Mathematics

The Gateway to Polish State Universities

GATAPU-General Aptitude Test for Admission to Polish Universities

The areas of Mathematics covered in the Aptitude Test :

Mathematics

Mathematical prerequisites:

Mathematics: knowledge of elementary mathematics will be assumed.  Questions may require the manipulation of mathematical expressions in a physical context. 

Algebra: properties of polynomials, including the solution of quadratics.  Graph sketching and transformations of variables. Solving linear equations and systems of linear equations.   Inequalities and their solution.

Geometry: planar- points, lines, planes, etc. areas: rectangles, triangles, polygons, circles; Pythagorean theorem. Basic properties and calculation of areas and volumes of: cubes, prisms, pyramids, cylinders, cones and spheres.

Elementary trigonometry including relationships between sin, cos and tan.

Elementary coordinate geometry.

Calculus: Differentiation as finding the slope of a curve, and the location of maxima, minima and points of inflection.

1. Numbers and number sets, basic mathematical logic

  • sets and their elements,
  • set algebra - operations of union, intersection, complementation as well as theirbasic properties,
  • logic - propositions, operations of conjunction, alternative, implication and equivalence,
  •  number sets - natural, integer, rational, irrational and real numbers; basic properties of algebraic operations,
  • modulus of a real number - its definition and properties; finding solutions of equations and inequalities involving absolute values.

2. Functions and their properties

  • a function, its argument, domain, range, graph; composition; the greatest and least value of a function over an interval; monotonicity of a function; definitions of an injective function, even/odd function; transformations of graphs (translation, mirror reflection, scaling).

3. Polynomials and rational functions

  • linear function - definition and graph,
  • quadratic function - definition, graph; Viete's formulae; finding solutions of equations and inequalities,
  • polynomials - definition; factorization, Bezout's theorem; finding solutions of equations and inequalities,
  • homographic functions - definition and graphs; finding solutions of equations and inequalities involving rational expressions.

4. Exponential and logarithmic functions

  • definitions, properties and graphs of exponential and logarithmic functions; finding solutions of equations and inequalities involving logarithms and exponentials.

5. Trigonometric functions

  • measuring angles; right triangle trigonometry; sine, cosine, tangent and cotangent functions, their graphs and properties; trigonometric identities; finding solutions of equations and inequalities.

6. Sequences

  • definition of a sequence; arithmetic and geometric sequences.

7. Plane geometry

  • points, lines, triangles, quadrilaterals, etc,
  • triangles - internal angles, exterior angles, area of a triangle; solving a triangle, triangle centers; the circles of a triangle; similar triangles,
  • transformations of 2-D space - translation, rotation, mirror reflection, scaling.

8. Analytic geometry in 2-D

  • vector algebra, a straight line, a circle and disc; distance in 2-D.

9. Solid geometry

  • incidence of planes and lines; dihedral angle; the cube the tetrahedron and other pyramids, cones and cylinders, the sphere; volume and area of these geometric objects

10. Probability theory and statistics

  • basic combinatorics - permutations with and without repetitions, variations with and without repetitions, combinations with and without repetitions; binomial coefficient; probability - its definition and properties; binomial experiment, basic descriptive statistics -mean, variance, standard deviation and their interpretation.


GATAPU 2008 in India

26-27 July 2008

GATAPU test shall be held in India by Polish Universities on 26th and 27th July.It shall be held simultaneously in four Indian Metropolitan cities

New Delhi

Kolkata

Mumbai

Chennai

Registration Centers

Approved Registration centers in India

GATAPU Application Form

Application form for GATAPU can be downloaded online

The Application form has to be dully filled. Approved Registration Centers shall need to check the Educational certificates before accepting and issuing the code number to the Candidates

Application forms without academical documents shall not be accepted.