MATHEMATICS
Mathematics at WGSB not only prepares students for GCSE and GCE assessments, but to also equips them with the quantitative analysis and logical reasoning skills that are essential to succeed in a range of fields beyond school. The department strives to provide students with a challenging yet enjoyable experience of learning maths in a way which allows students to see the application and uses of maths on a regular basis.
In Key Stage 3 and Key Stage 4, all students follow the same course and are assessed in the following main topic areas:
- Number
- Algebra
- Geometry
- Ratio and Proportion
- Probability and Statistics
GCSE students follow the AQA specification.
A Level students follow the Edexcel specification.
Year 7
Year 7
| Term | Topic | Learning Outcomes |
| 1 | Number Skills Algebra | Operations with directed (negative and positive) numbersOrder of operationsMultiplying and dividing numbers using non-calculator strategiesCompare and simplify fractionsWriting a number as a fraction of anotherComparing decimals Collecting like termsSubstitution into expressionsWriting expressionsSolving one step linear equations |
| 2 | Sequences Number Theory Area and Perimeter | Pattern recognition in different types of sequencesFinding the nth term of an arithmetic sequence Prime factors, HCF and LCM Including circles and compound shapesArc lengths and sector areas |
| 3 | Fractions, Decimals, and Percentages | Operations (addition, subtraction, multiplication and division) with proper fractions, improper fractions and mixed numbers.Decimal operations using non-calculator and calculator-based techniques.Converting between fractions, decimals and percentagesCalculating percent of a numberUsing multipliers to calculate percent increase and decreaseReverse percentagesCompound interest |
| 4 | Angle geometry Algebraic Expressions and Equations | Angles on a straight lineAngles rules on a transversalInterior and exterior anglesSimple geometric proof Expanding single bracket expressionsSolving multi step linear equationsProblem solving by setting up and solving linear equations |
| 5 | Data Handling Rounding and Approximation Pythagoras | Pie charts, bar charts, frequency polygons, averages, measures of spread, grouped data Rounding, significant figures, estimating calculations Using Pythagoras to solve for unknown sides |
| 6 | Ratios Transformations of Shapes 3D Shapes | Simplifying, converting to fractions, and sharing into ratiosMaps and scale drawings Translations, reflections, rotations Volumes of cuboids, prims, cylinders and pyramidsPlans and elevation |
Year 8
Year 8
| Term | Topic | Learning Outcomes |
| 1 | Number Skills Algebraic Expressions and Equations Geometry | Recap of operations with directed (negative and positive) numbers Simplifying expressionsSubstitution into expressionsExpanding single bracket and introduction to double bracket expressionsSolving multi-step linear equationsForming and solving equationsRearranging formulae Constructions (no Loci)Recap of angles propertiesProperties of 2D shapes |
| 2 | Straight Line Graphs Probability | Plotting using a table of valuesGradients and intercepts of linesFinding the equation of a lineParallel and perpendicular lines The counting principleSample spaces, mutually exclusive events, relative frequency |
| 3 | Data Handling | Types of sampling and biasScatter graphs and correlationsQuartiles, IQR, measures of spreadBox plots and cumulative frequencyGrouped data |
| 4 | Indices Measurement | Index rulesNegative indicesStandard FormSquare and cube roots in index form Metric unit conversions for length, area and volumeCompound measures |
| 5 | Algebraic Expressions and Equations | Expanding double and triple bracket expressionsDifference of two squaresFactorising by finding the HCF and basic quadratic expressionsSolving linear equations with fractionsSimplifying algebraic fractions |
| 6 | Bearings Sets and Set Notation Bounds | Drawing and calculating bearings using angle facts Unions, intersections, compliments using Venn diagrams Finding upper and lower bounds and using them in calculations |
Year 9
Year 9
| Term | Topic | Learning Outcomes |
| 1 | Number Skills Proportions Algebra and Sequences | Recap of operations with directed (negative and positive) numbers Perform simple numerical direct and inverse proportion calculations Solve multi-step linear equationsSolving simultaneous equations algebraically using substitution and eliminationProblem solving using equationsFinding the nth term of linear and quadratic sequencesRecognising geometric progressions,Fibonacci sequences and triangular numbersFactorising expressions using a variety of techniques |
| 2 | Indices Triangle Geometry Number Skills | Index rules (including negative and fractional indices) Similarity and similar trianglesPythagorasUsing trigonometric ratios to find unknown angles and side lengths Converting between recurring decimals and fractions |
| 3 | Transformations Surds Algebra | Translations, rotations, reflections and enlargements of shapes Operations with surdsRationalising the denominator Solving quadratic equations by factorising |
| 4 | Geometry and Measurement Algebra | Plans and elevationsConstructions and lociScale drawings and bearingsUnit conversion of metric units Solving linear inequalitiesDrawing inequalities on a number line |
| 5 | Number Skills Circle Geometry Probability and Sets | Using multipliers to compound percent changesReverse percentages Understand and apply circle theoremsFinding arc lengths and sector areas Using Venn diagrams and set notationUnderstanding mutually exclusive eventsUnderstanding difference between independent and dependent eventsUsing Tree diagrams and two-way tablesCalculating relative frequency and expected values |
| 6 | Algebra | Solve quadratic equations using the quadratic formulaComplete the square and apply to solving equationsSketching quadratic graphs |
Years 10 & 11
Year 10
| Term | Topic | Learning Outcomes |
| 1 | Number Skills Geometry Algebra | Recap of operations with directed (negative and positive) numbersRecap of fraction operations and index rulesChange of baseStandard form calculations Understand and apply circle theorems Changing the subject of a formula |
| 2 | Algebra Trigonometry | Straight line graphs and coordinate geometry Recap of PythagorasUsing trigonometric ratios to find unknown angles and side lengthsSine Rule, Cosine RuleAreas of triangles (including sectors)a3D trigonometrySolving problems with bearingExact trig values |
| 3 | Data Handling Algebra | Charts and averagesGrouped dataHistograms Solving quadratic equationsCompleting the square to find turning points and solve equationsKey features of quadratic graphs |
| 4 | Algebra | Direct and inverse proportionEquation of a circle graphSolving non-linear simultaneous equations algebraically and by graphing |
| 5 | Number Geometry Algebra | Bounds, error intervals, truncation Volume and surface areas of 3D objects including cones and spheresVolume and area scale factors Finding the equations of tangents to circles |
| 6 | Algebra | Linear inequalitiesFinding regions using inequalitiesSolving quadratic inequalitiesIterationsIntro to Functions |
Year 11
| Term | Topic | Learning Outcomes |
| 1 | Number Skills Algebra | Fraction operation recap Operations with algebraic fractionsFunction notation, composite functions, inverse functionsProperties of exponential functions and reciprocal functionsGraph transformationsSolving equations by graphing |
| 2 | Geometry Number Probability and Sets | Vectors IterationCounting principle Using Venn diagrams and set notationUnderstanding mutually exclusive eventsUnderstanding difference between independent and dependent eventsUsing Tree diagrams and two-way tablesCalculating relative frequency and expected values |
| 3 | Measurement and Rates Algebra | Compound measures and rates of flow Estimating rates of changeEstimating area under graphsAlgebraic proof |
| 4 | Geometry Number Algebra | Congruency, similarity and geometric proof Prime factors, number properties using prime factors, HCF, LCM using prime factors Arithmetic, geometric, and quadratic progressionsFibonacci sequence |
| 5 | Revision | |
| 6 |
Post 16 at WG6
Year 12
| Topic | Learning Outcomes | |
| Term 1 | Pure 1: Algebraic Expressions Pure 2: Quadratics Pure 3: Equations and Inequalities Pure 4: Graphs and Transformations Pure 12: Differentiation Pure 5: Straight Line Graphs | Index Laws Expanding Brackets Factorising Negative and Fractional Indices Surds Rationalising Denominators 2.1 Solving Quadratic Equations 2,2 Completing the Square 2.3 Functions 2.4 Quadratic Graphs 2.5 The Discriminant 2.6 Modelling with Quadratics 3.1 Linear Simultaneous Equations 3.2 Quadratic Simultaneous Equations 3.3 Simultaneous Equations on Graphs 3.4 Linear Inequalities 3.5 Quadratic Inequalities 3.6 Inequalities on Graphs 4.1 Cubic Graphs 4.2 Quartic Graphs 4.3 Reciprocal Graphs 4.4 Points of Intersection 4.5 Translating Graphs 4.6 Stretching Graphs 4.7 Transforming Functions 12.1 Gradients of Curves 12.2 Finding the Derivative 12.3 Differentiation xnxn 12.4 Differentiation Quadratics 12.5 Differentiation functions with two or more terms 12.6 Gradients, tangents and normal 12.7 Increasing and decreasing functions 12.8 Second order derivatives 12.9 Stationary Points 12.10 Sketching gradient functions 12.11 Modelling with differentiation 5.1 y=mx+cy=mx+c 5.2 Equations of straight lines 5.3 Parallel and perpendicular lines 5.4 Length and area 5.5 Modelling with straight lines |
| Term 2 | Pure 11: Vectors Stats 1: Data Collection Stats 2: Measures of Location and Spread Stats 3: Representations of Data Stats 4: Correlation Mechs 8: Modelling in Mechanics Mechs 9: Constant Acceleration Pure 6: Circles | 11.1 Vectors 11.2 Representing vectors 11.3 Magnitude and direction 11.4 Position vectors 11.5 Solving geometric problems 11.6 Modelling with vectors Populations and samples Sampling Non-random sampling Types of data The large data set 2.1 Measures of Central Tendency 2.2 Other Measures of Location 2.3 Measures of Spread 2.4 Variance and Standard Deviation 2.5 Coding 3.1 Outliers 3.2 Box Plots 3.3 Cumulative Frequency 3.4 Histograms 3.5 Comparing Data 4.1 Correlation 4.2 Linear Regression 8.1 Constructing a Model 8.2 Modelling Assumptions 8.3 Quantities and Units 8.4 Working with Vectors 9.1 Displacement-time Graphs 9.2 Velocity-time Graphs 9.3 Constant Acceleration Formulae 1 9.4 Constant Acceleration Formulae 2 9.5 Vertical Motion Under Gravity 6.1 Midpoints and Perpendicular Bisectors 6.2 Equation of a Circle 6.3 Intersections of Straight Lines and Circles 6.4 Use Tangent and Chord Properties 6.5 Circles and Triangles |
| Term 3 | Pure 13: Integration Pure 9: Trigonometric Ratios Pure 10: Trigonometric Identities and Equations Pure 14: Exponentials and Logarithms Mechs 10: Forces and Motion | 13.1 Integrating xnxn 13.2 Indefinite Integrals 13.3 Finding Functions 13.4 Definite Integrals 13.5 Areas under Curves 13.6 Areas under the x-axis 13.7 Areas between Curves and Lines 9.1 The cosine rule 9.2 The sine rule 9.3 Areas of Triangles 9.4 Solving triangle problems 9.5 Graphs of sine, cosine, and tangent 9.6 Transforming trigonometric graphs 10.1 Angles in all four Quadrants 10.2 Exact values of trigonometrical ratios 10.3 Trigonometric Identities 10.4 Simple Trigonometric Equations 10.5 Harder Trigonometric Equations 10.6 Equations and Identities 14.1 Exponential Functions 14.2 y=exy=ex 14.3 Exponential Modelling 14.4 Logarithms 14.5 Laws of Logarithms 14.6 Solving Equations using Logarithms 14.7 Working with Natural Logarithms 14.8 Logarithms and Non-Linear Data 10.1 Force Diagrams 10.2 Forces as Vectors 10.3 Forces and Acceleration 10.4 Motion in 2 Dimensions 10.5 Connected Particles 10.6 Pulleys |
| Term 4 | Stats 5: Probability Stats 6: Statistical Distributions Mechs 11: Variable Acceleration Pure 7: Algebraic Methods | 5.1 Calculating Probabilities 5.2 Venn Diagrams 5.3 Mutually Exclusive and Independent Events 5.4 Tree Diagrams 6.1 Probability Distributions 6.2 The Binomial Distributions 6.3 Cumulative Probabilities 11.1 Functions of time 11.2 Using differentiation 11.3 Maxima and minima problems 11.4 Using integration 11.5 Constant acceleration formulae 7.1 Algebraic Fractions 7.2 Dividing Polynomials 7.3 The factor theorem 7.4 Mathematical Proof 7.5 Methods of Proof |
| Term 5 | Stats 7: Hypothesis Testing Pure 8: The Binomial Expansion | 7.1 Hypothesis Testing 7.2 Finding Critical Values 7.3 One-tailed tests 7.4 Two-tailed tests 8.1 Pascal’s Triangle 8.2 Factorial Notation 8.3 The Binomial Expansion 8.4 Solving Binomial Problems 8.5 Binomial Estimation |
| Term 6 | (Y13) Pure 5: Radians (Y13) Pure 1: Algebraic Methods (Y13) Pure 2: Functions and Graphs (Y13) Pure 4: Binomial Expansion | 5.1 Radian Measure 5.2 Arc Length 5.3 Areas of Sectors and Segments 5.4 Solving Trigonometric Equations 5.5 Small Angle Approximations Proof by Contradiction Algebraic Fractions Partial Fractions Repeated Factors Algebraic Division 2.1 The Modulus Function 2.2 Functions and Mapping 2.3 Composite Functions 2.4 Inverse Functions 2.5 y=|f(x)|y=f(x) and y=f(|x|)y=f(x) 2.6 Combining Transformations 2.7 Solving Modulus Problems 4.1 Expanding (1+x)n(1+x)n 4.2 Expanding (a+bx)n(a+bx)n 4.3 Using Partial Fractions |
Year 13
| Topic | Learning Outcomes | |
| Term 1 | Pure 2: Functions and Graphs Pure 3: Sequences and Series Pure 4: Binomial Expansion Mechs 5: Forces and Friction Mechs 6: Projectiles Pure 6: Trigonometric Functions | 2.1 The Modulus Function 2.2 Functions and Mapping 2.3 Composite Functions 2.4 Inverse Functions 2.5 y=|f(x)|y=f(x) and y=f(|x|)y=f(x) 2.6 Combining Transformations 2.7 Solving Modulus Problems 3.1 Arithmetic Sequences 3.2 Arithmetic Series 3.3 Geometric Sequences 3.4 Geometric Series 3.5 Sum to Infinity 3.6 Sigma Notation 3.7 Recurrence Relations 3.8 Modelling with Series 4.1 Expanding (1+x)n(1+x)n 4.2 Expanding (a+bx)n(a+bx)n 4.3 Using Partial Fractions 5.1 Resolving Forces 5.2 Inclined Planes 5.3 Friction 6.1 Horizontal Projection 6.2 Horizontal and Vertical Components 6.3 Projection at any Angle 6.4 Projectile motion formulae 6.1 Secant, cosecant and cotangent 6.2 Graphs of sec x, cosec x and cot x 6.3 Using sec x, cosec x and cot x 6.4 Trigonometric Identities 6.5 Inverse Trigonometric Functions |
| Term 2 | Pure 7: Trigonometry and Modelling Pure 8: Parametric Equations Pure 9: Differentiation Stats 1: Regression, correlation and hypothesis testing Stats 2: Conditional Probability | 7.1 Addition Formulae 7.2 Using the angle addition formulae 7.3 Double-angle formulae 7.4 Solving Trigonometric Equations 7.5 Simplifying acosx ±bsinxacosâ¡x ±bsinâ¡x 7.6 Proving Trigonometric Identities 7.7 Modelling with Trigonometric Functions 8.1 Parametric Equations 8.2 Using Trigonometric Identities 8.3 Curve Sketching 8.4 Points of Intersection 8.5 Modelling with Parametric Equations 9.1 Differentiating sinx andcosxsinâ¡x andcosâ¡x 9.2 Differentiation exponentials and logarithms 9.3 The chain rule 9.4 The product rule 9.5 The quotient rule 9.6 Differentiating trigonometric functions 9.7 Parametric differentiation 9.8 Implicit differentiation 9.9 Using second derivatives 9.10 Rates of change Exponential models Measuring correlation Hypothesis testing for zero correlation 2.1 Set Notation 2.2 Conditional Probability 2.3 Conditional Probabilities in Venn Diagrams 2.4 Probability Formulae 2.5 Tree Diagrams |
| Term 3 | Stats 3: The Normal Distribution | 3.1 The normal distribution 3.2 Finding probabilities for normal distributions 3.3 The inverse normal distributions 3.4 The standard normal distribution 3.5 Finding μ |
