Title: InkMaths / Further Maths: core results
On every note of this deck, unless a note says otherwise:
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Front: STANDARD RESULT — LEARN IT
Cubic root relations:
az^3 + bz^2 + cz + d = 0: α + β + γ = ?
Back: α + β + γ = -ba

Front: STANDARD RESULT — LEARN IT
Hyperbolic identity:
cosh^2 x - sinh^2 x = ?
Back: cosh^2 x - sinh^2 x = 1

Front: STANDARD RESULT — LEARN IT
Multiplying complex numbers:
|zw| = ?, arg(zw) = ?
Back: |zw| = |z||w|, arg(zw) = arg z + arg w

Front: STANDARD RESULT — LEARN IT
Standard result:
Σ r^2 = ?
Back: Σ r^2 = n(n+1)(2n+1)6

Front: STANDARD RESULT — LEARN IT
Volume of revolution:
V = ? (about the x-axis)
Back: V = π ∫ y^2 dx

Front: STANDARD RESULT — LEARN IT
Second order equations:
ay'' + by' + cy = 0: auxiliary equation?
Back: am^2 + bm + c = 0

Front: STANDARD RESULT — LEARN IT
Definition:
cosh x = ?
Back: cosh x = e^x + e^-x2

Front: STANDARD RESULT — LEARN IT
2 × 2 determinant:
rows (a, b), (c, d): det = ?
Back: det = ad − bc

Front: STANDARD RESULT — LEARN IT
Logarithmic form:
arsinh x = ?
Back: arsinh x = ln(x + √x^2 + 1)

Front: STANDARD RESULT — LEARN IT
De Moivre's theorem:
(cos θ + i sin θ)^n = ?
Back: (cos θ + i sin θ)^n = cos nθ + i sin nθ

Front: STANDARD RESULT — LEARN IT
Polar area:
A = ?
Back: A = 12 ∫ r^2 dθ

Front: STANDARD RESULT — LEARN IT
Integrating factor:
dydx + P(x)y = Q(x): IF = ?
Back: IF = e^∫ P dx