A level Mathematics Programme of Study 2025-2026
A level Mathematics
INTENT: One of the requirements of the new A-level specification is to test the content synoptically and for students to apply the knowledge they have in unfamiliar areas. Students will be aiming to ‘draw together information from different areas of the specification’ and ‘apply their knowledge and understanding in practical and theoretical contexts’. Use of calculators in exams is more important now and students will learn to use the modes and abilities of their calculator efficiently.
The course consists of material that covers both Pure and Applied Mathematics. Two thirds of the course is focused on Pure Mathematics covering subjects such as advanced algebra and calculus. One third is split evenly between statistics and mechanics. There are two versions of the program of study depending on whether the lead teacher is a statistics or mechanics specialist.
TEACHER 1 Trigonometry
● Sine and Cosine Rule
● Trigonometric graphs
● Solving equations through CAST diagrams
● Trigonometric Identities
Quadratics
● Quadratic Functions
● Simultaneous Equations
● Inequalities
Calculus –Differentiation
● From first principles
● Differentiation
● Liebnitz notation
● Linear coordinate geometry
● Tangents and Normals
TEACHER 2
Factor Theorem and Cubics
● Factor theorem
● Algebraic Long division
● Solving Cubics
Indices
● Index laws
Curve Sketching
● Sketching Cubic, quartic and reciprocal grams
● Curve sketching graph transformations
TEACHER 1 Integration
● Introduction to integration
● Reverse differentiation
Logarithms and Exponentials
● Laws of logarithms
● Solving logarithmic equations
● Solving exponential equations
Binomial Expansion
● With n as an integer
TEACHER 2
Indices and Surds
● Manipulating surds
● Rationalising a denominator
STATISTICS T1
Sampling and Definitions
● Sampling Methods
● Key definitions
● Large Data Set
Probability
● Notation
● Tree diagrams
● Venn diagrams
● Independence and Mutually exclusive
Describing Data
● Means and Standard deviation
MECHANICS T2
Forces and Units
● Standard units and basic dimensions
● Force units and balanced forces
● Resultant forces
Motion in a straight line
● Displacement time graphs
● Velocity time graphs
Constant Acceleration
● SUVAT Proof
●SUVAT equations
TEACHER 1
Calculus - Differentiation
● Maxima and minima
● Optimisation Problems
Calculus – Integration
● Areas under graphs Coordinate Geometry
● Equation of a circle
● Coordinate geometry problems
Logarithms and Exponentials
2
● e*x and ln x
● Real life exponentials Logarithmic Data
TEACHER 1
Proof
● By exhaustion
● Algebraic
● Disprove by counter example
Year 13 content
● Partial Fractions
● Radians, arc length and sectors
TEACHER 2 – Year 13 content
Calculus - Differentiation
● Differentiating trigonometry
● Differentiating ex and ln x
TEACHER 1 -Year 13 content
Numerical Methods
● Iteration
● Location of roots
● Spider and staircase diagrams
STATISTICS T1
Describing Data
● Histogram
● Means and Standard deviations
● Comparing Distributions
● Bivariate Data
Discrete Probability
● Discrete random variables
● Binomial Distribution
Hypothesis Testing Binomial hypothesis testing p-value and critical regions
T2 MECHANICS T2
Vectors
● Notation
● Magnitude
● Unit vectors
● Angles with an axis
Variable Acceleration
● Calculating displacement, velocity and acceleration using calculus
● Use of F=ma
● Cars pulling trailers
● Lifts
● Pulleys
TEACHER 1 -Year 13 content Trigonometry
● Reciprocal trigonometric functions
● Exact values Functions
● Domains and ranges
● Mapping
● Composite functions
● Inverse functions
TEACHER 2- Year 13 content
Algebraic Fractions
● Simplify
● Add, subtract, multiply and divide
Numerical Methods
● Trapezium Rule
Differentiation
Chain rule differentiating trigonometry, logarithms and exponentials.
Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction and precise statements
Understandand use mathematical language and syntax as set out in the content.
Understandand use language and symbols associated with set theory, as set out in the appendices. Apply to solutions of inequalities and probability.
Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, includingthose relating to applications of mathematics.
Recognise the underlying mathematical structureina situation and simplify and abstract appropriately to enable problems to besolved.
Construct extended arguments tosolve problems presented in an unstructured form, including problems in context.
Interpret and communicate solutions in the context of the original problem.
Evaluate, includingby making reasoned estimates, the accuracy or limitations of solutions.
Understandthe concept of a mathematical problem solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle
Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics.
Translate a situation in context into a mathematical model, making simplifying assumptions.
Use a mathematical model with suitableinputs to engage with and exploresituations (for a given model or a model constructed or selected by the student).
Interpret the outputs of amathematical model in the context of the original situation (for a given model or a model constructed or selected by the student).
Understandthat a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate.
Understandand use modelling assumptions
TEACHER 1 Trigonometry
● Sine and Cosine Rule
● Trigonometric graphs
● Solving equations through CAST diagrams
● Trigonometric Identities
Quadratics
● Quadratic Functions
● Simultaneous Equations
● Inequalities
Calculus –Differentiation
● From first principles
● Differentiation
● Liebnitz notation
● Linear coordinate geometry
● Tangents and Normals
TEACHER 2 Factor Theorem and Cubics
● Factor theorem
● Algebraic Long division
● Solving Cubics
Indices
● Index laws
Curve Sketching
● Sketching Cubic, quartic and reciprocal grams
●Curve sketching graph transformations
TEACHER 1 Integration
● Introduction to integration
● Reverse differentiation
Logarithms and Exponentials
● Laws of logarithms
● Solving logarithmic equations
● Solving exponential equations
Binomial Expansion
● With n as an integer
TEACHER 2 Indices and Surds
● Manipulating surds
● Rationalising a denominator
TEACHER 1
Calculus - Differentiation
● Maxima and minima
● Optimisation Problems
Binomial Expansion
● With n as an integer
Calculus – Integration
● Introduction to integration
● Reverse differentiation
● Areas under graphs
Coordinate Geometry
● Equation of a circle
● Coordinate geometry problems
TEACHER 1 Proof
● By exhaustion
● Algebraic
● Disprove by counter example
Year 13 content
● Partial Fractions
● Numerical Methods
● Iteration
● Location of roots
● Spider and staircase diagrams
TEACHER 2 – Year 13 content
Calculus - Differentiation
● Differentiating trigonometry
● Differentiating ex and ln x
MECHANICS T1 MECHANICS T1
Forces and Units
● Standard units and basic dimensions
● Force units and balanced forces
● Resultant forces
Motion in a straight line
● Displacement time graphs
● Velocity time graphs
Constant Acceleration
● SUVAT Proof
● SUVAT equations
Vectors
● Notation
● Magnitude
● Unit vectors
● Angles with an axis
Variable Acceleration
● Calculating displacement, velocity and acceleration using calculus
Dynamics
● Use of F=ma
Connected Particles
● Cars pulling trailers
● Lifts Pulleys
STATISTICS T2
Sampling and Definitions
● Sampling Methods
● Key definitions
● Large Data Set
Probability
● Notation
● Tree diagrams
● Venn diagrams
● Independence and Mutually exclusive
Describing Data
● Means and Standard deviations
● Comparing Distributions
STATISTICS T2
Describing Data
● Histogram
● Means and Standard deviations
● Comparing Distributions
● Bivariate Data
Discrete Probability
● Discrete random variables
STATISTICS T2
Discrete Probability
● Binomial Distribution
Hypothesis Testing
● Binomial hypothesis testing p-value and critical regions
TEACHER 1 -Year 13 content
● Radians, arc length and sectors
TEACHER 1 -Year 13 content Trigonometry
● Reciprocal trigonometric functions
● Exact values Functions
● Domains and ranges
● Mapping
● Composite functions
● Inverse functions
TEACHER 2- Year 13 content Algebraic Fractions
● Simplify
● Add, subtract, multiply and divide
Numerical Methods
● Trapezium Rule
Differentiation
Chain rule differentiating trigonometry, logarithms and exponentials.
Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction and precise statements
Understandand use mathematical language and syntax as set out in the content.
Understandand use language and symbols associated with set theory, as set out in the appendices. Apply to solutions of inequalities and probability.
Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, includingthose relating to applications of mathematics.
Recognise the underlying mathematical structureina situation and simplify and abstract appropriately to enable problems to besolved.
Construct extended arguments tosolve problems presented in an unstructured form, including problems in context.
Interpret and communicate solutions in the context of the original problem.
Evaluate, includingby making reasoned estimates, the accuracy or limitations of solutions.
Understandthe concept of a mathematical problem solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle
Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics.
Translate a situation in context into a mathematical model, making simplifying assumptions.
Use a mathematical model with suitableinputs to engage with and exploresituations (for a given model or a model constructed or selected by the student).
Interpret the outputs of amathematical model in the context of the original situation (for a given model or a model constructed or selected by the student).
Understandthat a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate.
Understandand use modelling assumptions
TEACHER 1
Trigonometry
●Additionrule
●Double angle rules
●Inverse trigonometric functions
●Identities
●R Formula
●Small angleapproximations
●Differentiation of trig from first principles
Calculus - Differentiation
●Chain, product and quotient
●Derivations of inverses
●Shapes of functions
TEACHER 2
Sequences and Series
●Recurrance relationships
●Arithmetic Sequences
●Geometric Sequences
TEACHER 1
Calculus - Integration
●Area between twocurves
●Integration by cover up
●Rational functions
●Partial fractions
●Trigonometric identities
TEACHER 1
Calculus - Integration
●By parts
●Substitution
●StandardResults
Numerical Method
●Newton Rapheson
Modulus
●Graphs
●Solving equations
TEACHER 2
Binomial Expansion with fractional and negative powers
Calculus - Differentiation
●Implicit differentiation
●Normals, tangents and turning points
STATISTICS T1
Conditional Probability
●Applied to tree diagrams and Venn diagrams
Normal Distribution
●Finding probabilities
●Working backwards
●Z values and finding mean and standard deviation
MECHANICS T2 MECHANICS T2
Statics
●At an angle
●Coefficient of friction
Dynamic
●At an angle
●Coefficient of friction
MATHS
TEACHER 1
Parametric Equations 1
●The graphs of parametric equations
●Parametric tocartesian
●Differentiating parametrics
●Integrating parametrics
Solving Differential Equations
●Connected rates of change
●Separation of variables
Vectors
●In 3D
●SUVAT
●Vectors with variable acceleration
STATISTICS T1 STATISTICS T1
Hypothesis Testing
●Normal hypothesis testing pvalue
●Correlation hypothesis testing p-value
Approximating Distributions
●Approximating Binomial with a normal distribution
●Normal distribution hypothesis testing
MECHANICS T2
Projectiles
●From ground level
●From a height
●At an angle
Moments
●Multiple pivots and suspensions
Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction; precise statements involving correct use of symbols and connecting language
Understandand use mathematical language and syntax as set out in the content.
Understandand use language and symbols associated with set theory, as set out in the appendices. Apply to solutions of inequalities and probability
Understandand use the definition of a function; domain and range of functions.
Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, includingthose relating to applications of mathematics.
Recognise the underlying mathematical structureina situation and simplify and abstract appropriately to enable problems to besolved.
Construct extended arguments tosolve problems presented in an unstructured form, including problems in context.
Interpret and communicate solutions in the context of the original problem.
Understandthat many mathematical problems cannot be solved analytically, but numerical methods permit solution to a required level of accuracy.
Evaluate, includingby making reasoned estimates, the accuracy or limitations of solutions, including those obtained using numerical methods.
Understandthe concept of a mathematical problem solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle
Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics.
Translate a situation in context into a mathematical model, making simplifying assumptions.
Use a mathematical model with suitableinputs to engage with and exploresituations (for a given model or a model constructed or selected by the student).
Interpret the outputs of amathematical model in the context of the original situation (for a given model or a model constructed or selected by the student).
Understandthat a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate. Understandand use modelling assumptions
TEACHER 1
Trigonometry
●Additionrule
●Double angle rules
●Inverse trigonometric functions
●Identities
●R Formula
●Small angleapproximations
●Differentiation of trig from first principles
Calculus - Differentiation
●Chain, product and quotient
●Derivations of inverses
●Shapes of functions
TEACHER 2
Sequences and Series
●Recurrance relationships
●Arithmetic Sequences Geometric Sequences
TEACHER 1
Calculus - Integration
●Area between twocurves
●Integration by cover up
●Rational functions
●Partial fractions
●Trigonometric identities
TEACHER 2
Binomial Expansion with fractional and negative powers
TEACHER 1
Calculus - Integration
●By parts
●Substitution
●StandardResults
TEACHER 2
Numerical Method
●Newton Rapheson
Calculus -
Differentiation
●Implicit differentiation
●Normals, tangents and turning points
Modulus
●Graphs
●Solving equations
Statics
●At an angle
●Coefficient of friction
Dynamic
●At an angle Coefficient of friction
Vectors
●In 3D
●SUVAT
●Vectors with variable acceleration
Conditional Probability
●Applied to tree diagrams and Venn diagrams
Normal Distribution
●Finding probabilities
●Working backwards
●Z values and finding mean and standard deviation
Projectiles
●From ground level
●From a height
●At an angle
Moments
Multiple pivots and suspensions
TEACHER 1
Parametric Equations 2
●Differentiating parametric
●Integrating parametric
Solving Differential Equations
●Connected rates of change
●Separation of variables
TEACHER 2
Proof
Proof by contradiction
Revision
Approximating
Distributions
●Approximating Binomial with a normal distribution
●Normal distribution hypothesis testing
Construct and present mathematical arguments through appropriate use of diagrams; sketching graphs; logical deduction; precise statements involving correct use of symbols and connecting language
Understandand use mathematical language and syntax as set out in the content.
Understandand use language and symbols associated with set theory, as set out in the appendices. Apply to solutions of inequalities and probability
Understandand use the definition of a function; domain and range of functions.
Comprehend and critique mathematical arguments, proofs and justifications of methods and formulae, includingthose relating to applications of mathematics.
Recognise the underlying mathematical structureina situation and simplify and abstract appropriately to enable problems to besolved.
Construct extended arguments tosolve problems presented in an unstructured form, including problems in context.
Interpret and communicate solutions in the context of the original problem.
Understandthat many mathematical problems cannot be solved analytically, but numerical methods permit solution to a required level of accuracy.
Evaluate, includingby making reasoned estimates, the accuracy or limitations of solutions, including those obtained using numerical methods.
Understandthe concept of a mathematical problem solving cycle, including specifying the problem, collecting information, processing and representing information and interpreting results, which may identify the need to repeat the cycle
Understand, interpret and extract information from diagrams and construct mathematical diagrams to solve problems, including in mechanics.
Translate a situation in context into a mathematical model, making simplifying assumptions.
Use a mathematical model with suitableinputs to engage with and exploresituations (for a given model or a model constructed or selected by the student).
Interpret the outputs of amathematical model in the context of the original situation (for a given model or a model constructed or selected by the student).
Understandthat a mathematical model can be refined by considering its outputs and simplifying assumptions; evaluate whether the model is appropriate.
Understandand use modelling assumptions