8-Week Weekly Breakdown (2 lessons per week, 1 hour each)

Each session:

• 30 minutes Maths (Edexcel A Level)
• 30 minutes Physics (AQA A Level)

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Week 1

Maths:
Topic: Algebraic Methods – Partial Fractions & Functions
Learning Objectives:

• Use partial fraction decomposition to simplify rational expressions.
• Understand function notation and composition.
• Relate algebraic manipulation to real-world modelling.
  Activities:
• Guided practice decomposing complex rational expressions into partial fractions.
• Function transformation and composition exercises linked to problem-solving contexts.
• Exam technique tip: recognising functional inverses and domains in applied questions.
  National Curriculum Reference:
• Edexcel A Level Maths Content Domain: Pure Mathematics - Algebra, functions and equations (NSa1, NSa3)

Physics:
Topic: Mechanics – Forces and Motion (Newton's Laws)
Learning Objectives:

• Recall and apply Newton’s three laws of motion.
• Use free body diagrams to analyse forces on objects in equilibrium and motion.
• Solve problems involving resultant forces and acceleration.
  Activities:
• Draw and interpret free-body diagrams for multiple force scenarios.
• Solve numerical problems combining vectors and Newton’s laws.
• Exam tip: Identify which law applies to the scenario and check units meticulously.
  National Curriculum Reference:
• AQA Physics Topic 5.1 & 5.2 (Forces, Newton’s Laws - A Level specification)

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Week 2

Maths:
Topic: Coordinate Geometry – Circles and Tangents
Learning Objectives:

• Derive equations of circles and find equations of tangents.
• Understand geometric loci and intersection points between lines and circles.
  Activities:
• Work through circle equation problems involving centre-radius form.
• Practice tangent line calculations, including perpendicularity conditions.
• Exam technique tip: Writing precise steps for equation rearrangement to avoid algebraic slip-ups.
  National Curriculum Reference:
• Edexcel A Level Maths: Geometry & Measures (NC1, NGf)

Physics:
Topic: Kinematics – SUVAT Equations and Graph Analysis
Learning Objectives:

• Use SUVAT equations in solving linear motion problems.
• Interpret velocity-time and displacement-time graphs.
  Activities:
• Apply SUVAT formulae to problems with constant acceleration.
• Analyse graphs to determine acceleration, displacement, and velocity.
• Exam technique tip: Carefully define variables before solving; consider sign conventions.
  National Curriculum Reference:
• AQA Physics Topic 5.3 & 5.4 (Kinematics - A Level specification)

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Week 3

Maths:
Topic: Differentiation – Techniques and Applications
Learning Objectives:

• Differentiate polynomials, products, quotients, and composite functions.
• Apply differentiation to find gradients, stationary points, and optimisation problems.
  Activities:
• Stepwise differentiation exercises using formal rules.
• Solve problems involving maxima, minima, and points of inflection.
• Exam tip: Check differentiation steps by substitution to reduce careless errors.
  National Curriculum Reference:
• Edexcel A Level Pure Maths: Calculus (NSb1, NSb2)

Physics:
Topic: Dynamics – Work, Energy and Power
Learning Objectives:

• Understand and use work done by a force, kinetic and potential energy concepts.
• Apply conservation of energy principle to solving problems.
  Activities:
• Calculate work done in various force contexts; kinetic-potential energy problem-solving.
• Discuss real-world examples such as rollercoasters or pendulums.
• Exam technique tip: Write down energy conservation equations clearly before manipulating.
  National Curriculum Reference:
• AQA Physics Topic 5.5 & 5.6 (Work, Energy and Power)

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Week 4

Maths:
Topic: Integration – Techniques and Problem Solving
Learning Objectives:

• Integrate polynomials and basic composite functions using substitution.
• Calculate areas under curves and interpret integration in physics context.
  Activities:
• Practise definite and indefinite integrals.
• Apply integration to find displacement given velocity functions.
• Exam technique tip: Always state constants of integration unless dealing with definite integrals.
  National Curriculum Reference:
• Edexcel A Level Calculus (NSc1, NSc2)

Physics:
Topic: Circular Motion – Uniform Circular Motion and Forces
Learning Objectives:

• Understand velocity, acceleration, and forces acting in circular motion.
• Calculate centripetal force and acceleration.
  Activities:
• Solve quantitative problems on uniform circular motion (e.g., cars on bends).
• Sketch force diagrams and interpret resultant forces directionality.
• Exam tip: Keep track of vector directions and make clear diagrams for clarity.
  National Curriculum Reference:
• AQA Physics Topics 5.7 (Circular Motion)

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Week 5

Maths:
Topic: Vectors – Geometry and Applications
Learning Objectives:

• Perform vector operations and understand geometric interpretations.
• Use vectors in solving geometry problems including lines and planes.
  Activities:
• Vector addition, scalar multiplication, and dot product practice.
• Solve problems finding angles and distances using vectors.
• Exam technique tip: Always write vectors in component form before calculations.
  National Curriculum Reference:
• Edexcel A Level Vectors (NSe1)

Physics:
Topic: Oscillations – Simple Harmonic Motion (SHM)
Learning Objectives:

• Describe characteristics of SHM and its equations.
• Solve problems involving displacement, velocity, and acceleration in SHM.
  Activities:
• Use SHM formula to model physical systems such as springs.
• Sketch displacement, velocity, and acceleration graphs against time.
• Exam tip: Remember phase relationships between quantities in SHM questions.
  National Curriculum Reference:
• AQA Physics Topic 6.1 (Oscillations)

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Week 6

Maths:
Topic: Exponentials and Logarithms
Learning Objectives:

• Manipulate exponential and logarithmic expressions and solve related equations.
• Use exponential growth and decay models relevant in physics contexts.
  Activities:
• Solve equations involving e^x and log functions.
• Apply growth and decay formulae to example problems (e.g., radioactive decay).
• Exam tip: Pay attention to the base of logarithm; clarify domain restrictions.
  National Curriculum Reference:
• Edexcel Pure Maths – Exponentials and Logarithms (NSe3)

Physics:
Topic: Thermal Physics – Kinetic Theory and Ideal Gases
Learning Objectives:

• Explain the principles of kinetic theory of gases.
• Use the ideal gas equation in various problem scenarios.
  Activities:
• Interpret PV=nRT problems, including unit conversions.
• Discuss real gas limitations and link to microscopic theory.
• Exam technique tip: Don't confuse state variables; always include units in final answers.
  National Curriculum Reference:
• AQA Physics Topic 7.1 (Thermal Physics)

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Week 7

Maths:
Topic: Differential Equations – First Order
Learning Objectives:

• Solve simple separable first-order differential equations.
• Apply to modelling growth and decay processes.
  Activities:
• Work through integrating factor and separation of variables methods.
• Model physics problems such as cooling or radioactive decay.
• Exam tip: Show all algebraic manipulation clearly and justify integration steps.
  National Curriculum Reference:
• Edexcel Calculus Applications (NSc3)

Physics:
Topic: Electric Circuits – Current, Potential Difference, and Resistance
Learning Objectives:

• Understand circuit components and their behaviour.
• Use Ohm’s law and combinations of resistors in circuits.
  Activities:
• Analyse series and parallel circuits.
• Calculate total resistance, current distribution and voltage drops.
• Exam tip: Draw labelled circuit diagrams; annotate values to assist problem solving.
  National Curriculum Reference:
• AQA Physics Topic 8.1 & 8.2 (Electricity)

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Week 8

Maths:
Topic: Probability and Statistics – Binomial and Normal Distributions
Learning Objectives:

• Understand binomial distribution formulas and their applications.
• Use normal distribution to calculate probabilities and percentiles.
  Activities:
• Worked examples calculating binomial probabilities and cumulative distributions.
• Apply normal approximation to binomial distribution questions.
• Exam technique tip: Clearly define the random variable and set up probability statements.
  National Curriculum Reference:
• Edexcel Statistics – Discrete and Continuous Distributions (NSp1, NSp2)

Physics:
Topic: Nuclear Physics – Radioactivity and Half-Life
Learning Objectives:

• Describe radioactive decay and the concept of half-life.
• Solve problems involving exponential decay and activity.
  Activities:
• Calculate remaining nuclei over time using decay formula.
• Discuss practical applications and safety of nuclear physics.
• Exam tip: Convert units to seconds or years consistently when calculating half-life.
  National Curriculum Reference:
• AQA Physics Topic 8.6 (Nuclear Physics)

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End of Plan

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Additional Notes for Tutors:

• Begin each lesson with a 5-minute recap quiz from prior week topics to boost retention.
• Encourage linking Maths techniques directly with Physics models to foster interdisciplinary understanding.
• Use past paper exam questions regularly for both subjects, focusing on mark scheme language and exam strategies.
• Allocate time for reflection and questions at the end of each lesson segment to check comprehension.

By weaving together core Edexcel Maths and AQA Physics topics and embedding exam technique practice, this plan aims to elevate comprehensive understanding and exam confidence for Year 12 & 13 students, fully aligned with the National Curriculum (England).