Ashbourne’s A level Maths Easter Revision courses run in morning or afternoon sessions over five days and are taught by a selection of Ashbourne tutors including longstanding members of staff Chella Nathan and Barry Rhule. Chella has a BSc in Maths and Physics and B.Eng and has been teaching for more than twenty years. Barry also has a BSc in Maths and Physics and a PhD in Physics. He is also a member of the London Mathematical Society and has been teaching at the college for many years.
What is covered in the Easter Revision course?
This is a joint module course and covers:
Powers, indices: the laws, solving simple equations in powers using prime factorisation. Surds and rationalising denominators.
Roots of quadratic equations: discriminants; completing the square; application to graphs of parabolas; condition for tangency when intersection straight lines
Inequalities: multiplying/dividing by negative numbers.
Transformation of graphs: translation, enlargement; f(x), kf(x), f(x+k), f(x) + k
The remainder theorem, integer and non-integer factors and roots
Logarithmic and exponential equations
The binomial theorem
Geometric series: infinite gps
Radian measure; sine and cosine rules; circle theorems
Equations of circles
Simple trigonometry: angles greater than ninety degrees, trigonometric equations; at least 2 solutions
Simple differentiation and integration: areas under curves, equations of tangents and normals, max/min problems
Trapezium rule for approximating areas
Functions and inverse functions. Range and domain and finding inverse functions. Graphs of inverse functions. Particular emphasis on logarithmic and exponential functions.
Differentiation – Product, quotient and chain rule. Implicit differentiation. Tangents and normal.
Trigonometric equations and identities – Particular emphasis on Rcos(x + a).
Transformation of functions and their graphs. Emphasis on modulus functions.
Approximation of roots. Establishing integer bounds to roots and finding an approximation to required degree of accuracy.
Exponential and logarithms – Growth and decay.
Binomial series for fractional and negative indicies. Condition for convergence.
Trapezium rule for approximation of areas.
Implicit and parametric differentiation – Tangents and normal
Differential equations – Particular emphasis on exponential growth and decay
Integration partial fractions, integration by parts, integration by substitution. Volumes of solids of revolution.
Vectors – Equations of lines and their intersection. Vector dot product, angles between vectors, perpendicular vectors and equation of a right bisector of a line.
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
Mathematical models in probability and statistics
Representation and summary of data
Correlation and regression
Discrete random variables
The Normal distribution
Algorithms on graphs
The route inspection problem
Critical path analysis