Mathematics AS / A2

The aims of the course are to:

• Teach and clarify methods which you may have previously found difficult.

• Improve problem solving and examination technique.

• Recommend a strategy for effective revision.

AS courses: either C1 C2 M1 or C1 C2 S1

A2 courses: either C3 C4 M2 or C3 C4 S2

For those who wish to combine AS and A2 units the following combinations are possible:

C1 C2 S2 or C1 C2 M2

C3 C4 S1 or C3 C4 M1

A breakdown of the topics we will cover is given below. Students should check with their teachers before signing up for the course if they are in doubt as to its suitability.

Core 1 (C1)

Basic algebra, indices surds, the quadratic function, inequalities, simultaneous equations, straight line graphs, curve sketching and transformations. Differentiation and integration of xn. Tangents and normals. Sequences and series – arithmetic progressions.

Core 2 (C2)

Remainder and factor theorems, coordinate geometry of the circle, the geometric series, the binomial expansion for positive integer powers. Trigonometry – sine and cosine rules, radian measure, identies tan = sin θ/cos θ, cos2 θ + sin2 θ = 1, solving trigonometric equations. Logarithms. Differentiation – maximum and minimum values and associated problems. Definite integrals, area under a curve. Approximate integration – trapezium rule.

Core 3 (C3)

Functions, combined graphical transformations, reciprocal trig ratios, compound angle formulae, r - ∝ method. Differentiation of ex, lnx, and trig functions. Chain rule, product and quotient rules. Iterative techniques for solving equations.

Core 4 (C4)

Parametric equations. Parametric and implicit differentiation. Exponential growth and decay. Integration by substitution. Volume of revolution. Integration by parts. Differential equations, partial fractions and applications to expand series, to assist integration and differentiation. Vectors in three dimensions, the scalar product, equations of lines.

Mechanics 1 (M1)

Linear kinematics

Vectors in mechanics

Newton’s laws of motion, pulleys, inclined planes

Statics - equilibrium, sum of force zero, sum of moments zero

Momentum and impulse

Statistics (S1)

Representation of data

Measures of central tendency and dispersion

Probability

Correlation and linear regression

Discrete random variables E(X) Var(X)

Normal distribution

Statistics 2 (S2)

Binomial, and Poisson distributions

Continuous random variables - mean, mode, median variance

Normal Distribution as an approximation to the binomial and Poisson distributions

Hypothesis testing

Mechanics2 (M2)

Centre of Mass of simple shapes and composite laminas

Projectiles

Work, Energy Power

Conservation of momentum; Newton’s experimental law

More moments e.g. ladder problems