Free Practice Questions for Estonian Basic-School Mathematics Exam
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Key Facts: Estonian Basic-School Mathematics Exam Exam
50 points / 7 tasks / 180 minutes
Single written paper: 5 mandatory tasks worth 8 points each (40 pts) plus 2 alternative tasks worth 10 points each of which the candidate solves only one (10 pts)
Harno, Põhikooli matemaatika lõpueksami eristuskiri
25/50 points (50%) to pass
Minimum score for the exam to count as 'sooritatud' (completed) toward the basic-school graduation requirement
Haridus- ja Teadusministeerium, Põhikooli lõpetamise ja vastuvõtuprotsess
20% / 30% / 50% cognitive-level split
Tasks are weighted roughly 20% recall of facts/procedures, 30% application to routine problems, and 50% reasoning, justification and non-routine/real-life problems
Harno, Põhikooli matemaatika lõpueksami eristuskiri
15,066 candidates, 66.39% avg (2026)
Spring 2026 candidates and average score, up from 63.87% in 2025; about a third scored 90-100% and nearly a quarter scored below 50%
ERR / Harno, 'Eksamite tulemused püsivad mullusega võrreldaval tasemel' (June 2026)
12.49-point language-medium gap (2026)
Score gap between candidates who sat the exam in Estonian versus Russian, flagged by Harno's assessment centre as a widening, 'worrying' polarization trend
ERR / Harno, 'Eksamite tulemused püsivad mullusega võrreldaval tasemel' (June 2026)
29 April 2026, 10:00
2025/2026 exam date and start time for the Matemaatika lõpueksam
Haridus- ja Teadusministeerium, EKSAMITE KALENDER 2026
Free 100-question MCQ study bank for Estonia's põhikooli matemaatika lõpueksam (Grade 9), covering the computation skills behind the full III kooliaste (7.-9. klass) curriculum: numbers/powers/percentages, algebraic expressions and equations, functions and graphs, planimetry, solid geometry, and statistics/probability. Official exam: single 180-minute written paper, 50 points across 7 tasks (5 mandatory @ 8 pts + 1 of 2 optional @ 10 pts), scheduled 29 April 2026 at 10:00. Pass threshold is 25/50 points (50%). Ordinary non-programmable calculator allowed; no formula sheets or textbooks. In 2026, 15,066 candidates averaged 66.39% (up from 63.87% in 2025), with roughly a third at 90-100% and nearly a quarter below 50%. Compulsory for every basic-school graduate (not an elective), alongside an Estonian-language exam and one valikeksam. No fee, since basic education is free. Not an official-format simulation - the real exam requires full written, partial-credit solutions.
Sample Estonian Basic-School Mathematics Exam Practice Questions
Try these sample questions to review concepts for the Estonian Basic-School Mathematics Exam exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1Evaluate using the correct order of operations: -3 + 5 x (-2).
2What is 35% of 240?
3A jacket originally costs 80 euros. Its price is reduced by 25% in a sale. What is the new price?
4Simplify: 2^3 x 2^2.
5What is the value of the square root of 169?
6A recipe requires flour and sugar in the ratio 5:2. If 15 kilograms of flour are used, how much sugar is needed?
7A shop increases the price of a chair from 120 euros to 150 euros. What is the percentage increase?
8Simplify: (-2)^4.
9A students' savings decreased from 90 euros to 63 euros over a month. By what percentage did the savings decrease?
10Simplify the expression: 3/4 + 5/6 (write as a single fraction in lowest terms).
About the Estonian Basic-School Mathematics Exam Exam
The Estonian Basic-School Final Examination in Mathematics (põhikooli matemaatika lõpueksam) is the national Grade 9 exam that Haridus- ja Noorteamet (Harno) administers each spring as one of three compulsory exams every basic-school graduate must pass, alongside an Estonian-language exam (Eesti keel or Eesti keel teise keelena) and one valikeksam (elective) chosen from subjects like biology, physics, history or English. Unlike those nine elective options, Matemaatika itself is compulsory for every candidate - there is no opting out. The exam is a single 180-minute written paper worth 50 points across 7 tasks: 5 mandatory tasks worth 8 points each (40 points) plus 2 alternative tasks worth 10 points each, of which the candidate answers only one (10 points), scheduled for Wednesday, 29 April 2026 at 10:00. Tasks require full worked solutions rather than bare answers and are graded across three cognitive levels - roughly 20% recall of facts and procedures, 30% application of methods to routine problems, and 50% reasoning, justification and non-routine or real-life problems - covering the full three-year (7.-9. klass) III kooliaste curriculum: rational-number arithmetic and percentages, algebraic simplification and factoring, linear and quadratic equations and inequalities, functional relationships and graphs, planimetry, basic solid geometry, and statistics/probability. Candidates may use only an ordinary, non-programmable, non-graphing calculator; textbooks, handbooks and outside formula sheets are banned. At least 25 of 50 points (50%) is needed to pass. In spring 2026, 15,066 candidates sat the exam, averaging 66.39% (up from 63.87% the year before), with roughly a third scoring 90-100% and nearly a quarter scoring below 50% - a polarization officials called 'worrying,' alongside a widening 12.49-percentage-point score gap between Estonian-medium and Russian-medium candidates. This free bank of 100 original multiple-choice questions is an English-language MCQ study adaptation built around genuine worked calculations - solving equations, computing percentages, areas, volumes and probabilities, and evaluating functions - across the whole Grade 9 curriculum. It is not a simulation of the official exam, which requires full, partial-credit written solutions to a 6-task paper (5 mandatory plus 1 chosen optional task).
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 ühtne põhikooli lõpueksam administered once a year each spring by Haridus- ja Noorteamet (Harno) under the Põhikooli- ja gümnaasiumiseadus and its implementing final-examination regulation. Every Grade 9 graduate must pass an Estonian-language exam, Matemaatika, and one valikeksam (elective) to receive the põhikooli lõputunnistus. Unlike the nine valikeksam choices, Matemaatika is compulsory for every candidate and tests the full three-year (7.-9. klass, III kooliaste) national curriculum: rational-number arithmetic, powers and roots, ratio and percentage calculations, algebraic expressions and factoring, linear and quadratic equations and inequalities, simple functional relationships (direct/inverse proportion, linear and quadratic functions) and their graphs, planimetry (triangles, quadrilaterals, circles, the Pythagorean theorem, perimeter and area), basic solid geometry (surface area and volume of prisms, cylinders, pyramids, cones and spheres), and descriptive statistics and probability. Harno's annually published eristuskiri can narrow the exact scope tested in a given year - for example, standard form and negative integer exponents, spreadsheet-based data-characteristic tasks, computer-assisted equation solving/graphing, and cylinder/cone/sphere/pyramid surface area or volume were excluded from the 2025 and 2026 sittings - but these remain part of the underlying curriculum and can reappear in other years. Permitted aids are an ordinary, non-programmable calculator that cannot graph functions, connect to the internet, or store/exchange data; textbooks, handbooks and outside formula sheets are not permitted. This bank is a unified MCQ study adaptation covering the underlying computations across the whole Grade 9 mathematics curriculum - it does not reproduce the official exam's full written-solution, partial-credit response format.
Time Limit
180 minutes (3 hours) for the single written paper. For the 2025/2026 school year, the Matemaatika lõpueksam is scheduled for Wednesday, 29 April 2026, starting at 10:00 - one week after the Eesti keel/Eesti keel teise keelena exam (21 April 2026) and before the valikeksam window of 6-8 May 2026.
Passing Score
Scored out of 50 points (5 mandatory tasks worth 8 points each, plus one of two optional 10-point tasks chosen by the candidate). At least 25 of 50 points (50%) is needed for the exam to be recorded as 'sooritatud' (completed) and count toward the basic-school graduation requirement. In spring 2026, 15,066 candidates sat the exam, averaging 66.39% (up from 63.87% in 2025); roughly a third scored 90-100%, nearly a quarter scored below 50%, and officials flagged a widening 12.49-percentage-point gap between Estonian-medium and Russian-medium candidates as a 'worrying' polarization trend.
Exam / Certification Fees
No fee. Estonian basic education is free, and Matemaatika is one of the three compulsory unified final exams that Harno administers each spring to every regularly enrolled Grade 9 student at no cost.
Exam sponsor websiteFees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.
Official sources
- Harno - Põhikooli matemaatika lõpueksam
- Harno - Põhikooli lõpueksamid (Basic-School Final Exams overview)
- Haridus- ja Teadusministeerium - Ühtsed põhikooli lõpueksamid
- Haridus- ja Teadusministeerium - EKSAMITE KALENDER 2026
- Riigi Teataja - Põhikooli riiklik õppekava (ainevaldkond matemaatika)
- Harno - Eksamite tulemused püsivad mullusega võrreldaval 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.
Numbers, Powers and Percentages
Operations with rational numbers and order of operations, powers and roots, ratio and proportion, and percentage-change/percentage-of word problems.
Algebraic Expressions and Equations
Simplifying and factoring expressions, linear equations and inequalities, quadratic equations by factoring or formula, fractional equations, and simple systems of two linear equations.
Functions and Graphs
Direct and inverse proportionality, linear functions (slope/intercept), basic quadratic functions, and reading values and behaviour from graphs.
Planimetry (Plane Geometry)
Triangle angle sums, congruence/similarity, quadrilateral and circle properties, the Pythagorean theorem, and perimeter/area formulas.
Solid Geometry Basics
Surface area and volume of prisms, cylinders, pyramids, cones and spheres, and simple composite solids.
Statistics and Probability
Mean, median, mode and range from data sets and frequency tables, plus classical probability and basic counting problems.
Preparing for the Estonian Basic-School Mathematics Exam Exam
What You Need to Know
- Passing score: Scored out of 50 points (5 mandatory tasks worth 8 points each, plus one of two optional 10-point tasks chosen by the candidate). At least 25 of 50 points (50%) is needed for the exam to be recorded as 'sooritatud' (completed) and count toward the basic-school graduation requirement. In spring 2026, 15,066 candidates sat the exam, averaging 66.39% (up from 63.87% in 2025); roughly a third scored 90-100%, nearly a quarter scored below 50%, and officials flagged a widening 12.49-percentage-point gap between Estonian-medium and Russian-medium candidates as a 'worrying' polarization trend.
- Assessment: Official national ühtne põhikooli lõpueksam administered once a year each spring by Haridus- ja Noorteamet (Harno) under the Põhikooli- ja gümnaasiumiseadus and its implementing final-examination regulation. Every Grade 9 graduate must pass an Estonian-language exam, Matemaatika, and one valikeksam (elective) to receive the põhikooli lõputunnistus. Unlike the nine valikeksam choices, Matemaatika is compulsory for every candidate and tests the full three-year (7.-9. klass, III kooliaste) national curriculum: rational-number arithmetic, powers and roots, ratio and percentage calculations, algebraic expressions and factoring, linear and quadratic equations and inequalities, simple functional relationships (direct/inverse proportion, linear and quadratic functions) and their graphs, planimetry (triangles, quadrilaterals, circles, the Pythagorean theorem, perimeter and area), basic solid geometry (surface area and volume of prisms, cylinders, pyramids, cones and spheres), and descriptive statistics and probability. Harno's annually published eristuskiri can narrow the exact scope tested in a given year - for example, standard form and negative integer exponents, spreadsheet-based data-characteristic tasks, computer-assisted equation solving/graphing, and cylinder/cone/sphere/pyramid surface area or volume were excluded from the 2025 and 2026 sittings - but these remain part of the underlying curriculum and can reappear in other years. Permitted aids are an ordinary, non-programmable calculator that cannot graph functions, connect to the internet, or store/exchange data; textbooks, handbooks and outside formula sheets are not permitted. This bank is a unified MCQ study adaptation covering the underlying computations across the whole Grade 9 mathematics curriculum - it does not reproduce the official exam's full written-solution, partial-credit response format.
- Time limit: 180 minutes (3 hours) for the single written paper. For the 2025/2026 school year, the Matemaatika lõpueksam is scheduled for Wednesday, 29 April 2026, starting at 10:00 - one week after the Eesti keel/Eesti keel teise keelena exam (21 April 2026) and before the valikeksam window of 6-8 May 2026.
- Exam / certification fees: No fee. Estonian basic education is free, and Matemaatika is one of the three compulsory unified final exams that Harno administers each spring to every regularly enrolled Grade 9 student at no cost. 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 Basic-School Mathematics Exam: Suggested Study Strategy
Frequently Asked Questions
Is the official exam multiple-choice?
No. The written paper mixes short-answer and extended-response tasks that require full worked solutions, graded for partial credit at each step according to Harno's published grading rubric - not selective-response MCQ items. This bank is an MCQ study adaptation for learning and checking the underlying computations - it is not a simulation of the official full-solution written format.
Is mathematics an elective or a required exam?
It is compulsory for every basic-school graduate, not an elective. Every Grade 9 student must pass an Estonian-language exam, Matemaatika, and a separate valikeksam (elective) chosen from subjects like biology, history, physics or English. Matemaatika itself is not one of those nine elective choices - there is no way to substitute a different subject for it.
How is the exam structured and scored?
It is a single 180-minute written paper worth 50 points across 7 tasks: 5 mandatory tasks worth 8 points each (40 points), plus 2 alternative tasks worth 10 points each of which the candidate solves only one (10 points). Tasks are graded across three cognitive levels: roughly 20% recall of facts and procedures, 30% application of methods to routine problems, and 50% reasoning, justification and non-routine or real-life problems.
What score do I need to pass?
At least 25 of the 50 points, i.e. 50%, for the exam to be recorded as 'sooritatud' (completed) and count toward the basic-school graduation requirement. In spring 2026, the national average was 66.39%, with roughly a third of candidates scoring 90-100% and nearly a quarter scoring below 50%.
What calculators or reference materials are allowed?
Only an ordinary, non-programmable calculator that cannot graph functions, connect to the internet, or store/exchange data. If the calculator has built-in one-touch formula functions, the candidate must still write out the formula used in their solution. Textbooks, handbooks and outside formula sheets are not permitted.
Does the exam cover the whole three-year curriculum, or does the scope change each year?
The underlying III kooliaste (7.-9. klass) curriculum stays constant, but Harno's annually published eristuskiri can narrow which parts are actually tested in a given year's paper. For example, standard form and negative integer exponents, spreadsheet-based statistics tasks, computer-assisted equation solving/graphing, and the surface area or volume of cylinders, cones, spheres and pyramids were excluded from both the 2025 and 2026 sittings, even though they remain part of the taught curriculum and can return in future years. This bank studies the full curriculum rather than only one year's narrowed scope.
When is the 2026 exam?
Wednesday, 29 April 2026, starting at 10:00, running 180 minutes. It falls one week after the Eesti keel/Eesti keel teise keelena exam (21 April 2026) and before the valikeksam window of 6-8 May 2026.
Is there an exam fee?
No. Basic education in Estonia is free, and this compulsory final exam is administered by Harno at no cost to regularly enrolled Grade 9 students.