AS and A Level Maths
Course Guide 2016-17
AS and A Level Maths Course Guide
Welcome to AS Level Maths. In this course you will develop your mathematical skills from GCSE, and
will learn many new and powerful techniques that can be used in many other areas such as Science,
Pharmacy, Finance, and Computer Programming to name but a few. This course also gives you the
building blocks for any further study in a course that depends heavily on mathematical ideas, for
example Physics, Engineering, and of course Maths!
Course Overview
For AS Maths you will study three modules: Core 1, Core 2, and Mechanics 1, all of which contribute
an equal amount to your final exam grade. Should you choose to continue on to A Level Maths, you
will study a further three modules: Core 3, Core 4 and Mechanics 2. Your A Level grade will be
determined from all of your modules studied, and each will contribute the same amount to your
overall grade. There is no coursework; all of the units are 100% exam.
AS Maths
AS students usually study Core 1 up to the end of Term 1, and then Core 2 up to the exam.
Mechanics 1 is taught throughout the year by a separate teacher. For the Core modules, you will be
expected to provide your own folder. Your teacher will provide you with extensive class notes which
will guide you through the course, and plenty of supporting exercises that will help you to practise
the basics, and develop your problem-solving skills. Able students can expect to be stretched by
some optional, very demanding exercises. You must bring your full folder to each lesson, as you will
constantly need to refer to earlier topics.
For Mechanics 1, it would be a good idea to have a separate folder. The emphasis in Mechanics is on
problem-solving. A greater proportion of time therefore will be spent on problem-solving, and you
will not be provided with a set of class notes.
AS maths moves considerably more rapidly than GCSE, but we are sensitive to the differing needs of
pupils, and recognise that not all students will progress through the course at the same speed. We
do not therefore devote a set amount of time to each module; some modules will be completed very
quickly, but some will need a greater amount of time for key ideas to sink in. All MCHS Maths staff
are very supportive, and you should ask them for help whenever necessary. Your teacher will tell you
when support is available.
At the end of each module you will be given an assessment. This will be marked with feedback on a
PLC which will tell you which areas you were good at, and which need further improvement. You will
receive a WWW and an EBI. The EBI will typically be further exercises on areas that you found
difficult, or extension work for those who performed well in all areas.
There will be regular tests and exams which will be marked and graded according to AS Level grade
boundaries. These will form the basis of your reports.
Term 1
Core 1 (one third of AS Maths)
Teachers: Mrs L Riggs, Mr C Arrowsmith
This course offers some bridging material from GCSE to A Level study, and ensures that you are able
use these ideas fluently before moving on to more advanced topics. Towards the end of the course
you will meet calculus. This is a powerful technique that deals with how things change, and forms
the basis of many “applied” topics, particularly the maths underlying Physics. The course is split into
8 units: (Note: you are NOT allowed a calculator for Core 1, so you will need to be able to do
fractions, negatives, indices etc without the use of one)
Unit 1 (Algebra):
- Recaps and develops algebraic skills from GCSE such as simplifying, brackets, factorising,
indices, surds. A lot of emphasis will be placed on self-study, with support if needed.
Unit 2 (Quadratic Functions):
- Recaps and develops quadratic equations (factorising, using the formula, completing the
square),
Unit 3 ( Equations and inequalities)
linear and non-linear simultaneous equations, linear and quadratic inequalities, and using
the discriminant to determine the number of solutions to a quadratic
Unit 4 (Graph Sketching):
- Sketching cubics, reciprocal graphs, quadratics. Interpreting the intersection of graphs as
solutions to equations. Using transformations eg f(x) + a.
Unit 5 (Coordinate Geometry):
- Gradient and intercept. Equation of a line in various forms. Parallel and perpendicular lines.
Solving problems. Note: all of this material will be relied upon for Unit 7
Unit 6 (Arithmetic Progression):
- Understand un notation, recurrence relations and sigma notation. Prove the formula for the
sum to n terms, and use to solve problems
Unit 7 (Differentiation):
- Understand what differentiation means, and understand the notation. Find gradients of
curves, and the equation of the tangent and the normal. Find rates of change, and the
second differential.
Unit 8 (Integration):
- Understand that integration is the inverse of differentiation. Find the indefinite integral of
expressions involving indices. Find f(x) given f’(x) and a coordinate.
Assessment: 1 ½ hour exam (non-calculator) in Summer
Supporting text: Edexcel AS and A Level Mathematics Core 1
Terms 2 and 3
Core 2 (another third of AS Maths)
Teachers: Mrs L Riggs, Mr C Arrowsmith
This course develops the ideas from Core 1 and introduces some other important concepts such as
radians and logarithms. It also develops your techniques of calculus and shows how they can be used
to solve increasingly complex problems. You are allowed the use of a calculator for Core 2.
Unit 1 (Algebra):
- Simplifying algebraic fractions, division of algebraic expressions, Factor-Remainder Theorem
Unit 2 (Geometry):
- Sine rule, cosine rule etc. (Note: the emphasis will be on self-study here)
Unit 3 (Logarithms):
- Definition of a logarithm, logarithm laws, solving equations, change of base (Note: logs are
very useful for Unit 7)
Unit 4 (Coordinate Geometry):
- Equation of a circle, tangents, chords, diameter
Unit 5 (Binomial Theorem):
- Understanding factorial notation, nCr, xpanding (a +b)n and (1 + x) n
Unit 6 (Radian Measure):
- Understand the definition of a radian and understand why they are used, Arc length, sector
area, area of a segment. Use of calculator in RAD mode.
Unit 7 (Geometric Progression):
- Term to term rules, understand nth term formula, prove the formula for the sum to n terms
and use to solve problems
Unit 8 (Trigonometric graphs). Note: This may be combined with Unit 10
- Plot and sketch graphs of sin, cos, tan. Transform functions using eg f(x) + a. Find exact
values for 30, 45, 60 degrees etc
Unit 9 (Differentiation):
- Determine criteria for a function to be increasing/ decreasing/ stationary. Classify stationary
points. Solve problems involving maxima and minima
Unit 10 (Trigonometric identities and equations):
- Prove and use trigonometric identities to simplify expressions and solve equations.
Determine all possible solutions using a CAST diagram or a graph.
Unit 11 (Integration):
- Use integration to find the area bounded by a curve and the x axis, a curve and a line, or two
curves. Understand the meaning of negative area. Use the Trapezium Rule to estimate areas,
and determine whether it is an under or over estimate.
Assessment: 1 ½ hour exam in Summer (calculator allowed)
Supporting text: Edexcel AS and A Level Mathematics Core 2
Terms 1,2&3
Mechanics 1
Teacher: Miss G Goodwin
This is very much an “applied” course, and shows how maths can be used to model and predict the
behaviour of physical systems, for example the motion of a ball thrown off a cliff top. The emphasis
is on applying Newton’s laws of motion and their resulting formulae, and these fundamental ideas
will serve as a building block for more complicated ideas. A lot of the course complements ideas
from Physics, but we treat it in a far more mathematical way. Topics studied are briefly described
below. Again, there is no set time for each unit, as it sometimes takes longer for these fundamental
ideas to sink in.
Mathematical models in mechanics
- Understand the assumptions made when using maths to model a mechanical system.
Understand the physical meaning of words such as “smooth”, light”, “inextensible”,
“particle” etc and how these affect the system. Know how to draw effective force diagrams
Kinematics of a particle moving in a straight line
- Memorise the equations of motion. Describe motion under gravity. Use distance-time and
velocity-time graphs
Statics of a particle
- Identify all forces acting in a system, and draw them effectively on a diagram. Know how to
resolve a force in a given direction, in particular perpendicular and parallel to an inclined
slope. Understand how to model friction. Understand equilibrium.
Dynamics of a particle
- Use: Sum of forces acting on a particle = ma to solve problems. Solve connected particles
problems, eg pulley systems. Thrust in a towbar/ tension in a tow rope, reaction force in a
lift ( your weight doesn’t change, but your reaction force does)
Momentum and impulse
- Use momentum and impulse to find speeds of particles before and after collisions. Model
particles connected by a string.
Moments
- Define moment/ turning force, and use to solve problems for systems in equilibrium
Vectors
- Use vectors to model dynamic and static systems.
Assessment: 1 ½ hour exam in Summer (calculator allowed)
Supporting text: Edexcel AS and A Level Mathematics Mechanics 1
A Level Maths
A Level Maths follows much the same format as AS Maths in terms of assessment and timings, but
you can expect to meet a higher degree of challenge at this level
In Core 3 and Core 4, you will further develop some of the ideas introduced in AS, such as
differentiation, integration and trigonometry, and you will begin to look at developing precision, eg
the construction of proofs and formal definitions of functions. For Mechanics 2, you will build on
skills developed in Mechanics 1, and look in more detail at modelling more complex situations.
When you have completed C0re 3 and 4, you will have learned all the trigonometry and
differentiation you will ever need for a higher level course involving maths. If only the same were
true of integration…
In addition to this, you will be given Independent Learning Projects (ILPs). The majority of these are
intended to recap information from AS Maths, and to help embed the basic ideas. You will be set
one of these at the start of a new topic.
The assessment is exactly the same as for AS Maths, but the timings of the courses are slightly
different. Core 3 is started at the end of the AS exams in Year 12 (Term 3) and continued until
Christmas the following year (Term 4). You will then study Core 4 during terms 5 and 6. Mechanics 2
is started in year 13, and continues throughout the year.
Terms 3 and 4
Core 3
Teachers in Year 13: Mrs L Riggs and Mr C Starr
Unit 1 (Algebraic Fractions):
- Simplifying algebraic fractions by cancelling common factors. Add, subtract, multiply and
divide algebraic fractions. Use algebraic division to simplify fractions
Unit 2 (Functions):
- Function notation and definition including domain and range. Classifying functions as oneone, many-one etc. Composite functions, inverse functions and sketching the graph of the
inverse.
Unit 3 (The exponential function):
- Define the exponential function ex. Find the inverse lnx. Sketch graphs and transform them,
eg f(x) + 3, and solve equations
Unit 4 (Numerical methods):
- Determine intervals in which a solution lies, and use graphs to determine the number of
solutions. Derive and use an iterative formula, and show that a solution is correct to a given
number of decimal places
Unit 5 (The modulus function):
- Define the modulus function f(x) = │x│. Use the modulus func on in transforma ons of
graphs. Solve modulus equations.
Unit 6 (Trigonometry):
- Definition of sec, cosec, cot, and their graphs. Definition of arcsin, arccos, arctan and their
graphs. Further Pythagorean identities, use to prove identities and solve equations. Find
exact trigonometric ratios using CAST.
Unit 7 (Further trigonometry):
- Addition formulae, double and half angle formulae, Rcos(θ-α), sums of sines and cosines.
Use all to prove identities and solve equations.
Unit 8 (Differentiation):
- Chain rule, product rule, quotient rule. Prove and use differential of ex, lnx, trig ratios etc
Supporting text: Edexcel AS and A Level Mathematics Core 3
Terms 5 and 6
Core 4
Teachers in Year 13: Mrs L Riggs and Mr C Starr
Unit 1 (Partial Fractions):
- Decompose a fraction into its partial fractions. Recognise the different methods required
Unit 2 (Binomial Theorem):
- Use binomial theorem when n is not a positive integer. Determine the range of values for
which the series converges. Use the binomial theorem to estimate eg √2. Use partial
fractions to simplify
Unit 3 (Parametric equations):
- Express a Cartesian equation in terms of parametric equations and vice versa. Solve
problems eg intersections of curves with axes etc.
Unit 4 (Further Differentiation):
- Implicit and parametric differentiation. Prove the rules for ax and logax
Unit 5 (Integration):
- Integration as the inverse of differentiation, integration of f(ax+b) . Using trigonometric
identities, especially integrals of sin2x and cos2x .Using partial fractions, particularly with
limits. Integration by substitution. Integration by parts. Comparing exact and approximate
answers using the trapezium rule. Parametric integration
- Volume of revolution using Cartesian and parametric equations
- Shortcuts: -Integrating f’(x)fn(x) and f’(x)/f(x).
Unit 6 (Vectors):
- Recap basic definitions of vectors and use to prove geometric theorems. Use the scalar
product. Find the vector equation of a line in 3D space. Determine whether or not a pair of
lines intersect, and find the angle between two lines.
Supporting text: Edexcel AS and A Level Mathematics Core 4
Terms 4,5 and 6
Mechanics 2
Teacher: Mr C Starr
Topics covered:
Kinematics of a particle moving in a straight line or plane:
- Projectiles
- Velocity and acceleration when displacement is a function of time
- Differentiating and integrating vectors, and finding the motion of a particle in a plane
Centre of Mass:
- Find the centre of mass of a system of particles, or a combination of 2D shapes (plane
lamina)
- Determine equilibrium conditions for a lamina on an inclined plane, or hanging from a fixed
point
Work, Energy, Power:
- Definitions of work, energy and power. Types of energy: potential, kinetic, and energy lost
due to friction. Conservation of energy, and change in energy for a particle. Power: moving
vehicles.
Collisions:
- Elastic collisions. Inelastic collisions and the coefficient of restitution. Impact, or successive
impacts of a particle with a fixed surface. Energy lost in an inelastic collision
Statics of rigid bodies.
- Moment of a force, and conditions for equilibrium. Lots and lots of problems involving
ladders…
Supporting text: Edexcel AS and A Level Mathematics Mechanics 2