Notation And Manipulation

Algebra is arithmetic with the numbers left out on purpose. A letter stands for a number you do not yet know, or for any number at all, and once you can write the four basic arithmetic processes with letters instead of digits you can say something true about every case at once. That is why this topic sits at the front of the Algebra section: everything after it, from solving equations to differentiating a curve, is manipulation of the objects defined here.

You will use letters to express generalised numbers, substitute into formulae and transform them, tell an expression from an equation from an identity, collect like terms and expand brackets, factorise by taking out common factors and by recognising the difference of two squares, apply the index laws, and handle algebraic fractions. On the Extension Tier you will transform complex formulae where the subject appears twice, expand products of two or three binomials, factorise quadratics with a leading coefficient, work with fractional powers and algebraic denominators, and construct proofs.