Free Practice Questions for Estonian Upper-Secondary Broad Mathematics Exam
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Key Facts: Estonian Upper-Secondary Broad Mathematics Exam Exam
12 tasks, 100 points
Part I: four 5-point plus three 10-point tasks (50 points); Part II: five 10-point tasks (50 points)
Kitsa ja laia matemaatikakursuse riigieksami eristuskiri (Harno, 25.09.2025)
20 May 2026
2025/2026 exam date for the written mathematics riigieksam (both kitsas and lai, same day); lisaeksam 3 June 2026
Riigi Teataja, 'Riigieksamite vormid ja ajad ... 2025/2026. oppeaastal' (04.04.2025 nr 14)
5,670 candidates, 59.2 avg (2026)
Broad-track (lai) candidates and their average score out of 100 in spring 2026, up 0.9 points from the prior year; 63 scored a perfect 100
ERR, 'Harno: eksamitulemused pusivad mullusega sarnasel tasemel' (2026)
4,855 candidates, 35.4 avg (2026)
Narrow-track (kitsas) candidates and their average score out of 100 in spring 2026, down 3.7 points from the prior year
ERR, 'Harno: eksamitulemused pusivad mullusega sarnasel tasemel' (2026)
270 minutes + 45-minute break
Part I (120 min) and Part II (150 min) working time, separated by a 45-minute break, starting at 10:00
Kitsa ja laia matemaatikakursuse riigieksami eristuskiri (Harno, 25.09.2025)
1 point of 100
Minimum score for the exam to count as sooritatud (completed) toward the compulsory graduation requirement
Haridus- ja teadusministri maarus nr 54, per Harno's eristuskiri
Free 100-question computational MCQ study bank for Estonia's lai matemaatika riigieksam, covering derivatives, trigonometry, vectors, probability, exponential/logarithmic functions, sequences and stereometry - the advanced curriculum content that distinguishes the broad track from the narrow (kitsas) mathematics exam. Official exam: two-part written paper, 12 tasks, 100 points (Part I 120 min, 45-min break, Part II 150 min), scheduled 20 May 2026 with a lisaeksam on 3 June 2026; scoring just 1 point of 100 satisfies the graduation requirement, though the numeric result matters heavily for STEM university admission. Spring 2026: 5,670 broad-track candidates averaged 59.2 of 100 points versus 4,855 narrow-track candidates averaging 35.4. Calculator (non-programmable, non-graphing) and a track-specific formula sheet are permitted; no textbooks. Not an official-format simulation - the real exam requires full handwritten, partial-credit solutions; no fee for regular gumnaasium candidates.
Sample Estonian Upper-Secondary Broad Mathematics Exam Practice Questions
Try these sample questions to review concepts for the Estonian Upper-Secondary Broad Mathematics Exam exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1Simplify the expression (x² − 9) / (x − 3) for x ≠ 3.
2Solve for x: 3x − 7 = 2x + 5.
3The quadratic equation x² − 5x + 6 = 0 has two real roots. What is the larger root?
4Write √50 in simplest radical form.
5Solve for x: 2/(x − 1) + 3 = 5/(x − 1).
6Solve the system 2x + y = 11 and x − y = 1. What is the value of x?
7Simplify (a³ − a) / (a² − 1) for a ≠ ±1.
8A rectangle's length is 3 cm more than twice its width. If the perimeter is 36 cm, find the width.
9Let y = x². Solving x⁴ − 5x² + 4 = 0 gives several real roots for x. What is the largest one?
10Simplify (2³ · 2⁻¹) / 2² as a power of 2, then evaluate it.
About the Estonian Upper-Secondary Broad Mathematics Exam Exam
The Estonian Upper-Secondary State Examination in Broad Mathematics (lai matemaatika riigieksam) is the more advanced of the two national mathematics riigieksamid that Haridus- ja Noorteamet (Harno) administers each spring, alongside the kitsas (narrow) matemaatika exam, on a single shared exam day. Mathematics is one of the compulsory riigieksamid every gumnaasium graduate must sit, and students choose, by around 20 January, whether to prepare for and sit the narrow or the broad curriculum's exam paper - both share an identical two-part written format and identical 100-point scoring, differing only in the depth of content each ainekava (course syllabus) covers. The lai ainekava spans roughly 14 mandatory course units across three years, building from algebra, inequalities and basic right-triangle trigonometry through general-angle trigonometric identities, vectors and analytic geometry, exponential and logarithmic functions, probability and statistics, limits, derivatives and their applications, definite integrals, and three-dimensional stereometry - a materially heavier calculus and geometry load than the narrow track, and the track generally expected for STEM-oriented university admission in Estonia. Each exam paper has 12 tasks worth 100 points: Part I (120 minutes) has four 5-point and three 10-point tasks, and Part II (150 minutes, after a 45-minute break) has five 10-point tasks, with every task requiring a full handwritten, multi-step solution graded on a detailed partial-credit rubric rather than a single final answer. Candidates may use a personal non-programmable, non-graphing calculator without internet connectivity and an official track-specific formula sheet attached to the exam booklet, but no textbooks or other reference materials. In spring 2026, 5,670 candidates sat the broad track and averaged 59.2 of 100 points (a 0.9-point increase from the prior year, with 63 candidates achieving a perfect 100), compared with 4,855 candidates on the narrow track who averaged only 35.4 points (a 3.7-point decrease). This free bank of 100 original multiple-choice questions is a computational study adaptation designed to build and check the calculation skills - derivatives, trigonometric equations, vector operations, probability, exponential growth, and solid-geometry volumes and areas - that the riigieksam draws on. It is not a simulation of the official exam, which requires full handwritten, multi-step solutions with partial-credit scoring rather than a single selected answer.
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. Mathematics is one of the compulsory riigieksamid every gumnaasium graduate must sit, and candidates choose between two separate exam papers built from two separate ainekavad: kitsas matemaatika (narrow) or lai matemaatika (broad). Both are held on the same day, share an identical two-part written format (Part I, 120 minutes; a 45-minute break; Part II, 150 minutes) and identical 100-point scoring, and both permit a personal non-programmable, non-graphing calculator without internet connectivity plus an official track-specific valemileht (formula sheet) attached to the exam booklet. The lai (broad) ainekava is the more advanced of the two, adding limits, derivatives and their applications, definite integrals, general-angle trigonometric equations, vectors and analytic geometry, binomial and normal-distribution probability, and three-dimensional stereometry beyond what the narrow track covers, and is the track generally expected for STEM-oriented university admission. This bank is a multiple-choice study adaptation of the lai matemaatika computational skill set - it does not reproduce the official exam's full handwritten, partial-credit written-response format.
Time Limit
Both math tracks share one exam day, starting at 10:00: Part I runs 120 minutes, followed by a 45-minute break, then Part II runs 150 minutes - 270 minutes of working time in total. Per the Riigi Teataja regulation on riigieksamite vormid ja ajad for 2025/2026, the written mathematics riigieksam (both kitsas and lai) is scheduled for 20 May 2026, with a lisaeksam (makeup) sitting on 3 June 2026 for candidates with a valid excuse.
Passing Score
Scored out of 100 points (Part I: four 5-point plus three 10-point tasks = 50 points; Part II: five 10-point tasks = 50 points). Per the governing regulation, the exam counts as sooritatud (completed) once a candidate scores at least 1% of the maximum result - just 1 of 100 points - satisfying the compulsory graduation requirement; there is no higher fixed pass/fail line for graduation itself, though the numeric score matters greatly for university admission. In spring 2026, 5,670 candidates sat the broad track, averaging 59.2 points (up 0.9 from the prior year) with 63 candidates scoring a perfect 100, compared with 4,855 narrow-track candidates averaging only 35.4 points (down 3.7 points from the prior year).
Exam / Certification Fees
No fee for regularly enrolled gumnaasium candidates - riigieksamid are free state examinations administered by Harno. Every graduate must sit either the kitsas or lai matemaatika riigieksam; Harno's eristuskiri describes no international-certificate substitution route for mathematics comparable to the English riigieksam's Cambridge/IELTS/TOEFL option.
Exam sponsor websiteFees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.
Official sources
- Harno - Matemaatika riigieksam
- Harno - Riigieksamid (State Examinations overview)
- Riigi Teataja - Riigieksamite vormid ja ajad ... 2025/2026. oppeaastal
- Kitsa ja laia matemaatikakursuse riigieksami eristuskiri (2025)
- Oppekava.ee - Laia matemaatika kursused (curriculum outline)
- ERR - Harno: eksamitulemused pusivad mullusega sarnasel tasemel (2026 results)
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.
Limits and Derivatives
Limit evaluation, the derivative rules (power, product, quotient, chain), tangent lines, and derivatives of exponential/logarithmic functions.
Algebra: Expressions and Equations
Rational expressions, linear/quadratic/rational equations and systems, and word problems.
Vectors and Analytic Geometry
Vector magnitude, components, dot products, parallel vectors, and equations of lines and circles.
Probability and Statistics
Permutations, combinations, probability, binomial distribution and normal-distribution z-scores.
Stereometry and Solid Geometry
Volumes and surface areas of prisms, cylinders, cones, spheres, pyramids, tetrahedra and inscribed solids.
Trigonometric Functions and Identities
Unit circle values, radian-degree conversion, the Pythagorean identity, law of sines/cosines, and trig equations.
Functions and Sequences
Function evaluation and domain, arithmetic/geometric sequences and series, even/odd functions and composition.
Integrals and Derivative Applications
Definite/indefinite integrals, area under a curve, critical points, extrema and optimization.
Exponential and Logarithmic Functions
Logarithm evaluation and rules, exponential/logarithmic equations, compound interest and decay.
Inequalities and Basic Trigonometry
Linear/compound/quadratic inequalities and right-triangle sine/cosine/tangent ratios.
Exam Format and Scheduling
Two-part written structure, 100-point scoring, formula-sheet/calculator policy, 2026 dates, and how broad differs from narrow.
Preparing for the Estonian Upper-Secondary Broad Mathematics Exam Exam
What You Need to Know
- Passing score: Scored out of 100 points (Part I: four 5-point plus three 10-point tasks = 50 points; Part II: five 10-point tasks = 50 points). Per the governing regulation, the exam counts as sooritatud (completed) once a candidate scores at least 1% of the maximum result - just 1 of 100 points - satisfying the compulsory graduation requirement; there is no higher fixed pass/fail line for graduation itself, though the numeric score matters greatly for university admission. In spring 2026, 5,670 candidates sat the broad track, averaging 59.2 points (up 0.9 from the prior year) with 63 candidates scoring a perfect 100, compared with 4,855 narrow-track candidates averaging only 35.4 points (down 3.7 points from the prior year).
- 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. Mathematics is one of the compulsory riigieksamid every gumnaasium graduate must sit, and candidates choose between two separate exam papers built from two separate ainekavad: kitsas matemaatika (narrow) or lai matemaatika (broad). Both are held on the same day, share an identical two-part written format (Part I, 120 minutes; a 45-minute break; Part II, 150 minutes) and identical 100-point scoring, and both permit a personal non-programmable, non-graphing calculator without internet connectivity plus an official track-specific valemileht (formula sheet) attached to the exam booklet. The lai (broad) ainekava is the more advanced of the two, adding limits, derivatives and their applications, definite integrals, general-angle trigonometric equations, vectors and analytic geometry, binomial and normal-distribution probability, and three-dimensional stereometry beyond what the narrow track covers, and is the track generally expected for STEM-oriented university admission. This bank is a multiple-choice study adaptation of the lai matemaatika computational skill set - it does not reproduce the official exam's full handwritten, partial-credit written-response format.
- Time limit: Both math tracks share one exam day, starting at 10:00: Part I runs 120 minutes, followed by a 45-minute break, then Part II runs 150 minutes - 270 minutes of working time in total. Per the Riigi Teataja regulation on riigieksamite vormid ja ajad for 2025/2026, the written mathematics riigieksam (both kitsas and lai) is scheduled for 20 May 2026, with a lisaeksam (makeup) sitting on 3 June 2026 for candidates with a valid excuse.
- Exam / certification fees: No fee for regularly enrolled gumnaasium candidates - riigieksamid are free state examinations administered by Harno. Every graduate must sit either the kitsas or lai matemaatika riigieksam; Harno's eristuskiri describes no international-certificate substitution route for mathematics comparable to the English riigieksam's Cambridge/IELTS/TOEFL option. 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
Estonian Upper-Secondary Broad Mathematics Exam: Suggested Study Strategy
Frequently Asked Questions
Is the official Estonian broad mathematics riigieksam multiple-choice?
No. It is a two-part written exam with 12 tasks worth 100 points, and every task requires a full handwritten, multi-step solution graded on a detailed partial-credit rubric - not a single selected answer. This bank is a multiple-choice study adaptation for practicing the underlying computations (derivatives, trigonometric equations, vector operations, probability, volumes and more) - it is not a simulation of the official written-response format and does not replace practicing full worked solutions with proper justification steps.
What is the difference between kitsas (narrow) and lai (broad) matemaatika?
Both are separate riigieksamid built from separate national-curriculum syllabi (ainekavad), held on the same day with an identical two-part format and identical 100-point scoring. Lai (broad) is the more advanced of the two, adding limits, derivatives and their applications, definite integrals, general-angle trigonometric equations, vectors and analytic geometry, binomial and normal-distribution probability, and three-dimensional stereometry beyond what kitsas covers. Broad is generally the track expected or preferred for STEM-oriented university admission, while narrow covers a lighter subset of content.
What calculator and reference materials are allowed?
Candidates may use a personal, non-programmable calculator that cannot plot graphs, connect to the internet, or otherwise store/exchange information (aside from holding an intermediate calculation result in memory). Harno also attaches an official valemileht (formula sheet) specific to the lai matemaatika ainekava to the exam booklet. No textbooks, other reference books, mobile phones, smartwatches or cameras are permitted.
How is the exam scored, and what counts as passing?
The exam is scored out of 100 points: Part I contributes four 5-point tasks plus three 10-point tasks (50 points), and Part II contributes five 10-point tasks (50 points). Per the governing regulation, the exam counts as completed once a candidate scores at least 1% of the maximum result (1 point), satisfying the graduation requirement - there is no higher fixed pass/fail line for graduation itself, though the actual numeric score matters heavily for university admission, particularly for STEM-track programmes.
When is the 2026 exam, and is there a makeup date?
Per the Riigi Teataja regulation on riigieksamite vormid ja ajad for the 2025/2026 school year, the written mathematics riigieksam (both kitsas and lai) is scheduled for 20 May 2026. A lisaeksam (makeup sitting) for candidates with a valid excuse is scheduled for 3 June 2026.
How did students perform on the broad mathematics exam recently?
In spring 2026, 5,670 candidates sat the lai matemaatika riigieksam and averaged 59.2 of 100 points, an increase of 0.9 points from the prior year, with 63 candidates achieving a perfect 100-point score. By comparison, 4,855 candidates sat the kitsas (narrow) exam and averaged only 35.4 points, a decrease of 3.7 points from the prior year.
Can I substitute an international certificate for this exam, the way English riigieksam candidates can use Cambridge or IELTS?
No. Harno's eristuskiri for the mathematics riigieksam describes no international-certificate substitution route comparable to the English riigieksam's Cambridge/IELTS/TOEFL option. Every gumnaasium graduate must sit either the kitsas or lai matemaatika riigieksam directly.