# Framework curricula for secondary schools

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Probability, statistics

 DEVELOPMENTAL TASKS, ACTIVITIES CONTENTS PREREQUISITES OF MOVING AHEAD Considering circumstances as necessary. Comparing a priori estimates with calculations. Simple problems of probability calculation. The investigation of a few concrete distribution patterns. Operations with events in concrete probability calculations (‘and’, ‘or’, ‘not’). Learning how to construct models. Relative frequency. The classical model of probability. Awareness of the relationship between relative frequency and probability. Solving simple problems of probability. Using a PC to analyse statistical data and random phenomena. Interpreting everyday problems, analysing data in statistical publications and daily papers. Statistical sampling.

Year 12
Number of teaching hours per year: 128

Methods of thinking

 DEVELOPMENTAL TASKS, ACTIVITIES CONTENTS PREREQUISITES OF MOVING AHEAD Organising knowledge: establishing correlation between the various fields of mathematics. Equivalence, implication. Relations between set theory and logic. Organisation of knowledge. Prerequisites listed under lower grades. Improving deductive skills. The review of the acquired verification methods. Some examples to complete induction. Review of knowledge in connection with combination theory and graphs.

Arithmetic and algebra

 DEVELOPMENTAL TASKS, ACTIVITIES CONTENTS PREREQUISITES OF MOVING AHEAD Synthesis and review. Sets of numbers. Prerequisites listed under lower grades. The history of mathematics (library and Internet use) Review of number theory. Real numbers and subsets. The application of the concept of numbers and operations with certainty. Interpreting operations, properties of operations. Approximate values. Equations Learning to work in a planned and disciplined manner. The importance of self-checks. Special algebraic identities of the second and third degree. The methods of finding solutions to equations. The role of the fundamental set (domain). Inequalities. Equation / inequality systems. Expressions of the second degree. Equations of the second degree, Viete formulae. Expressions and equations with square roots. Exponential, logarithmoc and trigonometric expressions and simple equations. Improving problem solving skills, reading skills and analysing skills in connection with texts. Solving verbalised problems.

Functions and sequences

 DEVELOPMENTAL TASKS, ACTIVITIES CONTENTS PREREQUISITES OF MOVING AHEAD The application of mathematics in practical life. Problems from the history of mathematics. The concept of sequence. Arithmetic sequence and geometric sequence, the n-th element, the sum of the first n elements. The calculation of compound interest. Examples to other sequences (recursion). Calculating the n-th element and the sum of the first n elements in an arithmetic / geometric sequence in exercises. Using compound interest calculation in simple practical exercises. Synthesis and review Prerequisites listed under lower grades. Improving abstraction skills. Improving the way of looking at functions. Using functions in practice and in science. The review and synthesis of what has been learned about functions. The representation of the basic functions. Functional transformations. f(x) + c; f (x+c); c f (x); f (c x). The analysis of functions with the help of the plot of the function.

Geometry, measurement

 DEVELOPMENTAL TASKS, ACTIVITIES CONTENTS PREREQUISITES OF MOVING AHEAD Improving the way of looking at space. Improving aesthetic skills. The correlative position, distance and angle of spatial configurations. The theorem of the straight line perpendicular to a plane. Simple polyhedrons. In addition to the prerequisites listed under lower grades: knowing the definition of the correlate position, distance and angle of spatial configurations. The practical application of mathematics in the- geometry of space. Connecting plane geometry and the geometry of space. Establishing analogies. Review of calculations of area and circumference. The surface and volume of polyhedrons. Cylindric bodies, the surface and volume of a cylinder. Conical bodies, the surface and volume of a cone. The volume of the frustum of a cone / pyramid. The surface and volume of a sphere. Applying the learned formulae to calculate surface and volume in simple exercises. Synthesis and review The basic concepts of geometry, point sets. Improving the way of looking at functions. Improving deductive skills. Review of geometrical transformations. Theorems in connection with triangles and their applications. Theorems in connection with rectangles and their applications. Theorems in connection with circles Applying the correlation between the various fields of mathematics. Vectors and the co-ordinates of a vector. Vector operations, their properties and applications. The orthogonal co-ordinate system. the equation of configurations. Trigonometric relationships and their applications.

Probability, statistics

 DEVELOPMENTAL TASKS, ACTIVITIES CONTENTS PREREQUISITES OF MOVING AHEAD The practical role and application of descriptive statistics and probability calculation. Using a computer to handle statistical data and to investigate random phenomena. The investigation of statistical data and samples (opinion poll, quality control). Prerequisites listed under lower grades. Using a geometrical model to determine probability. The determination of probability with the help of a geometrical measure. Review: The properties of data sets: arithmetic mean, weighted geometrical mean, median, modal value, standard deviation. Frequency, relative frequency. The classical probability model. Solving simple probability calculation exercises.