Algebra
Outcomes
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Use and interpret algebraic notation, including:
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Ab in place of a x b
Examples
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3y in place of y + y + y and 3 x y
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A2 in place of a x a, a3 in place of a x a x a; a2b in place of a x a x b
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A/b in place of a ÷ b
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Brackets
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Ab in place of a x b
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Substitute numerical values into formulae and expressions, including scientific formulae
Examples
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Understand and use the concepts and vocabulary of expressions, equations, inequalities, terms and factors
Examples
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Simplify and manipulate algebraic expressions to maintain equivalence by:
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Collecting like terms
Examples
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Multiplying a single term over a bracket
Examples
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Taking out common factors
Examples
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Expanding products of two or more binomials
Examples
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Collecting like terms
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Understand and use standard mathematical formulae; rearrange formulae to change the subject
Examples
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Model situations or procedures by translating them into algebraic expressions or formulae and by using graphs
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Use algebraic methods to solve linear equations in one variable (including all forms that require rearrangement)
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Recognise, sketch and produce graphs of linear and quadratic functions of one variable with appropriate scaling, using equations in x and y and the Cartesian plane
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Interpret mathematical relationships both algebraically and graphically
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Reduce a given linear equation in two variables to the standard form y = mx + c; calculate and interpret gradients and intercepts of graphs of such linear equations numerically, graphically and algebraically
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Use linear and quadratic graphs to estimate values of y for given values of x and vice versa and to find approximate solutions of simultaneous linear equations
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Find approximate solutions to contextual problems from given graphs of a variety of functions, including piece-wise linear, exponential and reciprocal graphs
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Generate terms of a sequence from either a term-to-term or a position-to-term rule
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Recognise arithmetic sequences and find the nth term
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Recognise geometric sequences and appreciate other sequences that arise
Examples