Maths item of the month

Curriculum mapping

A list of Maths Items of the Month categorised by GCSE/A level topics can be seen at: Maths Items of the Month Curriculum mapping.


Recent Maths Items of the Month

July 2016
Perpendicular parabolas

perpendicular parabolas

If the curves y = (xp)2 + q and x = (yr)2 + s have four points of intersection will these four points always lie on a circle?


June 2016
MEI Conference taster - Odd and distinct partitions

O(n) is the number of ways of writing n as the sum of odd positive integers.
e.g. O(6)= 4:     {5+1, 3+3, 3+1+1, 1+1+1+1+1+1}

D(n) is the number of ways of writing n as the sum of distinct positive integers.
e.g. D(6) = 4:     {6, 5+1, 4+2, 3+2+1}

Does O(n)=D(n) for all natural numbers?

This problem is taken from the 2015 MEI Conference session Desert Island Mathematics. To see details of this year's sessions visit the conference website: conference.mei.org.uk


May 2016
MEI Conference - Sessions about famous mathematicians

The 2015 MEI conference featured a strand of sessions about 12 famous mathematicians. The following problem is from the session about John Conway.

There are only three numbers (>1) that can be written as the sum of fourth powers of their digits:

1634 = 14 + 64 +34 +44
8208 = 84 + 24 + 04 + 84
9474 = 94 + 44 + 74 + 44

Find the smallest number (>1) that can be written as the sum of fifth powers of its digits.

This year the 2016 Conference will feature a strand of sessions about a different set of 12 famous mathematicians. To see details of these, and other sessions, visit the conference website: conference.mei.org.uk


April 2016
Are you sure?

right-angled triangle

What’s the area?

Now read the research: Drawing attention to a lack of attention


March 2016
Cube Slice

A cube is sliced vertically along the line shown in the diagram and the smaller part is thrown away.

cube slice 1

The remaining prism is going to be sliced vertically downwards again by a line going through corner D.

Where would the slice have to be to split it into two equal volumes?

cube slice 1

This problem is taken from the FMSP GCSE Problem Solving Materials.


February 2016
50, 60, 70, ... ?

Find the size of the angle α.

50-60-70-triangle


January 2016
Happy 2016

2016 is a triangular number.

The first three triangular numbers are: 1, 3, 6. The first three pentagonal numbers are: 1, 5, 12.

triangular and pentagonal numbers

The pentagonal numbers 1, 5 and 12 are all one third of a triangular number.

Are all pentagonal numbers one third of a triangular number?

Solution