CTU FCE Department of Mathematics
Thákurova 7, 166 29 Praha 6
Phone: +420 / 224 354 390

# Entrance Exam from Mathematics

### Requirements for the Entrance Exam

1. Algebraic expression adjustments (operations with fractions, quadratic trinomial decomposition, special factors as a3 + b3, powers with rational exponents).
2. Equations and inequalities (linear equations, quadratic equations, equations with absolutes value resp. two absolute values, equations with parameter, irrational equations, systems of equations, linear inequalities, quadratic inequalities, inequalities with absolute value).
3. Sequences (arithmetic sequence, geometric sequence, a sequence entered recursively).
4. Functions, their properties and graphs (linear, quadratic, rational, exponential and logarithmic function). Simple exponential and logarithmic equations.
5. Complex numbers (algebraic form, trigonometric form, operations with complex numbers, the absolute value of complex numbers, De Moivre's formula, quadratic equations, binomial equations).
6. The similarity and congruence theorem of triangles, Pythagoras's theorem, Euclid's theorem.
7. Basic geometric shapes in space (mutual position of lines and planes, simple bodies, their graphic representation).
8. Perimeters, areas, surface areas and volumes of basic geometric shapes using trigonometry.
9. Trigonometry (trigonometric function, simple trigonometric identities, basic trigonometry theorems and their applications).
10. Analytic geometry of linear and quadratic objects in the plane (vectors, intersection of lines, angle of lines, equations of conic sections – standard and general form).

Constructive problems of Stereometry are not included in the entrance exam due to the nature of test. The knowledge of stereometry and the basics of Monge projection is examined in an entry test (at the beginning of November) in the subject Constructive Geometry.