1 questions since they are too simple for students applying to mathematics faculty and doing them is a bit like waste of time. It will be more effective for you to do all question papers of STEP2 and STEP3. You may also do question papers from 1988 to 1997, but since the syllabus changed in 1998, it might be confusing to do some early papers.
At the time doing STEPs, prepare a notebook for writing down some now knowledge or skill you have learned, like ' when we know a relationship in the form of A+B+C+D and want to prove a equality in the form of ABCD, let a=InA, b=InB, c=InC, d=InD and calculate a+b+c+d'. Also, organise the questions which you think are difficult but you can soon learn how to solve them, make a list, and finish them again before the week of taking STEPs.
5.
If you find some areas in STEP are particular difficult, like Mobius Transformation in complex number or dot product in vectors, try STEP Database. Find all the questions in some specific fields and do all of them to gain basic insights towards them.

That's all my suggests and all my experience during the study of this year. Hope that it is useful for you!

Here's some useful website:
STEP database: https://stepdatabase.maths.org/database/index.html#
AoPS database, consisting of almost all question paper from almost around the world, if you want to find STEP/AMC question papers, try this: https://artofproblemsolving.com/community/c3158_usa_contests
STEP modules:
https://maths.org/step/assignments
https://maths.org/step/assignments-stepii
https://maths.org/step/assignments-stepiii
AMC12: https://artofproblemsolving.com/wiki/index.php/AMC_12_Problems_and_Solutions
BMO1: https://bmos.ukmt.org.uk/home/bmo.shtml

GOOD LUCK!
(edited 1 month ago)

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