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Further Pure 2 formulae

The 5 results the Further Pure 2 notes display, each with the conditions it needs to be true and a link to the lesson that states it. Of the 5, the formulae booklet prints 1, 3 are yours to memorise and 1 is a working line the notes derive in front of you.

Further Maths · 5 lessons with formulae.

A result the Edexcel formulae booklet prints is marked as such; one it does not print is marked to learn; and a result badged derived in the lesson is a working line the notes build in front of you rather than a standard result to memorise.

5 lessons

Reduction formulae

n I_{n} = (n - 1) I_{n-2}, I_{n} = \text{∫}_{0}^{π/2} \sin^{n} x \, dx

NOT IN THE BOOKLET: DERIVED IN THE LESSONConditionsn ≥ 2, with Iₙ = ∫₀^π/2 sinⁿ x dx. The formula holds only for this integral with these limits.

Arc length and surface area

s = \text{∫} \sqrt{1 + (\frac{dy}{dx})^{2}} \, dx

IN THE FORMULAE BOOKLETConditionsy differentiable with a continuous derivative across the interval.

Eigenvalues and eigenvectors

\text{det}(\text{M} - λ\text{I}) = 0

NOT IN THE BOOKLET: LEARN ITConditionsM a square matrix.

Diagonalisation and the Cayley-Hamilton theorem

\text{P}^{-1}\text{MP} = \text{D}

NOT IN THE BOOKLET: LEARN ITConditionsM must have a full set of independent eigenvectors; P is then invertible with those eigenvectors as its columns.

Modular arithmetic and Fermat's little theorem

a^{p-1} \equiv 1 \, (\text{mod } p)

NOT IN THE BOOKLET: LEARN ITConditionsp prime, and p must not divide a.

Every formula in the library is indexed by unit on the equation index, and the Further Pure 2 notes are where these results are derived and used. The 3 the booklet does not print are on the list of every formula to memorise, alongside the rest of the course.

Also: Further Statistics 1 formulae · Further Statistics 2 formulae