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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).
A.-13
B.16
C.-16
D.4
Explanation: Multiplication is performed before addition: 5 x (-2) = -10, then -3 + (-10) = -13. Order of operations always requires multiplication and division to be done before addition and subtraction, unless parentheses say otherwise.
2What is 35% of 240?
A.84
B.72
C.96
D.168
Explanation: To find 35% of a number, convert the percentage to a decimal (0.35) and multiply: 0.35 x 240 = 84. This is the standard method for finding a percentage of a quantity.
3A jacket originally costs 80 euros. Its price is reduced by 25% in a sale. What is the new price?
A.60 euros
B.55 euros
C.65 euros
D.20 euros
Explanation: A 25% discount removes 0.25 x 80 = 20 euros from the price, leaving 80 - 20 = 60 euros. Equivalently, the new price is 75% of the original: 0.75 x 80 = 60 euros.
4Simplify: 2^3 x 2^2.
A.32
B.16
C.64
D.10
Explanation: When multiplying powers with the same base, add the exponents: 2^3 x 2^2 = 2^(3+2) = 2^5 = 32. This exponent rule applies whenever the bases are identical.
5What is the value of the square root of 169?
A.13
B.12
C.14
D.84.5
Explanation: The square root of 169 is the positive number that, when multiplied by itself, equals 169. Since 13 x 13 = 169, the square root of 169 is 13.
6A recipe requires flour and sugar in the ratio 5:2. If 15 kilograms of flour are used, how much sugar is needed?
A.6 kg
B.7.5 kg
C.5 kg
D.3 kg
Explanation: The ratio 5:2 means flour is 5 parts and sugar is 2 parts. Since 15 kg of flour is 3 times the 5-part unit (15 / 5 = 3), sugar must also scale by 3: 2 x 3 = 6 kg.
7A shop increases the price of a chair from 120 euros to 150 euros. What is the percentage increase?
A.25%
B.20%
C.30%
D.15%
Explanation: Percentage increase equals (change / original) x 100%. The change is 150 - 120 = 30 euros, so the increase is (30 / 120) x 100% = 25%.
8Simplify: (-2)^4.
A.16
B.-16
C.8
D.-8
Explanation: (-2)^4 means (-2) multiplied by itself 4 times: (-2) x (-2) x (-2) x (-2). Multiplying an even number of negative factors gives a positive result: (-2)^4 = 16.
9A students' savings decreased from 90 euros to 63 euros over a month. By what percentage did the savings decrease?
A.30%
B.27%
C.70%
D.33%
Explanation: The decrease is 90 - 63 = 27 euros. Percentage decrease is (decrease / original) x 100% = (27 / 90) x 100% = 30%.
10Simplify the expression: 3/4 + 5/6 (write as a single fraction in lowest terms).
A.19/12
B.8/10
C.15/24
D.4/5
Explanation: The least common denominator of 4 and 6 is 12. Converting: 3/4 = 9/12 and 5/6 = 10/12. Adding: 9/12 + 10/12 = 19/12, which cannot be simplified further.

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 website

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 ~18%

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.

Study emphasis ~30%

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.

Study emphasis ~14%

Functions and Graphs

Direct and inverse proportionality, linear functions (slope/intercept), basic quadratic functions, and reading values and behaviour from graphs.

Study emphasis ~20%

Planimetry (Plane Geometry)

Triangle angle sums, congruence/similarity, quadrilateral and circle properties, the Pythagorean theorem, and perimeter/area formulas.

Study emphasis ~8%

Solid Geometry Basics

Surface area and volume of prisms, cylinders, pyramids, cones and spheres, and simple composite solids.

Study emphasis ~10%

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

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Estonian Basic-School Mathematics Exam: Suggested Study Strategy

1Practise full worked solutions with intermediate steps shown, not just final answers, since the real exam awards partial credit at each step and is explicitly graded on how clearly reasoning is expressed, not only on the final result.
2Drill percentage and ratio word problems heavily (discounts, price changes, mixing problems), since these real-life applications recur across both the mandatory tasks and the optional-task pair.
3Master factoring and the quadratic formula together, since quadratic and fractional equations are consistently among the most heavily weighted algebra tasks on past papers.
4Review the Pythagorean theorem, triangle similarity, and circle/quadrilateral area formulas until automatic, since planimetry tasks reliably appear and often combine several formulas in one multi-step problem.
5Don't neglect solid-geometry formulas (prism, cylinder, cone, pyramid, sphere surface area and volume) just because a specific year's eristuskiri excluded some of them - the underlying curriculum still includes them and this bank studies the full three-year scope.
6Time yourself against the real exam's 180-minute, 6-task structure (5 mandatory plus 1 chosen optional task) so you build a realistic sense of pacing and know which optional task plays to your strengths.
7Practise with only an ordinary non-programmable calculator, exactly as permitted on exam day, since graphing calculators, phones and outside formula sheets are not allowed.

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.