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2. Algebra and graphs

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  1. C2.1 Introduction to algebra

    1. • Know that letters can be used to represent generalised numbers.

    2. • Substitute numbers into expressions and formulas.

  2. C2.2 Algebraic manipulation

    1. • Simplify expressions by collecting like terms.

    2. • Expand products of algebraic expressions.

    3. • Factorise by extracting common factors. Simplify means give the answer in its simplest form, e.g. 2a + 3b + 5a – 9b = 7a – 6b. e.g. expand 3x(2x – 4y). Includes products of two brackets involving one variable, e.g. expand (2x + 1)(x – 4). Factorise means factorise fully, e.g. 9x2 + 15xy = 3x(3x + 5y).

  3. C2.4 Indices II

    1. C2.4.1Understand and use indices (positive, zero and negative).

      • Understand and use indices (positive, zero and negative).

    2. C2.4.2Understand and use the rules of indices

      • Understand and use the rules of indices. e.g. 2x = 32. Find the value of x. e.g. simplify: • (5x 3) 2 • 12a 5 ÷ 3a –2 • 6x 7y 4 × 5x –5y. Knowledge of logarithms is not required.

  4. C2.5 Equations

    1. • Construct simple expressions, equations and formulas, including linear simultaneous equations.

    2. • Solve linear equations in one unknown.

    3. • Solve simultaneous linear equations in two unknowns.

    4. • Change the subject of a simple formula where the subject appears once and is not raised to a power or under a root.

  5. C2.6 Inequalities

    1. • Represent and interpret inequalities, including on a number line. When representing and interpreting inequalities on a number line: • open circles should be used to represent strict inequalities (<, >) • closed circles should be used to represent inclusive inequalities (⩽, ⩾) e.g. – 3 ⩽ x < 1 –/uni202F3– /uni202F2– /uni202F101 x

  6. C2.7 Sequences

    1. • Continue a given number sequence or pattern.

    2. • Recognise patterns in sequences, including the term-to-term rule, and relationships between different sequences.

    3. • Find and use the nth term of the following sequences: (a) linear (b) simple quadratic (c) simple cubic. e.g. write the next two terms in this sequence: 1, 3, 6, 10, 15, …, … e.g. find the nth term of 2, 5, 10, 17

  7. C2.9 Graphs in practical situations

    1. • Use and interpret graphs in practical situations, including travel and conversion graphs, and interpret the gradient of a straight-line graph as a rate of change.

    2. • Draw graphs from given data, including distance–time graphs representing journeys.

  8. C2.10 Graphs of functions

    1. • Construct tables of values, and draw, recognise and interpret graphs for functions of the following forms: • ax + b • ± x2 + ax + b • x a (x ≠ 0) where a and b are integer constants.

    2. • Solve associated equations graphically, including finding and interpreting roots by graphical methods. e.g. find the intersection of a line and a curve.

  9. C2.11 Sketching curves

    1. • Recognise, sketch and interpret graphs of the following functions: (a) linear (b) quadratic. Knowledge of symmetry and roots is required. Knowledge of turning points is not required.