STEP Prep Thread 2019

Probably not entirely helpful, but did you know you can "sing" the quadratic formula to the tune of "Pop goes the weasel"?

I think that if your interviewers knew that you had dropped one you would be at a disadvantage, whereas if you had only done 3 from the start you wouldn't IFSWIM.

@TheTroll73
Are you telling me you're going through A Levels Maths / Further Maths having to dive to the formula booklet for the compound angle formulae. Don't blame Siklos just because you've forced yourself into bad habits. Spend a few days doing questions without diving for the formulae booklet and the formulae should ingrain into your mind (Unless you have some kind of mental condition)

STEP is testing whether you are an able mathematician. Mathematicians at "STEP" level should be reasonably expected to know basic formulae like the back of their hand.
If you don't know them, you simply haven't used them enough and aren't familiar with them. You've just fallen into the bad habit of saying >I don't know them perfectly, so I'll reach for the formula booklet every time I do a question, and so you never give yourself the opportunity to learn them.

Alright... I will take on your advice and see how it goes, hopefully I won't get bored too much.

However, I still don't see how remembering formulae shows mathematical ability

@TheTroll73 your situation has probably already been over-discussed already, but I think I have quite a nice example of where memory was relevant for me in doing an older STEP question alongside a formula booklet. In case it's that deep for you, I've left this unnamed question in a spoiler at the bottom of the page.

The question was split into several definite integrals, so I began making headway with the first part, and I simplified it down to an integral that both looked pretty simple and looked as if it couldn't be further simplified. Having not done any integration over the past month or so, I immediately reached for the formula book, looked down all the given integrals, and couldn't find it. I played about with the integral again, and couldn't go anywhere, so I moved onto another question.

However, the relevant integral was in fact in the formula booklet, just in the form of a derivative rather than integral - and I hadn't looked there.

Of course, the organisation of the STEP formula booklet could be blamed here, but I think the issue was with my unfamiliarity with a standard integral - that's certainly how I felt coming back to relatively easily glide through the rest of that particular question after being told by @_gcx coincidentally.

I don't expect to feel intimidated by the lack of a formula booklet in STEP if I take it this June. FM content in STEP II? Possibly. Fewer questions? Again - a lot more significant a change than no formula booklet in my opinion.

To me it just shows familiarity. I have a horrible memory but can still give quite a few of them. For the integrals/derivatives, you could always just derive them if you're unsure. Particularly with differentiation because then you have the chain/product rule to plow through everything not so much with integration. If you go out to specifically remember them in my opinion you're more likely to make a mistake.

fwiw, there's no formula booklet for tripos exams either.

FWIW, there's no formula booklet for Tripos exams either.

do they give required formulae (more complex ones at least) in the question or do you have to remember all of the relevant formula?

So if I just dropped one without telling them I should be fine?

Can anyone help me with STEP 2 2009 QUESTION 6

I dont understand how they get the infinite GP. The approach of adding just the 5 terms and showing that it is greater than 3 is pretty simple, so I want to be able to understand the GP method.

Sorry I don't know how to write latex on tsr so this might be really unhelpful but... The inequality you show in the first part of (i) you can use to replace every term after the 3rd in the sequence with a term that is strictly smaller and forms a geometric series after the third term.

By iterating the inequality you should be able to deduce that $\frac{1}{F_i}>\frac{1}{2^{i-3}F_3}$ for $i\geq 4$ and hence that $\sum_{i=4}^\infty \frac{1}{F_i}>\sum_{i=4}^\infty \frac{1}{2^{i-3}F_3}$

Understand this part. Thanks. I guess I got super confused as to where they got the G.P from.



What do you mean by iterating the inequality. Sorry I am very stupid

Very possibly it's the incorrect terminology but I mean from the inequality and setting i=4 you have$\frac{1}{F_4}>\frac{1}{2F_3}$ and by setting i=5 you have $\frac{1}{F_5}>\frac{1}{2F_4}$ you can then combine these two inequalities to get $\frac{1}{F_5}>\frac{1}{4F_3}$ you can keep repeating this to gain an inequality for each term after the third in terms of $F_3$.

Also you're not being stupid I'm just doing a bad job explaning