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


-Coordinate geometry of straight lines and circles

-Quadratic functions


-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)2 and 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


-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


-Binomial Distribution

-Confidence Intervals



· Calculate the product moment correlation coefficient between x & y

Sxx=2.41 Syy=3.56 Sxy=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


– 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=8x + 1 can be transformed into the curve y = 2x 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


· A cable raising a load with an acceleration of 1.5 m s -2 has a tension of 15kN. Find the mass of the load · Students are expected to have a sound understanding of C1.