# Ratio & Proportion (Pre-GCSE)

## 4 files12/05/2016

(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.# Simultaneous Equations

## 3 files12/05/2016

(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.# Advanced Sequences

## 6 files12/05/2016

(Used for Tiffin Year 9 scheme of work)

Includes a 'levelled activity' where students advance through progressively difficult levels. Please note that the slides may be updated within the next month to include more of (d) below.

(a) Recap: Find/use nth term of a linear sequence.

(b) Find/use nth term of a quadratic sequence.

(c) Identify the formula for the nth term of a simple geometric sequence (e.g nth term of 2, 4, 8, 16, ... is 2^n)

(d) Extension: Solve sequence proofs and problems involving missing terms, using algebraic approaches.# Factorising Quadratics

## 7 files12/05/2016

(Used for Tiffin Year 9 scheme of work)

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.