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2 Equations, formulae and identities

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  1. 2.1 Use of symbols

    1. 2.1.ASymbols in equations, expressions and formulae

      understand that symbols may be used to represent numbers in equations or variables in expressions and formulae

    2. 2.1.BGeneralised arithmetic rules in algebra

      Understand that algebraic expressions follow the generalised rules of arithmetic.

    3. 2.1.CInteger index notation

      use index notation for positive and negative integer powers, including zero

    4. 2.1.DIndex laws

      use index laws in simple cases: xᵐ × xⁿ = xᵐ⁺ⁿ, xᵐ ÷ xⁿ = xᵐ⁻ⁿ and (xᵐ)ⁿ = xᵐⁿ

  2. 2.2 Algebraic manipulation

    1. 2.2.AEvaluate expressions by substituting numerical values

      evaluate expressions by substituting numerical values for letters

    2. 2.2.BCollect like terms

      collect like terms

    3. 2.2.CExpanding a single term over a bracket

      multiply a single term over a bracket

    4. 2.2.DTaking out common factors

      take out common factors

    5. 2.2.EProducts of two linear expressions

      expand the product of two simple linear expressions

    6. 2.2.FFactorising simple quadratic expressions

      understand the concept of a quadratic expression and factorise expressions limited to x² + bx + c

  3. 2.3 Expressions and formulae

    1. 2.3.AUnknowns and variables

      understand that a letter may represent an unknown number or a variable

    2. 2.3.BCorrect notational conventions for algebraic

      use correct notational conventions for algebraic expressions and formulae

    3. 2.3.CSubstitution in expressions and formulae

      substitute positive and negative integers, decimals and fractions for words and letters in expressions and formulae Evaluate 2x – 3y when x = 4 and y = −5

    4. 2.3.DFormulae from mathematics and other real-life contexts

      use formulae from mathematics and other real-life contexts expressed initially in words or diagrammatic form and convert to letters and symbols

    5. 2.3.EDerive a formula or expression

      derive a formula or expression

    6. 2.3.FChanging the subject of a formula

      change the subject of a formula where the subject appears once

  4. 2.4 Linear equations

    1. 2.4.ASolving linear equations

      solve linear equations with integer or fractional coefficients in one unknown, where the unknown appears on either or both sides

    2. 2.4.BForming linear equations

      set up simple linear equations from given data The three angles of a triangle are a°, (a + 10)°, (a + 20)°. Find the value of a

  5. 2.6 Simultaneous linear equations

    1. 2.6.A

      Calculate exact solutions of two simultaneous linear equations in two unknowns.

  6. 2.7 Quadratic equations

    1. 2.7.A

      solve quadratic equations by factorisation, limited to x² + bx + c = 0

  7. 2.8 Inequalities

    1. 2.8.AInequality symbols and compound inequalities

      understand and use the symbols >, <, ≥ and ≤, including double-ended inequalities

    2. 2.8.BOpen and closed intervals

      understand and use the convention for open and closed intervals on a number line

    3. 2.8.CSolving linear inequalities

      solve simple linear inequalities in one variable and represent the solution set on a number line

    4. 2.8.DLinear inequalities on Cartesian graphs

      Represent simple linear inequalities on rectangular Cartesian graphs.

    5. 2.8.ERegions defined by linear inequalities

      identify regions on rectangular Cartesian graphs defined by simple linear inequalities Conventions for the inclusion of boundaries are not required