100+ Free Přijímačky VŠE Matematika Practice Questions

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Key Facts: Přijímačky VŠE Matematika Exam

The VŠE mathematics entrance test is a Czech-language, five-option multiple-choice paper shared by faculties FFÚ, FMV and FPH, split into general-mathematics computations and word problems; it runs 60 minutes at FFÚ and FMV and 45 minutes at FPH, no calculators are allowed, and each dean sets the admission cut-off after the sitting.

Sample Přijímačky VŠE Matematika Practice Questions

Try these sample questions to test your Přijímačky VŠE Matematika exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1For n != 0 and n != +-1, simplify the algebraic expression: [(n + 3)/(n + 1) - (n - 3)/(n - 1)] * (n^2 - 1)/(4n).

A.-1

B.n

C.1

D.4

Explanation: Subtract the two fractions inside the brackets using the common denominator (n + 1)(n - 1) = n^2 - 1: [(n + 3)(n - 1) - (n - 3)(n + 1)] / (n^2 - 1) = [(n^2 + 2n - 3) - (n^2 - 2n - 3)] / (n^2 - 1) = 4n / (n^2 - 1). Multiplying by (n^2 - 1)/(4n) gives [4n / (n^2 - 1)] * [(n^2 - 1) / (4n)] = 1.

2For real numbers x and y such that x != y and x != -y, simplify the expression: (x^3 - y^3)/(x - y) - (x^3 + y^3)/(x + y).

A.0

B.2xy

C.2(x^2 + y^2)

D.-2xy

Explanation: Factor both numerators using sum and difference of cubes: x^3 - y^3 = (x - y)(x^2 + xy + y^2) and x^3 + y^3 = (x + y)(x^2 - xy + y^2). Dividing by the denominators yields (x^2 + xy + y^2) - (x^2 - xy + y^2) = x^2 + xy + y^2 - x^2 + xy - y^2 = 2xy.

3Simplify the radical expression for a > 0: (a^(1/2) * a^(2/3)) / a^(1/6).

A.a^(1/2)

B.a

C.a^2

D.1

Explanation: Apply the laws of exponents: a^(1/2) * a^(2/3) = a^(1/2 + 2/3) = a^(3/6 + 4/6) = a^(7/6). Dividing by a^(1/6) gives a^(7/6 - 1/6) = a^(6/6) = a^1 = a.

4Solve the linear equation in the set of real numbers R: (4x - 1)/3 - (x + 2)/2 = (x + 4)/6.

A.x = 0

B.x = 1

C.x = 2

D.x = 3

Explanation: Multiply every term by the common denominator 6: 2(4x - 1) - 3(x + 2) = x + 4. Expanding gives 8x - 2 - 3x - 6 = x + 4, which simplifies to 5x - 8 = x + 4. Transposing x to the left and -8 to the right yields 4x = 12, so x = 3. Substituting back: (12 - 1)/3 - (3 + 2)/2 = 11/3 - 5/2 = 7/6, and (3 + 4)/6 = 7/6.

5What is the sum of all real roots of the quadratic equation 2x^2 - 7x + 3 = 0?

A.3

B.7/2

C.3/2

D.-7/2

Explanation: By Vieta's formulas, for any quadratic equation ax^2 + bx + c = 0 with real roots, the sum of the roots is x_1 + x_2 = -b/a = -(-7)/2 = 7/2. Alternatively, solving using the quadratic formula gives discriminant D = 49 - 24 = 25, yielding roots x = (7 +- 5)/4, so x_1 = 3 and x_2 = 1/2; 3 + 1/2 = 7/2.

6Find all real solutions to the rational equation: (x + 2)/(x - 1) + 1/(x + 1) = 6/(x^2 - 1).

A.x = -5 and x = 1

B.x = -5 only

C.x = 1 only

D.No real solution

Explanation: The domain requires x != 1 and x != -1 because x^2 - 1 = (x - 1)(x + 1). Multiplying both sides by (x - 1)(x + 1) gives (x + 2)(x + 1) + (x - 1) = 6. Expanding yields x^2 + 3x + 2 + x - 1 = 6, which simplifies to x^2 + 4x - 5 = 0. Factoring gives (x + 5)(x - 1) = 0, so candidate solutions are x = -5 and x = 1. Since x = 1 makes the denominators zero, it is an extraneous root. Thus, x = -5 is the only valid solution.

7Solve the linear inequality in the set of real numbers R: (3x - 5)/2 - (x - 1)/3 <= 1.

A.(-infinity, 19/7]

B.[19/7, infinity)

C.(-infinity, 17/7]

D.(-infinity, 3]

Explanation: Multiply the inequality by 6 (a positive number, so the inequality sign does not change): 3(3x - 5) - 2(x - 1) <= 6. Expanding gives 9x - 15 - 2x + 2 <= 6, which simplifies to 7x - 13 <= 6. Adding 13 to both sides yields 7x <= 19, so x <= 19/7. The solution set is (-infinity, 19/7].

8Find the set of all real numbers x satisfying the quadratic inequality: x^2 - 2x - 15 <= 0.

A.(-infinity, -3] U [5, infinity)

B.[-3, 5]

C.(-5, 3)

D.[-5, 3]

Explanation: Factor the quadratic expression: x^2 - 2x - 15 = (x - 5)(x + 3). The roots are x = -3 and x = 5. The graph of y = x^2 - 2x - 15 is an upward-opening parabola, so it lies on or below the x-axis exactly between its roots, endpoints included. Therefore, the solution set is the closed interval [-3, 5].

9Find the set of all real numbers x in R satisfying the rational inequality: (x + 5)/(3x - 6) < 1.

A.(-infinity, 2] U [11/2, infinity)

B.(2, 11/2)

C.(-infinity, 2) U (11/2, infinity)

D.(11/2, infinity)

Explanation: Subtract 1 from both sides instead of multiplying by the denominator, whose sign is unknown: (x + 5)/(3x - 6) - 1 < 0. Over the common denominator this is [(x + 5) - (3x - 6)] / (3x - 6) = (-2x + 11) / (3x - 6) < 0. The numerator vanishes at x = 11/2 and the denominator at x = 2. Sign analysis: for x < 2 the numerator is positive and the denominator negative, so the quotient is negative; for 2 < x < 11/2 both are positive, so the quotient is positive; for x > 11/2 the numerator is negative and the denominator positive, so the quotient is negative. The solution set is therefore (-infinity, 2) U (11/2, infinity).

10Solve the absolute value equation in R: |2x - 5| = 3x - 2.

A.x = 7/5 and x = -3

B.x = 7/5

C.x = -3

D.No real solution

Explanation: Since the absolute value is non-negative, we must have 3x - 2 >= 0, so x >= 2/3. For 2x - 5 >= 0 (x >= 5/2): 2x - 5 = 3x - 2 => x = -3, which contradicts x >= 5/2 and x >= 2/3 (extraneous). For 2x - 5 < 0 (x < 5/2): -(2x - 5) = 3x - 2 => -2x + 5 = 3x - 2 => 5x = 7 => x = 7/5 = 1.4. Since 2/3 <= 1.4 < 5/2, x = 7/5 is the unique real solution.

About the Přijímačky VŠE Matematika Exam

The Přijímací zkouška z matematiky is the common mathematics entrance test used by three faculties of the Prague University of Economics and Business (Vysoká škola ekonomická v Praze — VŠE): the Faculty of Finance and Accounting (FFÚ), the Faculty of International Relations (FMV) and the Faculty of Business Administration (FPH). VŠE publishes a single content specification for all three. The test has two parts — computational problems from general mathematics (algebraic manipulation, equations and inequalities, systems, sequences, functions, exponential and logarithmic functions, trigonometric functions, complex numbers, combinatorics and analytic geometry) and applied word problems (proportion and shared work, propositions and sets with Venn diagrams, percentages and averages, combinatorics, sequences, and plane and solid geometry). Timing and scoring differ by faculty: FFÚ allows 60 minutes for a test marked out of 100 points, FMV allows 60 minutes on a 1,000-point scale, and FPH allows 45 minutes. Calculators, tablets, phones and mathematical tables are all forbidden, but a summary of key formulas from Katedra matematiky VŠE comes with the test paper. The Faculty of Informatics and Statistics (FIS) does not use this test; it admits on Scio NSZ results instead. This practice bank is an English-language, four-option MCQ study adaptation built from the official VŠE content specification. It is not an official translation and does not simulate the real paper, which is written in Czech and offers five options (a–e) per item.

Assessment

Two parts in one sitting: Part 1 (Příklady z obecné matematiky) with computational items, and Part 2 (Slovní úlohy) with word problems. On the official 2023 sample paper for FFÚ and FPH, Part 1 accounted for 60 of the 100 points and Part 2 for the remaining 40. Every item offers five choices (a–e) with exactly one correct answer, and the last choice is normally 'jiná odpověď' (another answer).

Time Limit

60 minutes at FFÚ and FMV; 45 minutes at FPH

Passing Score

No fixed university-wide pass mark. Each dean announces point cut-offs (bodové hranice) after the test, based on the applicant ranking. For 2026/2027 FMV required a minimum of 400 of 1,000 points on the mathematics test plus a programme total such as 1,540 points; FFÚ and FPH admit by rank on the combined mathematics and language score.

Exam Fee

1,050 CZK application fee per e-přihláška for admissions run in academic year 2026/2027 (Rector's Order PR 1/2026, effective 1 September 2026); the June 2026 round charged 990 CZK. The fee is non-refundable and covers one application, not the individual test. (Vysoká škola ekonomická v Praze (VŠE) — FFÚ, FMV and FPH; content specified by Katedra matematiky (KMAT))

Přijímačky VŠE Matematika Exam Content Outline

Not published

Úpravy výrazů, rovnice a nerovnice (Expressions, Equations & Inequalities)

Simplification of algebraic and rational expressions, factorisation, linear, quadratic, rational, irrational and absolute-value equations and inequalities, and systems of equations and inequalities.

Not published

Funkce, posloupnosti a řady (Functions, Sequences & Series)

Properties, graphs and domains of functions, exponential and logarithmic equations and inequalities, arithmetic and geometric progressions, and infinite geometric series.

Not published

Goniometrické funkce a komplexní čísla (Trigonometry & Complex Numbers)

Trigonometric values, identities and equations, and complex numbers in algebraic and trigonometric form including modulus, conjugates, Moivre's theorem and roots in C.

Not published

Analytická geometrie a kombinatorika (Analytic Geometry & Combinatorics)

Vector operations and the dot product, general and parametric equations of lines, mutual positions and distances, circles and conic sections, permutations, variations, combinations and the binomial theorem.

Not published

Slovní úlohy (Word Problems)

Part 2 of the paper: direct and inverse proportion and shared work, propositions, sets and Venn diagrams, percentages and averages, combinatorics, sequences, and plane and solid geometry, all tested through applied reasoning.

How to Pass the Přijímačky VŠE Matematika Exam

What You Need to Know

Passing score: No fixed university-wide pass mark. Each dean announces point cut-offs (bodové hranice) after the test, based on the applicant ranking. For 2026/2027 FMV required a minimum of 400 of 1,000 points on the mathematics test plus a programme total such as 1,540 points; FFÚ and FPH admit by rank on the combined mathematics and language score.
Assessment: Two parts in one sitting: Part 1 (Příklady z obecné matematiky) with computational items, and Part 2 (Slovní úlohy) with word problems. On the official 2023 sample paper for FFÚ and FPH, Part 1 accounted for 60 of the 100 points and Part 2 for the remaining 40. Every item offers five choices (a–e) with exactly one correct answer, and the last choice is normally 'jiná odpověď' (another answer).
Time limit: 60 minutes at FFÚ and FMV; 45 minutes at FPH
Exam fee: 1,050 CZK application fee per e-přihláška for admissions run in academic year 2026/2027 (Rector's Order PR 1/2026, effective 1 September 2026); the June 2026 round charged 990 CZK. The fee is non-refundable and covers one application, not the individual test.

Keys to Passing

Work through all 100 available questions
Review every answer and explanation
Track weak areas and revisit them
Use our AI tutor for tough concepts

Přijímačky VŠE Matematika Study Tips from Top Performers

1Review complex numbers thoroughly: unlike the CERMAT maturita common part, komplexní čísla are explicitly named in the VŠE specification, including algebraic and trigonometric form, modulus, and Moivre's theorem.

2Download the KMAT formula sheet from kmat.vse.cz before you start revising, so you know exactly which formulas are printed with the test and which you have to memorise.

3Practise multi-step arithmetic without a calculator. No aids are permitted, and at FPH you have only 45 minutes, so fraction and percentage work has to be fast and accurate.

4Master Venn diagrams and the negation of quantified statements: VŠE lists 'výroky a množiny, Vennův diagram' among the word-problem areas, and its sample papers use survey-style set problems.

5Work through both official sample papers and the 2023 papers for FFÚ/FPH and FMV published under 'Zkušební testy z minulých let' — note that the FMV variant uses the same items on a 1,000-point scale.

6Use the literature VŠE itself recommends: Klůfa J., Úvod do matematiky pro studenty VŠE (Ekopress, 2024) and Otavová M., Sýkorová I., Úvod do reálných funkcí pro studenty VŠE (Ekopress, 2022).

Frequently Asked Questions

Which VŠE faculties use this mathematics entrance test?

VŠE publishes one content specification headed 'Přijímací zkouška z matematiky – FFU, FMV, FPH', so the same scope applies to the Faculty of Finance and Accounting (FFÚ), the Faculty of International Relations (FMV) and the Faculty of Business Administration (FPH). The Faculty of Informatics and Statistics (FIS) does not use it and admits on Scio NSZ results instead.

How long is the test and how is it scored?

Timing and scoring are set by each faculty. FFÚ allows 60 minutes for a mathematics test marked out of a maximum of 100 points. FMV also allows 60 minutes but marks each of its three tests out of a maximum of 1,000 points, and required at least 400 of them for entry in 2026/2027. FPH allows 45 minutes for its mathematics test. VŠE does not publish a fixed number of items.

Are calculators or mathematical tables allowed during the exam?

No. The official specification states that no aids may be used — no calculator, tablet, mobile phone, or mathematical and physical tables. All arithmetic has to be done by hand.

What aids does VŠE provide to test takers?

A summary of the most important formulas prepared by the VŠE Department of Mathematics (Katedra matematiky) is supplied as part of the test assignment. The same sheet can be downloaded in advance from kmat.vse.cz, so you can learn exactly which formulas you will be given and which you must know by heart.

Can the mathematics test be waived?

Yes, through several routes that each faculty announces for the given round: strong secondary school grades in the relevant subjects, a qualifying result in the VŠE 'přijímačky nanečisto' mock exams (at least 60% per test at FMV and at least 70% per part at FPH in 2026), placement in national olympiad rounds, or completion of the VŠE 'nultý ročník' lifelong-learning year. FMV additionally converts a CERMAT Matematika rozšiřující result into points: grade 1 counts as 1,000 points, grade 2 as 900 and grade 3 as 800.

How does this practice bank compare with the official examination?

The official VŠE test is written in Czech and every item offers five options (a–e), with the fifth normally being 'jiná odpověď'. This bank is an English-language study adaptation on the site's standard four-option interface, built from the official VŠE content specification. It is a study aid for the examinable topics, not an official translation or a simulation of the real paper's format — work through the official sample papers on vse.cz for that.