Further Maths

What is Mathematics and Further Mathematics?

Mathematics and Further Mathematics is a more challenging double A level, designed for students with a love of, and talent for mathematics. It is a comprehensive and in-depth study of mathematical concepts, covering a wide range of topics comprising algebra, calculus, statistics, and mechanics. This course is an excellent opportunity to enhance your problem-solving skills, add depth to your prior GCSE knowledge and discover new mathematical concepts. You should choose maths if you enjoy being challenged, if you feel the reward from persevering until you find a solution and you want to further develop your logical thinking skills.

What will I study?

Year 12

Students study the full A level Mathematics course in year 12 and take the exam at the end of the year. The biggest component of the course is pure mathematics, developing your skills in algebra is key to being able to access the vast majority of the content including trigonometry and new topics such as calculus. You’ll learn the application of statistical and probability models which allow for analysis in real world contexts. We also look at the use of technology when analysing large sets of data. Finally, you’ll study mechanics, the mathematics of forces and motion, which will build on prior knowledge from GCSE Physics.

The main topics in the specification are listed below:

• Proof
• Algebra and functions
• Coordinate geometry in the plane
• Sequences and series
• Trigonometry
• Exponentials and logarithms
• Differentiation
• Integration
• Numerical methods
• Vectors
• Statistical sampling
• Data presentation and interpretation
• Probability
• Statistical distributions
• Statistical hypothesis testing
• Quantities and units in mechanics
• Kinematics
• Forces and Newton’s laws
• Moments

Year 13

These concepts are extended and new ideas, such as complex numbers, matrices and hyperbolic functions are introduced to complete the A level Further Mathematics course.

• Proof
• Complex numbers
• Matrices
• Further algebra and functions
• Further calculus
• Further vectors
• Polar coordinates
• Hyperbolic functions
• Differential equations
• Numerical methods
• Dimensional analysis
• Momentum and collisions
• Work, energy and power
• Circular motion
• Centres of mass and moments
• Discrete random variables (DRVs) and expectation
• Poisson distribution
• Continuous random variables (CRVs)
• Chi squared tests for association
• Exponential distribution
• Inference – one sample t – distribution
• Confidence Intervals

Assessments

There are three exams at the end of each year, each exam is two hours long.

Year 12

Paper 1 – Pure Mathematics

Paper 2 – Pure Mathematics and Mechanics

Paper 3 – Pure Mathematics and Statistics

Year 13

Paper 1 – Pure Mathematics

Paper 2 – Pure Mathematics

Paper 3 – Mechanics and Statistics

Trips, visits and enrichments:

• Experience inspiring maths speakers presenting mathematics live in the context of exciting, real-world applications at Maths Inspiration lecture shows and Maths Fest.
• UKMT Senior Maths Challenge, British Mathematical Olympiad, Olympiad for Girls and other regional challenges run each year.
• We also offer enrichments including the Cipher Challenge and Ritangle competition.

What can it lead to?

A-Level Mathematics and Further Mathematics is highly regarded and is a prerequisite for many university courses, particularly in science, technology, engineering, and mathematics (STEM) fields. It is known for its challenging curriculum, fostering critical thinking, problem-solving skills, and mathematical fluency, making it a valuable foundation for higher education and future careers.

Mathematics plays a fundamental role in various aspects of our lives, society, and the world at large. These are some key areas where mathematics plays on important role:

• Problem Solving: Mathematics equips individuals with essential problem-solving skills. It encourages logical thinking and teaches us how to break down complex issues into smaller, manageable parts.
• Scientific Advancement: Mathematics is the language of science. It underpins nearly all scientific disciplines, from physics and chemistry to biology and economics, enabling researchers to formulate hypotheses, analyse data, and make predictions.
• Technological Innovation: The development of technology and innovation heavily relies on mathematics. Everything from computer programming and software development to engineering and artificial intelligence requires a strong mathematical foundation.
• Economic and Financial Literacy: Understanding mathematical concepts like budgeting, interest rates, and statistics is crucial for personal financial management. On a broader scale, mathematical models and analyses are essential for making informed economic and financial decisions.
• Medical Research and Healthcare: Mathematical models are used in epidemiology to track the spread of diseases, in medical imaging for diagnosis, and in drug development for analysing clinical trial data.
• Engineering and Architecture: Engineers and architects use mathematics to design structures, analyse stress and load distributions, and ensure the safety and efficiency of buildings and infrastructure.
• Environmental Studies: Mathematics is used to model and analyse environmental data, such as climate change predictions, air and water quality assessments, and ecological studies.
• Data Analysis: In an age of big data, mathematics is essential for processing, analysing, and extracting meaningful insights from large datasets, which is crucial in fields like marketing, social sciences, and business.
• Global Challenges: Many global challenges, such as addressing climate change, managing resources, and planning sustainable cities, require mathematical modelling and analysis to find solutions.

Further Maths can only be studied as part of a four-subject programme, alongside Mathematics and two other subjects.