book used in all mathematics courses:

International Mathematics for Cambridge IGCSE (0607) Entended, David Rayner, Jim Fensom, Oxford University Press, ISBN 978 019 841 6906

pre-DP Mathematics 1 (2op) MAY1 Figures and equations (2op)

General objectives The aim of the course is that the student

• revises the principles of percentage calculation
• is able to use comparability in problem solving
• deepens the expertise in fractional calculations
• revises the power calculation rules
• strengthens the understanding of the concept of function
• understands the principles of solving an equation and a pair of equations
• learns how to use software to draw and observe functions, and solve equations

Key content

• number sets and basic calculations
• opposite number, inverse, and absolute value
• percentage calculation
• power calculation rules (exponential integer)
• directly and inversely comparability
• function, graph and interpretation
• solving the first-degree equation
• pair of equation
• square and cubic root
• power function and power equation (degrees 2 and 3)

Assessment of the course

The assessment of the course is based on versatile evidence, and the assessment supports the development of the student's mathematical thinking and self-confidence, and maintains and strengthens the motivation to study. The assessment guides the student to evaluate his/her own competence and to develop his/her mathematics skills and understanding and long-term working skills. The course is assessed numerically on a scale of 4 to 10.

pre-DP Mathematics 2 (3op) MAA2 Functions and Equations 1 (3op)

General objectives

The aim of the course is that the student

• learns about the mathematical modelling of phenomena through polynomial, rational and root functions, knows the characteristics of polynomial, rational and root functions, knows how to solve related equations, and knows the link between polynomial functions’ zeros and polynomial factors
• is able to solve simple polynomial equations
• is able to use software for mathematical modelling, researching polynomial, rational and root functions, and solving polynomial, rational and root equations and polynomial equations in connection with applications.

Key content

• polynomial function, equation and inequality
• quadratic formula
• polynomial product and binomial formulas (square of sum, product of sum and difference)
• polynomic factors
• power function and power equation (exponential positive integer)
• rational functions and equations
• root functions and equations

Refine content

• Polynomes: Simplification of polynomials and the application of factors by zero points. Construct a polynomial expression by using zeros and one value. Binomial formulas in both directions.
• Polynomial equations and inequalities: solving the first and second degree equations, discriminant and the zero rule of product. Solving the higher-degree equations of which is based on the zero rule of product, grouping and/or separating a common factor. Bikvadrate and other equations that return into the second degree equation. Common root and power equations. The polynomic inequality can be solved at zero points or using the graph or test points (polynomial function can only change its sign at zero).
• Functions: Typical features of the secondary and tertiary polynomial function and the power function graph. The domain of the function and its effect on the function descriptor and equation solutions. Rules of square root and the simplification of square root expressions. Solving the root equation and evaluating the solution obtained (by checking or by checking the increase in the definition and square of the equation on the basis of the condition). Handling and simplifying of rational expressions. Simple rational equations.

Assessment of the course

The evaluation draws attention to numeracy, methodological selection, mathematical thinking and problem solving skills, justifying and analyzing conclusions, activity during the lessons, and software selection and use.

The assessment scale is a numerical assessment (4-10).

pre-DP Mathematics 3 (op2) MAA3 Geometry (2op)

General objectives

The aim of the course is that the student

• is trained to perceive and describe space and shape information in both two- and three-dimensional situations
• is able to apply similarity of figures, the Pythagora’s rule and the trigonometry of a right triangle
• trains to format, justify and use phrases containing geometric data
• is able to use software when studying plane figures and 3d-shapes with related geometry.

Key content

• similarity of plane figures and 3d-shapes
• sine and cosine rule
• calculation of lengths, angles and areas in polygone
• the geometry of the circle and its parts and lines associated to circle
• calculation of lengths, areas and volumes related to the cylinder, direct cone and sphere

Refine content

• Right Triangle: Pythagora’s theorem, trigonometric ratios of acute angle and memory triangles.
• Triangles and other polygons: sum of polygon angles, characteristics of equilateral triangle and parallelogram, and regular polygons. Sine rule and cosine rule and area of triangle.
• Similarity of figures and shapes, scale factor, and ratio of areas of similar figures, ratio of volumes of similar shapes. An angle-angle statement of the similarity of triangles and an angle-half-sentence.
• Circle: Length of circumference, arc, and chord. The area of the circle, sector and segment. Circular angle statement, tangent and tangent angle statement.
• Space geometry: Concepts related to the shapes (e.g. edge, face, bottom, lateral face, cuboid, pyramid, tetraedre). It is enough for the student to calculate the length, area and volume related to the sphere, cylinder, cone, as well as simple space angle calculations (e.g. angles created inside the cube) and drawings.
• use of a calculator to find of the values of the cosine and tangent and the solving of an acute angle.

Assessment of the course

The evaluation draws attention to numeracy, methodological selection, mathematical thinking and problem solving skills, justifying and analyzing conclusions, activity during the lessons, and software selection and use.

The assessment scale is a numerical assessment (4-10).

pre-DP Mathematics 4 (op3) MAA4 Analytical geometry and vectors (3op)

General objectives

The aim of the course is that the student

• understands how analytical geometry creates connections between geometric and algebraic concepts
• understands the geometric significance of the equation
• is able to solve the absolute value equations like | f(x) | = a or | f(x) | = | g(x) |
• understands vector concept and familiarizes itself with the basics of vector calculation
• is able to explore points, distances and angles of the two-dimensional coordinate system using vectors
• is able to solve plane geometry problems with vectors
• is able to use software to study curves, vectors and related applications.

Key content

• curve equation
• line, circle and quadratic equation
• equation group
• parallel and perpendicular lines
• absolute value equation
• distance of a point from a line
• basic characteristics of vectors
• addition, subtraction and product by scalar of plane vectors
• dot product and angle between vectors in plane

Refine content

• Curve equation: Cartesian plane coordinate system and its point, line, circle and parabola; The xy-plane points forms the equation form an xy-level curve; Line and

circular equations (different formats) and square complementing in connection with the processing of a circle or parabola equation; Tangents of a circle; Parabola (axis parallel to coordinate axes, focus point and directrix line) and different representations of the equation of parabola (zero-point and vertex-point equation); A pair of equations and methods for solving different intersections (two straight lines, circle and line, parabola and line, etc.) and the solution principle of the linear equation group.

• Absolute value: Definition of absolute value and equations that are resolved by definition. (The square increase method can be introduced, but the absolute value equation has been removed from the curriculum content.)
• Basic characteristics of vectors: The vector has direction and length. It is an object that indicates a transition (a certain amount, in a certain direction). Definitions and markings of key concepts related to zero vector, opposite vector, parallelism (parallelism, opposite direction and perpendicular), vector length, unit vector and angle between vectors.
• Vectors: The focus of the review is on xy-plane vectors. Presentation of the vector in the coordinate system by means of x- and y-directional components (i- and j-basic vectors). The general concept of position can be ignored. The parallelism and perpendicular of the lines, the angle of direction and the angle between the lines can be treated by methods of analytical geometry (by means of an angle factor) or by means of vectors (parallel vectors, dot product).
• use of calculator to form vectors, dot product and calculation of the angle between vectors.

Assessment of the course

The evaluation draws attention to numeracy, methodological selection, mathematical thinking and problem solving skills, justifying and analyzing conclusions, activity during the lessons, and software selection and use.

The assessment scale is a numerical assessment