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Key Facts: Državna Matura Math A Exam

Administered centrally across Croatia by NCVVO (Nacionalni centar za vanjsko vrednovanje obrazovanja).

Regulatory framework governed by the Pravilnik o polaganju državne mature (NN 56/2026).

Total testing time is exactly 180 minutes in a single uninterrupted morning session.

The total score available is 60 points across multiple-choice, short-response, and extended-response items.

Minimum passing score is 25% (15.00 points) to achieve the grade dovoljan (2).

Candidates are provided an official standardized formula sheet containing algebraic, trigonometric, analytic, and calculus formulas.

Approved non-programmable scientific calculators without graphing or CAS features are permitted.

Examination results are directly integrated into the national central university application system (Postani-student).

The Croatian Državna matura Mathematics Level A is a 180-minute, 60-point national exam testing advanced algebra, calculus, geometry, and probability; 15/60 points (25%) is required to pass.

Sample Državna Matura Math A Practice Questions

Try these sample questions to review concepts for the Državna Matura Math A exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1An article's price is increased by 25%. By what percentage must the new price be decreased to return exactly to its original price?
A.25%
B.15%
C.20%
D.22.5%
Explanation: Let the original price be P. After a 25% increase, the new price is 1.25*P. To return to P, the price must decrease by 0.25*P. The percentage reduction relative to the new price is (0.25*P / 1.25*P) * 100% = (1/5) * 100% = 20%.
2What is the simplified exact value of the numerical expression (sqrt(5) + sqrt(3))^2 - sqrt(60)?
A.8 + 2*sqrt(15)
B.2
C.8
D.sqrt(8)
Explanation: Expanding the square gives (sqrt(5))^2 + 2*sqrt(5)*sqrt(3) + (sqrt(3))^2 = 5 + 2*sqrt(15) + 3 = 8 + 2*sqrt(15). Note that sqrt(60) = sqrt(4 * 15) = 2*sqrt(15). Subtracting this gives (8 + 2*sqrt(15)) - 2*sqrt(15) = 8.
3For the complex number z = (3 - 4i) / (1 + 2i), what is the value of its real part, Re(z)?
A.-1
B.1
C.2
D.-2
Explanation: Multiply numerator and denominator by the complex conjugate of the denominator, (1 - 2i): z = ((3 - 4i)(1 - 2i)) / ((1 + 2i)(1 - 2i)) = (3 - 6i - 4i + 8i^2) / (1 - 4i^2) = (3 - 10i - 8) / (1 + 4) = (-5 - 10i) / 5 = -1 - 2i. Thus, the real part is Re(z) = -1.
4What is the product of all real solutions to the equation |2x - 5| = 9?
A.14
B.-14
C.-7
D.7
Explanation: The equation |2x - 5| = 9 splits into two cases: 2x - 5 = 9 or 2x - 5 = -9. From the first case, 2x = 14 => x = 7. From the second case, 2x = -4 => x = -2. The product of the two solutions is 7 * (-2) = -14.
5Let x1 and x2 be the roots of the quadratic equation 2x^2 - 7x + 3 = 0. What is the value of (1 / x1) + (1 / x2)?
A.3/7
B.-7/3
C.7/2
D.7/3
Explanation: By Viète's formulas for ax^2 + bx + c = 0, the sum of roots is x1 + x2 = -b/a = 7/2 and the product of roots is x1 * x2 = c/a = 3/2. The expression simplifies to (1 / x1) + (1 / x2) = (x1 + x2) / (x1 * x2) = (7/2) / (3/2) = 7/3.
6For all real numbers x != 2 and x != -2, simplify the algebraic expression: (x / (x - 2)) - (8 / (x^2 - 4)) - (2 / (x + 2)).
A.(x - 2) / (x + 2)
B.0
C.(x + 4) / (x^2 - 4)
D.1
Explanation: Find a common denominator: x^2 - 4 = (x - 2)(x + 2). Bringing all fractions over this denominator gives [x(x + 2) - 8 - 2(x - 2)] / (x^2 - 4) = [x^2 + 2x - 8 - 2x + 4] / (x^2 - 4) = (x^2 - 4) / (x^2 - 4) = 1.
7What is the exact numerical value of log_3(54) - log_3(2) + log_3(1/9)?
A.-1
B.3
C.1
D.2
Explanation: Using the logarithmic properties log_b(x) - log_b(y) = log_b(x/y), we combine the first two terms: log_3(54) - log_3(2) = log_3(54/2) = log_3(27) = 3, because 3^3 = 27. Then log_3(1/9) = log_3(3^(-2)) = -2. Adding these values gives 3 + (-2) = 1.
8The first term of an arithmetic sequence is a1 = 7 and the common difference is d = 4. What is the sum of the first 20 terms, S20?
A.900
B.850
C.940
D.920
Explanation: The sum of the first n terms of an arithmetic sequence is given by Sn = (n / 2) * [2*a1 + (n - 1)*d]. Substituting n = 20, a1 = 7, and d = 4: S20 = (20 / 2) * [2(7) + (20 - 1)(4)] = 10 * [14 + 19 * 4] = 10 * [14 + 76] = 10 * 90 = 900.
9If z = 1 + i*sqrt(3), what is the exact value of z^9 in the set of complex numbers?
A.512
B.-512i
C.-512
D.512i
Explanation: Write z in polar (trigonometric) form: modulus r = sqrt(1^2 + (sqrt(3))^2) = sqrt(4) = 2. The argument is theta = arctan(sqrt(3)/1) = pi/3. By de Moivre's formula, z^9 = r^9 * [cos(9*theta) + i*sin(9*theta)] = 2^9 * [cos(3*pi) + i*sin(3*pi)]. Since cos(3*pi) = -1 and sin(3*pi) = 0, we have z^9 = 512 * (-1 + 0*i) = -512.
10An infinite geometric series with first term a1 and common ratio q (|q| < 1) has a sum of S = 18. If the sum of the squares of all its terms is S_squares = 108, what is the value of the common ratio q?
A.1/3
B.1/2
C.2/3
D.1/4
Explanation: For the original series, S = a1 / (1 - q) = 18, so a1 = 18(1 - q). For the series of squared terms, the first term is a1^2 and the common ratio is q^2: S_squares = a1^2 / (1 - q^2) = 108. Substituting a1 = 18(1 - q): [324(1 - q)^2] / [(1 - q)(1 + q)] = 324(1 - q) / (1 + q) = 108. Dividing both sides by 108 gives 3(1 - q) / (1 + q) = 1. Cross-multiplying: 3 - 3q = 1 + q => 4q = 2 => q = 1/2.

About the Državna Matura Math A Exam

The Državna matura in Mathematics Level A (Matematika viša razina) is the standardized national exit examination administered across Croatia by the National Centre for External Evaluation of Education (NCVVO). As the higher tier of the compulsory state matura mathematics requirement, Level A is designed for students seeking entrance into university faculties with intensive quantitative requirements, such as engineering (FER, FSB), natural sciences (PMF), medicine, economics, architecture, and computer science. The examination consists of 60 scoreable points administered over a single 180-minute testing session. Tasks span four structural domains: Numbers & Algebra (30%), Functions & Calculus (30%), Geometry & Trigonometry (25%), and Modeling & Statistics (15%). Candidates are provided an official formula booklet (knjižica formula) and are permitted an approved non-programmable scientific calculator without graphic or symbolic algebraic capabilities. Grading follows a national percentage scale where 25% (15.00 points) represents the threshold for a passing grade (dovoljan 2).

Exam sponsor: NCVVO (Nacionalni centar za vanjsko vrednovanje obrazovanja). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

60 questions

Time Limit

180 minutes

Passing Score

15 out of 60 points (25%)

Exam / Certification Fees

Free for regular seniors; fee per exam applies for re-sits/external candidates.

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.

30%

Brojevi i algebra (Numbers & Algebra)

Real and complex numbers (algebraic and trigonometric forms), powers, radicals, logarithms, linear and quadratic equations/inequalities, algebraic fractions, systems of equations, polynomials, and arithmetic and geometric sequences.

30%

Funkcije (Functions & Calculus)

Domain, range, symmetries, inverse and composite functions; polynomial, rational, exponential, logarithmic, and trigonometric functions; limits, derivatives, tangents, monotonicity, extrema, and definite/indefinite integrals.

25%

Geometrija (Geometry & Trigonometry)

Planar figures, solid geometry (prisms, pyramids, cylinders, cones, spheres), trigonometric ratios and equations, sine and cosine laws, 2D/3D vectors, dot product, and conic sections (circle, ellipse, hyperbola, parabola).

15%

Modeliranje i statistika (Modeling, Combinatorics, Probability & Statistics)

Permutations, combinations, variations, binomial theorem, classical and conditional probability, descriptive statistics (measures of central tendency and dispersion), and real-world mathematical modeling.

Preparing for the Državna Matura Math A Exam

What You Need to Know

  • Passing score: 15 out of 60 points (25%)
  • Exam length: 60 questions
  • Time limit: 180 minutes
  • Exam / certification fees: Free for regular seniors; fee per exam applies for re-sits/external candidates. Official sources

Using Our Practice Resources

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

Državna Matura Math A: Suggested Study Strategy

1Familiarize yourself thoroughly with the official NCVVO formula booklet (knjižica formula) so you know exactly which formulas are provided and where they are located, avoiding wasting time memorizing formulas already in the booklet.
2Practice full past exam papers under strict 180-minute timed conditions to develop pacing for the three distinct problem types (MCQs, short answer, and multi-step extended response).
3Focus heavily on calculus fundamentals: mastering product, quotient, and chain rules for derivatives, finding local extrema and points of inflection, and setting up definite integrals for geometric areas.
4Review analytic geometry thoroughly: know how to find tangent lines to circles, ellipses, and parabolas, as conic section problems regularly award high points on Level A exams.
5Master vector algebra in 3D: practice scalar products, angle calculations between vectors, vector collinearity, and computing areas or perpendicular projections using vector methods.
6Double-check domain restrictions (uvjeti) on all logarithmic, radical, and rational equations before selecting or recording solutions, as extraneous roots are a frequent trap.

Frequently Asked Questions

What is the difference between Level A (viša razina) and Level B (osnovna razina) in Croatian Državna matura Mathematics?

Level A (viša razina) covers the complete 4-year general gimnazija mathematics curriculum, including differential and integral calculus, complex numbers in trigonometric form, vectors in 3D, conic sections, and advanced stereometry. Level B (osnovna razina) covers core foundational mathematics and excludes calculus, complex numbers, conic sections, and advanced trigonometry. Level A is required or strongly rewarded by faculties of engineering, sciences, economics, and medicine.

How many points are required to pass the Državna matura Mathematics Level A exam?

The minimum passing score (prag prolaznosti for grade dovoljan 2) is 25%, which corresponds to 15.00 out of 60 points. Higher grades typically require: dobar (3) around 50% (30.00 pts), vrlo dobar (4) around 70% (42.00 pts), and odličan (5) around 85% (51.00 pts), though final cutoffs are verified annually by NCVVO.

What aids and calculators are allowed during the exam?

Candidates are allowed to use standard writing and drawing tools (blue or black ballpoint pen, pencil, eraser, ruler/triangle, compass) and an approved scientific calculator. The calculator must not have symbolic algebra (CAS), graphing display capabilities, or programmable memory. In addition, an official formula booklet (knjižica formula) containing standard algebraic, trigonometric, and calculus formulas is supplied directly inside the exam packet.

What is the structure and duration of the Level A Mathematics examination?

The exam lasts 180 continuous minutes without breaks. It carries a maximum of 60 points distributed among three types of questions: multiple-choice questions (closed items with 4 options), short constructed-response questions (where only the final numerical or algebraic answer is scored), and extended-response tasks (where full mathematical steps, proofs, and working must be presented on the designated lined pages).

When is the Državna matura Mathematics exam administered?

The exam is administered twice per academic year: the primary summer examination window (ljetni rok) takes place in late June, and the autumn re-sit window (jesenski rok) takes place in late August or early September for candidates retaking or improving scores.

Who must take the Mathematics Level A examination?

All gimnazija students must take either Level A or Level B mathematics to graduate. Vocational school students (strukovne škole) take it if they plan to apply to higher education institutions that mandate Level A for enrollment rankings via the Postani-student portal.

How does negative marking work on multiple-choice questions?

There is no negative marking on the Croatian Državna matura. Incorrect choices or blank answers simply earn 0 points, so candidates should ensure they attempt and mark an answer for every single item.