3U+4U math resources but so good it's almost like I put 5 state rankers in a room and took notes (1 Viewer)

[penny3709]

Math resources but so cracked its almost like i put 5 state rankers into a room and took notes

Math resources that make 3u and 4u look easy

tldr; i put every insane ext1/ext2 trick i learned into one place (aka The Vault), check it out here

thevaultexclusive.framer.website​

hello on this fine (rainy asf) evening yall

so i graduated from elite selective where as u might know everyone breathes maths

and i had like 3 diff extension teachers all telling me random hacks over the year, plus all my mates were state rankers or close enough (like 97+ is basically equivalent) and all went to du and ngo and all the top tutoring places

and i thought, why not just dump every single obscure little thing into one resource

so yeah, i made this thing called the vault and not to glaze but it's literally like i gathered together 5 state rankers in one room and js took notes on how they think

i’m not gonna do the whole fake hype thing lemme just show you

1)proof hack (the double swap)

when they throw Σ(k=1 to n) [k * r^k] at you in a series proof, everyone tries induction.
but heres the double swap trick
u write S = r + 2r² + 3r³ + ... + n r^n, then compute rS, subtract: S - rS = r + r² + ... + r^n - n r^(n+1), then simplify. you’ve got the closed form without induction
(looks complicated but dw tho Vault teaches you the “pattern catch” trick so you do stuff like this in 20 seconds flat)

2)vapourising complex locus qns
Show that if |z - 1| = |z + 1| then arg(z) = π/2 or -π/2.
Vault approach is don’t draw, don’t overthink
condition screams “perpendicular bisector” but algebra route is faster: |z - 1|² = |z + 1|² -> expand → cancel → Re(z) = 0. one line instead of some long ahhh geometric explanation

3)ext2 cheeky integral
Evaluate ∫ from 0 to π/2 of ln(sin x) dx
everyone panics and starts expanding with power series. the Vault way: use the identity ∫0→a f(x) dx = ∫0→a f(a - x) dx, pair it up with ln(cos x) and boom, you turn it into ∫ ln(sin x) + ln(cos x) dx = ∫ ln(sin 2x) dx - π ln(2).
after u use some dummy variable tricks (which vault teaches u to pattern-recognise in like 5 seconds of looking) then that reduces into a constant so clean its chefs kiss mwah

4)js a little recurrence shenanigans
sometimes they throw stuff like simplify recurrence Tₙ = 2Tₙ₋₁ + 3.
vault way is don’t iterate blindly, shift: let Uₙ = Tₙ+ c.
then u pick c to kill the constant.
here, Tₙ = 2Tₙ₋₁ +3. try Uₙ = Tₙ +3. then Uₙ = 2Uₙ₋₁. solved immediately → Uₙ = k·2ⁿ. then back-sub.
so Tₙ = k·2ⁿ −3

5)projectile motion boss trick
instead of splitting into two trig equations and getting lost, check if they gave you max height or range.
if they did, you can set u² sin(2θ) = R g and u² sin²(θ) = 2 H g, combine them straight away → boom, both unknowns dead in like what two lines
no annoying algebra to screw u up

and like… there’s full sections for
• parametric sketching cheats (when x² + y² pops up → polar switch instantly)
• vector hidden identities (dot product is your friend in circle proofs)
• the half-angle substitution hack in integrals that kills every sec² question

tbh this is just scratching surface, Vault is acc stacked with these “oh sht i never thought of that” type cheats

if ur grinding for high E4 im talking like easy 95+ and you want every little sneaky technique distilled into one that’s basically what The Vault is

ngl wasn’t even planning to share it beyond mates, but since a few ppl asked i js tossed it online.

not sure how long i’ll leave it up, probs till after trials. if you wanna squeeze some easy marks take a peek fellas


thevaultexclusive.framer.website

 

[O_Starkindler!]

ok so i grabbed vault from one of the discord messages like beginning of term 2 and idk how to explain it without spoiling half the fun but it actually cooks. like it doesn’t read like notes, its more like someone whispering “btw don’t do it the normal way, do this instead” and suddenly the whole question somehow folds? idk how to explain it

recurrence ones were the first time i felt that like usually id sit there iterating forever but with that “shift trick” they put in vault, the constant just disappears like cheating. then in 4u mechanics i had one of those projectile nightmares and instead of splitting into 2 pages of sin/cos algebra turned into a tiny combo move that killed both unknowns at once
i was there sitting like bruh that’s it?

also cant say too much but one of the complex qns had this sneaky parametrisation my tutoring centre didnt even show me. turns loci qns into basically one substitution + rearrange. like it shouldnt be that clean, but it is

same stuff with integrals like theres one identity they put in there that makes the ln(sinx) style questions collapse into a constant before you even blink

not gonna overhype like its not some magical free marks thing obv, but if you been grinding past papers and ur sick of the long messy algebra paths or just running out of time on hard qns, vault is defo like finding all the hidden shortcuts on a video game. like yeah you still gotta walk it, but feels like you know the secret tunnels now ykwim