Foundation plus - Algebraic manipulation - GCSE Mathematics

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Foundation plus - Algebraic manipulation

infoWhy this? We are teaching this unit so that pupils can confidently manipulate algebraic expressions, including expanding, factorising and substituting into linear and quadratic forms, enabling them to represent situations algebraically and construct clear, logical arguments

scheduleWhy now? We are teaching it now in Year 10 so that pupils can use these algebra skills to deepen their understanding of current topics such as equations, graphs and functions, and to tackle richer multi-step problems across the GCSE course

Like terms in algebraic expressions have the same variable(s) raised to the same power(s).
Terms can be collected (added or subtracted) only if they are like terms.
Multiplying and dividing algebraic terms involves using the laws of indices (powers).
The distributive law allows expansion of brackets: a(b + c) = ab + ac.
Expanding multiple single brackets involves applying the distributive law more than once.
Substitution means replacing variables with given numerical values, including positive and negative numbers.
Algebraic expressions can be formed from worded problems by identifying operations and variables.
Algebra can be used to construct mathematical arguments and proofs.
Factorising an expression means writing it as a product of its factors.
A quadratic expression is an expression of the form ax² + bx + c.
The difference of two squares is a² - b² = (a + b)(a - b).
Expanding double brackets involves multiplying each term in the first bracket by each term in the second bracket.
Factorising a quadratic with a unitary coefficient (x²) involves finding two numbers that multiply to give the constant term and add to give the coefficient of x.
Factorising quadratics with a non-unitary coefficient (ax²) may require splitting the middle term or using other methods.
Completing the square rewrites a quadratic expression in the form a(x + p)² + q.
Formulae are algebraic rules or equations that relate variables.

rocket_launchYou must be able to

Collect like terms in algebraic expressions and simplify the result.
Multiply and divide algebraic terms, applying the laws of indices correctly.
Expand single brackets and simplify the resulting expressions.
Expand and simplify expressions involving multiple single brackets.
Substitute positive and negative values into basic linear and non-linear algebraic expressions.
Form algebraic expressions from worded descriptions or problems.
Use algebraic expressions to form and construct simple mathematical arguments or proofs.
Factorise basic linear expressions (e.g., 3x + 6 = 3(x + 2)).
Expand and simplify double brackets (e.g., (x + 2)(x + 3)).
Factorise quadratic expressions with a unitary coefficient (x²) into double brackets.
Factorise quadratic expressions using the difference of two squares.
Expand and simplify triple brackets (e.g., (x + 1)(x + 2)(x + 3)).
Factorise quadratic expressions with a non-unitary coefficient (ax²) into double brackets.
Complete the square for a quadratic expression.
Substitute values into formulae, including rearranged and non-linear formulae.

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