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Exam Review

Key Facts: Slovakia Maturita Math Exam

The Slovak maturita external mathematics test (EČ MS) is administered centrally by NIVaM on behalf of the Ministry of Education (MŠVVaM SR).

The external mathematics test lasts 150 minutes on paper; the 2026/2027 specification sets 160 minutes for an electronic administration.

The test contains 30 one-point tasks: 20 open short-answer tasks and 10 closed tasks with five options (A-E).

NIVaM's 2026/2027 specification assigns 7 tasks to basics of mathematics, 8 to functions, 6 to planimetry, 5 to stereometry and 4 to combinatorics, probability and statistics.

A candidate passes with more than 25 % in the test and an oral grade of 1-3, or more than 33 % with an oral grade of 4.

Permitted aids are drawing tools, the printed formula overview and a calculator that cannot draw graphs or solve equations symbolically.

The test result is reported as a percentage and a national percentile, and both appear on the maturita certificate.

A failed external test can be retaken in September or in the March session of the following school year.

FEI STU waives its mathematics entrance test for 2026/2027 applicants with at least the 70th percentile in the external mathematics test.

The NIVaM external mathematics test (EČ MS) has 30 one-point tasks in 150 minutes, 20 short-answer and 10 five-option closed tasks; candidates pass with more than 25 % (oral grade 1-3) or more than 33 % (oral grade 4).

Sample Slovakia Maturita Math Practice Questions

Try these sample questions to review concepts for the Slovakia Maturita Math exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 103+ question experience with AI tutoring.

1What is the exact value of the expression (3/4 - 1/6) / (5/12 + 1/3)?
A.7/9
B.5/8
C.3/5
D.7/12
Explanation: Compute the numerator: 3/4 - 1/6 = 9/12 - 2/12 = 7/12. Compute the denominator: 5/12 + 1/3 = 5/12 + 4/12 = 9/12 = 3/4. Dividing numerator by denominator gives (7/12) / (9/12) = 7/9.
2Simplify the algebraic expression (2x^2 - 8) / (x^2 + 4x + 4) for all real values of x where it is defined.
A.2(x + 2) / (x - 2)
B.2(x - 2) / (x + 2)
C.(2x - 4) / (x - 2)
D.2 / (x + 2)
Explanation: Factor the numerator: 2x^2 - 8 = 2(x^2 - 4) = 2(x - 2)(x + 2). Factor the denominator: x^2 + 4x + 4 = (x + 2)^2. Canceling the common factor (x + 2) for x != -2 yields 2(x - 2) / (x + 2).
3What is the solution set in R of the linear equation 3(2x - 5) - 4(x - 2) = 5x - 1?
A.x = 3
B.x = -1
C.x = -2
D.x = 2
Explanation: Expand the left-hand side: 6x - 15 - 4x + 8 = 2x - 7. The equation becomes 2x - 7 = 5x - 1. Rearranging terms: 2x - 5x = -1 + 7, which gives -3x = 6, hence x = -2.
4What is the product of the real roots of the quadratic equation 3x^2 - 10x + 8 = 0?
A.10/3
B.8
C.-8/3
D.8/3
Explanation: By Vieta's formulas for ax^2 + bx + c = 0, the product of the roots is x_1 * x_2 = c/a. Here a = 3 and c = 8, so the product is 8/3. Factoring confirms it: (3x - 4)(x - 2) = 0 gives the roots 4/3 and 2, and 4/3 * 2 = 8/3.
5What is the solution set in R of the inequality |2x - 3| <= 5?
A.[-1, 4]
B.(-infinity, -1] U [4, infinity)
C.[-4, 1]
D.[-1, 5]
Explanation: The absolute value inequality |2x - 3| <= 5 is equivalent to the compound inequality -5 <= 2x - 3 <= 5. Adding 3 to all parts gives -2 <= 2x <= 8. Dividing by 2 yields -1 <= x <= 4, which is the closed interval [-1, 4].
6Evaluate the logarithmic expression log_2(32) + log_3(1/27) - log_5(sqrt(5)).
A.5/2
B.3/2
C.1
D.2
Explanation: Evaluate each term individually: log_2(32) = 5 since 2^5 = 32. log_3(1/27) = log_3(3^-3) = -3. log_5(sqrt(5)) = log_5(5^(1/2)) = 1/2. Combining these gives 5 + (-3) - 1/2 = 2 - 1/2 = 3/2.
7What is the solution in R of the exponential equation 4^(x + 1) = 8^(x - 1)?
A.x = 3
B.x = 4
C.x = 2
D.x = 5
Explanation: Express both bases as powers of 2: 4 = 2^2 and 8 = 2^3. The equation becomes (2^2)^(x + 1) = (2^3)^(x - 1), which simplifies to 2^(2x + 2) = 2^(3x - 3). Equating exponents: 2x + 2 = 3x - 3, which gives 3x - 2x = 2 + 3, so x = 5.
8What is the solution in R of the equation log_4(3x + 1) = 2?
A.3
B.7/3
C.5
D.5/3
Explanation: Convert the logarithmic equation to exponential form: 3x + 1 = 4^2 = 16. Subtracting 1 gives 3x = 15, so x = 5. Checking the argument: 3(5) + 1 = 16 > 0, which is strictly in the domain.
9What is the solution set in R of the rational inequality (2x - 6) / (x + 1) >= 0?
A.(-infinity, -1) U [3, infinity)
B.[-1, 3]
C.(-1, 3]
D.(-infinity, -1] U [3, infinity)
Explanation: Find critical points where the numerator or denominator is zero: 2x - 6 = 0 => x = 3; x + 1 = 0 => x = -1. Note that x != -1 because division by zero is undefined. Test the sign on the intervals (-infinity, -1), (-1, 3), and (3, infinity): for x < -1, (-)/(-) = +; for -1 < x < 3, (-)/(+) = -; for x >= 3, (+)/(+) = +. The inequality is satisfied for x in (-infinity, -1) U [3, infinity).
10For what values of the parameter k in R does the quadratic equation x^2 + (k - 2)x + (k + 1) = 0 have exactly one real solution (a double root)?
A.k = 0 and k = 4
B.k = 0 and k = 8
C.k = -2 and k = 4
D.k = 2 and k = -4
Explanation: A quadratic equation has exactly one real solution if and only if its discriminant D = 0. Here a = 1, b = k - 2, and c = k + 1. D = b^2 - 4ac = (k - 2)^2 - 4(1)(k + 1) = k^2 - 4k + 4 - 4k - 4 = k^2 - 8k. Setting D = 0 gives k(k - 8) = 0, which yields k = 0 or k = 8.

About the Slovakia Maturita Math Exam

Independent study practice for the maturita in mathematics (maturitná skúška z matematiky) in Slovakia, focused on its centralized external test (externá časť, EČ MS), which NIVaM (formerly NÚCEM) administers under the School Act (Zákon č. 245/2008 Z. z.) and Decree No. 224/2022 Z. z. on secondary schools. The official test has 30 one-point tasks in 150 minutes: 20 open short-answer tasks and 10 closed tasks with five options (A-E), drawn from the national target requirements (Cieľové požiadavky, ŠPÚ 2019) in five topic areas. A school-based oral part (ÚFIČ) completes the subject. Permitted aids are drawing instruments, the formula overview printed in the test booklet and a non-graphing calculator without symbolic algebra. This bank is an English-language, four-option multiple-choice study adaptation for practising the underlying concepts and calculations; it is not an official translation and does not simulate the Slovak- or Hungarian-language paper, its open-response tasks or the oral examination.

Exam sponsor: NIVaM (Národný inštitút vzdelávania a mládeže), on behalf of the Ministry of Education, Research, Development and Youth of the Slovak Republic. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

30 questions

Time Limit

150 minutes (paper test); 160 minutes if taken electronically under the 2026/2027 specification; oral part 20 + 20 minutes.

Passing Score

>25 % (at least 8/30 points) with oral grade 1–3, or >33 % (at least 10/30 points) with oral grade 4 under Decree No. 224/2022 Z. z.

Exam / Certification Fees

Free; centralized state examination fully funded by the Ministry of Education for enrolled secondary school students.

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

7 of 30 tasks (23%)

Základy matematiky (Basics of Mathematics)

Logic and sets, numbers, variables and expressions (powers, roots, percentages, positional numeral systems), elementary number theory, and equations, inequalities and their systems, including absolute-value, rational, exponential and logarithmic equations.

8 of 30 tasks (27%)

Funkcie (Functions)

Properties of functions and sequences; linear and quadratic functions and arithmetic sequences; power and linear fractional functions; exponential and logarithmic functions, geometric sequences and interest; trigonometric functions.

6 of 30 tasks (20%)

Planimetria (Plane Geometry)

Basic plane figures and their metric properties (triangles, sine and cosine rules, circles, polygons), plane analytic geometry (vectors, scalar product, equations of lines and circles, distances, angles), loci, similarity and congruence mappings, and construction tasks.

5 of 30 tasks (17%)

Stereometria (Solid Geometry)

Parallel projection, coordinates in space, positional and metric relations of lines and planes (angles, distances, cross-sections), and surface areas and volumes of cubes, cuboids, prisms, pyramids, cylinders, cones and spheres.

4 of 30 tasks (13%)

Kombinatorika, pravdepodobnosť a štatistika (Combinatorics, Probability and Statistics)

Counting rules, permutations, variations and combinations (with and without repetition), classical, complementary and geometric probability, independent events, and statistical measures (mean, median, mode, variance, standard deviation).

Preparing for the Slovakia Maturita Math Exam

What You Need to Know

  • Passing score: >25 % (at least 8/30 points) with oral grade 1–3, or >33 % (at least 10/30 points) with oral grade 4 under Decree No. 224/2022 Z. z.
  • Exam length: 30 questions
  • Time limit: 150 minutes (paper test); 160 minutes if taken electronically under the 2026/2027 specification; oral part 20 + 20 minutes.
  • Exam / certification fees: Free; centralized state examination fully funded by the Ministry of Education for enrolled secondary school students. Official sources

Using Our Practice Resources

  • Work through all 103 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Slovakia Maturita Math: Suggested Study Strategy

1Study the formula overview (prehľad vzťahov) printed on the last sheet of past NIVaM tests so you know which formulas are provided and which you must remember.
2Pay close attention to domain restrictions when solving rational, radical, and logarithmic equations; extraneous roots frequently arise from squaring or logarithmic transformations.
3For planimetry and stereometry problems, always draw a clear, labeled diagram identifying given angle measures and right triangles before applying the Pythagorean theorem or trigonometric laws.
4Practice setting up coordinate systems for analytic geometry questions to verify vector orthogonality using the dot product.
5Time yourself when completing multi-step calculation tasks to ensure you can complete 30 problems within the 150-minute allocation.

Frequently Asked Questions

What is the external test (EČ MS) of the Slovak maturita in mathematics?

It is the centralized external test (externá časť, EČ MS) of the maturita in mathematics, administered nationwide by NIVaM at Slovak gymnasia and secondary vocational schools under the School Act. The subject also includes a school-based oral part (ÚFIČ).

What is the passing score for Slovak Maturita mathematics in 2026?

Under Decree No. 224/2022 Z. z., as summarized in NIVaM's basic information for the 2026 maturita, a student passes the maturita in mathematics with an oral (ÚFIČ) grade of 1, 2 or 3 and more than 25 % in the external test (at least 8 of 30 points), or with an oral grade of 4 and more than 33 % in the test (at least 10 of 30 points).

How long is the test and what aids are permitted?

The paper test lasts 150 minutes; NIVaM's 2026/2027 specification allows 160 minutes when the test is taken electronically. Candidates may use writing and drawing instruments, the formula overview printed on the last sheet of the test booklet, and a calculator that is not part of a mobile phone and cannot draw graphs, simplify algebraic expressions or compute roots of equations.

Is this practice question bank an official NIVaM test?

No. This is independent practice by OpenExamPrep: an English-language, four-option multiple-choice study adaptation of the topics in the Slovak maturita in mathematics. It is not an official NIVaM test or translation and does not simulate the open-response tasks, the five-option closed tasks or the oral examination.