Submitted by maths123 on Sat, 06/13/2015 - 13:24
Can you quote formulas from the formula book in STEP? E.g the section titled coordinate geometry in the formula book has useful formulas – in STEP 3 2014 Q3 you could use the perpendicular distance from point to line
Do you get penalised for bad notation? E.g. putting a single implication instead of a double implication
In examiners reports, they often say that candidates accidently prove the converse of the result asked for? – How do you avoid this since it is easier to work from the statement you are asked to prove to a true/given statement than the other way e.g X>Y leads to 1>0? – do you have to rewrite the proof the other way? – this would be time consuming
What happens if you ‘verify’ instead of ‘show’ in STEP questions? In 2008 STEP 3 Q3 – for the last part, would you get marks for just substituting the coordinates of T into the equation of the circle? In STEP 2 2013 Q7i - aren't you verifying when you sub the values of x=3p + 4q, y=2p + 3q into the equation (*) ?
When you are asked to show an equation i.e X=Y; do you have to start from the LHS and work your way to the RHS or can you just manipulate the equation and come to a true statement? e.g X=Y leads to 1=1 hence X=Y is true
Thanks in advance
Quoting formulas: I think it
Quoting formulas: I think it depends. Sometimes the point of the question will clearly be to prove/derive a formula and in that case you obviously can't use it, but otherwise I think it's generally fine (hopefully someone who knows better than I do can answer though).
Notation: if the maths is right, you're fine. Better notation makes it easier for the examiner to follow, and if your notation is so bad you end up writing things that aren't true or not actually solving the problem, that'll cost you, but if it just means your answer doesn't look as pretty no-one will really care.
Converse: this also relates to your last question. If you show X=Y leads to 1=, you haven't shown that X=Y: for example, suppose the original equation is X=Y^2. Then X=Y implies X=X^2, which implies X=1 or X=0 (and, for example, taking X=Y=1 gives us 1=1). But X=Y^2 has many solutions which we haven't found like this, since there's a solution for any value of Y.
You're right that it's very often easier to start from the result and work backwards, but when you do this you have to think carefully about what deductions you can make. Adding things to both sides is something that works the same forwards or backwards, as does multiplying by a constant \emph{provided it is non-zero}, for example, so if you only use these steps (and check you've never multiplied by zero) then working backwards is fine.
'Verify' usually does just mean substitute. 'Show' is more ambiguous, and leaves it to you to work out the expected level of detail a little more: for both questions, they could have said verify (and just substituting is the right thing to do) but I guess they want to make sure you're confident about what it means for a point to lie on a circle etc. (I guess also with the second one, you have to do a bit of work to relate the equation for the new values to that with the old values, and maybe they thought people would expect it to be less work than that if they just said 'show').
Bounds of validity
often questions state show that .....for A<x<B - do we actually prove these bounds for x or do we take it as given and hence use it in our proofs? if we use them in our proofs do we lose marks if we do not quote them?
A good example is STEP 2 2011 Q3 where bounds for x are stated in brackets on the RHS of each expression needing to be proved - do you prove these bounds for x?
Bounds
If you're told to prove something for certain cases, they are the only ones you have to worry about. Sometimes you might prefer to work in generality and then see what conditions you need on $x$, but you don't have to do this if you don't want to. For example, in the first part of that question (STEP 2, 2011, q3), when you differentiate you find that $f'(x)=x \sin (x)$. It's not too hard to work out the most general conditions on $x$ for this to be non-negative, but they're only interested in the range they've given so it's probably not worth the effort. It's generally worth saying when you use the bounds as it makes it clear you understand what's going on.