100+ Free Érettségi Mathematics Practice Questions

Pass your Hungarian Érettségi — Mathematics (Matematika Érettségi) exam on the first try — instant access, no signup required.

✓ No registration✓ No credit card✓ No hidden fees✓ Start practicing immediately

100+ Questions

100% Free

1 / 100

Question 1

Score: 0/0

If the first term of a geometric sequence is 100 and the common ratio is 0.5, what is the 5th term?

6.25

12.5

to track

2026 Statistics

Key Facts: Érettségi Mathematics Exam

The Hungarian Érettségi Mathematics exam is a compulsory written school-leaving exam administered by the Oktatási Hivatal, offered at intermediate (180 min, ~96 pts) and advanced (240 min + oral) levels, graded 1–5 with 25% as the minimum pass.

Sample Érettségi Mathematics Practice Questions

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

1Let A = {1, 2, 3, 4, 5} and B = {3, 4, 5, 6, 7}. How many elements are in A ∪ B?

A.5

B.7

C.3

D.10

Explanation: A ∪ B contains all elements that are in A or B (or both). The elements are {1, 2, 3, 4, 5, 6, 7}, so |A ∪ B| = 7. Using the inclusion-exclusion principle: |A ∪ B| = |A| + |B| − |A ∩ B| = 5 + 5 − 3 = 7.

2Which of the following is the negation of the statement: 'All even numbers are divisible by 4'?

A.No even number is divisible by 4

B.Some even number is not divisible by 4

C.All even numbers are not divisible by 4

D.Some even number is divisible by 4

Explanation: The negation of 'All P are Q' is 'There exists a P that is not Q', i.e., 'Some even number is not divisible by 4'. This is true: for example, 2 and 6 are even but not divisible by 4.

3What is the remainder when 2026 is divided by 7?

A.0

B.3

C.5

D.6

Explanation: Divide 2026 by 7: 7 × 289 = 2023, so 2026 − 2023 = 3. Therefore 2026 ÷ 7 = 289 remainder 3. We can verify: 7 × 289 + 3 = 2023 + 3 = 2026 ✓.

4How many positive divisors does 360 have?

A.18

B.24

C.12

D.30

Explanation: First find the prime factorisation: 360 = 2³ × 3² × 5¹. The number of divisors is (3+1)(2+1)(1+1) = 4 × 3 × 2 = 24. Each divisor corresponds to a choice of exponents for each prime.

5Simplify: log₂(32) + log₂(8) − log₂(16)

A.3

B.4

C.5

D.6

Explanation: log₂(32) = 5 (since 2⁵ = 32), log₂(8) = 3 (since 2³ = 8), log₂(16) = 4 (since 2⁴ = 16). Therefore: 5 + 3 − 4 = 4.

6Solve for x: 3^(x+1) = 81

A.x = 2

B.x = 3

C.x = 4

D.x = 5

Explanation: Write 81 as a power of 3: 81 = 3⁴. So 3^(x+1) = 3⁴, giving x + 1 = 4, therefore x = 3.

7What is the 10th term of the arithmetic sequence with first term a₁ = 4 and common difference d = 3?

A.28

B.31

C.34

D.37

Explanation: The nth term of an arithmetic sequence is aₙ = a₁ + (n−1)d. For n = 10: a₁₀ = 4 + 9 × 3 = 4 + 27 = 31.

8A geometric sequence has first term a₁ = 2 and common ratio q = 3. What is the sum of the first 4 terms?

A.26

B.80

C.162

D.54

Explanation: The sum of the first n terms of a geometric sequence is Sₙ = a₁(qⁿ − 1)/(q − 1). Here: S₄ = 2(3⁴ − 1)/(3 − 1) = 2(81 − 1)/2 = 80. Alternatively: 2 + 6 + 18 + 54 = 80.

9For the quadratic equation x² − 5x + 6 = 0, which of the following correctly lists both solutions?

A.x = 1 and x = 6

B.x = 2 and x = 3

C.x = −2 and x = −3

D.x = −1 and x = −6

Explanation: Factor x² − 5x + 6 = (x − 2)(x − 3) = 0. Setting each factor to zero: x − 2 = 0 gives x = 2, and x − 3 = 0 gives x = 3. Verify: 2 + 3 = 5 = sum of roots, 2 × 3 = 6 = product of roots. ✓

10Which real values of x satisfy the inequality 2x − 3 < 7?

A.x < 2

B.x > 5

C.x < 5

D.x ≤ 5

Explanation: Add 3 to both sides: 2x < 10. Divide both sides by 2: x < 5. The solution set is (−∞, 5), i.e., all real numbers strictly less than 5.

About the Érettségi Mathematics Exam

The Hungarian Érettségi (school leaving examination) in Mathematics — known as matematika érettségi — is a compulsory component of the Hungarian matura taken by all secondary school students seeking the érettségi bizonyítvány certificate. The exam is offered at two levels: középszint (intermediate) and emelt szint (advanced). At középszint, the written exam lasts 180 minutes and is divided into Part I (12 short closed-answer problems worth approximately 32 points) and Part II (6 extended multi-step problems worth approximately 64 points). Calculator use is permitted throughout. At emelt szint, the written exam is 240 minutes and includes an additional 20-minute oral examination, covering more complex topics including calculus. Topics span sets and logic, number theory, algebra, functions, sequences, equations and inequalities, plane and solid geometry, trigonometry, coordinate geometry, combinatorics, probability, statistics, and (for emelt szint) limits, derivatives, and integrals. The exam is centrally developed and assessed by the Oktatási Hivatal. Past examination papers are publicly available on the official website and are the best preparation resource. The 2026 main session takes place in May–June 2026.

Questions

18 scored questions

Time Limit

180 minutes (középszint written exam): approximately 57 minutes for Part I (12 short problems), remaining time for Part II (6 extended problems). Emelt szint: 240 minutes written plus 20-minute oral.

Passing Score

Minimum 25% overall (and at least 12% per exam part) to pass. Graded 1–5: 25–39% = 2 (Elégséges/Pass), 40–59% = 3 (Közepes/Satisfactory), 60–79% = 4 (Jó/Good), 80–100% = 5 (Jeles/Excellent).

Exam Fee

Középszint is free as part of compulsory schooling. Emelt szint (advanced level, outside mandatory subjects) costs approximately 80,000 HUF (~€200) in 2026. (Oktatási Hivatal (Educational Authority, Hungary))

Érettségi Mathematics Exam Content Outline

12%

Algebra and Logarithms

Exponent rules, radicals, exponential equations, logarithmic expressions, and algebraic manipulation.

12%

Functions

Linear, quadratic, exponential, logarithmic, and trigonometric functions; domain, transformations, composition, and inverse.

12%

Plane Geometry

Triangles, circles, polygons; area and perimeter; Pythagorean theorem; similarity and Heron's formula.

10%

Sequences

Arithmetic and geometric sequences, nth-term formulas, sums, infinite geometric series, and financial applications.

10%

Equations and Inequalities

Linear, quadratic, radical, and exponential equations; linear and quadratic inequalities; systems of equations.

Number Theory and Arithmetic

Divisibility, primes, GCD, modular arithmetic, percentages, ratios, and interest calculations.

Solid Geometry

Volume and surface area of cylinders, cones, spheres, prisms, pyramids, and cubes.

Trigonometry

Trigonometric ratios, standard values, Pythagorean identity, Sine Rule, Cosine Rule, and equations.

Coordinate Geometry

Distance, midpoint, line equations, perpendicularity, circle equations, vectors, and section formula.

Combinatorics

Permutations, combinations, factorials, and systematic counting.

Probability

Classical probability, addition and multiplication rules, conditional probability, and independent events.

Statistics

Mean, median, mode, range, standard deviation, and the empirical rule.

Sets and Logic

Set operations, Venn diagrams, logical connectives, quantifiers, and negation.

Calculus (Emelt Szint)

Derivatives using the power rule, second derivative test, indefinite integrals, definite integrals, and area under curves.

How to Pass the Érettségi Mathematics Exam

What You Need to Know

Passing score: Minimum 25% overall (and at least 12% per exam part) to pass. Graded 1–5: 25–39% = 2 (Elégséges/Pass), 40–59% = 3 (Közepes/Satisfactory), 60–79% = 4 (Jó/Good), 80–100% = 5 (Jeles/Excellent).
Exam length: 18 questions
Time limit: 180 minutes (középszint written exam): approximately 57 minutes for Part I (12 short problems), remaining time for Part II (6 extended problems). Emelt szint: 240 minutes written plus 20-minute oral.
Exam fee: Középszint is free as part of compulsory schooling. Emelt szint (advanced level, outside mandatory subjects) costs approximately 80,000 HUF (~€200) in 2026.

Keys to Passing

Complete 500+ practice questions
Score 80%+ consistently before scheduling
Focus on highest-weighted sections
Use our AI tutor for tough concepts

Érettségi Mathematics Study Tips from Top Performers

1Download and practise all available official past papers from the Oktatási Hivatal website — the exam format has been stable since 2005, and pattern recognition is a major advantage.

2Learn to work precisely under time pressure: Part I of the középszint exam rewards fast, accurate short answers, so practise completing the 12-question section in under 60 minutes.

3Memorise exact values of trigonometric functions at standard angles (0°, 30°, 45°, 60°, 90°) and key algebraic identities, as these are tested repeatedly across exam papers.

4For Part II extended problems, always show full working — partial credit is awarded, so a correct method with an arithmetic error still earns marks.

5Focus on the five highest-weight topic areas (algebra, functions, plane geometry, sequences, equations) as they consistently account for the majority of points across both exam parts.

6For emelt szint, dedicate additional study time to calculus (derivatives, integrals, extrema) and to the oral examination topics published annually by the Oktatási Hivatal.

Frequently Asked Questions

What are the two levels of the Hungarian Érettségi Mathematics exam?

The exam is offered at középszint (intermediate level) and emelt szint (advanced level). Középszint is compulsory for all students; emelt szint is optional but earns extra university admission points and is required by some STEM degree programmes.

How is the középszint mathematics exam structured?

The középszint written exam lasts 180 minutes and has two parts: Part I contains 12 short closed-answer problems (approximately 32 points), and Part II contains 6 extended multi-step problems (approximately 64 points). Calculators are permitted throughout.

What score do I need to pass the mathematics érettségi?

You need at least 25% of total marks overall, with at least 12% in each exam part. Grade 5 (Jeles/Excellent) requires 80–100%; Grade 4 (Jó/Good) requires 60–79%; Grade 3 (Közepes/Satisfactory) requires 40–59%; Grade 2 (Elégséges/Pass) requires 25–39%.

What topics are covered in the middle-level mathematics érettségi?

Topics include sets and logic, number theory, algebra (powers, roots, logarithms), functions, sequences, equations and inequalities, plane geometry, solid geometry, trigonometry, coordinate geometry, combinatorics, probability, and statistics.

Is calculus included in the Hungarian mathematics érettségi?

Calculus (limits, derivatives, and integrals) is primarily an emelt szint (advanced level) topic. It may appear briefly at középszint but is not a major focus; at emelt szint it is a significant component alongside an oral examination.

Where can I find official past papers for the mathematics érettségi?

All official past examination papers with marking schemes are freely available on the Oktatási Hivatal website (oktatas.hu) going back to 2005. Practising these papers is the most effective preparation strategy, as the exam format is highly consistent year to year.