A: Algebra
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use and interpret algebraic manipulation, including:
use and interpret algebraic manipulation, including:
- ab in place of a × b
- 3y in place of y+y+y and 3×y
- a^2 in place of a×a, a^3 in place of a×a×a, a^2b in place of a×a×b
- b/a in place of a÷b
- coefficients written as fractions rather than as decimals
- brackets
substitute numerical values into formulae and expressions, including scientific formulae
substitute numerical values into formulae and expressions, including scientific formulae
understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors
understand and use the concepts and vocabulary of expressions, equations, formulae, identities, inequalities, terms and factors
simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by:
simplify and manipulate algebraic expressions (including those involving surds and algebraic fractions) by:
- collecting like terms
- multiplying a single term over a bracket
- taking out common factors
- expanding products of two or more binomials
- factorising quadratic expressions of the form x^2 + bx + c, including the difference of two squares; factorising quadratic expressions of the form ax^2 + bx + c
- simplifying expressions involving sums, products and powers, including the laws of indices
understand and use standard mathematical formulae; rearrange formulae to change the subject
understand and use standard mathematical formulae; rearrange formulae to change the subject
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
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
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’ (the use of formal function notation is expected)
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’ (the use of formal function notation is expected)