median
don steward
mathematics teaching 10 ~ 16

Saturday, 7 December 2019

frequency trees and percentages

a ppt is here








HKMO problem

note that a and b are complex numbers

students are supposed to use algebraic manipulation rather than finding a (= 3 + 2i) and b (= 3 - 2i)

it is not necessary to know the factorisations for the sum or difference of two cubes




not HKMO problems
but the same ilk

Friday, 29 November 2019

some square number patterns

all due to David Wells

proofs could involve expanding brackets and simplifying expressions
or use the difference of two squares equivalence
or could be considered by using diagrams




regular polygons with algebra

question 3 is from a Hong Kong Maths Olympiad paper



Tuesday, 26 November 2019

rings of circles

an application of trigonometry (in right angled triangles)

a ppt is here

the task is to relate the radius of the black circles (in the ring) to the radius of the red (centre) radius

it might be simpler to put the radius of the red circle, k = 1, and find the associated value of r
or vice versus

an intention is to work towards establishing a general rule
so that e.g. if you wanted to find the relationship between the radii for a 50 circle ring you could do so with a formula

surds can be involved for some of the cases

what relationships are there between the radii of the three different sized circles?


prove that r = k






Thursday, 21 November 2019

generalising probability GCSE questions

three probability questions, adpated from past GCSE (England) papers
thanks to the exam boards

exploring some examples and then maybe attempting some fairly demanding generalisations

a ppt is here













Monday, 18 November 2019

introducing angles

a whole turn is 360 degrees because the Babylonians said it should be
a convenient number, given that you want to subdivide it

a ppt is here
















I've lost the source for these images - my apologies

seems to be BHC 2004?


see also spokes