Mathematics

All students follow the same course and are assessed in the following main topic areas:

  • Number
  • Algebra
  • Shape, Space and Measures
  • Handling Data

Students are assessed at the beginning of Year 7 and this forms one of the five major assessments that take place over Years 7 & 8. These assessments allow the department to closely monitor the progress of students.

In addition to these assessments there are a further five Core Assessments. These assessments link to follow on Even Better If (EBI) tasks which are designed to ensure that students work on their areas of weakness. This progress on what was not fully understood in the core assessment is of great importance and is factored into the homework that is set.

Homework is set twice per week (although this may be organised as one longer homework). Students should be doing approximately one hour of Mathematics as homework per week.

Students are taught in their form groups.

Year 7

Year 7

Term

Topic

Learning Outcomes

1

Number Skills

 

 

 

 

 

 

 

Algebra

  • Operations with directed (negative and positive) numbers
  • Order of operations
  • Multiplying and dividing numbers using non-calculator strategies
  • Compare and simplify fractions
  • Writing a number as a fraction of another
  • Comparing decimals

 

  • Collecting like terms
  • Substitution into expressions
  • Writing expressions
  • Solving one step linear equations

2

Sequences

 

 

Number Theory

 

Area and Perimeter

 

  • Pattern recognition in different types of sequences
  • Finding the nth term of an arithmetic sequence

 

  • Prime factors, HCF and LCM

 

  • Including circles and compound shapes
  • Arc 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 percentages
  • Calculating percent of a number
  • Using multipliers to calculate percent increase and decrease
  • Reverse percentages
  • Compound interest

4

Angle geometry

 

 

 

 

Algebraic Expressions and Equations

  • Angles on a straight line
  • Angles rules on a transversal
  • Interior and exterior angles
  • Simple geometric proof

 

  • Expanding single bracket expressions
  • Solving multi step linear equations
  • Problem 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 ratios
  • Maps and scale drawings

 

 

 

  • Translations, reflections, rotations

 

  • Volumes of cuboids, prims, cylinders and pyramids
  • Plans 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 expressions
  • Substitution into expressions
  • Expanding single bracket and introduction to double bracket expressions
  • Solving multi-step linear equations
  • Forming and solving equations
  • Rearranging formulae

 

  • Constructions (no Loci)
  • Recap of angles properties
  • Properties of 2D shapes

2

Straight Line Graphs

 

 

 

 

Probability

 

 

  • Plotting using a table of values
  • Gradients and intercepts of lines
  • Finding the equation of a line
  • Parallel and perpendicular lines

 

  • The counting principle
  • Sample spaces, mutually exclusive events, relative frequency

3

Data Handling

 

 

 

  • Types of sampling and bias
  • Scatter graphs and correlations
  • Quartiles, IQR, measures of spread
  • Box plots and cumulative frequency
  • Grouped data

4

Indices

 

 

 

 

Measurement

  • Index rules
  • Negative indices
  • Standard Form
  • Square and cube roots in index form

 

  • Metric unit conversions for length, area and volume
  • Compound measures

5

Algebraic Expressions and Equations

 

  • Expanding double and triple bracket expressions
  • Difference of two squares
  • Factorising by finding the HCF and basic quadratic expressions
  • Solving linear equations with fractions
  • Simplifying 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 equations
  • Solving simultaneous equations algebraically using substitution and elimination
  • Problem solving using equations
  • Finding the nth term of linear and quadratic sequences
  • Recognising geometric progressions,
  • Fibonacci sequences and triangular numbers
  • Factorising expressions using a variety of techniques

2

Indices

 

Triangle Geometry

 

 

 

Number Skills

 

  • Index rules (including negative and fractional indices)

 

  • Similarity and similar triangles
  • Pythagoras
  • Using 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 surds
  • Rationalising the denominator

 

  • Solving quadratic equations by factorising

4

Geometry and Measurement

 

 

 

Algebra

  • Plans and elevations
  • Constructions and loci
  • Scale drawings and bearings
  • Unit conversion of metric units

 

  • Solving linear inequalities
  • Drawing inequalities on a number line

 

5

Number Skills

 

 

Circle Geometry

 

 

Probability and Sets

 

 

 

  • Using multipliers to compound percent changes
  • Reverse percentages

 

  • Understand and apply circle theorems
  • Finding arc lengths and sector areas

 

  • Using Venn diagrams and set notation
  • Understanding mutually exclusive events
  • Understanding difference between independent and dependent events
  • Using Tree diagrams and two-way tables
  • Calculating relative frequency and expected values

6

Algebra

 

 

 

  • Solve quadratic equations using the quadratic formula
  • Complete the square and apply to solving equations
  • Sketching quadratic graphs

 

Years 10 & 11

Year 10

Term

Topic

Learning Outcomes

1

Number Skills

 

 

 

 

Geometry

 

Algebra

 

 

  • Recap of operations with directed (negative and positive) numbers
  • Recap of fraction operations and index rules
  • Change of base
  • Standard form calculations

 

  • Understand and apply circle theorems

 

  • Changing the subject of a formula

 

2

Algebra

 

Trigonometry

 

  • Straight line graphs and coordinate geometry

 

  • Recap of Pythagoras
  • Using trigonometric ratios to find unknown angles and side lengths
  • Sine Rule, Cosine Rule
  • Areas of triangles (including sectors)a
  • 3D trigonometry
  • Solving problems with bearing
  • Exact trig values

 

3

Data Handling

 

 

 

Algebra

 

  • Charts and averages
  • Grouped data
  • Histograms

 

  • Solving quadratic equations
  • Completing the square to find turning points and solve equations
  • Key features of quadratic graphs

4

Algebra

 

 

 

  • Direct and inverse proportion
  • Equation of a circle graph
  • Solving 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 spheres
  • Volume and area scale factors

 

  • Finding the equations of tangents to circles

 

6

Algebra

 

  • Linear inequalities
  • Finding regions using inequalities
  • Solving quadratic inequalities
  • Iterations
  • Intro to Functions

Year 11

 

Term

Topic

Learning Outcomes

1

Number Skills

 

Algebra

 

 

  • Fraction operation recap

 

  • Operations with algebraic fractions
  • Function notation, composite functions, inverse functions
  • Properties of exponential functions and reciprocal functions
  • Graph transformations
  • Solving equations by graphing

 

2

Geometry

 

Number

 

 

Probability and Sets

 

  • Vectors

 

  • Iteration
  • Counting principle

 

  • Using Venn diagrams and set notation
  • Understanding mutually exclusive events
  • Understanding difference between independent and dependent events
  • Using Tree diagrams and two-way tables
  • Calculating relative frequency and expected values

3

Measurement and Rates

 

Algebra

 

 

  • Compound measures and rates of flow

 

 

  • Estimating rates of change
  • Estimating area under graphs
  • Algebraic 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 progressions
  • Fibonacci 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 

  1. Index Laws 

  1. Expanding Brackets 

  1. Factorising 

  1. Negative and Fractional Indices 

  1. Surds 

  1. 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 

 

  1. Populations and samples 

  1. Sampling 

  1. Non-random sampling 

  1. Types of data 

  1. 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 

 

  1. Proof by Contradiction 

  1. Algebraic Fractions 

  1. Partial Fractions 

  1. Repeated Factors 

  1. 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 ±bsinxacos⁡x ±bsin⁡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 andcosxsin⁡x andcos⁡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 

 

  1. Exponential models 

  1. Measuring correlation 

  1. 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