Algebra

Topics

Choose a topic to revise

Sample objectives

What this unit covers

• Notation, vocabulary and manipulation: [Foundation and Higher] Use and interpret algebraic notation for products, powers, division, fractional coefficients and brackets.
• Notation, vocabulary and manipulation: [Foundation and Higher] Substitute numerical values into formulae and expressions, including scientific formulae supplied in a question.
• Notation, vocabulary and manipulation: [Foundation and Higher] Understand and use algebraic vocabulary for expressions, equations, formulae, inequalities, terms and factors.
• Notation, vocabulary and manipulation: [Higher only] Include identities within algebraic vocabulary and reasoning.
• Notation, vocabulary and manipulation: [Higher only] Manipulate expressions involving surds and algebraic fractions, expand products of two or more binomials and factorise quadratics of the form ax^2 + bx + c.
• Notation, vocabulary and manipulation: [Foundation and Higher] Simplify and manipulate algebraic expressions by collecting like terms, expanding a single term over a bracket, taking out common factors and using index laws.
• Notation, vocabulary and manipulation: [Foundation and Higher] Understand and use standard mathematical formulae, including formulae written in words and symbols.
• Notation, vocabulary and manipulation: [Foundation and Higher] Rearrange formulae to change the subject.
• Notation, vocabulary and manipulation: [Foundation and Higher] Know the difference between an equation and an identity.
• Notation, vocabulary and manipulation: [Higher only] Construct algebraic proofs where required.
• Notation, vocabulary and manipulation: [Higher only] Interpret inverse functions and composite functions using expected function notation.
• Notation, vocabulary and manipulation: [Foundation and Higher] Interpret simple expressions as functions with inputs and outputs where appropriate.
• Graphs: [Foundation and Higher] Work with coordinates in all four quadrants.
• Graphs: [Foundation and Higher] Use y = mx + c to identify parallel lines and find equations of lines from points and gradients.
• Graphs: [Higher only] Use y = mx + c to identify perpendicular lines.
• Graphs: [Foundation and Higher] Identify and interpret gradients and intercepts of linear functions graphically and algebraically.
• Graphs: [Higher only] Deduce quadratic roots algebraically and deduce turning points by completing the square.
• Graphs: [Foundation and Higher] Identify and interpret roots, intercepts and turning points of quadratic functions graphically.
• Graphs: [Foundation and Higher] Include simple cubic and reciprocal functions where tier-appropriate.
• Graphs: [Higher only] Include exponential functions and trigonometric functions with degree arguments.
• Graphs: [Higher only] Sketch translations and reflections of a given function.
• Graphs: [Foundation and Higher] Apply graph interpretation to contexts such as distance, speed and acceleration.
• Graphs: [Higher only] Include reciprocal and exponential graphs in real-context graph problems.
• Graphs: [Higher only] Calculate or estimate gradients of graphs and areas under graphs, including non-linear graphs.
• Graphs: [Higher only] Interpret gradients and areas in contexts such as distance-time, velocity-time and financial graphs.
• Graphs: [Higher only] Recognise and use the equation of a circle with centre at the origin.
• Graphs: [Higher only] Find the equation of a tangent to a circle at a given point.
• Solving equations and inequalities: [Foundation and Higher] Include equations with the unknown on both sides where tier-appropriate.
• Solving equations and inequalities: [Foundation and Higher] Solve linear equations in one unknown algebraically, including equations with brackets.
• Solving equations and inequalities: [Foundation and Higher] Solve quadratic equations algebraically by factorising, including rearranged equations where tier-appropriate.
• Solving equations and inequalities: [Higher only] Solve quadratic equations by completing the square and using the quadratic formula.
• Solving equations and inequalities: [Foundation and Higher] Find approximate solutions to simultaneous equations using a graph.
• Solving equations and inequalities: [Foundation and Higher] Solve two simultaneous linear equations in two variables algebraically.
• Solving equations and inequalities: [Higher only] Use suffix notation in recursive formulae where required.
• Solving equations and inequalities: [Higher only] Find approximate solutions to equations numerically using iteration.
• Solving equations and inequalities: [Higher only] Solve linear inequalities in one or two variables and quadratic inequalities in one variable.
• Solving equations and inequalities: [Foundation and Higher] Solve linear inequalities in one variable and represent solution sets on a number line.
• Solving equations and inequalities: [Higher only] Derive and solve two simultaneous equations from a contextual problem.
• Solving equations and inequalities: [Foundation and Higher] Translate simple situations or procedures into algebraic expressions or formulae.
• Sequences: [Foundation and Higher] Generate terms of a sequence from a term-to-term rule or a position-to-term rule.
• Sequences: [Higher only] Include simple geometric progressions, other sequences and sequences involving surds where required.
• Sequences: [Foundation and Higher] Include Fibonacci-type and quadratic sequences where tier-appropriate.
• Sequences: [Foundation and Higher] Deduce expressions to calculate the nth term of linear sequences.
• Sequences: [Higher only] Deduce expressions to calculate the nth term of quadratic sequences.