Algebra: further quadratics, rearranging formulae and identities (8300 - Higher - Algebra)

Topic:

Algebra: further quadratics, rearranging formulae and identities

Specification references (in recommended teaching order)

	Specification content	Specification notes
A4	Simplify and manipulate algebraic expressions (including those involving surds) by: expanding products of two or more binomials factorising quadratic expressions of the form including the difference of two squares factorising quadratic expressions of the form simplifying expressions involving sums, products and powers, including the laws of indices
A5	Understand and use standard mathematical formulae Rearrange formulae to change the subject	including use of formulae from other subjects in words and using symbols
A6	Know the difference between an equation and an identity Argue mathematically to show algebraic expressions are equivalent, and use algebra to support and construct arguments and proofs
A7	Where appropriate, interpret simple expressions as functions with inputs and outputs Interpret the reverse process as the ‘inverse function’ Interpret the succession of two functions as a ‘composite function’	understand and use function notation: `f(x)`, `fg(x)`, `f^-1(x)` is expected at higher tier

The subject content (above) matches that set out in the Department for Education’s Mathematics GCSE subject content and assessment objectives document.

The expectation is that:

All students will develop confidence and competence with the content identified by standard type
All students will be assessed on the content identified by the standard and the underlined type; more highly attaining students will develop confidence and competence with all of this content
Only the more highly attaining students will be assessed on the content identified by bold type. The highest attaining students will develop confidence and competence with the bold content.

Teaching resources

Composite & inverse functions PowerPoint (part of Higher tier teaching pack)

Downloadable resource in ppt format. 29/04/2016

1.6 MB

Composite & inverse functions resources (part of Higher tier teaching pack)

Downloadable resource in doc format. 29/04/2016

641 KB

Multiplying three brackets

A straightforward powerpoint which explains a clear method for expanding three brackets.24/08/2015

Composition of Functions

An introduction to composition of functions followed by ten fairly demanding online multiple choice questions.19/08/2015

Expanding Polynomials

A straightforward game in which students roll dice to choose three sets of binomial expressions which they must expand. You will need to register for a TES account to access this resource, this is free of charge. 19/08/2015

Factorising Quadratics Tarsia (Harder)

A rhombus shaped tarsia activity containing difficult quadratics that should be factorised. You will need to register for a TES account to access this resource, this is free of charge. 19/08/2015

Tarsia - Composite Functions

A 'domino style' tarsia involving finding the numerical value of simple functions and composite functions. You will need to register for a TES account to access this resource, this is free of charge. 19/08/2015

Algebraic proof

A nice activity in which the basic 'tools' of mathematical proof are introduced and some standard types of mathematics proof at GCSE level are considered. You will need to register for a TES account to access this resource, this is free of charge. 19/08/2015

Factorising and expanding double brackets boxset

A fantastic Excel file which has a large number of exercises on expanding and factorising quadratic expressions, including the difference of two squares. You will need to register for a TES account to access this resource, this is free of charge. 19/08/2015

Algebra - Expanding two or more brackets

A video in which the method for expanding and simplifying various types of two or three bracket expressions is explained.19/08/2015