2. Algebra and graphs
- Syllabus
- 0580–2028–2029
- Section
- 2
- Level
- Core
Exam analysis
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In this section
Topic C2.1
C2.1 Introduction to algebra
Objectives in this topic
C2.1.1 Know that letters can be used to represent generalised numbers.
- Know that letters can be used to represent generalised numbers.
C2.1.2 Substitute numbers into expressions and formulas.
- Substitute numbers into expressions and formulas.
Topic C2.2
C2.2 Algebraic manipulation
Objectives in this topic
C2.2.1 Simplify expressions by collecting like terms.
- Simplify expressions by collecting like terms.
C2.2.2 Expand products of algebraic expressions.
- Expand products of algebraic expressions.
C2.2.3 Factorise by extracting common factors
- 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).
Topic C2.4
C2.4 Indices II
Objectives in this topic
C2.4.1 Understand and use indices (positive, zero and negative).
- Understand and use indices (positive, zero and negative).
C2.4.2 Understand 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.
Topic C2.5
C2.5 Equations
Objectives in this topic
C2.5.1 Construct expressions, equations and formulas
- Construct simple expressions, equations and formulas, including linear simultaneous equations.
C2.5.2 Solve linear equations
- Solve linear equations in one unknown.
C2.5.3 Solve simultaneous linear equations
- Solve simultaneous linear equations in two unknowns.
C2.5.4 Change the subject of simple formulas
- Change the subject of a simple formula where the subject appears once and is not raised to a power or under a root.
Topic C2.6
C2.6 Inequalities
Objectives in this topic
C2.6.1 Represent and interpret inequalities, including on a number line
- 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
Topic C2.7
C2.7 Sequences
Objectives in this topic
C2.7.1 Continue a given number sequence or pattern.
- Continue a given number sequence or pattern.
C2.7.2 Recognise patterns in sequences, including the term-to-term rule, and
- Recognise patterns in sequences, including the term-to-term rule, and relationships between different sequences.
C2.7.3 Find and use the nth term of the following sequences: (a) linear (b)
- 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
Topic C2.9
C2.9 Graphs in practical situations
Objectives in this topic
C2.9.1 Interpret practical graphs
- 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.
C2.9.2 Draw graphs from data
- Draw graphs from given data, including distance–time graphs representing journeys.
Topic C2.10
C2.10 Graphs of functions
Objectives in this topic
C2.10.1 Construct tables of values, and draw, recognise and interpret graphs
- 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.
C2.10.2 Solve associated equations graphically, including finding and
- Solve associated equations graphically, including finding and interpreting roots by graphical methods. e.g. find the intersection of a line and a curve.
Topic C2.11
C2.11 Sketching curves
Objectives in this topic
C2.11.1 Recognise, sketch and interpret graphs of the following functions: (a)
- 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.