In S4, students begin the more formal studying towards the eAssessment. At the end of S5 all students will sit the eAssessmemt at one of two levels: Standard is aimed at most students; Extended is aimed at the highest achieving students who might want to study Higher Level Maths at IB. At Europa we teach three groups at different levels. The Extended group will study for and sit the Extended eAssessment; the Standard Plus group will study the Standard course with some elements of the Extended course to prepare them better for AASL at IB or A-Level maths, but they will sit the Standard eAssessment; the Standard group will study for and sit the Standard eAssessment, but the teacher might teach some further bits if they think it is appropriate.
The structure of the courses is similar, with a few extra sub-topics in each unit for the Extended and Standard Plus groups. Student review and extend their knowledge of various number topics, such as indices and percentages, and then expand their knowledge with new topics in surds (Standard) and logarithms (Extended only). In algebra, students consolidate their knowledge of working with quadratics, and move on to solving quadratic equations, as well as developing algebraic fluency with algebraic fractions (Extended only). This is followed by increasing their knowlwedge of working with volumes and surface areas, and trigonometry, in both 2D and 3D. The year finishes with further development of understanding mathematical models, first developing their understanding of linear models, and then moving on to quadratic models.
S4 students will also begin to develop their more formal investigation and pattern spotting skills, a vital part of being a mathematician, which is assessed explicitly in the eAssessment. Student can practice their skills at finding the nth term of sequences, as well as the investigation structure.
S4 sees students develop their algebraic skills alongside modelling skills which are so vital in being able to answer a wide variety of mathematical problems.
In this unit students will learn about:
Linear sequences and finding the nth term
Combinations of linear sequences
Quadratic sequences and finding the nth term
Geometric sequences and finding the nth term
Formal notation for sequences (extended only)
The process and layout of a Mathematical Investigation
In this unit students will learn about:
The midpoint of two points
The distance between two points
Finding the gradient of lines
The equation of a straight line in the forms y=mx+c and ax+by=d
Working with parallel lines
Working with perpendicular lines (extended only)
Solving pairs of linear simultaneous equations
Finding perpendicular bisectors and shortest distances (extended only)
In this unit students will learn about:
Solving quadratic equations algebraically and graphically
Completing the square (extended only)
The different forms of a quadratic function
Solving pairs of simultaneous equations involving quadratics (extended only)
In this unit students will learn about:
The different types of number and their notations
Laws of indices
Working with bounds (extended only)
Absolute values
Surds
Logarithms (extended only)
In this unit students will learn about:
Direct and inverse proportion
Rearranging formulae
Algebraic Fractions (extended only)
Solving linear inequalities and representing these on the number line
Solving problems on linear programming involving linear inequalities in the Cartesian plane
Solving quadratic inequalities (extended only)
Simple Proof (Extended Only)
In this unit students will learn about:
What functions are
Graphing functions
Composite functions (extended only)
Inverse functions (extended only)
Domain and range (extended only)
Reciprocal functions
Exponential functions
Trigonometric functions
Circles (extended only)
Transforming functions (extended only)
In this unit students will learn about:
Circle theorems
Working with arcs and sectors of circles
Transformations of shapes (reflection, rotations, translations and enlargements)
Vectors (extended only)