'A Level' takes maths into a new dimension and consisits of three parts. AS-Level Modules in Year 12, three AS modules are taken: Core Mathematics 1, Core Mathematics 2, and Mechanics 1 or Statistics. The core maths modules extend and develop GCSE work on algebra, trigonometry and series. Surds and indices are extended, including the relationship between logarithms and indices. Differential and integral calculus are introduced. The mechanics (what used to be the old applied maths) deals with physical forces and their relation to motion or equilibrium, essential for would be engineers. Alternatively to mechanics is the option of statistics the idea of which is often meet with horror. However in this current age an understanding of statistics is almost obligatory and is essential for biologist and those in intending to go into research or the business world. The AS-Level is a qualification in its own right and counts for points to university entrance. A2 Modules this is necessary to qualify for the full A-Level, students take two more core maths modules and a statistics module in Year 13. In core maths they study further functions and calculus techniques, differential equations, and three-dimensional vectors. Statistics includes representation of data, probability distributions and measures of correlation. Anybody wishing to take up any of the scientific disciplines A-Level maths is a must as well as those who want to go into the financial and business world. Further Mathematics this offers opportunities to extend A-Level work on mechanics, statistics and calculus techniques through concepts of abstract algebra, mathematical techniques such as developing an algorithmic approach to problem-solving. In addition is the subject of 'Decision' maths. The most common combination would be the Pure papers P1 to P6, two Statistics units and four Mechanics papers, although, of course, other combinations are possible. It is reckoned that only those achieving A or A* at GCSE should attempt further maths but those with only a B or even a C could make the grade with effort. Useful for those who intend going on to study Maths, Physics or Engineering at university but you could find yourself repeating most of it there as the university course may have to cater for those who did not do it. Still for oversubscribed courses it could be the deciding factor in getting a place. These topics may not cover all the requirements of the various examination bodies AQA, EDEXCEL, OCR, WJEC or NICCEA but probably most of it. Any topic not found here and required can probably be catered for. A scientific calculator, one that can draw trig and exponential graphs is required to study A level. Forget the augment that A level is dumbing down, many of the topics covered here were not even approached until degree level in those supposed halcyon days of the 50s and 60s. Many of the questions in today's exams could also have come out of the exam papers of that time. True after the high failure rate and poor passes in 2001/2002 some of the 'harder' subjects were made optional and greater emphasis given to the core pure maths but some of the 'harder' subjects were perhaps a step too far. What is different to the 'old' is that instead or taking all the papers at the end of the second year they can now be taken as you go along and repeated to improve the grade. This is probably a fairer way.

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	Algebra		To simplify rational expression and partial fractions
	Binomial theorem		Expansion for a rational integer
	Coordinate geometry		Curve sketching in Cartesian and parametric form
	Trigonometry (1)		Acute angles negative angles in radians and degrees
	Trigonometry (2)		Graphs of trig functions, symmetries and periodicities
	Exponentials and logarithms		Exp(x) log(x ) (to base e) and related functions
	Differentiation (1)		Differentiation of trig and log functions
	Differentiation (2)		Applications for Graphs maxima and minima
	Differentiation (3)		The product and Quotient rules
	Differentiation (4)		Natural Log and exponential functions
	Integration (1)		By substitution
	Integration (2)		Change of variable for trig functions
	Integration (3)		Exponential functions
	Integration (4)		Natural Log integrals and using substitution
	Integration (5)		Trigonometric substitution
	Integration (6)		Volume of revolution and area of surface of revolution
	Integration (7)		Integration by parts
	Series		The Sigma notation, arithmetic and geometric progressions
	Functions		Evaluate and find the inverse of a function
	Surds		Add, subtraction, multiple, division and Rationalising
	The Binomial Series		Expansion of and Pascal's triangle
	Long Division of Polynomials		Dividing by a lower order polynomial
	Inequalities		Multiplying or dividing by, negative quantity
	The remainder theorem		p(x) divided by (x-a) to find the remainder p(a)
	Partial Fractions		To split into two or more fractions
	Simultaneous equations		Solution of simultaneous equations
	Logarithms		Adding and subtraction, changing base
	Numerical methods (1)		Approximation by the Newton-Raphson method
	Numerical methods (2)		Simpson’s rule
	Differential equations		First order solving
	Vectors		Use unit, position and displacement vetors
	Complex Numbers		Addition and subtraction multiplication De Moivre's Theorem
	Permutations and Combinations		Arrangements and other permutations n!(n factorial)
	Continuous random variables		Probability distributions
	Estimation and sampling		Distinguishing between sampling techniques
	Hypothesis testing		Type I and Type II errors, critical z-values
	Normal distribution		Properties of
	The binomial distribution		Properties of
	The poisson distribution		Properties of
	Confidence intervals; the t-distribution		Difference of population means
	chi (X2) tests		Goodness of fit tests
	Regression and correlation		Linear best line of fit and correlation coefficient
	Newton's laws of motion		conservation of momentum, acceleration
	Kinematics'		Projectiles, variable acceleration
	Centres of mass		Finding cm in one and two dimensions. Solid of rotation
	Energy, work, power		kinetic and potential energy, masses on inclines
	Collisions		Conservation of momentum, loss of energy in collision
	Simple harmonic motion		Definitions maximum speed and maximum acceleration
	Kinematics in two and three dimensions		Collisions between spheres
	Uniform circular motion		Angular speed and centripetal force.
	Elastic springs and strings		Hook’s law, energy in a spring
	Motion in a circle		In a horizontal circle, banked tracks
	Equilibrium of a rigid body		Balances and leaning ladders
	Variable acceleration		Using differential equations
	Coefficient of restitution		Bouncing balls
	Game theory		Zero-sum game, play safe strategies.
	Flows in a network		Bottlenecks, cuts and variations.
	Critical path analysis		Organising a event to minimise time, Gantt diagrams
	Recurrence relations		Solving first order linear recurrence relations
	Coding		Binary code and hamming distance and error detection
	Matrices		Definitions, addition, sub, multiple, solve linear equations