Title: InkMaths / Further Pure 1: results and forms
On every note of this deck, unless a note says otherwise:
Footer: Continue on inkmaths.co.uk · © 2026 InkMaths. All rights reserved.

Front: STANDARD RESULT — LEARN IT
Parabola:
y^2 = 4ax: parametric point?
Back: (at^2, 2at), tangent ty = x + at^2

Front: STANDARD RESULT — LEARN IT
Hyperbola:
x^2a^2 - y^2b^2 = 1: b^2 = ?
Back: b^2 = a^2(e^2 - 1), foci (±ae, 0)

Front: DEFINE
Define: L'Hospital's rule.
Back: For an indeterminate form 0/0 or ∞/∞, the limit of f/g equals the limit of f'/g', provided that second limit exists.

Front: STANDARD RESULT — LEARN IT
t-formula:
t = tan θ2: cos θ = ?
Back: cos θ = 1 - t^21 + t^2

Front: STANDARD RESULT — LEARN IT
Vector product:
|a × b| = ?
Back: |a||b| sin θ, the parallelogram's area

Front: STANDARD RESULT — LEARN IT
Taylor series:
f(x) = ? about x = a
Back: f(a) + f'(a)(x - a) + f''(a)2!(x - a)^2 + …

Front: STANDARD RESULT — LEARN IT
Scalar triple product:
tetrahedron volume = ?
Back: 16 a · b × c

Front: SPOT THE ERROR
Say what is wrong with this claim:
To solve x/(x − 2) < 3, multiply both sides by x − 2 and solve the result.
Back: x − 2 is negative when x < 2, and multiplying by a negative reverses the inequality. Subtract to one side, combine over a common denominator, and read a sign diagram; the shortcut loses the whole interval x < 2.

Front: STANDARD RESULT — LEARN IT
Weierstrass substitution:
t = tan x2: dx = ?
Back: dx = 2 dt1 + t^2

Front: STANDARD RESULT — LEARN IT
t-formula:
t = tan θ2: sin θ = ?
Back: sin θ = 2t1 + t^2

Front: STANDARD RESULT — LEARN IT
Simpson's rule:
∫ y dx ≈ ?
Back: h3(y_0 + 4y_1 + 2y_2 + … + 4y_n-1 + y_n)

Front: STANDARD RESULT — LEARN IT
Ellipse:
x^2a^2 + y^2b^2 = 1: b^2 = ?
Back: b^2 = a^2(1 - e^2), foci (±ae, 0)