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100+ Free Estonian Upper-Secondary Broad Mathematics Exam Practice Questions

Estonian Upper-Secondary State Examination — Broad Mathematics (Lai matemaatika) practice questions are available now; exam metadata is being verified.

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2026 Statistics

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 test your Estonian Upper-Secondary Broad Mathematics Exam exam readiness. 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.
A.x + 3
B.x − 3
C.x² + 3
D.9 − x
Explanation: The numerator is a difference of squares: x² − 9 = (x − 3)(x + 3). Dividing by (x − 3) cancels the common factor, leaving x + 3.
2Solve for x: 3x − 7 = 2x + 5.
A.12
B.2
C.−12
D.5
Explanation: Subtract 2x from both sides to get x − 7 = 5, then add 7 to both sides to get x = 12.
3The quadratic equation x² − 5x + 6 = 0 has two real roots. What is the larger root?
A.3
B.2
C.5
D.−3
Explanation: Factoring gives (x − 2)(x − 3) = 0, so the roots are x = 2 and x = 3. The larger of the two roots is 3.
4Write √50 in simplest radical form.
A.5√2
B.25√2
C.2√5
D.10√5
Explanation: 50 = 25 × 2, and √25 = 5, so √50 = √25 · √2 = 5√2.
5Solve for x: 2/(x − 1) + 3 = 5/(x − 1).
A.2
B.1
C.3
D.−2
Explanation: Subtracting 2/(x − 1) from both sides gives 3 = 3/(x − 1), so x − 1 = 1, meaning x = 2. Checking x = 2 in the original equation confirms it does not make any denominator zero.
6Solve the system 2x + y = 11 and x − y = 1. What is the value of x?
A.4
B.3
C.7
D.−4
Explanation: From the second equation, x = y + 1. Substituting into the first gives 2(y + 1) + y = 11, so 3y = 9 and y = 3, meaning x = 4.
7Simplify (a³ − a) / (a² − 1) for a ≠ ±1.
A.a
B.a²
C.a − 1
D.1/a
Explanation: Factor the numerator as a(a² − 1). Dividing by (a² − 1) cancels the common factor, leaving just a.
8A rectangle's length is 3 cm more than twice its width. If the perimeter is 36 cm, find the width.
A.5 cm
B.4.5 cm
C.6 cm
D.15 cm
Explanation: Let w be the width, so the length is 2w + 3. Half the perimeter equals w + (2w + 3) = 3w + 3 = 18, giving 3w = 15, so w = 5 cm.
9Let y = x². Solving x⁴ − 5x² + 4 = 0 gives several real roots for x. What is the largest one?
A.2
B.4
C.1
D.−2
Explanation: Substituting y = x² gives y² − 5y + 4 = 0, which factors as (y − 1)(y − 4) = 0, so y = 1 or y = 4. This means x = ±1 or x = ±2, and the largest of these values is 2.
10Simplify (2³ · 2⁻¹) / 2² as a power of 2, then evaluate it.
A.1
B.2
C.4
D.1/2
Explanation: Using exponent rules, 2³ · 2⁻¹ = 2², and dividing by 2² gives 2⁰, which equals 1.

About the Estonian Upper-Secondary Broad Mathematics Exam Practice Questions

Verified exam format metadata for Estonian Upper-Secondary State Examination — Broad Mathematics (Lai matemaatika) is pending. The practice questions above remain available while official exam length, timing, passing score, fee, and administrator details are reviewed.