Mathematics

What is the nature of Mathematics at IGCSE level?

IGCSE Mathematics at SJII is a curriculum that challenges students at all levels. Our goals include preparing students for whatever mathematics subject they choose in the IB and to give students the opportunity to extend themselves in developing a deeper appreciation of the discipline. Some of the more able students are also introduced to Additional Mathematics, a course that prepares them well for the rigours of higher level Mathematics at IB level.

What is the approach to learning?

Learning is student-centered. Students will learn through different teaching methods and styles, including pair and group work, activities which promote thinking skills and creativity and IT-based lessons. The emphasis is on building skills in mathematics based on a thorough understanding of mathematical principles and their application. Students will also be encouraged to undertake their own mathematical investigations under the guidance of their teacher, devise their own strategies for problem-solving and to raise questions relating to mathematical concepts and methods.

What is the subject content?

The following content will be used as a basis to help students achieve the outcomes described above. In this way, although students will become familiar with traditional topics in mathematics, these are seen as a vehicle for promoting mathematical thinking rather than being laboured over for their own sake.

Extended Mathematics (International Mathematics)

Number

Area Topics

decimals, fractions, ratio, rounding, exponents, surds; Patterns

Algebra

Functions

expansion, factorisation, algebraic fractions, linear & quadratic equations & inequalities, simultaneous equations notation, composite, inverse, modulus,; graphs of functions Geometry lines, angles, polygons, symmetry, circle geometry, Pythagoras Transformations transformation of graphs and geometric figures Mensuration perimeter, area, volume, surface area Coordinate Geometry equation of a straight line, graphs of linear inequalities

Statistics and Probability

discrete, continuous and grouped data; measures of central tendency; measures of spread; Set Theory nrobability - simple and compound events; Listing proceduresnotation and set operations; Venn Diagrams Trigonometry solution of triangles; Bearings; trigonometric ratios; trigonometric graphs; trigonometric equations

Vectors graphical representations of vectors; basic mathematical operations with vectors; physical applications of vectors

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Area Topics

Functions language and notation of functions, absolute functions, inverse functions, composite functions; transformation of functions

Algebra simultaneous equations; quadratics; exponents; logarithms; polynomials, sequence & series Straight Line Equation of a straight line; linearization

Graphs

Calculus Differentiation differentiation of various functions including integer, fractional and negative indices; differentiation of composite functions; products and quotients, trigonometric functions, logarithmic and exponential functions; investigating gradients; higher derivatives and their use in determining turning points; applications of differentiation

Calculus Integration integration of polynomials, trigonometrical functions, selected composite, quotients and exponential functions. definite integrals – areas under curves

Applied Mathematics application of differentiation and integration to analyse motion and to solve equations of motion

Trigonometry solution of triangles, circular measure, graphs of trigonometric functions, trigonometric identities, trigonometric equations

Permutations & Combinations permutations and combinations, binomial expansions

Vectors Vectors in two dimensions

What is the nature of assessment?

Both the International Mathematics and the Additional Mathematics courses are assessed by external exams at the end of Grade 10. Throughout the course, students will sit for topic tests, end-of-year exams, complete extended tasks for homework, as well as a number of mathematical investigations and modelling projects to develop their mathematical skills as well as their mathematical initiative and problem-solving skills. Students may also be required to make oral presentations.

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