**Subject**: Mathematics

Mathematics in years 12 and 13 at Paddington builds on students’ prior knowledge gained at key stage 4 such as coordinate geometry, trigonometry and sequences and series, deepening their understanding and connecting different aspects of Mathematics. Fundamental new concepts are introduced such as calculus. There is a strong emphasis on the use of logical deduction to solve problems, and the course is embedded with opportunities to apply their knowledge to the real world. The course is divided into Pure and Applied Mathematics, providing students with statistical and mechanical methods.

Further Mathematics (an additional A level) introduces new branches of mathematics such as complex numbers and differential equations, within which students begin to learn the deeper connections underlying mathematics. In addition to Further Pure Mathematics, students develop a deeper knowledge of methods in Statistics and Mechanics, providing more sophisticated tools to understand the world around them.

- Algebraic expressions, quadratic graphs, vectors in 2-D, straight-line graphs, modelling in mechanics, constant acceleration, equations and inequalities.
- Graphs and transformations, circles, algebraic methods and proof, binomial expansion, trigonometric ratios, forces and motion, differentiation.
- Trigonometric identities and equations, integration, variable acceleration, exponentials and logarithms, sequences and series.

- Radians, functions and graphs, regression and correlation, trigonometric functions, trigonometry and modelling.
- Differentiation, conditional probability, integration, parametric equations, numerical methods.
- The normal distribution, further calculus, vectors in 3-D.

**Students taking A Level Further Mathematics will study all the Single Maths content listed above in Year 12, and then in Year 13 they will study:**

- Core Pure Mathematics: Complex numbers, methods in calculus, series, differential equations, matrix algebra, proof, polar coordinates, hyperbolic functions, volumes of revolution.
- Further Statistics 1: Statistical distributions (Binomial, Poisson, Geometric, Negative binomial, normal), further hypothesis testing and test evaluation, probability generating functions.
- Further Mechanics 1: Momentum and impulse, work, power and energy, elastic collisions in 1 and 2 dimensions.

At Paddington, all students will receive regular feedback from formative assessment tasks. Within the curriculum, specific tasks are allocated for feedback. This ensures all students gain regular feedback. Teachers will mark student work and provide targeted feedback that enables students to improve their work and make progress. To support student understanding, teachers plan high-quality re-teach time to prepare students for their feedback. Across each term, students will receive feedback from multiple tasks.

**Exam board:** Edexcel

A Level Mathematics – 3 papers are sat at the end of year 13. Each paper is worth 1/3 of the total marks.

- Pure 1: 100 marks (120 minutes)
- Pure 2: 100 marks (120 minutes)
- Statistics and Mechanics: 100 marks (120 minutes)

A Level Further Mathematics – 4 papers are sat at the end of year 13. Each paper is worth 1/4 of the total marks.

- Core Pure 1: 75 marks (90 minutes)
- Core Pure 2: 75 marks (90 minutes)
- Further Statistics 1: 75 marks (90 minutes)
- Further Mechanics 1: 75 marks (90 minutes)

- Course textbooks available to borrow from school - they contain exam questions and examples to support all the learning.
- Homework booklets - weekly retrieval practice of pure and applied knowledge
- DrFrostMaths.com for retrieval practice / exam questions / videos to support
- https://sites.google.com/view/tlmaths/home TLMaths - video walkthroughs covering examples for the entire A Level and Further Maths A Level specification.
- Knowledge organisers provided by school
- Online student folders of extra practice questions.

Extension opportunities are also provided at KS5, with support for the UKMT Senior Maths Challenge and MAT/STEP guidance.

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