I am taking STEP2 tomorrow. I have read that we are advised not to try more than 6 questions. Does anyone disagree with this? What are the chances of getting a 1 if i do 8 questions half-way, completing only 2 or 3? Is there any other particular strategy you would recommend?

Solving the differential equation in part ii, I'm unsure what happens to the constant term - or why there isnt one?
Also in the solutions what does "straight lines... in the direction of the tangents to the circle at that point" mean? Would the lines meet?
Thanks

Both Q14 and Q16 are given as 2013 S3 Q7, and I don't think Q14 is

I am currently in Lower Sixth and am planning to take STEP 1 tomorrow. I was wondering that, if hypothetically, I have a bad day and fail to get a 1 or an S, would I still have to declare my STEP 1 mark and grade when applying next year?

For the part where you have to show that the integral of the function of theta from 0 to pi/4 is equal to two times the integral from 0 to pi/8. Is it enough to show that the function of theta is symmetrical about theta=pi/8 and then deduce the result or do you have to use a substitution and show it through manipulation of the integral?

For the deduction at the end of the question you have to use the substitution x=u^2 to get the left hand side, my question is how is it justified to then set u=x?

Hi! (See title for source). The question asks us to prove that $\ln\left(\frac{2y+1}{2y-1}\right)>\frac1y$ using power expansions of $\frac1y$ (where $y>\frac12$). Is it okay to use the Maclaurin series of $e^x$ in the proof? Something like this:

Hi, this may seem like a very basic question, but it has thrown me slightly. The question regards working out the probabilities of two distributions and combining them. The way they have added the probabilities I don't get. The hints and answers booklet states the answer to be: $$\frac{0.6 ( b - 0.5 ) + 0.4 ( a - b )}{0.6b + 0.4a} = \frac{0.4a + 0.2b - 0.3}{0.6b + 0.4a}$$

Whereas I got: $$\frac{0.6 ( b - 0.5)}{b} - \frac{0.4 ( a - b )}{a}$$

There is obviously something I'm missing, but I can't find it. Thanks in advance for any help.

I am stuck trying to prove $$(2n+4)I_n =(2n+1)aI_n-1$$

I think it should be done by parts, as change of variable would mess the limits, but I really wonder how the $a$ ended there.

I was wondering approximately how many marks are allocated to small parts of questions that kind of stand alone to the rest of the question? For example in STEP III 2005 q2 you are asked do find the equation of a curve from a differential equation then sketch it. If you missed out the sketch, how many marks would you be likely to lose?

In the STEP III Statistics module, when the distribution of $Y$ is being worked out given $Y=X^2$, I'm having some trouble understanding the following lines:
$$
\begin{aligned}
\mathrm{F}_Y(y)&=\mathrm{P}(Y \leqslant y)\\
&=\mathrm{P}(X^2 \leqslant y)\\
&=\mathrm{P}(X \leqslant \sqrt{y})\\
&=\int_{-\infty}^{\sqrt{y}} \mathrm{f}(t)\mathrm{d}t
\end{aligned}
$$
I'm confused because I don't see how it isn't as follows:
$$
\begin{aligned}