A Level Mathematics

“For the things of this world cannot be made known without knowledge of mathematics.” – Roger Bacon

A-level Mathematics is a prestigious subject that is highly regarded by the majority of Universities as it enables students to establish a wide range of skills. Students can use this A-Level to progress further into a range of professions including Teaching, Engineering, Accounting and Finance, Economics and Medicine.

Here at BTC, we encourage our AS and A2-Level students to reinforce their mathematical skills by comprehending mathematical problems and processes and developing their understanding of these concepts in a confident way. We also enable them to recognise how different situations are represented mathematically.

We recognise that Mathematics is a challenging A-level and in view of this we enable our students to appreciate a range of mathematical techniques that are used to solve difficult, unstructured problems.

The following modules are assessed at AS-Level:

Module

Exemplar Content

Exemplar Questions

Expectations:

Core Maths 1

-Surds

-Coordinate geometry of straight lines and circles

-Quadratic functions

-Polynomials

-Simultaneous equations

-Differentiation and Integration

· Find the coordinates of the points on the curve y= X³ -9x + 5 where the gradient is equal to 3

· Given that f’(x) = (x-1)²and f(0) = 2. Find f(x)

-Students should be able to:

·Expand brackets

·Solve linear equations

·Understand and comprehend Pythagoras’ Theorem

·Appreciate and use Trigonometry as a tool in problem solving

Core Maths 2

-Indices

-Further Differentiation

-Further integration and the Trapezium rule

-Exponentials and logarithms

-Geometric Series

Factorials and binomial expansions

-Simple transformation of graphs

· Describe the geometrical transformation that maps the graph of y=1 – x⁵ onto the graph of y=1 + X⁵

·Students are expected to have a sound understanding of C1.

Statistics 1

-Numerical Measures

-Probability

-Binomial Distribution

-Confidence Intervals

-Correlation

-Regression

· Calculate the product moment correlation coefficient between x & y

S_xx=2.41 S_yy=3.56 S_xy=1.87

· Students are expected to know a wide range of mathematical formulae.

The following modules are assessed at A2-Level:

Module	Content	Exemplar Questions
Core Maths 3	-Functions – Transformations of graphs and the modulus function -Inverse trigonometric functions and secant, cosecant and cotangent -The number e and calculus -Further differentiation -Volume of revolution and numerical integration	· Describe geometrically how the curve y=8^{x + 1}can be transformed into the curve y = 2^x by a sequence of transformations	· Students are expected to have a sound understanding C1 and C2.
Core Maths 4	-Binomial series expansion -Rational functions and division of polynomials -Partial fractions and applications -Parametric equations -Further trigonometry with integration -Exponential growth and decay -Differential Equations -Vector equations of lines	· Find the distance between the points (-5, 3, 7) and (-2,-2,6)	· Students are expected to have a sound understanding C1, C2 and C3.
Mechanics 1	-Mathematical models in mechanics -Vectors and their application in mechanics -Kinematics of a particle -Statics of a particle -Dynamics of a particle of moving in a straight line or plane -Moments	· A cable raising a load with an acceleration of 1.5 m s ^-2has a tension of 15kN. Find the mass of the load	· Students are expected to have a sound understanding of C1.