# Mathematics A Level at St Francis of Assisi Catholic Technology College

## Course description

Mathematics at AS and A level is a course worth studying in its own right. It is intellectually stimulating, challenging but interesting. It builds on work you will have met at GCSE, but also involves new ideas that some of the greatest minds in history have produced. It serves as a very useful support for many other qualifications as well as being a sought-after qualification for the workplace and courses in Higher Education.

While studying Mathematics you will be expected to:

- Use mathematical skills and knowledge to solve problems.

- Solve quite complicated problems by using mathematical arguments and logic.

- You will also have to understand and demonstrate what is meant by proof in mathematics.

- Simplify real life situations so that you can use mathematics to model what is happening and what might happen in different circumstances.

- Use the mathematics that you learn to solve problems that are given to you in a real-life context.

- Use calculator technology, computers and other resources (such as formulae booklets or statistical tables) effectively and appropriately; understand its limitations and when it is inappropriate to use such technology.

- Statistically analyse large data sets.

## Course content

Mathematics at AS and A level at St. Francis of Assisi is divided into several branches:

Core Mathematics

When studying Core Mathematics at AS and A2 level you will be extending your knowledge of such topics as algebra and trigonometry as well as learning some brand new ideas such as calculus. If you enjoyed the challenge of problem solving at GCSE using such mathematical techniques then you should find the prospect of this course very appealing. Key content includes:

- y = ex and y = ln x including (informally) differentiating y = ekx

- use of exponential growth and decay in modelling

- use of logarithmic graphs to estimate parameters in relationships of the form y = axn and y = kbx

- differentiation from first principles

- vectors in 2D

- proof by contradiction (including specific examples of irrationality of √2 and infinity of primes)

- use of functions in modelling, including consideration of limitations and refinements of models

- small angle approximations for sin, cos and tan

- exact values for sin, cos and tan

- proofs of addition formulae

- find your own substitutions for integration

- Newton-Raphson method

- trapezium rule

You will also study two applied modules; Statistics and Mechanics.

Statistics

When you study Statistics you will learn how to analyse and summarise numerical data in order to arrive at conclusions about it. You will extend the range of probability problems that you started for GCSE by using the new mathematical techniques studied
on the Core Mathematics course. Key content includes:

- sampling techniques

- interpreting diagrams

- interpreting regression lines

- measures of central tendency and variation, including calculating standard deviation

- binomial distribution as a model

- hypothesis testing using binomial model

- use of large data sets (may be provided by exam boards); use of technology to explore/interpret them

- conditional probability, Venn diagrams

- modelling with probability

- the normal distribution

- hypothesis testing with correlation coefficients

- hypothesis tests for the mean of a Normal distribution with known, given or assumed variance

- interpretation in context

Mechanics

When you study Mechanics you will learn how to describe mathematically the motion of objects and how they respond to forces acting upon them, from cars in the street to satellites revolving around a planet. You will learn the technique of mathematical modelling;
that is, of turning a complicated physical problem into a simpler one that can be analysed and solved using mathematical methods. Key content includes:

- vectors in 2D

- suvat equations

- displacement/time and Velocity/time graphs, gradients and areas

- use calculus in kinematics

- Newton’s laws

- motion in a straight line, including motion under gravity

- equilibrium (simple cases)

- projectile motion

- resolving forces

- dynamics for motion in a plane

- friction

- moments in simple static contexts

## Entry requirements

You will be expected to have achieved at least a grade 6 in your GCSE Mathematics. The demands of the course require a very strong mathematical ability.

## Future opportunities

AS level Mathematics is very valuable as a supporting subject to many courses at A level and degree level, especially in the sciences, geography, psychology and medical courses.

A Level Mathematics is a much sought-after qualification for entry to a wide variety of full-time courses in Higher Education. There are also many areas of employment that see a Mathematics A level as an important qualification and it is often a requirement for the vocational qualifications related to these areas. Higher Education courses or careers that either require A Level Mathematics or are strongly related, include:

- Economics

- Medicine

- Architecture

- Engineering

- Accountancy

- Teaching

- Psychology

- Environmental Studies

- Computing

- Information Communication Technology

If you wanted to continue your study of Mathematics after A levels you could follow a course in Mathematics at degree level or even continue further as a postgraduate and get involved in mathematical research.

## How to apply

If you want to apply for this course, you will need to contact St Francis of Assisi Catholic Technology College directly.