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Mathematics

"As a subject in its own right, Mathematics presents frequent opportunities for creativity."
"As a subject in its own right, Mathematics presents frequent opportunities for creativity."

Mathematics is the means of looking at the patterns that make up our world and the intricate and beautiful ways in which they are constructed and realised. Numeracy is the means of making that knowledge useful.

Mathematics contributes to the school curriculum by developing pupils’ abilities to calculate; to reason logically, algebraically, and geometrically; to solve problems and to handle data. Mathematics is important for pupils in many other areas of study, particularly Science and Technology. It is also important in everyday living, in many forms of employment, and in public decision-making. As a subject in its own right, Mathematics presents frequent opportunities for creativity, and can stimulate moments of pleasure and wonder when a problem is solved for the first time, or a more elegant solution to a problem is discovered, or when hidden connections suddenly manifest.

  • YEAR 7 TO 9
    • Subject: Mathematics
    • Year : 7 to 9
    • Hours per week: 4

    Course description

    In each year, students study 5 units of work which each contain a topic from the four strands of Mathematics. There is a built-in natural progression with topics that are covered in Year 7, being re-visited and then extended to a higher level in Year 8, and then again in Year 9 with a few new additions; below is a summary.


    Year 7  Units

    Number

    1. Arithmetic
    2. Rounding & Estimating
    3. Negative Numbers
    4. Fractions, Decimals and Percentages
    5. Special Numbers & Patterns

    Algebra

    1. Rules of Algebra
    2. Solving Equations
    3. Co-ordinates & Graphs
    4. Inequalities
    5. Conversion & Travel Graphs

    Shape and Space

    1. Angles
    2. Units and Measures
    3. Symmetry
    4. Area & Perimeter
    5. Circles & Loci

    Data Handling

    1. Averages & Range
    2. Probability
    3. Representing Data
    4. Pie Charts
    5. Venn Diagrams

    Year 8 Units

    Number

    1. Fractions
    2. Factors, Multiples & Primes
    3. Roots & Accuracy
    4. Fractions, Decimals & Percentages
    5. Ratio

    Algebra

    1. Solving Equations
    2. Trial & Improvement
    3. Linear Sequences
    4. Expressions & Brackets
    5. Straight Line Graphs

    Shape and Space

    1. Area & Volume
    2. Transformations
    3. Angles
    4. Circles
    5. 3D Shapes

    Data Handling

    1. Continuous Data & Frequency Polygons
    2. Data Collections & Pie Charts
    3. Scatter Graphs
    4. Averages & Range
    5. Probability

    Year 9 Units

    Number

    1. Laws of Indices
    2. Ratio & Percentages
    3. Accuracy & Standard Form
    4. Fractions
    5. Error Bounds

    Algebra

    1. Solving Equations and Brackets
    2. Formulae & Plotting Graphs
    3. Simultaneous Equations
    4. Inequalities & Regions
    5. Quadratic Sequences

    Shape and Space

    1. Transformations
    2. Pythagoras’ Theorem
    3. Trigonometry
    4. Volume & Compound Measures
    5. Construction

    Data Handling

    1. Grouped Continuous Data
    2. Probability
    3. Set Notation & Venn Diagrams
    4. Cumulative Frequency

    Mathematics Groups, Acceleration and Assessment

    All lessons are taught in ability groups determined by end of term tests, formal assessment tasks and teacher input. All end of term tests are based on the previous term’s content and help to give an accurate summary of each student’s progress over that time frame. Individual student performances are monitored and students may move groups at the teacher’s discretion at given points in the year to give them the best opportunity to achieve their potential. The setting of groups allows for class acceleration and also for targeted support for individuals. Higher ability groups that work at a faster pace than their peers progress to the next level quicker, with the aim of completing their International GCSE in Mathematics at the end of Year 10 or January of Year 11.

  • YEAR 10 AND 11

    Year 10

    UNIT 1

    • Fractions & Decimals, BIDMAS, Ratio & Proportion, Multiples/Factors/Primes.
    • Simplifying Algebraic Expressions, Solving Equations, Factorising, Substitution & Sequences.
    • Angles, Constructions & Circle Theorems.
    • Venn Diagrams & Set Notation.

    UNIT 2

    • Rounding & Estimating, Standard Form & Error Bounds.
    • Straight-line Graphs, Simultaneous Equations, Inequalities & Changing the Subject of Formulae.
    • Pythagoras & Right-Angled Trigonometry.
    • Displaying Data & Averages.

    UNIT 3

    • Percentage Revision, Compound & Reverse Percentages.
    • Quadratic Graphs, Expanding Brackets & Solving Quadratics by Factorising.
    • Transformations.
    • Probability & Tree Diagrams.

     UNIT 4

    • Rules of Indices.
    • Graphical & Quadratic Inequalities.
    • Converting Measures, Circles, Surface Area & Volume, Compound Measures, Similarity (including Area & Volume.)
    • Cumulative Frequency.

    Year 11

    UNIT 5

    • Recurring Decimals.
    • Cubic & Reciprocal Graphs, Using Graphs to Solve Equations, Non-Linear Simultaneous Equations, Tangents to Curves.
    • Intersecting Chords & Tangents.
    • Histograms.

    UNIT 6

    • Direct & Inverse Proportion.
    • Algebraic Fractions.
    • Vectors & Vector Geometry.
    • Shading Venn Diagrams & Set Builder Notation.

    UNIT 7

    • Irrational Numbers & Surds.
    • Differentiation, Turning Points, Travel Graphs & Kinematics. 
    • Non Right-Angled Trigonometry (Sine & Cosine Rules), Area of a Triangle.
    • Domain & Range of Functions, Composite & Inverse Functions.
    • Revision and Exam Preparation.

    PAST EXAMINATION PAPERS AND PRACTICE.


    Final Assessment

    Examination (100%)

    • Two written papers, taken at the end of the course (May/June of Year 11.) There is no coursework. 
    • Each paper is assessed through a two-hour examination set and marked by Edexcel. In both papers a calculator is allowed. 
    • The total number of marks for each paper is 100 and both are weighted at 50% of the qualification. 
    • Two tiers of entry available: Foundation is targeted at grades C – G (4MA0/1F & 4MA0/2F)   Higher is targeted at grades A* – D (4MA0/3H & 4MA0/4H)
  • YEAR 11 - FURTHER PURE MATHEMATICS

    For students who have been accelerated and taken their International GCSE Mathematics at the end of Year 10 or during Year 11 


    Course Content

    Year 11

    • Indices, Surds and Logarithms.
    • Solving Quadratic Equations by Completing the Square and the Quadratic Formula, Functions of the roots of a Quadratic Equation.
    • Factorising Polynomials, The Remainder Theorem, Solving and Graphing Linear and Non-Linear Inequalities and Linear Programming.
    • Sketching Graphs, Exponential Functions and Solving Equations using Graphs.
    • Arithmetic and Geometric Sequences and Series.
    • The Binomial Expansion.
    • Scalars and Vectors, Vector Arithmetic and Modulus.
    • Co-ordinate Geometry, Perpendicular Gradients, Equations of Straight-Lines and Distance between Points.

    • Calculus – Differentiation (including  and the trigonometry ratios), Gradients and Stationary Points, Chain/ Product and Quotient Rules, Integration and Finding Areas under Curves, Volumes of Revolution. 
    • Trigonometry – Radian Measure, Arc Length and Area of Sectors, Graphs of the Trigonometry Ratios, Sine and Cosine Rules, 3D Problems, Using Trigonometric Identities and Solving Trigonometric Equations.

    Final Assessment

    Examination (100%)

    Two written papers, taken at the end of the course (May/June of Year 11.) There is no coursework. Each paper is assessed through a two-hour examination set and marked by Edexcel. In both papers a calculator is allowed. The total number of marks for each paper is 100 and both are weighted at 50% of the qualification. Examination codes for the two papers are (4PM0/01 & 4PM0/02).

  • YEAR 12 MATHEMATICS

    Course Content

    Students complete two modules, one compulsory Core Mathematics module and one Applied Mathematics module chosen from either Mechanics or Statistics. Both examinations are taken in May/June of Year 12.


    Core 12 Content

    • ALGEBRA - Collecting Terms & Brackets, Indices, Surds, Algebraic Fractions & Polynomials
    • QUADRATICS - Factorising, Completing the Square, the Quadratic Formula, the Discriminant & Sketching Graphs
    • EQUATIONS & INEQUALITIES - Simultaneous Equations & Inequalities
    • SKETCHING CURVES - Cubic & Reciprocal Graphs, Graphs & Simultaneous Equations & Transformations
    • COORDINATE GEOMETRY - Equation of a Straight Line & Perpendicular Gradients,  Midpoints, Distance between Coordinates & the Equation of a Circle
    • SEQUENCES AND SERIES - nth Term Formulae, Recurrence Relations, Arithmetic Sequences & Series, Geometric Sequences & Series
    • DIFFERENTIATION - Finding the Derivative, Stationary Points & Applications of Differentiation
    • INTEGRATION - Finding the Integral, Finding the Constant of the Integral, Area under a Curve and Numerical Integration
    • TRIGONOMETRY – Sine/Cosine Rules, Area of a Triangle, Trigonometric values beyond  , Trigonometric Graphs
    • TRIGONOMETRIC IDENTITIES – Identities & Solving Equations
    • EXPONENTIALS & LOGARITHMS - Exponential Graphs, Using Logarithms and Solving Equations 
    • RADIANS - Radian Measure, Arc Length & Area of a Sector
    • THE BINOMIAL EXPANSION

    Statistics 1 Content

    • MODELLING, TYPES OF DATA & AVERAGES - Mathematical Modelling, Types of Data & Averages
    • MEASURES OF SPREAD - Quartiles, Percentiles, Variance & Standard Deviation
    • REPRESENTING DATA - Stem and Leaf, Box & Whisker Diagrams, Outliers, Histograms & Analysis of Data
    • PROBABILITY - Diagrams, Conditional Probability, Tree Diagrams, Independent & Mutually Exclusive Events
    • CORRELATION - Finding the Product Moment Correlation Coefficient
    • REGRESSION - Calculating the Least Squares Regression Line, Interpreting Regression Lines
    • DISCRETE RANDOM VARIABLES - Probability Distributions, Cumulative Distribution Function, Expectation & Variance
    • THE NORMAL DISTRIBUTION - The Standard & General Normal Distributions

    Mechanics 1 Content

    • KINEMATICS IN A STRAIGHT LINE - The Constant Acceleration Formulae, Distance & Speed – Time Graphs
    • DYNAMICS - Newton’s Second Law & Friction, Inclined Planes, Connected Particles, Momentum
    • STATICS – Equilibrium & Friction
    • MOMENTS - Calculating Moments, Equilibrium & Centres of Mass
    • VECTORS - Vector Arithmetic & Using Vectors in 2D
  • YEAR 12 AND 13 FURTHER MATHEMATICS

    Course Content

    Students take Further Mathematics in addition to the standard A level.  In total, students need to take 10 different modules to obtain a full A Level in both Mathematics and Further Mathematics.  Compulsory units for Further Mathematics can be made up from any combination of the Applied Mathematics Units in Mechanics, Statistics or Decision not already used as part of the standard A Level.


    Further Pure 1 Content

    • COMPLEX NUMBERS – i, Complex Arithmetic, Argand Diagrams, Modulus-Argument, Solving Polynomials
    • NUMERICAL SOLUTIONS TO EQUATIONS – Interval Bisection, Linear Interpolation, Newton-Raphson
    • COORDINATE SYSTEMS – Parametric Equations, Parabolas, Hyperbolas, Tangents & Normals
    • ROOTS OF QUADRATICS – Using root identities to form new equations with related roots
    • MATRICES – Adding/Subtracting Matrices, Matrix Multiplication, Transformations, 2x2 Inverses, The Determinant, Solving Simultaneous Equations
    • SERIES - ∑ notation, Formulae for ∑r, ∑r2, ∑r3, more Complex Series
    • PROOF – Proof by Induction

    Further Pure 2 Content

    • INEQUALITIES – Solving by Algebraic Manipulation & Graphically
    • SERIES– Method of Differences
    • FURTHER COMPLEX NUMBERS – Euler’s Relation, De Moivre’s Theorem, Finding the nth Root, Locus of Points & Regions on Argand Diagrams, Transformations
    • FIRST ORDER DIFFERENTIAL EQUATIONS – Separation of Variables, Sketching Solution Curves, Solving Exact Equations, Solving dy/dx +Py = Q, Using Substitution 
    • SECOND ORDER DIFFERENTIAL EQUATIONS – General Solutions to a(d2y/d x2) + b(dy/dx) + cy = 0, Complementary Functions & Particular Integrals, Boundary Conditions & Specific Solutions, Using Substitution
    • MACLAURIN & TAYLOR SERIES – Finding Higher Derivatives, Expressing Functions as Infinite Series using Maclaurin’s Expansion, Composite Functions, Finding an Approximation to a Function using Taylor’s Expansion, Solving Differential Equations using the Taylor Series Method

    The remaining 4 modules of International A Level Further Mathematics can be made up from any of the following modules (not including ones already used to complete the standard A Level in Mathematics):
    Further Pure 3 Mechanics 1,2,3,4 & 5 Statistics 1,2,3,4 Decision Mathematics 1

  • YEAR 13 MATHEMATICS

    Course Content

    Students complete two modules, one compulsory Core Mathematics module and one Applied Mathematics module chosen from either Mechanics or Statistics. Both examinations are taken in May/June of Year 13.


    Core 34 Content

    • ALGEBRA – Algebraic Fractions
    • FUNCTIONS – Notation & Terminology, Domain and Range, Composite & Inverse Functions
    • Exponential & Log Functions – The Exponential Function (y =  ) & Natural Logarithms (y = lnx)
    • NUMERICAL METHODS – Approximating Roots to Equations by Change of Sign & Iterative Methods
    • TRANSFORMING GRAPHS – The Modulus Function & Sketching Transformations of Curves
    • TRIGONOMETRY – The Reciprocal & Inverse Trigonometric Functions & Associated Identities
    • FURTHER TRIGONOMETRY – Addition, Double & Factor Formulae, the Forms Rsin(x ±α) & Rcos(x±α)
    • DIFFERENTIATION – Chain, Product & Quotient Rules, Differentiating , lnx and the Trigonometric Functions, Parametric & Implicit Differentiation, Rates of Change & Differential Equations
    • PARTIAL FRACTIONS – Adding & Subtracting Partial Fractions, 2/3/Repeated Factors in the Denominator
    • COORDINATE GEOMETRY – Parametric Equations
    • BINOMIAL EXPANSIONS – Expansions with Fractional or Negative Indices & Using Partial Fractions
    • VECTORS – Vector Arithmetic, 3 Dimensions, Angle between Vectors, Vector Equation of a Line
    • INTEGRATION – Trigonometric Functions & Using Identities, By Substitution & By Parts, Numerical Integration, Areas & Volumes, Solving Differential Equations

    Statistics 2 Content

    • BINOMIAL DISTRIBUTION – Factorials, nCr, Binomial CDF, Mean & Variance
    • POISSON DISTRIBUTION – Poisson CDF, Mean & Variance, Approximating Binomial
    • CONTINUOS RANDOM VARIABLES – Probability Density Function (PDF), Cumulative Distribution Function (CDF), Mean & Variance of a PDF, Mode/Median & Quartiles
    • CONTINOUS UNIFORM DISTRIBUTION – Rectangular Distribution & its Properties
    • NORMAL APPROXMINATIONS – Approximating Poisson & Binomial, Continuity Corrections
    • POPULATION & SAMPLES – Populations, Censuses & Samples, Sampling Methods, Concept of a Statistic
    • HYPOTHESIS TESTING – Hypothesis Tests, Significance Levels, 1 & 2 Tailed Tests, Tests with Poisson & Binomial, Critical regions

    Mechanics 2 Content

    • KINEMATICS IN A STRAIGHT LINE - The Constant Acceleration Formulae in a Vertical Plane, Use of Calculus
    • CENTRES OF MASS – Finding Centres of Mass in 1D, 2D & for Uniform or Composite Laminas, Frameworks & Equilibrium
    • COLLISIONS – Impulse & Momentum, Conservation of Momentum, Restitution, Successive Impacts & Energy Changes
    • STATICS OF RIGID BODIES – Moments, Equilibrium & Limiting Equilibrium 
"As a subject in its own right, Mathematics presents frequent opportunities for creativity."