Mathematics at ‘A’ Level at Ashbourne College
Why study Mathematics?
Mathematics at AS and A2 level is both challenging and demanding. It is fundamentally different from the study of Mathematics at GCSE requiring strong skills in algebraic manipulation and a disciplined approach to study. Students who opt for A level Mathematics often choose it in conjunction with two sciences selected from either Physics, Chemistry or Biology. However many
others select it alongside other subjects such as Statistics, Accounts, Economics, Computer Studies or Information technology. Students wishing to pursue a degree course in the sciences, medicine, business, economics, accounting, engineering or computing (as well of course as mathematics or statistics) will find Mathematics at AS and A2 Level useful, if not indeed,
essential.
Prerequisites
Students intending to study Mathematics at AS and A2 Level should ideally possess A*, A or B at GCSE Higher Level. However it is possible for a student with a grade C at intermediate level to be successful in their study of A Level Mathematics. Success in this subject is achieved by students who adopt a consistent work pattern and who are capable of reworking assignments
until they are of an appropriate standard. Students who have a tendency to ‘cram at the last minute’ are usually unsuccessful in this subject.
Course Content and Design
The course is designed for the Edexcel specification but contains topics common to the core specification of other major boards. The objectives of the examination are to test student proficiency in the following options: Pure Mathematics; Statistics; Mechanics and Decision Mathematics.
Pure Mathematics involves a great deal of algebraic processing skills involving
solving quadratic equations and further polynomials. Great emphasis is placed upon curve sketching. Geometry, trigonometry and various numerical techniques are all studied at A Level.
Statistics involves the study of probability and various methods of representing sample data. The student will also study discrete and continuous distribution.
Mechanics is based upon particle
motion and kinematics and therefore a good grade at GCSE, whilst desirable, is not essentia.l Students will receive tuition in all types of examination question, whether short answer questions, source based stimulus response questions or essays and techniques in preparing for and answering compulsory questions. All sixth form students can expect a minimum of 6 hours of classroom tuition, plus 2 X one-hour test periods per week.
The Programme
The programme consists of an examination of the relevant areas of the specification, a summary of the key facts and principles relevant to the area under study, past paper questions and reference, where instructive, to the Chief Examiner’s Reports. Students study three modules for an AS in their first year and a further three in their second year for the full A level. Retake and Upper sixth students will follow the old specification. Students will regularly receive modest amounts of homework between lessons as well as one or two substantial pieces of homework based on previous past papers per week.
The 20 units have been designed to produce Advanced Subsidiary and Advanced GCE examinations which enable schools and colleges to provide courses which will encourage candidates to:
a) develop their understanding of mathematics and mathematical processes in a way that promotes confidence and fosters enjoyment
b) develop abilities to reason logically and recognise incorrect reasoning, to generalise and to construct mathematical proofs
c) extend their range of mathematical skills and techniques and use them in more difficult, unstructured problems
d) develop an understanding of coherence and progression in mathematics and of how different areas of mathematics can be connected
e) recognise how a situation may be represented mathematically and understand the relationship between ‘real-world’ problems and standard and other mathematical models and how these can be refined and improved
f) use mathematics as an effective means of communication
g) read and comprehend mathematical arguments and articles concerning applications of mathematics
h) acquire the skills needed to use technology such as calculators and computers effectively, recognise when such use may be inappropriate and be aware of limitations
i) develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general
j) take increasing responsibility for their own learning and the evaluation of their own mathematical development.
Specification Content
C1 Algebra and functions; coordinate geometry in the ( x , y) y plane; sequences and series; differentiation; integration.
C2 Algebra and functions; coordinate geometry in the ( x , y) y plane; sequences and series; trigonometry; exponentials and logarithms; differentiation; integration.
C3 Algebra and functions; trigonometry; exponentials and logarithms; differentiation; numerical methods.
C4 Algebra and functions; coordinate geometry in the ( x , y) y plane; sequences and series; differentiation; integration; vectors.
Further Pure Mathematics
Unit Summary of unit content
FP1 Series; complex numbers; numerical solution of equations; coordinate systems, matrix algebra, proof.
FP2 Inequalities; series, first order differential equations; second order differential equations; further complex numbers, Maclaurin and Taylor series.
FP3 Further matrix algebra; vectors, hyperbolic functions; differentiation; integration, further coordinate systems.
Mechanics
Unit Summary of unit content
M1 Mathematical models in mechanics; vectors in mechanics; kinematics of a particle moving in a straight line; dynamics of a particle moving in a straight line or plane; statics of a particle; moments.
M2 Kinematics of a particle moving in a straight line or plane; centres of mass; work and energy; collisions; statics of rigid bodies.
M3 Further kinematics; elastic strings and springs; further dynamics; motion in a circle; statics of rigid bodies.
M4 Relative motion; elastic collisions in two dimensions; further motion of particles in one dimension; stability.
M5 Applications of vectors in mechanics; variable mass; moments of inertia of a rigid body; rotation of a rigid body about a fixed smooth axis.
Statistics Unit
Summary of unit content
S1 Mathematical models in probability and statistics; representation and summary of data; probability; correlation and regression; discrete random variables; discrete distributions; the Normal distribution.
S2 The Binomial and Poisson distributions; continuous random variables; continuous distributions; samples; hypothesis tests.
S3 Combinations of random variables; sampling; estimation, confi dence intervals and tests; goodness of fi t and contingency tables; regression and correlation.
S4 Quality of tests and estimators; one-sample procedures; two-sample procedures.
Decision Mathematics
Unit Summary of unit content
D1 Algorithms; algorithms on graphs; the route inspection problem; critical path analysis; linear programming; matchings.
D2 Transportation problems; allocation (assignment) problems; the travelling salesman; game theory; further linear programming, dynamic programming; flows in networks.
CLICK HERE FOR LINK TO SPECIFICATION
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