### ENTRANCE EXAM

1. The arrangement of algebraic expressions (operations with fractions, factoring of quadratics and a3 + b3, powers with rational exponents).
2. Equations and inequalities (linear and quadratic equations, equations with absolute values, irrational equations, set of equations, linear and quadratic inequalities, inequalities with absolute value).
3. Sequences (arithmetic, geometric, recursive).
4. Functions, their characteristics and graphs (linear, quadratic, rational, exponential and logarithmic functions). Simple exponential and logarithmic equations.
5. Complex numbers (algebraic form, goniometric form, operations with complex numbers, absolute value of complex numbers, Moivre theorem, solving quadratic equations, binomial equations).
6. Geometric congruence and similarity of triangles, constructive problems in the xy-plane using Thales theorem, Pythagoras theorem, Euclidean theorems, theorems of central and inscribed angles, equal and similar representations in xy-plane).
7. Basic geometric shapes in 3D (the relative position of straight lines and planes, simple solids and their graphic representations).
8. Calculating perimeters / circumferences, areas and volumes of basic geometric shapes with the application of trigonometry.
9. Goniometry and Trigonometry (goniometric functions of general angles, sum theorems, simple goniometric equations, basic trigonometric theorems and their applications).
10. Analytic geometry of linear and quadratic shapes in the xy-plane (vectors, line intersections, deviations of two lines, equations of conic shapes in basic and translated positions).