100+ Free NVO Grade 10 Mathematics Practice Questions

Prepare for the Bulgaria National External Assessment Grade 10 Mathematics with Integration of Other Subjects (НВО по математика с интегриране на други учебни предмети, край на X клас) exam with instant access — no signup required.

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2026 Statistics

Key Facts: NVO Grade 10 Mathematics Exam

18 tasks

Official 2025/2026 Grade 10 mathematics NVO length: 12 mathematics tasks plus integrated science/economics free-response items

MON NVO Grade 10 page and 2026 sitting notices

120 minutes

Official working time for the 2026 Grade 10 mathematics NVO (30 minutes longer than the previous model)

MON 2026 NVO sitting notice for VII and X class

19 June 2026, 08:00

National sitting date and start time for Grade 10 Mathematics with integration of other subjects

MON NVO Grade 10 timetable for 2025/2026

0–100 points

Maximum NVO result under Ordinance No. 11; Grade 10 mathematics is reported in points, not a published pass/fail cut

Ordinance No. 11 of 1 September 2016; MON NVO reporting practice

30.34 points

National mean on the 2026 Grade 10 integrated mathematics NVO (first year of the new model; not directly comparable to 2025)

MON 2026 NVO results briefing, 30 June 2026

Free 100-question English MCQ study bank for Bulgaria NVO Grade 10 Mathematics. Official 2026 exam: Bulgarian mixed 18-task paper (math plus integrated science/economics), 120 minutes, 19 June 2026 at 08:00, 0–100 points under Ordinance 11. Not an official-format simulation; no fee for regular school candidates.

Sample NVO Grade 10 Mathematics Practice Questions

Try these sample questions to test your NVO Grade 10 Mathematics exam readiness. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Solve 3x − 7 = 8. What is x?

A.3

B.15

C.−1

D.5

Explanation: Add 7 to both sides to get 3x = 15. Divide by 3 to obtain x = 5. Substituting back, 3(5) − 7 = 8, so the solution checks.

2Simplify √50 to lowest terms with a rational factor outside the radical.

A.25√2

B.2√5

C.10√5

D.5√2

Explanation: Factor 50 = 25 × 2. Then √50 = √(25 × 2) = 5√2. No further perfect-square factor remains inside the radical.

3What are the roots of x² − 5x + 6 = 0?

A.1 and 6

B.−2 and −3

C.2 and 3

D.5 and 6

Explanation: The quadratic factors as (x − 2)(x − 3) = 0, so the roots are 2 and 3. By Vieta, the sum is 5 and the product is 6, which matches the coefficients.

4For the linear function f(x) = −2x + 7, what is the slope of its graph?

A.7

B.−2

C.2

D.−7

Explanation: In slope-intercept form y = mx + b, m is the slope. Here m = −2, so the line falls 2 units for each 1 unit increase in x. The intercept 7 is a different feature of the graph.

5A right triangle has legs 6 cm and 8 cm. What is the hypotenuse?

A.14 cm

B.7 cm

C.10 cm

D.48 cm

Explanation: By the Pythagorean theorem, c² = 6² + 8² = 36 + 64 = 100, so c = 10 cm. This is a scaled 3-4-5 triangle (scale factor 2).

6A rectangle measures 5 cm by 12 cm. What is its area?

A.17 cm²

B.34 cm²

C.60 cm²

D.30 cm²

Explanation: Area of a rectangle is length times width: 5 × 12 = 60 cm². Perimeter would be 2(5 + 12) = 34 cm, a different quantity.

7What is the exact value of sin 30°?

A.√3 / 2

B.1/2

C.√2 / 2

D.1

Explanation: In a 30°-60°-90° triangle the side opposite 30° is half the hypotenuse, so sin 30° = 1/2. This is a required exact value in the grades 8–10 curriculum.

8The scores 4, 8, 6, 10, and 7 are recorded. What is their arithmetic mean?

A.6

B.7

C.8

D.35

Explanation: The mean is the sum divided by the count: (4 + 8 + 6 + 10 + 7) / 5 = 35 / 5 = 7. The median of this ordered list is also 7, but that is a coincidence of this data set.

9What is 20% of 80?

A.4

B.20

C.60

D.16

Explanation: 20% means 20/100 = 1/5, and (1/5) × 80 = 16. Equivalently, 0.20 × 80 = 16. Percent of a number is always that fraction of the given whole.

10An arithmetic sequence begins 3, 7, 11, 15, … What is the next term?

A.18

B.19

C.20

D.17

Explanation: The common difference is 7 − 3 = 4. Adding 4 to 15 gives 19. In general a_n = 3 + (n − 1) · 4, so the fifth term is 3 + 16 = 19.

About the NVO Grade 10 Mathematics Exam

NVO Grade 10 Mathematics is Bulgaria’s national external assessment at the end of the first gymnasium stage (grades 8–10), administered by the Ministry of Education and Science under Ordinance No. 11. For 2025/2026 the paper is Mathematics with integration of other subjects: 18 mixed Bulgarian tasks in 120 minutes on 19 June 2026 at 08:00, covering algebra, functions, plane and solid geometry, introductory trigonometry, sequences, statistics and probability, plus applied biology, chemistry, physics, and geography/economics contexts. Maximum 100 points. The official exam is not multiple choice only and is not offered as an English sitting. This free English MCQ bank trains first-stage mathematics and integrated modelling before students practise official Bulgarian constructed-response tasks.

Assessment

Official NVO Grade 10 Mathematics (2025/2026 integrated model) is a written Bulgarian test of 18 tasks lasting 120 minutes. Twelve tasks assess mathematics competencies from the grades 8–10 general-education curricula (selected response and constructed response). The remaining tasks are short free-response items that still require mathematics but also check expected outcomes from biology and health education, chemistry and environmental protection, physics and astronomy, and geography and economics. Scoring is 0–100 points under Ordinance No. 11. This 100-question bank is an English MCQ study adaptation only — it does not simulate the official mixed paper, language, or free-response marking.

Time Limit

120 minutes, 19 June 2026, start 08:00.

Passing Score

Scored 0–100 points under Ordinance No. 11 of 1 September 2016. Grade 10 NVO mathematics results are recorded as a point total; MON does not publish a pass/fail cut score for this assessment. The 2026 national mean was 30.34 points on the new integrated paper.

Exam Fee

No exam fee for regular school candidates; NVO is a compulsory state school assessment. External-candidate or makeup arrangements, if any, are school/authority-specific and not a published fee. (Ministry of Education and Science of the Republic of Bulgaria (Министерство на образованието и науката, МОН))

NVO Grade 10 Mathematics Exam Content Outline

Study emphasis ~22%

Algebra and equations

Reals and radicals, quadratics and Vieta, rational/irrational equations, inequalities, and systems.

Study emphasis ~18%

Functions and trigonometry

Linear and quadratic functions; sin/cos/tan at 30°, 45°, 60°; right-triangle trigonometry.

Study emphasis ~25%

Geometry and stereometry

Similarity, Pythagoras, sine/cosine laws, circles, areas, and 3D surface/volume formulas.

Study emphasis ~20%

Sequences, statistics, and probability

Progressions, compound interest, averages, classical probability, and combinatorics.

Study emphasis ~15%

Integrated science and economics

Mathematics applied to biology, chemistry, physics, geography, and simple financial models.

How to Pass the NVO Grade 10 Mathematics Exam

What You Need to Know

Passing score: Scored 0–100 points under Ordinance No. 11 of 1 September 2016. Grade 10 NVO mathematics results are recorded as a point total; MON does not publish a pass/fail cut score for this assessment. The 2026 national mean was 30.34 points on the new integrated paper.
Assessment: Official NVO Grade 10 Mathematics (2025/2026 integrated model) is a written Bulgarian test of 18 tasks lasting 120 minutes. Twelve tasks assess mathematics competencies from the grades 8–10 general-education curricula (selected response and constructed response). The remaining tasks are short free-response items that still require mathematics but also check expected outcomes from biology and health education, chemistry and environmental protection, physics and astronomy, and geography and economics. Scoring is 0–100 points under Ordinance No. 11. This 100-question bank is an English MCQ study adaptation only — it does not simulate the official mixed paper, language, or free-response marking.
Time limit: 120 minutes, 19 June 2026, start 08:00.
Exam fee: No exam fee for regular school candidates; NVO is a compulsory state school assessment. External-candidate or makeup arrangements, if any, are school/authority-specific and not a published fee.

Keys to Passing

Work through all 100 available questions
Review every answer and explanation
Track weak areas and revisit them
Use our AI tutor for tough concepts

NVO Grade 10 Mathematics Study Tips from Top Performers

1Master quadratic equations, Vieta formulas, and reducing rational/irrational equations to linear or quadratic form without extra roots.

2Know exact sin/cos/tan of 30°, 45°, and 60°, then practise law of sines and cosines on non-right triangles.

3Keep a one-page formula sheet for prism, pyramid, cylinder, cone, and sphere surface area and volume, and decompose 3D problems into plane figures.

4Drill arithmetic and geometric progressions plus compound interest; 2026 analysis highlighted combinatorics and probability as especially difficult.

5After MCQ concept work, practise official Bulgarian free-response modelling (science and economics contexts) under timed conditions — MCQs build recognition, not written justification.

Frequently Asked Questions

Is the official NVO Grade 10 Mathematics exam a multiple-choice test in English?

No. The official paper is a Bulgarian mixed selected-response and free-response test of 18 tasks (mathematics plus integrated natural-science and geography/economics items). This bank is an English-language MCQ study adaptation — not an official translation or format simulation.

What changed in the 2026 Grade 10 mathematics NVO?

The 2025/2026 model is Mathematics with integration of other subjects: 18 tasks in 120 minutes (30 minutes longer than the previous 90-minute model). Twelve tasks assess mathematics; the remaining short free-response tasks apply mathematics to biology, chemistry, physics, and geography/economics.

When is the 2026 Grade 10 mathematics NVO?

19 June 2026, starting at 08:00, with 120 minutes of working time.

How is the exam scored, and is there a pass mark?

The maximum is 100 points under Ordinance No. 11. Results are recorded as points. MON does not publish a pass/fail cut score for Grade 10 mathematics NVO. The 2026 national mean on the new integrated paper was 30.34 points.

Is there an exam fee?

No. NVO is a compulsory state school assessment; regular school candidates pay no fee. External or makeup arrangements, where they exist, are school/authority-specific and not a published fee.

100+ Free NVO Grade 10 Mathematics Practice Questions

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