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Exam Review

Key Facts: Estonian Upper-Secondary Narrow Mathematics Exam Exam

8 compulsory courses (ROK Lisa 3)

Kitsas matemaatika's national curriculum annex covers number sets/equations, trigonometry, vectors/line equations, probability/statistics, functions, sequences/derivative, planimetry/integral, and stereometry

Gumnaasiumi riiklik oppekava, Lisa 3 - Kitsas matemaatika ainekava

100 points / 12 tasks / 270 minutes

Two-part written exam: Part I (120 min, 7 tasks, 50 pts) and Part II (150 min, 5 tasks, 50 pts), separated by a 45-minute break, starting at 10:00

Kitsa ja laia matemaatikakursuse riigieksamite eristuskiri (SA Innove/Harno)

1% to pass (1 point)

The exam counts as 'sooritatud' (completed) at just 1% of the maximum result; there is no higher numeric pass/fail threshold

Haridus- ja teadusministri maarus nr 54, ptk 4 par 37

4,855 candidates, 35.4 avg (2026)

Kitsas matemaatika candidates and average score in spring 2026 (down 3.7 points from 2025), versus 5,670 candidates and a 59.2 average on the lai (broad) paper

ERR, 'Harno: eksamitulemused pusivad mullusega sarnasel tasemel' (June 2026)

20 May 2026

2025/2026 exam date for the gumnaasiumi riigieksam Matemaatika (kitsas and lai sat the same day); makeup sessions 25-29 May and 3 June 2026, results published 18 June 2026

Haridus- ja Teadusministeerium, EKSAMITE KALENDER 2026

Formula sheet added to booklet (2026)

Harno now includes an official valemileht inside the exam booklet itself, though its assessment center director noted this did not raise average scores versus the prior year

ERR, 'Harno: eksamitulemused pusivad mullusega sarnasel tasemel' (June 2026)

Free 100-question MCQ study bank for Estonia's kitsas matemaatika riigieksam (narrow-course mathematics), covering the computations behind all 8 official ROK Lisa 3 courses: algebra/equations/inequalities, trigonometry, vectors and line/circle equations, probability and statistics, functions/logarithms/percentages, sequences and the derivative, planimetry and the integral, and stereometry. Official exam: two-part written paper, 100 points across 12 tasks (Part I 120 min/50 pts, 45-min break, Part II 150 min/50 pts), officially starting 10:00, scheduled 20 May 2026 (same day as the lai/broad paper); considered completed at just 1% (1 point), with no separate pass threshold. In 2026, 4,855 candidates sat kitsas (35.4-point average, 2 perfect scores) versus 5,670 on lai (59.2 average, 63 perfect scores). Registration and track choice due 20 January; personal calculator and writing/drawing instruments allowed, plus an official Harno-provided formula sheet in the booklet as of 2026 - no outside reference materials. Not an official-format simulation; free for regular gumnaasium candidates.

Sample Estonian Upper-Secondary Narrow Mathematics Exam Practice Questions

Try these sample questions to review concepts for the Estonian Upper-Secondary Narrow Mathematics Exam exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Solve for x: 3x - 7 = 2x + 5.

A.12

B.-2

C.2

D.-12

Explanation: Subtract 2x from both sides to get x - 7 = 5, then add 7 to both sides to find x = 12. Always move variable terms to one side and constant terms to the other before combining.

2Evaluate: |-3| + |2 - 5|.

A.6

B.0

C.4

D.-6

Explanation: The absolute value of -3 is 3, and 2 - 5 = -3, whose absolute value is also 3. Adding these gives 3 + 3 = 6.

3Simplify: x^3 * x^(-1), for x ≠ 0.

A.x^2

B.x^3

C.x^(-3)

D.x^4

Explanation: When multiplying powers with the same base, add the exponents: 3 + (-1) = 2, giving x^2.

4Solve for x: 2^x = 8.

A.3

B.4

C.2

D.16

Explanation: Since 8 = 2^3, the equation 2^x = 2^3 gives x = 3 by matching exponents on equal bases.

5Solve for x: x^2 - 5x + 6 = 0.

A.x = 2 or x = 3

B.x = -2 or x = -3

C.x = 1 or x = 6

D.x = 2 or x = -3

Explanation: Factor the quadratic as (x-2)(x-3)=0, so the solutions are x=2 and x=3, since these are the two numbers that multiply to 6 and add to 5.

6Solve the inequality: x^2 - 4x + 3 > 0.

A.x < 1 or x > 3

B.1 < x < 3

C.x ≤ 1 or x ≥ 3

D.x < -1 or x > -3

Explanation: Factor as (x-1)(x-3)>0. Since the parabola opens upward, the expression is positive outside the roots, so the solution is x<1 or x>3.

7Solve the system: 2x + y = 7 and x - y = 2.

A.x = 3, y = 1

B.x = 1, y = 3

C.x = 3, y = -1

D.x = 2, y = 3

Explanation: Adding the two equations eliminates y: 3x = 9, so x = 3. Substituting back gives y = 7 - 2(3) = 1.

8Solve for x: (x + 3)/(x - 1) = 2.

A.x = 5

B.x = -5

C.x = 1

D.x = -1

Explanation: Multiply both sides by (x-1): x + 3 = 2(x-1) = 2x - 2, so 5 = x. Checking, x=5 does not make the denominator zero, so it is valid.

9Solve for x: √(2x + 3) = 5.

A.x = 11

B.x = 14

C.x = 1

D.x = 22

Explanation: Square both sides: 2x + 3 = 25. Subtract 3: 2x = 22, so x = 11.

10Simplify: (x^2 - 9)/(x - 3), for x ≠ 3.

A.x + 3

B.x - 3

C.x^2 - 3

D.x + 9

Explanation: Factor the numerator as a difference of squares: (x-3)(x+3). Dividing by (x-3) leaves x+3.

About the Estonian Upper-Secondary Narrow Mathematics Exam Exam

The Estonian Upper-Secondary State Examination in narrow-course mathematics (kitsas matemaatika riigieksam) is one of two parallel mathematics riigieksamid that Haridus- ja Noorteamet (Harno) administers each spring, alongside the more advanced lai matemaatika (broad) exam, both given as separate papers on the same day. Every gumnaasium graduate must choose one track - kitsas or lai, never both - as one of their three compulsory riigieksamid, alongside Eesti keel (or Eesti keel teise keelena) and a foreign-language riigieksam. Kitsas matemaatika is built from 8 compulsory courses set out in Lisa 3 of the gumnaasiumi riiklik oppekava (national curriculum annex): number sets/expressions/equations/inequalities, trigonometry, vectors in the plane with line and circle equations, probability and statistics, functions (including logarithms and percentage/compound-growth applications), sequences together with the function derivative, planimetry together with the definite integral, and stereometry. Contrary to a common assumption, the curriculum does include a basic derivative course (tangent lines, monotonic behaviour, simple extremum problems) and a basic definite-integral topic (area under simple polynomial curves via the Newton-Leibniz formula) - it is genuinely less advanced than lai matemaatika's 14-course sequence, but not calculus-free. The exam itself is a two-part written paper worth 100 points across 12 tasks - Part I (120 minutes, 7 tasks worth 50 points) and Part II (150 minutes, 5 tasks worth 50 points), separated by a 45-minute break, starting at the official time of 10:00 - mixing selective-response items with open-response items graded for partial credit at each solution step. In spring 2026, 4,855 candidates sat the kitsas paper, averaging 35.4 points (down 3.7 from 2025) with just 2 perfect scores, compared with 5,670 candidates and a 59.2-point average on the lai paper that year - a gap that reflects the two tracks' different curricular purposes rather than a simple difficulty scale, since kitsas matemaatika is designed around applying mathematics to everyday and scientific-literacy contexts rather than preparing students for STEM higher education. Registration, including the choice between kitsas and lai and between Estonian and Russian as the exam language, is due by 20 January. This free bank of 100 original multiple-choice questions is an MCQ study adaptation designed to build and check command of the computations behind all 8 kitsas matemaatika courses. It is not a simulation of the official exam, which requires full written solutions with partial credit awarded at each step of a 12-task, two-part paper.

Exam sponsor: Haridus- ja Noorteamet (Harno) - the Estonian Education and Youth Board, under the Haridus- ja Teadusministeerium (Ministry of Education and Research). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Official national gumnaasiumi riigieksam administered once a year each spring by Haridus- ja Noorteamet (Harno) under the Pohikooli- ja gumnaasiumiseadus and its implementing final-examination regulation. Every gumnaasium graduate must sit exactly one of two mathematics tracks - kitsas matemaatika (narrow) or lai matemaatika (broad) - never both, with both papers given on the same day. Kitsas matemaatika is built from 8 compulsory ROK Lisa 3 courses: number sets/expressions/equations/inequalities, trigonometry, vectors in the plane and line/circle equations, probability and statistics, functions (including logarithms and percentage/compound-growth applications), sequences and the function derivative, planimetry and the definite integral, and stereometry. The curriculum does include one basic derivative course (tangent lines, increasing/decreasing behaviour, simple extremum problems) and one basic definite-integral topic (area under simple polynomial curves), contrary to the common assumption that the narrow track omits calculus entirely - it simply stops short of the deeper calculus and additional geometry/modelling courses that lai matemaatika's 14-course sequence covers. Candidates choose their track and exam language (Estonian or Russian) when registering by 20 January. Permitted aids are limited to personal writing/drawing instruments and a basic pocket calculator; no textbooks, handbooks or outside formula sheets are allowed, though as of the 2026 sitting Harno itself includes an official valemileht (formula sheet) inside the exam booklet. This bank is a unified MCQ study adaptation covering the underlying computations across all 8 kitsas matemaatika courses - it does not reproduce the official exam's two-part written, partial-credit response format.

Time Limit

Part I runs 120 minutes and Part II runs 150 minutes, separated by a 45-minute break (270 minutes of working time plus the break); the official start time is 10:00. For the 2025/2026 school year, per Harno's confirmed EKSAMITE KALENDER 2026, the gumnaasiumi riigieksam Matemaatika (both kitsas and lai, sat the same day) is scheduled for 20 May 2026, with riigieksamite lisaeksamid (makeup sessions) running 25-29 May and 3 June 2026, and results published 18 June 2026.

Passing Score

Scored on a 0-100 point scale across 12 tasks (Part I: 4 tasks worth 5 points + 3 tasks worth 10 points = 50 points; Part II: 5 tasks worth 10 points = 50 points). The exam is considered 'sooritatud' (completed) once a candidate reaches at least 1% of the maximum result (a single point) - there is no higher numeric pass/fail threshold, since graduation requires completing rather than exceeding a specific score on each compulsory riigieksam. In spring 2026, 4,855 candidates sat the kitsas paper, averaging 35.4 points (down 3.7 from 2025) with only 2 perfect scores, versus 5,670 candidates on the lai paper averaging 59.2 points with 63 perfect scores.

Exam / Certification Fees

No fee for regularly enrolled gumnaasium candidates - riigieksamid are free state examinations administered by Harno. Kutseoppeasutuse final-year students, previous graduates retaking or improving a result, and holders of a foreign or Estonian secondary credential may also sit it at no cost.

Exam sponsor website

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

Official sources

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.

Study emphasis ~14%

Algebra: Equations, Inequalities and Expressions

Linear, quadratic, rational and radical equations and inequalities, absolute value, exponent/radical simplification and systems of equations.

Study emphasis ~10%

Trigonometry

Trigonometric functions of any angle, special-angle values, identities, the Law of Sines and Cosines, triangle and sector area.

Study emphasis ~12%

Vectors and Line/Circle Equations

Vector operations, magnitude, dot product, collinearity, and the equations of lines and circles including tangent lines.

Study emphasis ~11%

Probability and Statistics

Classical probability, permutations and combinations, independent events, and descriptive statistics (mean, median, variance).

Study emphasis ~13%

Functions, Logarithms and Percentages

Function evaluation and domain, logarithm laws, exponential/logarithmic equations, and percentage/compound-interest applications.

Study emphasis ~12%

Sequences and the Derivative

Arithmetic and geometric sequences and series with financial applications, plus basic derivatives, tangent lines and extremum problems.

Study emphasis ~13%

Planimetry and the Integral

Areas and the Pythagorean theorem for triangles, quadrilaterals and polygons, plus basic definite integrals for area under simple curves.

Study emphasis ~15%

Stereometry

Volume and surface area of prisms, pyramids, cylinders, cones and spheres, plus 3D distance calculations.

Preparing for the Estonian Upper-Secondary Narrow Mathematics Exam Exam

What You Need to Know

Passing score: Scored on a 0-100 point scale across 12 tasks (Part I: 4 tasks worth 5 points + 3 tasks worth 10 points = 50 points; Part II: 5 tasks worth 10 points = 50 points). The exam is considered 'sooritatud' (completed) once a candidate reaches at least 1% of the maximum result (a single point) - there is no higher numeric pass/fail threshold, since graduation requires completing rather than exceeding a specific score on each compulsory riigieksam. In spring 2026, 4,855 candidates sat the kitsas paper, averaging 35.4 points (down 3.7 from 2025) with only 2 perfect scores, versus 5,670 candidates on the lai paper averaging 59.2 points with 63 perfect scores.
Assessment: Official national gumnaasiumi riigieksam administered once a year each spring by Haridus- ja Noorteamet (Harno) under the Pohikooli- ja gumnaasiumiseadus and its implementing final-examination regulation. Every gumnaasium graduate must sit exactly one of two mathematics tracks - kitsas matemaatika (narrow) or lai matemaatika (broad) - never both, with both papers given on the same day. Kitsas matemaatika is built from 8 compulsory ROK Lisa 3 courses: number sets/expressions/equations/inequalities, trigonometry, vectors in the plane and line/circle equations, probability and statistics, functions (including logarithms and percentage/compound-growth applications), sequences and the function derivative, planimetry and the definite integral, and stereometry. The curriculum does include one basic derivative course (tangent lines, increasing/decreasing behaviour, simple extremum problems) and one basic definite-integral topic (area under simple polynomial curves), contrary to the common assumption that the narrow track omits calculus entirely - it simply stops short of the deeper calculus and additional geometry/modelling courses that lai matemaatika's 14-course sequence covers. Candidates choose their track and exam language (Estonian or Russian) when registering by 20 January. Permitted aids are limited to personal writing/drawing instruments and a basic pocket calculator; no textbooks, handbooks or outside formula sheets are allowed, though as of the 2026 sitting Harno itself includes an official valemileht (formula sheet) inside the exam booklet. This bank is a unified MCQ study adaptation covering the underlying computations across all 8 kitsas matemaatika courses - it does not reproduce the official exam's two-part written, partial-credit response format.
Time limit: Part I runs 120 minutes and Part II runs 150 minutes, separated by a 45-minute break (270 minutes of working time plus the break); the official start time is 10:00. For the 2025/2026 school year, per Harno's confirmed EKSAMITE KALENDER 2026, the gumnaasiumi riigieksam Matemaatika (both kitsas and lai, sat the same day) is scheduled for 20 May 2026, with riigieksamite lisaeksamid (makeup sessions) running 25-29 May and 3 June 2026, and results published 18 June 2026.
Exam / certification fees: No fee for regularly enrolled gumnaasium candidates - riigieksamid are free state examinations administered by Harno. Kutseoppeasutuse final-year students, previous graduates retaking or improving a result, and holders of a foreign or Estonian secondary credential may also sit it at no cost. Official sources

Using Our Practice Resources

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Estonian Upper-Secondary Narrow Mathematics Exam: Suggested Study Strategy

1Work through all 8 kitsas matemaatika courses in curriculum order - algebra, trigonometry, vectors/line equations, probability and statistics, functions/logarithms/percentages, sequences and the derivative, planimetry and the integral, and stereometry - since Harno's own eristuskiri and ROK Lisa 3 curriculum are structured exactly this way.

2Practise full worked solutions with intermediate steps shown, not just final answers, since the real exam awards partial credit at each step of the open-response tasks even when the final numeric answer is wrong.

3Drill percentage and compound-growth word problems (discounts, interest, depreciation) heavily, since these real-life applications are explicitly emphasised in the kitsas matemaatika curriculum's functions course and appear frequently on past papers.

4Don't skip the basic derivative and integral topics assuming they belong only to lai matemaatika - the kitsas curriculum does include simple extremum and area-under-a-curve problems, so practise the power rule and the Newton-Leibniz formula for polynomials.

5Time yourself against the real exam's structure (120 minutes for 7 tasks in Part I, 150 minutes for 5 tasks in Part II) so you build a realistic sense of pacing across a 270-minute working session.

6Review stereometry and planimetry formulas (volumes, surface areas, the Pythagorean theorem) until they are automatic, since these consistently carry significant point weight on past exams and this bank's category distribution.

7Use a basic pocket calculator during practice exactly as permitted on exam day, since graphing calculators, phones and outside reference materials (beyond the official formula sheet now included in the booklet) are not allowed.

Frequently Asked Questions

Is the official kitsas matemaatika riigieksam multiple-choice?

Only in part. The two-part written exam mixes selective-response items (multiple-choice, matching, true/false, ranking) with open-response items that require a full written solution, graded for partial credit at each step according to Harno's published hindamisjuhend (grading rubric). This bank is an MCQ study adaptation for learning and checking the underlying computations - it is not a simulation of the official partial-credit written format.

What is the difference between kitsas and lai matemaatika?

They are two separate exam papers given on the same day, and every graduate sits exactly one. Kitsas matemaatika has 8 compulsory ROK Lisa 3 courses focused on applying mathematics to everyday and scientific-literacy contexts, while lai matemaatika has 14 courses with deeper calculus, geometry and applied-modelling content aimed at students continuing into STEM higher education. In 2026, kitsas candidates averaged 35.4 points versus 59.2 for lai, reflecting this different calibration.

Does the narrow track really include derivatives and integrals?

Yes, to a basic degree - this is a common misconception. The official 8-course ROK Lisa 3 curriculum for kitsas matemaatika includes one course covering the function derivative (tangent lines, increasing/decreasing behaviour, simple extremum problems) and one topic on the definite integral (area under simple polynomial curves via the Newton-Leibniz formula). It omits the deeper calculus (limits, trigonometric-function derivatives, extended integration techniques) that lai matemaatika covers.

How is the exam structured and scored?

It is a two-part written exam worth 100 points across 12 tasks: Part I (120 minutes) has 4 tasks worth 5 points each plus 3 tasks worth 10 points each (50 points total), and Part II (150 minutes) has 5 tasks worth 10 points each (50 points total). The two parts are separated by a 45-minute break, and the exam officially begins at 10:00.

What score do I need to pass?

Very little, numerically - the exam is considered 'sooritatud' (completed) once a candidate reaches at least 1% of the maximum result, i.e. a single point out of 100. There is no higher numeric pass/fail threshold, since gumnaasium graduation requires completing (not exceeding a specific score on) each of the three compulsory riigieksamid. The numeric result matters most for university admission and scholarship purposes.

What calculators or reference materials are allowed?

Candidates may use personal writing and drawing instruments and a basic pocket calculator. Textbooks, handbooks, notes and outside formula sheets are not permitted, and correction fluid/tape and erasable pens are banned. As of the 2026 sitting, however, Harno itself includes an official valemileht (formula sheet) inside the exam booklet, a change that its assessment center director noted did not raise average scores compared with the prior year.

When is the 2026 exam, and can I retake it?

Per Harno's confirmed EKSAMITE KALENDER 2026, the gumnaasiumi riigieksam Matemaatika (both kitsas and lai, sat the same day) is scheduled for 20 May 2026, with results published 18 June 2026. Candidates with a valid medical or personal reason for missing the main sitting, or who wish to retake the exam to improve an earlier score, may apply for a lisaeksam (makeup session), which for 2026 runs 25-29 May and 3 June.