Ratio & Proportion (Pre-GCSE)
(Used for Tiffin Year 9 scheme of work)
(a) Methods for solving problems involving direct and indirect proportion, including the unitary method (but not quadratic/cubic/root relationships).
(b) Problems involving ratio.
(c) Extension: 3 way relationships, e.g. "If it takes a men b hours to dig c holes..."
This (intentionally) does not make reference to the GCSE method of establishing the constant of proportionality.
(Used for the Tiffin Year 9 scheme of work) (a) Solve simultaneous equations using graphical methods (i.e. finding points of intersection of straight lines).
(b) Solve simultaneous equations using elimination.
(c) Solve simultaneous equations using substitution.
(d) Appreciate graphically when we will have 0, 1 or infinitely many solutions.
(e) Solve worded problems requiring formation of simultaneous equations.
GCSE Factorising Quadratics
Covers 6 different methods of factorising quadratics and other types of expressions (e.g. cubics), the last two of which are extension:
(a) Factorising out a single term (b) Factorising expressions of the form x^2 + bx + c, (c) Difference of two squares (d) Expressions of the form ax^2 + bx + c (where a is not 1) ,
(e) 'Intelligent guessing' (e.g. bx - x + ab - a = (x + a)(b - 1)) and (f) Pairwise factorisation.
Includes expressions which require multiple types of factorisation.