## Why do we learn further maths?

Further maths is a challenging and rigorous A level, moving at a fast pace. We cover the A level Maths curriculum in year 12 and the Further Maths curriculum in year 13. This allows us to be flexible in the modules with teach to the FM students in year 13, tailoring them to the strengths and ambitions of the students.

## Our approach

We follow broadly the sequencing of the Pearson Edexcel textbooks, progressing the topics in order of approximate difficulty. This lets the students take ownership of their learning, as they know exactly what is coming up, and have a permenant bank of examples and practice questions.

We wrap the content of each topic into "fertile question" equiries, each of which is phrased to emphasise the key idea behind the mathematics. The connects the theme of the topic to a wider context, challenging and motivating the students.

All of our teachers teach everything. We want our students to be fully immersed in one topic at a time, and we want our teacher to all be able to support students across the whole curriculum.

We push our students by running a maths society each week, DIGITS, in which both teachers and students present and discuss extra curricular ideas. We run trips to Bletchley Park and enter Ritangle and UKMT competitions. In addition, we support students in preparing to take university entrance exams such as STEP and MAT.

## Head of Department

## Ms Burney

## Year 12

Autumn 1 | Autumn 2 |
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What makes a stand out function? How does changing the power of x change an equation? How are models of growth and decay related? What can calculus tell us about a function? How does maths get you to the moon? Do sin, cos and tan have hidden identities? Is it possible to differentiate and integrate all functions? What does it mean to prove something? | |

Functions and Modulus Binomial Expansion Exponentials and Logarithms Introduction to Calculus |
Trigonometric Identities Further Calculus Proof |

Spring 1 | Spring 2 |
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How many ways are there to represent a vector? How might an understanding of forces help a sportsperson? What is the kinematics behind cricket? How many ways can you balance a pencil? How does an engineer design a stable structure? Can sample of weather tell us about long term trends? How accurately can mathematics predict black swan events? How do statisticians test a hypothesis? How can we model the height of a population? | |

Vectors Forces Kinematics in one and two dimensions Moments |
Statistics Probability Hypothesis testing Probability distributions |

Summer 1 | Summer 2 |
---|---|

What is a better name - complex numbers or imaginary numbers? How do computers do mathematics? What is the cheekiest trick in mathematics? | |

Complex Numbers Matrices Proof by induction |
Revision End of year exams |

## Year 13

Autumn 1 | Autumn 2 |
---|---|

How did Leibniz help start a revolution? How can vectors help us handle three dimensions? What's the most beautiful equation in maths? When are Cartesian coordinates not the best frame of reference? What exactly do hyperbolic and trigonometric functions have in common Gibt es andere Methoden in der Infinitesimalrechnung? What does harmony have to do with differential equations? What does it mean for a car to have horsepower? What does the coefficient of restitution say about a ball? | |

Volumn of revolution Vectors in three dimensions Maclaurin series Further complex numbers Hyperbolic functions Indefinite integrals |
First and second order differential equations Work, energy and power Collisions in one and two dimensions |

Spring 1 | Spring 2 |
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How far does a spring extend? How far can the Poisson distribution help hospitals plan shifts? How many cards do I need to pick before I get four aces? How likely is it that the sample accurately represents the population? | |

Springs and strings Poisson, geometric, negative binomial distributions |
Chi squared test Central limit theorem Probability generating functions Revision Mock Exams |

Summer 1 | Summer 2 |
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Revision | Exams |