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STEP Support Programme

Assignment 8

Assignment 8 is now published and ready.

The "hints and partial solutions" for all the assignments have been updated (and now include some answers). Please let us know if you find a mistake!

I've struggled to prove part 2 of the warm up. Do you have advise a way to begin the proof further to splitting the first fraction?

"Advise a way", sorry

Using "the stem" (bit before the question parts start) we can say that $\dfrac{p+q} 2 \ge \sqrt{pq}$ and so we have $\dfrac{p+q} 4 \ge \dfrac {\sqrt{pq}} 2$.

You can do something similar with $r$ and $s$. Finally use the stem with $a=\sqrt{pq}$ ....

I'm not sure but I think the answer should be (0,5) for the intersection point rather than (5,0) as the hints and solutions say

Yep, agreed. You're correct.

I'll put in on my list of corrections to make!

Useful Links

Underground Mathematics: Selected worked STEP questions

STEP Question database

University of Cambridge Mathematics Faculty: What do we look for?

University of Cambridge Mathematics Faculty: Information about STEP

University of Cambridge Admissions Office: Undergraduate course information for Mathematics

Stephen Siklos' "Advanced Problems in Mathematics" book (external link)

MEI: Worked solutions to STEP questions (external link)

OCR: Exam board information about STEP (external link)

AMSP (Advanced Maths Support programme): Support for University Admission Tests (external link)