Hi all,

Assignment 5 is now up and ready. There is also a "Follow up" for assignment 4 available, do please have a look at this as it will give some hints and hopefully useful remarks for tackling similar problems.

Do please keep using the forum if you want to ask anything - and you can still ask questions on assignments 1-4!

Have fun!

Should Assignment 4 Warm Down include: For each card there is a number on one side and a letter on the other?

I have done question 3 part i and i am happy with my answer. Not sure how to tackle part ii though. Any hints please? Thanks in advance.

We hope you have enjoyed working through the three introductory modules, and if you haven't done so there is still plenty of time!

The next module (Assignment 4) will be released on Monday 12th September and future modules will be released weekly.

Hope everyone has had a great summer!

There are now "Follow up" files available for assignments 1, 2 and 3. These give suggested ways you could tackle the question, discussion of similar types of question and alerts to common pitfalls to avoid.

For a "show that" question, would you have to tackle it as a proof by induction or just show it works for a certain set of values? (Assignment 3 STEP Question)

Hi all! This is what I've done for part vii)
y=x²+2kx where 2≥x≥2 and -2>k>2
When k>0 let k=a, when k<0 let k=-a

When k>0, y=x²+2ax
This can be rewritten as:
y=(x+a)²-(a²) or y=x(x+2a)
Therefore the parabola passes through the origin and -2a with minimum at (-a,-(a²)). Hence, the smallest value = -(a²)
f(2) = 4+4a
f(-2) = 4-4a
Therefore 4+4a is the greatest value.

If anyone is looking for an interesting question, I have found a good one on a older STEP paper.
*hint*
If you are stuck on part (ii) remembering the property that ln(x) + ln(y) = ln(xy) is useful when trying to find a suitable function.
The question doesnt require any A2 maths knowledge which makes it more accessible.
http://www.admissionstestingservice.org/Images/7922-step-specification.zip

When a STEP question asks for a sketch, does this have to be orthonormal and ruler-traced, or can it be more approximative ("sketchy"?) ? Also, how would you sketch a graph where more than one curve is possible, for example in assignment 2 where there are a number of parameters : do you just trace several possibilities ?

After solving the problem I found that it had a somewhat quick and neat solution (one that is generally quite pleasant to work with). The discussion after the problem mentioned that this can be generalised for any closed curve, and that this is Holditch's theorem. I thought this was quite interesting so I found a proof if anyone wants to give it a read.
http://www.math.pitt.edu/~troy/sflood/holditch.pdf