Description
This International A Level Further Mathematics provides the techniques in Algebra, Geometry, Trigonometry and Calculus that form the fundamental building blocks of further study in a variety of subjects including Science and Engineering. You will also find this course extremely valuable if you are looking for a progression route for further training whilst employed.
International A Level Mathematics CAIE exams can be taken in June and November .
International A Level Mathematics Edexcel Exams can be taken in January and June (Some units are available in October).
Our courses at International Home Study allow our students to work at their own pace and we work to ensure all our student’s needs are met. Our resources will cover the requirements of the course making sure you stay on track with the subject you choose.
Support
The course will be delivered online including Tutor Support for two years. All assignments are marked by one of our professional Tutors who will offer regular feedback and guide you through your course. Postal assignments cannot be accepted without prior permission from the tutor and you must have access to email in order to contact your Tutor.
Throughout your course, you'll have the support of a Tutor to guide you. Additionally, you can reach out to the Student Support Team for help with any other questions you may have. You can be assured that you will receive unlimited support for your home study course, so there is no need to struggle or feel isolated during your studies.
Assessment
The course contains a number of assignments which your tutor will mark and give you valuable feedback on. You will also have access to a range of online resources.
Students will be required to arrange and pay for their examinations at an approved centre when an examination forms part of the course. We can provide an extensive list of these centres for you.
Whats included?
Students will be provided with logins for the student portal where they will find all the study materials they need to complete their course. They will also be provided with an e-textbook to assist them in completing their assignments.
Students will be provided with a Tutor who will help guide them through their course, and their Tutor will expect them to submit a number of assignments in order that their progress can be monitored. These assignments will be graded for them and feedback provided. You will also be able to ask the Tutor any questions about the course or for more help if needed. Once their course has been completed, they will then be allocated practice exam papers to ensure that they are familiar with the procedure and layout of their exams. Learners will be expected to complete these under exam conditions (i.e.. stick to the time scales allowed and try to find somewhere quiet), their Tutor can then provide them with a grade and feedback. More practice papers can be provided if required.
Difference between Cambridge & Edexcel Exam Boards
Cambridge and Edexcel A Levels are international qualifications. Cambridge A-Levels can be taken worldwide including the United Kingdom, whereas Edexcel A-Levels can only be taken outside of the United Kingdom. Both exam boards offer a similar specification however different courses can have a different structure. Both the Cambridge and Edexcel courses are full A Level qualifications.
Fees
Course fees for payment in full include:
- Assessment and feedback on all assignments.
- Access to your personal Tutor via our online portal.
- Access to a range of online resources, student materials, assessments, assignments, eBooks etc
- Practice exam papers to prepare you for the real thing.
- Help with UCAS application if attending University.
- Tutor references and predicted grades once a satisfactory amount of work has been completed.
- Help finding an exam centre for you to sit your exam.
Cambridge Exam Board
Awarding Body: Cambridge
Cambridge Course Code: 9231
Cambridge Exams: June and November
Cambridge Study Hours: 300 – 360 hours
This International A’ Level Further Mathematics Course with Cambridge develops and extends a set of transferable skills. These include the skill of working with mathematical information, as well as the ability to think logically and independently, consider accuracy, model situations mathematically, analyse results and reflect on findings.
This syllabus is intended for high ability learners who have achieved, or are likely to achieve, a high grade in the A Level Mathematics examination. Knowledge of the whole content of the Cambridge International A Level Mathematics syllabus is assumed. Learners will find that the additional time spent studying Further Mathematics will support their understanding of A Level Mathematics.
The key concepts for Cambridge International AS & A Level Further Mathematics are:
Problem solving
Mathematics is fundamentally problem solving and representing systems and models in different ways. These include:
- Algebra: this is an essential tool which supports and expresses mathematical reasoning and provides a means to generalise across a number of contexts.
- Geometrical techniques: algebraic representations also describe a spatial relationship, which gives us a new way to understand a situation.
- Calculus: this is a fundamental element which describes change in dynamic situations and underlines the links between functions and graphs.
- Mechanical models: these explain and predict how particles and objects move or remain stable under the influence of forces.
- Statistical methods: these are used to quantify and model aspects of the world around us. Probability theory predicts how chance events might proceed, and whether assumptions about chance are justified by evidence.
Communication
Mathematical proof and reasoning is expressed using algebra and notation so that others can follow each line of reasoning and confirm its completeness and accuracy. Mathematical notation is universal. Each solution is structured, but proof and problem solving also invite creative and original thinking.
Mathematical modelling
Mathematical modelling can be applied to many different situations and problems, leading to predictions and solutions. A variety of mathematical content areas and techniques may be required to create the model. Once the model has been created and applied, the results can be interpreted to give predictions and information about the real world.
There are four components that can be combined in specific ways (please see below):
Paper 1: Further Pure Mathematics 1
Paper 2: Further Pure Mathematics 2
Paper 3: Further Mechanics
Paper 4: Further Probability & Statistics
All AS Level candidates take two written papers. All A Level candidates take four written papers.
AS Level Further Mathematics
The Cambridge International AS Level Further Mathematics qualification offers two different options:
- Further Pure Mathematics 1 and Further Mechanics (Paper 1 and Paper 3)
OR
- Further Pure Mathematics 1 and Further Probability & Statistics (Paper 1 and Paper 4).
A Level Further Mathematics
Cambridge International A Level Further Mathematics includes all four components:
- Paper 1: Further Pure Mathematics 1
- Paper 2: Further Pure Mathematics 2
- Paper 3: Further Mechanics
- Paper 4: Further Probability & Statistics.
Modules:
- Further Pure Mathematics 1 (Paper 1)
- Roots of polynomial equations
- Rational functions and graphs
- Summation of series
- Matrices
- Polar coordinates
- Vectors
- Proof by induction
- Further Pure Mathematics 2 (Paper 2)
- Hyperbolic functions
- Matrices
- Differentiation
- Integration
- Complex numbers
- Differential equations
- Further Mechanics (Paper 3)
- Motion of a projectile
- Equilibrium of a rigid body
- Circular motion
- Hooke’s law
- Linear motion under a variable force
- Momentum
- Further Probability & Statistics (Paper 4)
- Continuous random variables
- Inference using normal and t-distributions
- c2 – tests
- Non-parametric tests
- Probability generating functions
Exam Papers
Paper 1: Further Pure Mathematics 1
Written Examination: 2 hours
Availability: June and November
Assessment overview: 6 to 8 structured questions based on the Further Pure Mathematics 1 subject content
75 marks
Paper 2: Further Pure Mathematics 2
Time: 1 hour 2 hours
Availability: June and November
Assessment overview: 7 to 9 structured questions based on the Further Pure Mathematics 2 subject content
75 marks
Paper 3: Further Mechanics
Written examination: 1 hour 30 minutes
Availability: June and November
Assessment overview: 5 to 7 structured questions based on the Further Mechanics subject content
50 marks
Paper 4: Probability and Statistics
Practical examination: 1 hour 30 minutes
Availability: June and November
Assessment overview: 6 to 8 structured questions based on the Further Probability & Statistics subject content.
50 marks
Edexcel Exam Board
Awarding Body: Edexcel
Specification Codes:
AS in Further Mathematics (XFM01)
A Level in Further Mathematics (YFM01)
Edexcel Exams: January and June (some units will be available in October)
Edexcel Study Hours: 300 – 360 hours
The purpose of this course, based on the syllabus is to enable students to:-
- Develop their understanding of mathematics and mathematical processes in a way that promotes confidence and foster enjoyment.
- Develop abilities to reason logically and recognise incorrect reasoning, to generalise and to construct mathematical proofs.
- Extend their range of mathematical skills and techniques and use them in more difficult, unstructured problems.
- Develop an understanding of coherence and progression in mathematics and of how different areas of mathematics can be connected.
- Recognise how a situation may be represented mathematically and understand the relationship between ‘real-world’ problems and standard and other mathematical models and how these can be refined and improved.
- Use mathematics as an effective means of communication
- Read and comprehend mathematical arguments and articles concerning applications of mathematics.
- Acquire the skills needed to use technology such as calculators and computers effectively, recognise when such use may be inappropriate and be aware of limitations.
- Develop an awareness of the relevance of mathematics to other fields of study, to the world of work and to society in general.
- Take increasing responsibility for their own learning and the evaluation of their own mathematical development.
All AS Level candidates take three written papers, they have one compulsory unit, and choose two additional units.
Compulsory Unit
Further Pure Mathematics 1 (FP1)
Optional Units
Further Pure Mathematics 2 (FP2)
Further Pure Mathematics 3 (FP3)
Mechanics 1 (M1)
Mechanics 2 (M2)
Mechanics 3 (M3)
Statistics 1 (S1)
Statistics 2(S2)
All A Level candidates take three written papers, they have two compulsory units and choose four additional units.
Compulsory Units
Further Pure Mathematics 1 (FP1) and Further Pure Mathematics 2 (FP2)
OR
Further Pure Mathematics 1 (FP1) and Further Pure Mathematics 3 (FP3)
Optional Units
Further Pure Mathematics 2 (FP2)
Further Pure Mathematics 3 (FP3)
Mechanics 1 (M1)
Mechanics 2 (M2)
Mechanics 3 (M3)
Statistics 1 (S1)
Statistics 2(S2)
Modules:
Further Pure Mathematics 1
- Complex numbers
- Roots of quadratic equations
- Numerical solution of equations
- Coordinate systems
- Matrix algebra
- Transformations using matrices
- Series
- Proof
Further Pure Mathematics 2
- Inequalities
- Series
- Further complex numbers
- First order differential equations
- Second order differential equations
- Maclaurin and Taylor series
- Polar coordinates
Further Pure Mathematics 3
- Hyperbolic functions
- Further coordinate systems
- Differentiation
- Integration
- Vectors
- Further matrix algebra
Mechanics 1
- 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
- Moments
Mechanics 2
- Kinematics of a particle moving in a straight line or plane
- Centres of mass
- Work and energy
- Collisions
- Statics of rigid bodies
Mechanics 3
- Further kinematics
- Elastic strings and springs
- Further dynamics
- Motion in a circle
- Statics of rigid bodies
Statistics 1
- Mathematical models in probability and statistics
- Representation and summary of data
- Probability; correlation and regression
- Discrete random variables
- Discrete distributions
- The Normal distribution
Statistics 2
- The Binomial and Poisson distributions
- Continuous random variables
- Continuous distributions
- Samples
- Hypothesis tests
Exam Papers
FP1: Further Pure Mathematics 1
Written Examination: 1 hour 30 minutes
Availability: January and June
Assessment overview: Structured questions based on the Further Pure Mathematics 1 subject content. Students may use a calculator in this examination.
75 marks
FP2: Further Pure Mathematics 2
Written Examination: 1 hour 30 minutes
Availability: January and June
Assessment overview: Structured questions based on the Further Pure Mathematics 1 subject content. Students may use a calculator in this examination.
75 marks
FP3: Further Pure Mathematics 3
Written Examination: 1 hour 30 minutes
Availability: January and June
Assessment overview: Structured questions based on the Further Pure Mathematics 3 subject content. Students may use a calculator in this examination.
75 marks
M1: Mechanics 1
Written Examination: 1 hour 30 minutes
Availability: January, June and October
Assessment overview: Structured questions based on the Mechanics 1 subject content. Students may use a calculator in this examination.
75 marks
M2: Mechanics 2
Written Examination:
Availability: January, June and October
Assessment overview: Structured questions based on the Mechanics 2 subject content. Students may use a calculator in this examination.
75 marks
M3: Mechanics 3
Written Examination:
Availability: January, June and October
Assessment overview: Structured questions based on the Mechanics 3 subject content. Students may use a calculator in this examination.
75 marks
S1: Statistics 1
Written Examination:
Availability: January, June and October
Assessment overview: Structured questions based on the Statistics 1 subject content. Students may use a calculator in this examination.
75 marks
S2: Statistics 2
Written Examination:
Availability: January, June and October
Assessment overview: Structured questions based on the Statistics 2 subject content. Students may use a calculator in this examination.
75 marks