UKMT SMC QUESTION

[final yarrow]

i need a step by step explanation pls

[wet crater]

ew

[final yarrow]

?

[wet crater]

looks ugly

[wispy flame]

<@&791435371564892232>

[final yarrow]

<@&791435371564892232>

[muted oracle]

That's quite easy

[final yarrow]

do it bro

[wooden girder]

guys i got this

nvm gl guys

[split talon]

work out radius, work out the sector times that by 3

give me a minute

[wooden girder]

how do you know to times by 3

i knew to work out the first sector

but didnt know where to go from there

[spiral flax]

u do all maths qualification possible

should be able to do it

[split talon]

the point at which the 2 “flat” semi circles meet and X Y form an equaliateral triangle

then each sector has a 30 degree angle

could be wrong

[chrome creek]

8 root 34

[split talon]

i got 12

[chrome creek]

its 8 root 34

[split talon]

no way

fairs it’s an answer not there ur so op captain

[chrome creek]

i know right

[wooden girder]

ah smart

[chrome creek]

they should make me an oxford professor

[wooden girder]

?

how does it work

[split talon]

i’m not gonna the best at explaining ibsr better of waiting lol

[wispy flame]

@final yarrow told u

[spiral flax]

A by inspection

[split talon]

bean

[spiral flax]

Bean

[chrome creek]

Well, tickle my toes and call me a tap-dancer! I didn’t see that coming!

[split talon]

i’m never helping u again

[final yarrow]

explain pls

[split talon]

the three shaded regions r the exact same

[final yarrow]

how

[final yarrow]

@wispy flame is this block worthy

[wispy flame]

he js got into imperial tho

[final yarrow]

fairs

[wispy flame]

lowk

yk the question

i think there is an equilateral triangle

if i think of it as loci

@final yarrow

[final yarrow]

how

[wispy flame]

if they are the same radius

and u draw a locus of points around X and Y

i feel like where they intersect

[final yarrow]

js send a photo

[wispy flame]

shows 60 60 69

60*

i havent drawn in

[wooden girder]

the equilateral triangle part is easy

its the way to figure out that all the regions are the same

which i dont get

[upbeat oxide]

sigma

[spiral flax]

💔

[final yarrow]

guys i need an explanation pls

someone save the soul society

[upbeat oxide]

If you want more rigorous justification as to why those areas are the same then you can just draw lines and radii

And use angles ig

[chrome creek]

@upbeat oxide r u online

[upbeat oxide]

Perchance

[chrome creek]

can i ask a question

[upbeat oxide]

Depends if it's a nice one

[chrome creek]

do you know the way when u differentiate a quadratic

you have like e.g 3+2x-x^2

[upbeat oxide]

Yeah

[chrome creek]

do you know the 2x, when u differentiate that why isnt it 2x power 0

since as it is, in the equation 2x power 1

[upbeat oxide]

x⁰=1

So 2x⁰=2×1=2

[split talon]

🙂‍↔️

[chrome creek]

OH YEAH

sorry gang

wait so

if u have

6=0.5x^2+3/2(x)

is that

[upbeat oxide]

Ew

[chrome creek]

x+3/2?

sorry not 6=, y=

[upbeat oxide]

Gonna be honest the forms a bit ambiguous

3/2(x) could be 3 / (2x) or (3/2)x

[chrome creek]

hold on

[upbeat oxide]

And then the 0.5x²+3/2(x) you be a whole fraction itself or 0.5x² and whatever the last one means

[chrome creek]

this

[upbeat oxide]

x + 3/2

[chrome creek]

ohhh

ok ty

[faint salmon]

fr

[final yarrow]

how long did this take

[upbeat oxide]

Just like depends how quickly you spot things and whether you actually prove it

Could take pretty much anywhere from 10 seconds to like 5 minutes

Assuming you actually know to try and look for shortcuts

[final yarrow]

hypothetically it couldn’t end in root 3 right?

[upbeat oxide]

Well in this specific case it can't be because there's only 1 answer

But in a similar question there's no reason it couldnt

Could have some pythagoras

[simple whale]

https://youtube.com/shorts/2ETwyWb0UVU?si=RPpNU03rCszO1uMT

[final yarrow]

arizus

[simple whale]

It all ends up being just a quarter circle

[final yarrow]

how do you see this

in the exam

[simple whale]

I knew the answer would be something nice otherwise they wouldn't set it as a question

So i just kinda went looking for a way to rearrange the areas

[final yarrow]

ohh that makes so much sense

arizus may i ask you a question

[simple whale]

Yes

[final yarrow]

2 things how did you get into trinity cambridge maths - cs thts my dream

also apparently you did eduqas lit and lang

how did you get 9s in those

[simple whale]

I mean i think it's a just a lot of work over the past 3+ years

I'd say olympiads were very important (indirectly)

[final yarrow]

did you get into imo?

[simple whale]

At the end of they say you just have to get through as many questions as you can at the interview

[simple whale]

No, but i got onto a camp

U don't need to be imo level or anything like that

[final yarrow]

what is the difference

[simple whale]

The camp is used to select people for the imo (and a couple other competitions)

[final yarrow]

ohhh and the camp is held at cambridge?

[simple whale]

One of the camps is yes

[final yarrow]

do you think your youtube contributed

[simple whale]

They have one at oxford (for younger students) and one in Budapest, hungary over Christmas

[simple whale]

Indirectly yes

Directly no, cuz they don't really care about personal statement much

[final yarrow]

how did you improve ur bmo skills

and smc

[simple whale]

Practice

Over many years

[final yarrow]

is it too late?

[simple whale]

It's never "too" late

Just depends how much work you want to put in

[final yarrow]

do you think smc is harder then bmo

[simple whale]

Bmo is orders of magnitude harder

[final yarrow]

what do you mean?

[simple whale]

Like bmo is much much much harder

[final yarrow]

bmo1 seems easier then smc

[simple whale]

They're not really even comparable, but i always found smc (and imc and jmc) super easy

[simple whale]

It's definitely harder lol

Proof writing is a different skill

[final yarrow]

did you ever get into ukmt summer school

[final yarrow]

wait is bmo not just 10 marks for the right answer

[simple whale]

No but that's a luck based thing

[simple whale]

Nope

You can get the right answer and get 0/10

[final yarrow]

is bmo gcse or alevel

[simple whale]

If you don't prove EVERY step you can't get more than 3/10

[simple whale]

I think the summer school is only y10s and 11s

It's randomly selected based on imc scores

[final yarrow]

really?

[simple whale]

I'm pretty sure yeah

[final yarrow]

is alevel content needed for bmo2?

[simple whale]

Nope

You don't even need gcse content

Honestly all you need is some geometry theorems, proof by induction and knowing how to logically write proof

You can logic your way through all the questions

[final yarrow]

geometry theorems?

[simple whale]

Like circle theorems

Plus maybe triangle centers

I mean there is lots and lots of theory

But u won't need it at bmo2 (and definitely not bmo1)

[final yarrow]

what is this?

[simple whale]

Incenters, circumcenters, centroids and orthocenters

You can google

They each have their own properties and stuff

[final yarrow]

sounds interesting

did you get an SS in STEP

[simple whale]

I still need to do step this summer

[final yarrow]

you are year 13?

[simple whale]

Yeah

[final yarrow]

how have you finded step questions

[simple whale]

Not too bad

I'm not too worried about getting 1,1

But i want to get S,S

[final yarrow]

for trinity you need 1,1?

[simple whale]

Yeah that's my offer

[final yarrow]

and what about for your alevels?

[simple whale]

2 a*s and an a

It's the standard offer than most people get

[final yarrow]

did you apply to trinity specifically

also for bmo proof by contradiction and induction

or just induction

[simple whale]

Yes

[simple whale]

I mean you'll need all types of proof yes

Just induction is kinda specific

All other types of proof are super general

[final yarrow]

so only two proofs that you need to learn

what does super general mean