a ppt is here

## Saturday, 7 December 2019

### 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

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

proofs could involve expanding brackets and simplifying expressions

or use the difference of two squares equivalence

or could be considered by using diagrams

## 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

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

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

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