At this 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 and logarithms. There is a balance between the
development of new ideas as an end in itself, and the emergence of these ideas
in the solution of actual problems. A concept that appears at first sight
rather abstract often has a surprisingly powerful role to play in the solution to
a real-world problem, and likewise mathematical ideas developed in the solution
of a problem can acquire a fascinating life of their own outside the context of
the original problem. It is the balance between these approaches that provides
so much of the intrigue and creativity in the study of Pure Mathematics.
At School level, Applied
Mathematics is divided between the areas of Mechanics, Statistics and Decision
In 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 mathematical modelling; that is, how to turn a complicated physical
problem into a simpler one that can be analysed and solved using mathematical
In the AS Mechanics module (M1), sophisticated
mathematical ideas such as calculus and vectors are used to describe simplified
mechanical situations and Newton’s laws of motion are used to analyse them and
make predictions about their future behaviour.
The A2 Mechanics module (M2) is an extension of these ideas, and gives a
taste of the structure of more advanced mathematical modelling, where concepts
are introduced because they turn out to be very helpful rather than obviously
The two Mechanics modules are an excellent choice
for girls studying Physics at A-level, and also for those wishing to pursue
further study in Physics or Structural/Mechanical Engineering beyond the Sixth Form.
In Statistics you will learn how to analyse and
summarise numerical data in order to arrive at conclusions about it, such as
judging whether an observed pattern in an experiment could most likely be
attributable to coincidence, or whether it is perhaps a reflection of some
underlying relationship. You will extend the work begun for IGCSE by using new
mathematical techniques studied in the Pure Mathematics course.
In the AS level module (S1), topics such as
Probability Distributions, Correlation and Regression and the Theory of
Probability are developed, while in the A2 module (S2), this work is extended
to cover more sophisticated distributions and continuous Random Variables.
The Statistics modules are helpful for any girl
wishing to pursue further study of the Life Sciences, Psychology or Economics
beyond the Sixth Form.
In Year 13 girls get the option to study a module
in Decision Mathematics (D1). This is a very modern branch of the subject and
covers ideas such as how to order alphabetically or numerically large amounts
of data (and how to judge the relative efficiency of these methods), how best
to traverse a network series of different places and how to maximise business
profits subject to constraints such as the availability of raw materials and
labour costs. This module gives a taste of the kind of reasoning and
mathematical ideas that would be encountered in the further study of Computer
Science or Operational Research beyond the Sixth Form.
Further Mathematics can
only be studied in addition to Mathematics, so it requires girls to devote two
of their AS option choices to the subject area, one choice being Mathematics,
the other choice being Further Mathematics.
Full details of the
Mathematics course can be found in the relevant section and should be read
first, before continuing with this section.
Mathematics and Further
Mathematics is an option combination that girls who wish to study Mathematics
at university should seriously consider following (although it is not
necessarily a prerequisite for such study), as should anyone wishing to study Maths,
Physics, Engineering or Economics at the very top universities.
It is a demanding course
of study that requires a capacity for abstract reasoning as well as very strong
algebraic skills, However, it is highly rewarding for those who choose to
Girls studying the
single-subject Mathematics option must complete six modules by the end of Year
13: the four compulsory Pure modules and two elective Applied ones. In both of Years
12 and 13 this study is completed over four lessons per week, with two
During both Year 12 and
Year 13, girls choosing the Mathematics and Further Mathematics options will
receive eight lessons per week, delivered by four different teachers, and complete
six modules in each year. This is exactly double the amount of teaching time,
and twice the number of modules studied.
During Year 12, girls
choosing the Mathematics and Further Mathematics options study three of the
four Pure Mathematics modules that are compulsory for the single Mathematics
award. They will also study the AS Statistics (S1) and the AS Mechanics (M1)
modules. The sixth module studied is the Further Pure Mathematics 1 module,
which explores some more unusual concepts and ideas (such as Matrices and
Complex numbers) that are not covered anywhere in the single-subject syllabus.
This module is an AS level one, and is not necessarily harder than the other AS
During Year 13, girls must complete another
six modules, one of which is the remaining Pure Module that is necessary for
the single-subject course, another of which is Further Pure Mathematics 2, a
more advanced Pure Maths module in which the mathematics gets considerably more
sophisticated and difficult, and more interesting! The remaining four modules
required for the Further Maths A2 qualification are elective (from M2, M3, S2,
S3, FP3, D1, D2), and we are able to deliver almost any combination of Applied
modules that a girl may wish to follow.