skip to content

STEP Support Programme

S3 2001 Q3

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.

The MEI solution "shades out" so shades out the region you don't want. You are correct that you need the part under the curve c=(b^2)/4 in the first quadrant.

This graph shows the region if you "shade in" - i.e. it is the part that is shaded three times.

This graph shows the region if you "shade out" - i.e. the unshaded bit is the one you want. I had to swap the inequalities to draw this, on paper I would just shade out the portion that did not satisfy the inequality. I think this graph makes the required region easier to see!

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)