I used the substitution u = coshx for the first part and similarly tried to use u = sinhx for the second part, but once I try to evaluate my integral I get the natural log of -1.
My integral is 1/(1 + 2u^2) which I evaluated to 1/sqr(2) * ln((u *sqr(2) + 1)/(u *sqr(2) - 1)) and my upper and lower bounds are sinha and 0 respectively

...has now been published! Enjoy!

Hello,

I am not from the UK, hence I am not doing A-levels,
I am a bit confused with the syllabuses. I am taking STEP II & III.

I have found some formulae and statistical tables on the STEP booklet which I think don't fit into any of the topics listed on the official STEP syllabus. In particular: correlation and regression, distribution-free (non-parametric) tests, the T distribution, the x^2 distribution, Wilcoxon signed rank test and Wilcoxon rank sum test...

Are these topics required? If not, why are they on booklet?

After using the hints, I found the Fibonacci question (Q5) of the Step 2 mixed pure quite doable, but I'm not sure I'd have ever figured out the $F_i>2F_{i-2}$ trick on my own.

The solutions for that question have a mistake on the last line. It should be $S<3\frac{29}{60}<3\frac{1}{2}$.

For the last part of the question you have to prove,

2(1-e^2)>f(1-4e^2)

Can you say that ...

(1-e^2)>(1-4e^2)

And

2>f

Or is it necessary to consider the different cases of the value of e?

Thank you :-)

Can I get some help on how to do the proof by induction?

I am able to prove the base case n=0.

I have tried to substitute in the expression the cases n= k+1 and n=k-1, but that leads me nowhere. I have as well unsuccessfully tried to integrate and differentiate the given expression.

I think strong induction may be needed here....

Thank you!

The STEP II Mechanics module is now available here.
Questions and Topic Notes have just gone up; hints and solutions will follow shortly!
As always, feedback/comments/spotting mistakes welcome.

Struggling to link the final quartic with previous parts of the question. Any hints would be appreciated.

Hi I am a university counselor and 3 of my year 12 students want to take step tests in year 12. I note often year 13 students take the test as part of their conditional offer but does the test results last more then one year and is there any point in the year 12 students taking the test?

Tim Jervis

Hey so I'm currently stuck on the last part of Q9 where you have to find a necessary and sufficient condition for d. I understand that you probably have to find an inequality of some sort to show that friction is acting upwards that also gets rid of mu but I've come stuck on what this is going to be. I have horizontal and vertical force components and have taken moments about A which I know are probably right from part (i) working but it would be difficult to use the result in (i) as that assumes limiting equilibrium