Announcement on preparatory mathematics classes for the State Matura

Free Online Preparatory Mathematics Classes for the State Matura Examination

Dear Secondary-School Graduates and Future Students,

The Faculty of Computer Science and Engineering (FCSE) is pleased to announce FREE online preparatory classes in MATHEMATICS for the external examination subject MATHEMATICS within the State Matura examination, during the period 9 May 2026 – 3 June 2026.

The classes will be delivered by FCSE professors and teaching assistants.

The preparatory classes are organised to help secondary-school graduates—our future students—achieve the best possible results in the Mathematics examination for the State Matura, which will be held on 6 June 2026.

The preparatory classes will comprise 57 teaching hours (42 hours of core instruction + 15 hours of supplementary instruction), distributed evenly across 13 days and will cover all content prescribed by the Mathematics Examination Programme for the State Matura in general and vocational secondary education, which includes the following five areas:

• AREA 1: MATHEMATICAL LOGIC AND SETS (weighting: 7%)
• AREA 2: REAL AND COMPLEX NUMBERS (weighting: 12%)
• AREA 3: ALGEBRA (weighting: 40%)
• AREA 4: GEOMETRY (weighting: 34%)
• AREA 5: TRIGONOMETRY (weighting: 7%)

Class Schedule

Classes will be held according to the following schedule:

A further 15 hours (3 days × 5 hours) will be held to solve problems submitted by participants during the classes, according to the following schedule:

Mathematics Examination Programme for the State Matura

The Mathematics Examination Programme for the State Matura is provided below.

A. CONTENT

AREA 1: MATHEMATICAL LOGIC AND SETS

1. MATHEMATICAL LOGIC

• The concept of a proposition
• Logical operations (negation, conjunction, disjunction, implication and equivalence)
• Compound propositions
• Laws of logic (commutative, associative and distributive laws; implication replacement; law of non-contradiction; law of the excluded middle; De Morgan’s laws; modus ponens; modus tollens; and hypothetical syllogism)

2. SETS

• The concepts of a set and a subset
• Methods of defining sets
• Operations on sets
• Laws governing operations on sets

AREA 2: REAL AND COMPLEX NUMBERS

1. NUMBERS

• Natural numbers
• Integers
• Rational numbers
• Real numbers
• Complex numbers

2. OPERATIONS ON NUMBERS

• Natural numbers
• Integers
• Rational numbers
• Real numbers
• Complex numbers

3. PROPORTIONALITY OF QUANTITIES

• Ratios and proportions; direct and inverse proportionality
• Simple and compound rule of three
• Percentage calculations: percentage, below one hundred and above one hundred
• Proportional division
• Percentage calculations: of one hundred, below one hundred and above one hundred
• Interest calculations

AREA 3: ALGEBRA

1. ALGEBRAIC RATIONAL EXPRESSIONS

• Powers with natural-number exponents
• Integral rational expressions: monomials and polynomials
• Fractional rational expressions

2. LINEAR EQUATIONS AND LINEAR INEQUALITIES

• Linear equations in one unknown
• Linear inequalities in one unknown

3. LINEAR FUNCTIONS, SYSTEMS OF LINEAR EQUATIONS AND SYSTEMS OF LINEAR INEQUALITIES

• Real-valued functions
• Linear functions
• Systems of two linear equations in two unknowns
• Systems of two linear inequalities in one unknown

4. QUADRATIC EQUATIONS AND QUADRATIC FUNCTIONS

• Incomplete and complete quadratic equations
• Nature of the solutions of a quadratic equation
• Vieta’s formulas and their application
• The concept of a quadratic function
• Graphs of elementary quadratic functions
• Canonical form of a quadratic function; vertex of a parabola

AREA 4: GEOMETRY

1. GEOMETRIC FIGURES IN THE PLANE

• Basic geometric figures
• Rays, line segments and half-planes
• Circumference and circle
• Angles and types of angles
• Polygonal lines and polygons
• Vectors; operations on vectors

2. PERIMETER AND AREA OF PLANE FIGURES

• The concepts of perimeter and area
• Perimeter and area of rectangles, triangles, quadrilaterals and regular polygons
• Circumference of a circle and length of a circular arc
• Area of a circle and parts of a circle

3. GEOMETRIC SOLIDS

• Points, lines and planes
• Geometric solids
• Polyhedra and solids of revolution
• Intersections of geometric solids with a plane

4. SURFACE AREA AND VOLUME OF GEOMETRIC SOLIDS

• The concepts of surface area and volume of a solid
• Prisms
• Pyramids
• Cylinders
• Cones
• Spheres

AREA 5: TRIGONOMETRY

1. TRIGONOMETRIC FUNCTIONS IN A RIGHT-ANGLED TRIANGLE

• Measurement of angles (degrees and radians)
• Concept and definition of the trigonometric functions of an acute angle
• Trigonometric functions of complementary angles
• Values of the trigonometric functions of the angles 30°, 45° and 60°
• Fundamental trigonometric identities
• Solving a right-angled triangle