Good luck everyone who is sitting STEP 1 tomorrow!

I have two questions:

1. STEP 2 2017 Q5: the last part asks "Deduce that |PN| is at minimum when Q is at origin. " Doesn't that mean I should use the fact that Q is at origin to deduce that |PN| is at minimum? But the marking scheme answer is the other way around and says only 1/3 marks will be given to answers like mine. Why?

Apologies if this solution is available on an assignment (I am currently working from the past papers)

For part (i):

I am confused as to what the shaded region is (the diagram is not clear). The solution I am referring to is the MEI solutions (on the 'useful links' list on the side). The inequalities satisfied so far are c > 0, b > 0, c ≤ b²/4.

The way I have drawn the diagram is the shaded region under the curve c = b²/4 where c is the y-axis and b is the x-axis.

Thank you to everyone involved for their time and effort in making this resource.

I am asking for further help with 4.(v) of assignment 23 - the one about the blue eyed islanders. I don't fully understand the inductive step used in the solution sheet, but I'm not fully convinced by the argument in my own solution either.

For part (ii) :

the solution states that the different cases that arise from the shortest distance to a circle and a parabola are:

a) p ≤ 2a

b < p < 2a ⇒ shortest distance = p - b

p ≤ b < 2a ⇒ shortest distance = 0 (as circle must pass through the origin and so does the parabola, and the circle intersects the parabola when p < b )

b ≤ p = 2a ⇒ shortest distance = 2a - b

Hi, I have just started my preparation for STEP 1 and had a question regarding the sketching of graphs.....
Will we be provided with graph sheets while sketching or will we have to sketch on the plain blank sheets ?

For the shape of the quadrilateral I obtained that opposite sides of the quadrilateral are equal and parallel. I incorrectly came to the conclusion that it is a square. what is an easy way to determine that it was in fact a parallelogram?

Could you please check the working below:

p = λ(a) + (1-λ)b and q = c + μ(a - c)

CQ × BP = AB × AC

⇒ ⟦μ(a -c)⟧⟦λ(a-b)⟧=⟦b-a⟧⟦c-a⟧
⇒⟦μ⟧ = 1/⟦λ⟧
since λ and μ > 0
μ = 1/λ

IF PQ intersects point D then :

r = OP + t(PQ) = d for a parameter t / OP and PQ are vectors

After finishing the preparation part for assignment 12, I found there may be some difference between CIE statistics and STEP statistics, just the question (iv):(b) and (c) in preparation

below is the link:

https://maths.org/step/sites/maths.org.step/files/assignments/assignment...
https://maths.org/step/sites/maths.org.step/files/Feedback_A12_2.pdf

The solution appears to depend on division by 0.

I am a student from China, as I solving the problem on the basic module, assignment 11, I had a little problem with the first question. the answer says we need to show this question with the billiard ball. can anyone show me an image about it (I guess it may be the image of the sum of arithmetic sequence on the book)
thanks a lot