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2 Equations, formulae and identities

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  1. 2.1 Use of symbols

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

    2. Understand that algebraic expressions follow the generalised rules of arithmetic.

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

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

  2. 2.2 Algebraic manipulation

    1. evaluate expressions by substituting numerical values for letters

    2. collect like terms

    3. multiply a single term over a bracket

    4. take out common factors

    5. expand the product of two simple linear expressions

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

  3. 2.3 Expressions and formulae

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

    2. use correct notational conventions for algebraic expressions and formulae

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

    5. derive a formula or expression

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

  6. 2.7 Quadratic equations

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

  7. 2.8 Inequalities

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

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

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

    4. Represent simple linear inequalities on rectangular Cartesian graphs.

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