Specification points

WJEC GCSE Mathematics and Numeracy (Double Award) 3320QD

225 points in 4 topics, with WJEC's codes and titles.

Codes and titles are read by a script from WJEC's published specification and have not been checked by a person. What each point covers is in the specification itself: WJEC’s specification.

1 Number

1.1 Number and rounding
1.1.1 Reading and writing whole numbers
1.1.2 Round whole numbers to the nearest 10, 100, 1000, etc
1.1.3 Place value
1.1.4 Rounding decimals
1.1.5 Round numbers to a given number of significant figures
1.1.6 Directed numbers
1.1.7 Rounding up or down in context
1.1.8 Check methods and solutions using appropriate strategies
1.1.9 Estimating by approximation
1.2 Number properties including prime factor decomposition
1.2.1 Properties of numbers
1.2.2 The meaning of the terms square, square root, cube and cube root
1.2.3 Reciprocals
1.2.4 Prime factors in index form
1.2.5 LCM and HCF by prime factor decomposition
1.2.6 Using prime factor decomposition
1.3 Index laws including standard form
1.3.1 The notation for positive integral indices
1.3.2 The notation for zero and negative indices
1.3.3 The notation for fractional indices
1.3.4 Rules of indices for positive integer powers
1.3.5 Rules of indices for negative and fractional powers
1.3.6 Converting to and from standard form
1.3.7 Using standard form
1.4 Fractions, decimals, percentages and ratio
1.4.1 Equivalent fractions
1.4.2 Equivalent fractions, decimals and percentages
1.4.3 Converting between fractions, decimals and percentages
1.4.4 Order and compare whole numbers, decimals, fractions and percentages
1.4.5 Simplifying fractions
1.4.6 One number as a fraction or percentage of another
1.4.7 Fractions and percentages of quantities
1.4.8 Fractional and percentage change
1.4.9 Multipliers
1.4.10 Repeated proportional change
1.4.11 Calculating with ratios
1.4.12 Direct and inverse proportion problems
1.4.13 Reverse proportional change
1.5 Proficiency in calculations
1.5.1 Number operations and order of operations
1.5.2 Add, subtract, multiply and divide whole numbers, including large whole numbers
1.5.3 Add, subtract, multiply and divide decimals, fractions and negative numbers
1.5.4 Number machines
1.5.5 Using a calculator efficiently
1.5.6 Trigonometric functions on a calculator
1.6 Limits of accuracy
1.6.1 Rounding answers to a sensible accuracy
1.6.2 Measurement as approximate
1.6.3 Upper and lower bounds
1.6.4 Bounds in calculations
1.6.5 Effects of premature rounding
1.7 Extraction, interpretation and presentation of information
1.7.1 Interpreting mathematical information
1.7.2 Plans and schedules
1.7.3 Venn diagrams
1.8 Personal/household finance and enterprise
1.8.1 Calculating with money
1.8.2 Personal and household finance
1.8.3 Simple and compound interest
1.8.4 Calculations with multiple rates
1.8.5 Annual Equivalent Rate (AER)
1.8.6 Annual Percentage Rate (APR)
1.9 Rational and irrational numbers
1.9.1 Recurring decimals and exact fractions
1.9.2 Converting recurring decimals to fractions
1.9.3 Rational and irrational numbers
1.9.4 Manipulate and simplify numerical expressions involving surds
1.9.5 Simplifying more complex surd expressions
1.9.6 Using pi in exact calculations
1.9.7 Using surds in exact calculations

2 Algebra

2.1 Algebraic conventions and manipulation of expressions and formulae
2.1.1 Conventions of algebra
2.1.2 Substituting into formulae and expressions
2.1.3 Equations, expressions and formulae
2.1.4 Identities, equations, expressions and formulae
2.1.5 Form and simplify expressions
2.1.6 Collecting like terms
2.1.7 Expand expressions – single bracket
2.1.8 Multiply and divide terms by applying rules of indices
2.1.9 Simplifying algebraic fractions
2.1.10 Simplifying more complex algebraic fractions
2.1.11 Expand two linear expressions in one or two variables
2.1.12 Expanding linear and quadratic expressions
2.1.13 Factorising linear or quadratic expressions by a common factor
2.1.14 Factorising more complex expressions by common factors
2.1.15 Factorising quadratic expressions
2.1.16 Changing the subject of a formula
2.1.17 Changing the subject with repeated terms
2.2 Equations and inequalities – algebraic method
2.2.1 Solving linear equations
2.2.2 Solving more complex linear equations
2.2.3 Simple linear inequalities
2.2.4 More complex linear inequalities
2.2.5 Solving quadratics by factorisation
2.2.6 Simultaneous linear equations
2.2.7 Equations with linear denominators
2.2.8 Solving quadratics by formula
2.2.9 Trial and improvement for cubic equations
2.2.10 Equations for direct and inverse proportion
2.3 Sequences
2.3.1 Patterns in number
2.3.2 Term-to-term rules
2.3.3 Generating sequences from the nth term
2.3.4 nth term of linear sequences
2.3.5 nth term of quadratic sequences
2.4 Coordinates, linear and non-linear graphs
2.4.1 Coordinates in four quadrants
2.4.2 Graphs of vertical, horizontal and straight lines
2.4.3 The equation y = mx + c
2.4.4 Quadratic graphs
2.4.5 Straight-line graphs and inequality regions
2.4.6 Parallel and perpendicular lines
2.4.7 Solving simultaneous equations graphically
2.4.8 Graphs of quadratic, reciprocal and other functions
2.4.9 Graphs of quadratic and cubic functions
2.4.10 Solving equations graphically
2.4.11 Graphs with y given implicitly
2.5 Real-life graphs
2.5.1 Conversion, travel and real-life graphs
2.5.2 Misleading graphs in the media
2.5.3 Tangents and rates of change
2.5.4 Area under a graph
2.5.5 The trapezium rule

3 Geometry and measures

3.1 Geometric terms, vocabulary and properties of shape
3.1.1 Geometric terms
3.1.2 Properties of 2-D shapes
3.1.3 Properties of 3-D shapes
3.2 Use of mathematical equipment for measurement and accurate drawing
3.2.1 Measuring and accurately drawing lines, circles and angles
3.2.2 Accurate constructions with ruler, protractor and compasses
3.2.3 Loci and regions in two dimensions
3.3 Maps, scale drawings, bearings and 2-D representation of 3-D shapes
3.3.1 Reading scales
3.3.2 Using maps
3.3.3 Scale drawings
3.3.4 Three-figure bearings
3.3.5 Plans and elevations
3.3.6 3-D shapes on isometric paper
3.3.7 Nets of 3-D shapes
3.4 Angle facts
3.4.1 Angle properties of points, lines and parallel lines
3.4.2 Angle properties of triangles and quadrilaterals
3.4.3 Angles in polygons
3.4.4 Circle theorems
3.4.5 Geometric proofs
3.5 Units and measure
3.5.1 Units of time
3.5.2 Metric units
3.5.3 Calculations with time
3.5.4 Converting units of time
3.5.5 Time zones
3.5.6 Estimating metric measurements
3.5.7 Converting metric and imperial units
3.5.8 Compound measures: speed and fuel consumption
3.5.9 Other compound measures: density and flow rates
3.5.10 Converting units of area and volume
3.6 Perimeter, area and volume
3.6.1 Perimeter and area of 2-D shapes
3.6.2 Arc length and area of sectors and segments
3.6.3 Surface area and volume of 3-D shapes
3.7 Pythagoras’ theorem and trigonometry
3.7.1 Pythagoras' theorem in 2-D
3.7.2 Pythagoras' theorem in 3-D
3.7.3 Trigonometry in right-angled triangles, bearings and elevation
3.7.4 Sides and angles of right-angled triangles in 2-D and 3-D
3.7.5 Extend trigonometry to angles of any size
3.7.6 Trigonometry for any angle; sine and cosine rules
3.7.7 Area of a triangle using ½ab sin C
3.7.8 Graphs of trigonometric functions
3.8 Position, symmetry and transformations
3.8.1 Coordinates from geometrical information
3.8.2 Shapes with line symmetry
3.8.3 Lines of symmetry
3.8.4 Rotational symmetry
3.8.5 Reflections, rotations, translations and enlargements
3.8.6 Two successive transformations
3.9 Similar shapes and congruence
3.9.1 Congruent and similar shapes
3.9.2 Similar shapes as enlargements
3.9.3 Corresponding dimensions of similar shapes
3.9.4 Corresponding angles in similar and congruent shapes
3.9.5 Lengths, areas and volumes of similar shapes
3.9.6 Congruence of triangles: SSS, SAS, AAS and RHS

4 Statistics and probability

4.1 Data handling cycle – collection methods
4.1.1 The statistical problem-solving process
4.1.2 Specifying and testing hypotheses
4.1.3 Questionnaire design, fairness and bias
4.1.4 Sample size and reliability of data
4.1.5 Tallying methods
4.1.6 Frequency tables
4.1.7 Sorting and tabulating qualitative and quantitative data
4.1.8 Grouping data into class intervals
4.1.9 Specify the data needed and consider potential sampling methods
4.1.10 Random, systematic and stratified sampling
4.2 Data handling cycle – represent, interpret and display results
4.2.1 Pictograms, bar charts and pie charts
4.2.2 Vertical line diagrams
4.2.3 Line graphs over time
4.2.4 Scatter diagrams
4.2.5 Lines of best fit
4.2.6 Correlation in scatter diagrams
4.2.7 Correlation and causality
4.2.8 Mean, median, mode and range of a list
4.2.9 Grouped frequency diagrams and frequency polygons
4.2.10 Averages and range of a frequency distribution
4.2.11 Estimated mean of grouped data
4.2.12 Estimated median of grouped data
4.2.13 Modal category and modal class
4.2.14 Group containing the median
4.2.15 Choosing measures of central tendency
4.2.16 Comparing distributions
4.2.17 Measures of spread, including interquartile range
4.2.18 Cumulative frequency tables and diagrams
4.2.19 Box-and-whisker diagrams
4.2.20 Histograms with unequal class widths
4.2.21 Misleading graphs
4.2.22 Look at data to find patterns and exceptions
4.2.23 Drawing inferences and conclusions from data
4.3 Probability – single event/experiment
4.4 Probability – more than one event/experiment