AS/A Level Mathematics

You can develop a fuller understanding of mathematics and mathematical processes, and their importance for Science, Commerce and other aspects of modern life.

Unit information

You will be studying six modules in all. This consists of 4 pure maths modules (C1,C2,C3,C4), 1 mechanics module (M1) and 1 statistics module (S1), which together gives you a broad experience in using and applying mathematical methods. You will be engaged using learning methods such as group work, short tests as well as the more traditional lectures and tutorials. Students wishing to sit the AS-level examinations will be required to study the modules C1, C2 and S1. Students wishing to continue their studies for a full A-level qualification in their second year will study the modules C3, C4 and M1.

AS Module: C1

Topics covered in this module include algebra, which is an essential component of the entire course, coordinate geometry, binomial expansions and differentiation. Students will get to try their hand at graph-sketching and how this can be applied to solve real problems.

AS Module: C2

The second pure maths module is essentially an extension of C1, where students get to understand and apply more advanced mathematics. Some of the topics covered in this module will include group work.

AS Module: S1

The statistics module covers probability theory, random variables, and probability distributions.

A2 Module: C3

This pure maths module continues from C1 and C2, and covers more advanced mathematical analysis.

A2 Module: C4

Continuing from C1, C2 and C3, the C4 module completes the pure maths element of the course.

A2 Module: M1

This mechanics module introduces the student to the application of mathematics to real-world problems. It is particularly useful for students studying physics (or engineering), and includes topics such as motion in a straight line, friction and momentum.

The course can be taken as part of a full-time programme of study in conjunction with other AS subjects, or possibly with other Level 3 qualifications. Physics combines particularly well with maths, and the work on statistics will help with interpretation in several academic disciplines. Our staff will be happy to help you put together a programme most suited to your needs. The course can also be taken on a part-time basis by mature students.

Unit information

The course covers many aspects of mathematics, and is designed to develop both a broad and in-depth understanding of the subject, as well as enjoyment and achievement. The emphasis on mathematical modelling and context means that you will be able to recognise and use mathematics in numerous aspects of daily life. The models include the nature of distributions within statistics, and the effect of forces within kinematics. The course requires an excellent understanding of algebra and trigonometry, and will develop these topics and introduce others such as calculus, probability distributions and Newton’s laws.

Year 1 (AS) (40%)

U1 (Pure – 25%) : Quadratic and simultaneous equations, inequalities, completing the square, surds, trigonometric equations and proofs, coordinate and circle geometry, differentiation and turning points, curve sketching, integration and evaluating areas, the binomial theorem, vectors, logarithms and exponential functions and proofs.

U2 (Applied – 15%):

• Statistics

Sampling, statistical diagrams and measures, regression, rules of probability, Venn diagrams, the Binomial, Poisson and discrete Uniform distributions, Hypothesis testing and working with large data sets

• Mechanics

Equations of motion, travel graphs, vertical motion, rectilinear motion, Newton’s laws, lifts and connected particles, pulleys and vectors within kinematics.

Year 2 (A2) (60%)

U3 (Pure – 35%) : Arithmetic and geometric progressions, further binomial expansion, partial fractions, arcs and sectors, reciprocal trig functions, derivative of trigonometric, exponential and logarithmic functions, differentiation of composite, product and quotient functions, composite angles, harmonic trig functions, modulus, sketching and transforming functions, implicit and parametric differentiation, points of inflection, integration by parts and by substitution, functions and their inverses, iterative methods, differential equations within geometry.

U4 (Applied – 25%):

• Statistics

The uniform and normal distributions, further hypothesis testing, correlation and causation, independence of events, conditional probability, Bayes’ theorem.

• Mechanics

Resolving forces, equilibrium, friction, further pulley systems, motion in two dimensions, vector kinematics, vector calculus .

• Differential equations

Forming, solving and modelling with differential equations

The course can be taken as part of a full-time programme of study in conjunction with other AS subjects, or possibly with other Level 3 qualifications. Physics combines particularly well with maths, and the work on statistics will help with interpretation in several academic disciplines. Our staff will be happy to help you put together a programme most suited to your needs. The course can also be taken on a part-time basis by mature students.

Unit information

The course covers many aspects of mathematics, and is designed to develop both a broad and in-depth understanding of the subject, as well as enjoyment and achievement. The emphasis on mathematical modelling and context means that you will be able to recognise and use mathematics in numerous aspects of daily life. The models include the nature of distributions within statistics, and the effect of forces within kinematics. The course requires an excellent understanding of algebra and trigonometry, and will develop these topics and introduce others such as calculus, probability distributions and Newton’s laws.

Year 1 (AS) (40%)

U1 (Pure – 25%) : Quadratic and simultaneous equations, inequalities, completing the square, surds, trigonometric equations and proofs, coordinate and circle geometry, differentiation and turning points, curve sketching, integration and evaluating areas, the binomial theorem, vectors, logarithms and exponential functions and proofs.

U2 (Applied – 15%):

• Statistics

Sampling, statistical diagrams and measures, regression, rules of probability, Venn diagrams, the Binomial, Poisson and discrete Uniform distributions, Hypothesis testing and working with large data sets

• Mechanics

Equations of motion, travel graphs, vertical motion, rectilinear motion, Newton’s laws, lifts and connected particles, pulleys and vectors within kinematics.

Year 2 (A2) (60%)

U3 (Pure – 35%) : Arithmetic and geometric progressions, further binomial expansion, partial fractions, arcs and sectors, reciprocal trig functions, derivative of trigonometric, exponential and logarithmic functions, differentiation of composite, product and quotient functions, composite angles, harmonic trig functions, modulus, sketching and transforming functions, implicit and parametric differentiation, points of inflection, integration by parts and by substitution, functions and their inverses, iterative methods, differential equations within geometry.

U4 (Applied – 25%):

• Statistics

The uniform and normal distributions, further hypothesis testing, correlation and causation, independence of events, conditional probability, Bayes’ theorem.

• Mechanics

Resolving forces, equilibrium, friction, further pulley systems, motion in two dimensions, vector kinematics, vector calculus .

• Differential equations

Forming, solving and modelling with differential equations

The course covers many aspects of mathematics and is designed to develop both a broad and in-depth understanding of the subject. You will study key areas of algebra and functions, as well as mathematical models (kinematics and vectors in mechanics). You will also learn aspects of calculus, coordinate geometry, binomial theorem, logarithms and sequences.

Unit information

Year 1 (AS)

• C1: Algebra andamp; functions , Coordinate Geometry, Differentiation
• C2: Sequences, Coordinate Geometry, Trigonometry, Integration
• S1: Discrete Probability Distribution, Binomial andamp; Poisson Distribution, Continuous Probability Distribution
• M1: Rectilinear Motion, Friction, Momentum, Statics

Year 2 (A2)

• C3: Trigonometry, Exponentials, Differentiation, Integration
• C4: Trigonometry, Differentiation, Equations, Integration, Vectors
• S2: Continuous Probability Distributions, Two or more Variables, Hypothesis Testing andamp; Confidence Intervals
• M2: Expanding previous knowledge on Rectilinear Motion, Dynamics of a Particle, Motion under Gravity, Vectors, Circular Motion.

The course covers many aspects of mathematics and is designed to develop both a broad and in-depth understanding of the subject. You will study key areas of algebra and functions, as well as mathematical models (kinematics and vectors in mechanics). You will also learn aspects of calculus, coordinate geometry, binomial theorem, logarithms and sequences.

Unit information

Year 1 (AS)

• C1: Algebra andamp; functions , Coordinate Geometry, Differentiation
• C2: Sequences, Coordinate Geometry, Trigonometry, Integration
• S1: Discrete Probability Distribution, Binomial andamp; Poisson Distribution, Continuous Probability Distribution
• M1: Rectilinear Motion, Friction, Momentum, Statics

Year 2 (A2)

• C3: Trigonometry, Exponentials, Differentiation, Integration
• C4: Trigonometry, Differentiation, Equations, Integration, Vectors
• S2: Continuous Probability Distributions, Two or more Variables, Hypothesis Testing andamp; Confidence Intervals
• M2: Expanding previous knowledge on Rectilinear Motion, Dynamics of a Particle, Motion under Gravity, Vectors, Circular Motion.