tldr; i put every insane ext1/ext2 trick i learned into one place (aka The Vault), check it out here
thevaultexclusive.framer.website
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+ which 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 looked through my hs notes and made something called the vault and i promise this isnt just a glaze but it's literally like i gathered together 5 state rankers in one room and just took notes on how they think
i’m not gonna do the whole fake hype thing, lemme just show you the type of stuff i mean
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 here’s 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)ext1 MCQ elimination trick
question says: A parabola with vertex (0,0) and focus (a,0) has equation y² = 4ax. Find the tangent with slope m.
Vault shortcut teaches u to js not bother with focus-directrix definitions
straight formula is y = m x + (a / m). works for ALL parabolas in that form and shows up like every second year
3)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
4)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
[/B]5)js a little recurrence shenanigans[/B]
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
6)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)
• complex shortcuts (dont expand cis form unless you want pain)
• the half-angle substitution hack in integrals that kills every sec² question
tbh this is just scratching surface, Vault is stacked with these “oh sht i never thought of that” type cheats. not like im smarter than anyone, i just collected the battle scars so u dont have to
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
legit the 20% of effort that gets you the 80% of results
i wasn’t even planning to share it beyond mates, but since a few ppl asked i just 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
