Cambridge International AS and A Level Mathematics - Further (9231)
This course 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.
*Course available from September 2020, for first exams in June 2022.
This course is available as a single year course only. Consequently Pamoja does not currently offer Further Mathematics at AS Level.
The course covers the following topics:
- Mechanics 1 – including projectile motion, moments, equilibrium, centre of mass, circular motion
- Matrices and Vectors
- Calculus – including hyperbolic and inverse trigonometric functions, second derivatives, differential equations, and applications
- Complex numbers – de Moivre’s theorem
- Statistics 1 – including discrete and continuous random variables, statistical distributions, sampling and hypothesis testing
- Statistics 2 – including expectation and variance, goodness of fit and non-parametric tests
- Series & sequences
- Proof by induction
- Polynomials (cubic and quartic)
- Polar coordinates
- Mechanics 2 – including Hooke’s Law, work, momentum,
- Newton’s Laws
In each year there is also time for revision and trial examinations.
Activities and assessments
The course includes the following activities: readings and practice questions on each topic, quizzes, self-assessments and marked assignments. Teachers will review and grade assignments during the course. There are also unit discussions to support students with each topic.
The final examination consists of four externally-assessed papers:
- Paper 1—2 hours, 30% AL, structured questions on Further Pure Mathematics 1
- Paper 2—2 hours, 30% AL, structured questions on Further Pure Mathematics 2
- Paper 3—1 hour 30 minutes, 20% AL, structured questions on Further Mechanics
- Paper 4—1 hour 30 minutes, 20% AL, structured questions on Further Probability and Statistics
Advice from our teachers
This course is twice the pace of a standard two-year A Level course. In order to succeed in International A Level Further Mathematics in a single year, we recommend students set aside twenty to thirty hours a week to study. It is important that students regularly keep up with the readings and the course activities in a timely manner. And that they contact their teacher if they fall behind or need help with assignments.
Hodder Education eTextbook
This course is dependent on student etextbooks provided by Hodder Education and hosted on the Dynamic Learning platform. Please ensure you check the Hodder Dynamic Learning guidance to ensure your systems are able to access this service. This service is provided as part of the Pamoja course fee - find out more.
Minimum entry requirements
The Cambridge International A Level Mathematics Further (9231) syllabus requires students to have already studied mathematics to an advanced level. This School Taught course assumes that students already have covered the curriculum specified in Cambridge International A Level Mathematics (9709), and taken the following papers:
- Pure Mathematics 1
- Pure Mathematics 3
- Probability and Statistics 1
A student may have taken an alternative qualification or papers, and it will be the school’s responsibility to check that any qualifications cover the expected prior knowledge, or that the student will be able to undertake additional study alongside their Further Mathematics course.
If you also require a Mathematics International A Level course to use alongside this Further Mathematics course we recommend you choose our Route A option to ensure the prior learning is covered.
Cambridge International calculator guidance
International AS and A Level Mathematics students will require a scientific calculator when studying the course and for examinations. As stated below, Cambridge International allows for a wide range of calculators to be used in examinations. Pamoja teachers have suggested the Casio ClassWiz models as suitable for this course, such as the fx-991 EX.
Candidates can use programmable calculators [in examinations]. However, calculators with any of the following facilities are not allowed, unless stated otherwise in the syllabus:
- graphic display
- data banks
- language translators
- retrieval or manipulation of text or formulae
- QWERTY keyboards
- built-in symbolic algebraic manipulations (output must be numeric not algebraic)
- symbolic differentiation or integration (output must be numeric not algebraic)
- capability of any remote communication
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