The term "Combined Maths" typically refers to the subject known as "Further Mathematics" or "Additional Mathematics" in some educational systems. However, the exact content and syllabus can vary depending on the educational board or country. Without specific information about the educational system you're referring to, I'll provide a general overview based on what is commonly understood as Additional Mathematics or Further Mathematics.
Key Components of a Combined Maths or Further Mathematics Syllabus:
Advanced Algebra:
Polynomial equations and functions.
Complex numbers and their properties.
Sequences and series.
Coordinate Geometry:
Equations of circles, ellipses, hyperbolas.
Parametric equations.
Advanced topics in coordinate geometry.
Trigonometry:
Further development of trigonometric functions.
Trigonometric identities and equations.
Applications of trigonometry.
Calculus:
Differentiation and integration.
Applications of calculus in various contexts.
Techniques of integration.
Vectors:
Vector algebra and geometry.
Scalar and vector products.
Applications of vectors.
Statistics and Probability:
Probability distributions.
Statistical methods and analysis.
Hypothesis testing.
Matrices and Transformation Geometry:
Matrix algebra.
Transformation matrices.
Further topics in transformation geometry.
Differential Equations:
Solution of first and second-order differential equations.
Applications of differential equations.
Important Considerations:
Educational System: The syllabus may vary based on the educational system (e.g., A Levels, Advanced Placement, IB).
Local Educational Board: Different countries and educational boards may have specific syllabi for Further Mathematics or Combined Maths. For example, Cambridge International Examinations (CIE) has its own A Level Further Mathematics syllabus.
Language of Instruction: The syllabus you're referring to, especially if it's in English, may be associated with an English-medium curriculum.
To provide more accurate information, you may want to specify the educational system or the examination board you are referring to, as this will help in tailoring the information to a specific context.
The aim of education is to turn out creative children who would suit the modern world. To achieve this, the school curriculum should be revised according to the needs of the time.
Thus, it had been decided to introduce a competency based syllabus in 2009. The earlier revision of the G.C.E. (Advanced Level) Combined Mathematics syllabus was conducted in 1998. One of the main reason for the need to revise the earlier syllabus had been that in the Learning - Teaching- Assessment process, competencies and competency levels had not been introduced adequately. It has been planned to change the existing syllabus that had been designed on a content based approach to a competency based curriculum in 2009. In 2007, the new curriculum revision which started at Grades 6 and 10 had introduced a competency based syllabi to Mathematics. This was continued at Grades 7 and 11 in 2008 and it continued to Grades 8 and 12 in 2009. Therefore, a need was arisen to provide a competency based syllabus for Combined Mathematics at G.C.E.(Advanced Level) syllabus the year 2009.
After implementing the Combined Mathematics syllabus in 2009 it was revisited in the year 2012. In the following years teachers view’s and experts opinion about the syllabus, was obtained and formed a subject comittee for the revision of the Combined Mathematics syllabus by acommodating above opinions the committee made the necessary changes and revised the syllabus to implement in the year 2017.
The student who has learnt Mathematics at Grades 6-11 under the new curriculum reforms through a competency based approach, enters grade 12 to learn Combined Mathematics at Grades 12 and 13 should be provided with abilities, skills and practical experiences for his future needs. and these have been identified and the new syllabus has been formulated accordingly. It is expected that all these competencies would be achieved by pupils who complete learning this subject at the end of Grade 13.
Pupils should achieve the competencies through competency levels and these are mentioned under each learning outcomes
It also specifies the content that is needed for the pupils to achieve these competency levels. The number of periods that are needed to implement the process of Learning-Teaching and Assessment also mentioned in the syllabus.
Other than the facts mentioned regarding the introduction of the new curriculum, what had already been presented regarding the introduction of Combined Mathematics Syllabus earlier which are mentioned below too are valid
• To decrease the gap between G.C.E. (Ordinary Level) Mathematics and G.C.E. (Advanced Level) Combined Mathematics.
• To provide Mathematics knowledge to follow Engineering and Physical Science courses.
• To provide a knowledge in Mathematics to follow Technological and other course at Tertiary level.
• To provide Mathematics knowledge for commercial and other middle level employment.
• To provide guidance to achieve various competencies on par with their mental activities and to show how they could be developed throughout life.
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