Please read the information on this page before applying.

Please note that applicants from Croatia and EU who are applying through the National IT System of Applications to Higher Education Institutions www.postani-student.hr do not need to apply through this page.

**Before you start your bachelor’s application**

Make sure you have all your supporting documents scanned and ready to upload. Required documents include:

- Certificate of citizenship/passport photocopy
- Original Certificate of completed upper secondary school degree from your country along with an official translation into English or Croatian (if issued in a different language to these)
- Original Transcript of grades for all years of secondary school along with official translations into English or Croatian (if issued in a different language to these)
- Proof of knowledge of the English language
- Proof of knowledge of intermediate level mathematics in Croatian or English language
- Curriculum Vitae in the English language
- Motivation letter in the English language.

**Admission requirements**

To meet the entry requirements for bachelor's level studies, all students must fulfill the following requirements:

**General requirement**: A successfully completed upper secondary (high school) education**English language requirement**: Documented proficiency in English**Specific requirement**: Documented knowledge in Mathematics - intermediate level (the equivalent of Croatian State Matura exam from Mathematics - Higher/Extended level (A)).

**Meeting the requirements**

Candidates with Croatian matriculation certificates

**Meeting the general requirement**

To document your eligibility, please submit the Secondary School Certificate and transcript of grades for all four upper secondary years (Svjedodžba, razred 1 - 4). Please note that with the graduation year of 2010 and later, a state matura exam (državna matura) is also required.

**Meeting the English language requirement**

The English language requirement you can meet with your upper secondary studies with English at the advanced level as part of your Matura exam (državna matura) with the graduation year of 2010 and later.

You can also demonstrate that you meet the English language requirement through an internationally approved English test equivalent to B2 English level according to the Common European Framework of Reference for Languages - CEFRL.

**Meeting the specific requirement**

You can meet the requirement with your upper secondary studies with Mathematics at the advanced level as part of your written Matura exam (državna matura) with the graduation year of 2010 and later. Please submit the results of the Croatian State Matura exam from Mathematics, Higher/Extended level (A) is required.

Candidates with other matriculation certificates

**Meeting the general requirement**

Each applicant must deliver an officially authorized copy of an upper secondary school graduation certificate and, if the school certificate does not clearly show the content and scope of subjects that were studied, also certified secondary school transcripts with an official translation into English or Croatian (if issued in a different language to these).

**Meeting the English requirement**

English language proficiency equivalent to the Croatian Matura exam from English at the advanced level is required. The requirement can be satisfied through a result equal to, or higher than, those stated in the following (or similar) internationally recognized English tests:

- IELTS Academic/IELTS UKVI: an overall mark of 5.5 and no section below 5.0
- TOEFL iBT Paper-based: Score of 4.0 (scale 1 - 6) in written test, the total score of 530
- TOEFL iBT Internet-based: Score of 17 (scale 0 - 30) in written test, the total score of 72
- University of Cambridge ESOL Examinations (Cambridge ESOL): B2 First (FCE), or Cambridge English: First (First Certificate in English) grade A, B, or C

The language requirement can also be fulfilled through previous university and upper secondary school studies equivalent to the above-stated tests.

**Meeting the specific requirement**** - Qualifications **

The list below summarizes the minimum requirements for the bachelor programmes at FER. You must have **at least one of the qualifications listed** here or provide us comparable results for other recognized qualifications (specifically required scores for internationally recognized qualifications may be provided on request). Any test results should not be older than three years.

List of qualifications:

- SAT Composite Score (Math Reading & Writing)
- In the New SAT: Min composite score: 1240, including a score in Mathematics of at least 620
- In the Old SAT: Min composite Score (Math Reading Writing) 1790, including a score in Mathematics of at least 620

- SAT Subject Test in Mathematics, level I or II
- Min score: 700

- ACT Composite Score
- Min composite score: 26, including a score in Mathematics of at least 26

- International Baccalaureate Diploma
- Min composite score: 32, including a score in Mathematics HL or Further Mathematics HL of at least 6

- GCE AS Levels or GCE A-Levels (not including General Studies, Critical Thinking or Key Skills)
- Min score: AAB, including an A in Mathematics

**Meeting the specific requirement**** - Mathematical knowledge**

Students are expected to master mathematical knowledge from the following topics:

- Number sets N, Z, Q, R i C
- understand number sets N, Z, Q, R and C (natural numbers, integers, rational numbers, real numbers and complex numbers)
- compare numbers
- understand and use intervals and interval notation
- write down subsets of real numbers as intervals and represent them on a number line
- use standard and trigonometric form of complex numbers

- Elementary operations
- add, subtract, multiply and divide
- determine the rounded numbers and the absolute value of the numbers
- use a calculator

- Percentage and ratios
- understand and use percentages
- understand and use ratios

- Algebraic expression and algebraic fractions
- calculate with powers and roots
- add, subtract and multiply algebraic expressions
- use identities for square and cub of binomial, for difference of squares and cubes and for sum of
- add, subtract, multiply and divide algebraic fractions
- isolating a one variable by another from algebraic equation
- understand and apply binominal theorem

- Units of measurements
- use fundamental measures (units of length, , area, volume, mass, time and money)
- Convert unit of measurement
- Use unit of measurement in geometry and word problems

- Mathematical modeling
- apply mathematical models related to algebraic expressions and calculations to solve problems in everyday life

- Functions – definition of a function
- use functions define algebraically, graphically, numerically in tables, or by verbal descriptions
- add, subtract, multiply, divide and compose functionsž

- Linear and quadratic functions, absolute value functions, second root function, polynomial and rational functions, exponential and logarithmic functions, trigonometric functions
- determine the domain of a function
- find the image of a function
- calculate function values
- draw/sketch/construct the graph of a function
- sketch the table of a function
- interpret the graph of a function
- calculate zeros of the function
- find the point of intersection between function graph and x/y-axis
- determine the function which corresponds to the given graph
- determine intervals on which the function increases/decreases
- interpret the graph of the function
- determine if a function is even or odd
- Quadratic functions
- determine coefficients and discriminate
- find the local minimum/maximum and the vertex of parabola
- Polynomial and rational functions
- draw the graph of polynomials (of degree 1, 2 and 3)
- draw the graph of rational function (with polynomials of degree 1 or 2 in numerator and denominator)
- Exponential and logarithmic functions
- draw the graph of composition of linear and exponential or logarithmic functions
- apply exponential and logarithmic basic identities
- Trigonometric functions
- define trigonometric functions on the unit circle
- determine the fundamental period of a function and apply properties of periodic function to trigonometric functions
- use basic trigonometric identities
- apply trigonometric formulas for angle sum
- apply product-to-sum and sum-to-product trigonometric identities
- recognize and graph trigonometric functions of thr form
- f(x) = Asin(Bx C) D
- f(x) = Acos(Bx C) D

- Sequences
- recognize the given sequences
- recognize the arithmetic sequences
- determine the nth term and the term sum of arithmetic sequence
- recognize the geometric sequences
- determine the nth term and the term sum of geometric sequence

- Derivation of functions
- find derivation of the constant function, polynomial functions and trigonometric functions
- find the derivation of the sum, difference, product, quotient and composition of functions
- determine the tangent line at a point of the graph of the differential function
- use the differential calculus to analyze functions
- apply mathematical models related to algebraic expressions and calculations to solve problems in everyday life

- Mathematical modeling
- apply mathematical models related to functions to solve problems in everyday life

- Linear equations and inequations
- solve linear equations and inequations

- Quadratic equations and inequations
- solve quadratic equations and inequations
- use Vieta’s formulas

- Absolute value equations and inequations, root equations and inequations
- solve absolute value equations and inequations
- solve root equations and inequations

- Simple polynomials and rational equations and inequations
- solve equations/ inequations by factoring
- solve equations/ inequations by substitution; for instance biquadratic equation

- Exponential and logarithmic equations and inequations
- solve exponential equations/ inequations with same base
- solve equations/ inequations using definition of logarithm
- solve equations/ inequations by logarithm both sides of equation/inequation
- solve equations/inequations using basic properties of logarithms and exponents
- solve equations/inequations which can be reduced to quadratic equation/inequation by substitution

- Trigonometric equations
- find general and particular solution of trigonometric equation using definition of trigonometric functions
- find general and particular solution of trigonometric equation using trigonometric identities

- Systems of equations and inequations
- solve systems of equations or inequations algebraically and graphically
- explain graphical solutions of system of equations or inequations

- Mathematical modeling
- use mathematical models related to equations or inequations to solve problems in everyday life

- Geometry basics in planimetry
- measure angles
- classify triangles
- use notions of congruent and similar triangles
- determine congruent triangles
- determine similar triangles
- calculate the scale (homotetic) factor
- apply Pythagorean theorem
- use properties of parallelograms, trapezoids and regular polygons
- determine and use parts of circle and disc (center, radius, arc, sector, central and inscribed angle, chord and tangent)
- use the Inscribed angle theorem and Thales theorem
- calculate the area and the circumference of circle

- Interrelation among geometric objects in tree-dimensional space
- determine the relationship between lines and planes in 3D space
- determine the intersection of a line and plane in 3D space
- determine the orthogonal projection of a point and a line segment onto a plane
- determine the angle between two lines and between a line and a plane

- Geometry basics in stereometry (prisms, pyramids, cylinders, cones, sphere)
- recognize and name of these solids
- determine parts of these solids (base, apex, height – altitude, lateral faces)
- find the surface area and the volume of these solids

- Trigonometry for right-angle triangles; Trigonometry for scalene triangles
- use the definition of sine, cosine and tangent in a right-angled triangle
- use the law of sine and the low of cosine
- aplly trigonometry in planimetry and stereometry (solid geometry )

- Coordinate system on a line and on a plane
- read and plot coordinates in the coordinate system
- calculate the distance between two given points
- find the coordinates of the midpoint of a line segment

- Vectors
- understand vector operations
- use coordinate vector
- find the length of a vector
- find the angle between two vectors

- Equations of a line
- use explicit and implicit equation of a line
- find the equation of the line given by a point and a slope
- find the equation of the line given by two points
- find the angle between two lines
- use the condition for parallel and perpendicular lines
- calculate the distance from a point to a line

- Second-order curves
- determine the equation of a circle in standard form
- determine the equation of a ellipse in standard form
- determine the equation of a hyperbola in standard form and find the equation of asymptotes
- determine the equation of a parabola in standard form
- find the interrelation between a second-order curve and a line
- determine the equation of tangent line to a curve
- apply the condition for a line to be tangent to the second –order curve

- Mathematical modeling
- use mathematical models related to geometry to solve problems in everyday life