Algebra

Expanding and factorising, indices, rearranging formulae, linear and simultaneous equations, algebraic fractions and inequalities.

Algebra is the language of the rest of the course. The Higher paper rewards fluent, well-set-out manipulation, so practise until it is automatic.

Expanding and factorising

To expand double brackets, multiply every term (FOIL): $(x+3)(x-5) = x^2 - 2x - 15$ . To factorise is to reverse this:

Common factor:

6x^2 - 9x = 3x(2x - 3)

Difference of two squares:

x^2 - 49 = (x+7)(x-7)

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Expanding and factorising

To expand double brackets, multiply every term (FOIL):

(x+3)(x-5) = x^2 - 2x - 15

. To factorise is to reverse this:

Common factor:

6x^2 - 9x = 3x(2x - 3)

Difference of two squares:

x^2 - 49 = (x+7)(x-7)