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State Graduation Exam — Grade 9 (ГВЭ-9) (Russia)

Practice Questions
Exam Review

Key Facts: GVE-11 Exam

235 min

Standard exam duration for each written subject paper

FIPI

14 tasks

Task count on the 2026 written mathematics examination

FIPI

5 points

Minimum primary points required for a passing grade 3 in mathematics

Rosobrnadzor

2 subjects

Compulsory subjects for high school certification: Russian and Math

FIPI

ГВЭ-11 is held in written or oral form for students with ОВЗ or disabilities, students in closed or penal institutions, and some vocational students. The 2026 written mathematics paper has 14 tasks in 235 minutes, and the Russian paper is a free-topic essay scored out of 17. This independent bank is an English-language MCQ study adaptation of both subjects.

Sample GVE-11 Practice Questions

Try these sample questions to review concepts for the GVE-11 exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.

1Calculate the numerical value of the expression: $\frac{3}{4} + \frac{5}{6} - \frac{7}{12}$.
A.1
B.$\frac{1}{2}$
C.$\frac{5}{4}$
D.$\frac{4}{3}$
Explanation: To calculate $\frac{3}{4} + \frac{5}{6} - \frac{7}{12}$, find the least common denominator, which is 12: $\frac{3 \times 3}{12} + \frac{5 \times 2}{12} - \frac{7}{12} = \frac{9 + 10 - 7}{12} = \frac{12}{12} = 1$.
2A winter jacket originally priced at 4,000 rubles is discounted by 15% during a store promotion. What is the final discounted price of the jacket?
A.3,600 rubles
B.3,400 rubles
C.3,200 rubles
D.3,800 rubles
Explanation: The discount amount is $15\%$ of $4\,000$, which is $0.15 \times 4\,000 = 600$ rubles. Subtracting the discount from the original price gives $4\,000 - 600 = 3\,400$ rubles (or equivalently $4\,000 \times 0.85 = 3\,400$ rubles).
3Solve the linear equation for $x$: $4(2x - 3) - 3(x + 1) = 10$.
A.3
B.4
C.5
D.7
Explanation: Expand both brackets: $8x - 12 - 3x - 3 = 10$. Combine like terms: $5x - 15 = 10$. Add 15 to both sides: $5x = 25$. Divide by 5: $x = 5$.
4Find the roots of the quadratic equation $x^2 - 7x + 10 = 0$. What is the value of the smaller root?
A.5
B.-5
C.-2
D.2
Explanation: Factoring the quadratic yields $(x - 2)(x - 5) = 0$, giving the roots $x_1 = 2$ and $x_2 = 5$. The question specifically asks for the smaller root, which is 2.
5Evaluate the numerical value of the exponential expression: $\frac{2^7 \cdot 2^{-3}}{2^2}$.
A.4
B.8
C.16
D.2
Explanation: Using the laws of exponents: in the numerator, $2^7 \cdot 2^{-3} = 2^{7 + (-3)} = 2^4$. Dividing by $2^2$ gives $2^{4 - 2} = 2^2 = 4$.
6Simplify the radical expression and find its exact value: $\sqrt{48} - \sqrt{27} + \sqrt{12}$.
A.$5\sqrt{3}$
B.$3\sqrt{3}$
C.$2\sqrt{3}$
D.$4\sqrt{3}$
Explanation: Extract square factors from each radicand: $\sqrt{48} = \sqrt{16 \times 3} = 4\sqrt{3}$, $\sqrt{27} = \sqrt{9 \times 3} = 3\sqrt{3}$, and $\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}$. Combining the like radical terms: $4\sqrt{3} - 3\sqrt{3} + 2\sqrt{3} = (4 - 3 + 2)\sqrt{3} = 3\sqrt{3}$.
7On a topographical map with a scale of $1 : 50\,000$, the straight-line distance between two settlements is measured as $6\text{ cm}$. What is the actual distance between them in kilometers?
A.0.3 km
B.30 km
C.3 km
D.12 km
Explanation: A scale of $1 : 50\,000$ means $1\text{ cm}$ on the map corresponds to $50\,000\text{ cm}$ in reality. Therefore, $6\text{ cm} \times 50\,000 = 300\,000\text{ cm}$. Converting to meters: $300\,000 / 100 = 3\,000\text{ m}$. Converting to kilometers: $3\,000 / 1\,000 = 3\text{ km}$.
8Solve the rational equation for $x$: $\frac{6}{x - 2} = \frac{9}{x + 3}$.
A.10
B.8
C.6
D.12
Explanation: Cross-multiply: $6(x + 3) = 9(x - 2)$. Expand both sides: $6x + 18 = 9x - 18$. Rearrange terms: $18 + 18 = 9x - 6x$, which simplifies to $36 = 3x$. Dividing by 3 gives $x = 12$. Neither denominator is zero at $x = 12$, so this is the valid solution.
9A delivery van travels from Warehouse A to Warehouse B, a distance of $180\text{ km}$, at an average speed of $60\text{ km/h}$. On the return trip along the exact same route, it travels at $90\text{ km/h}$. What was the average speed of the van for the entire round trip?
A.$72\text{ km/h}$
B.$75\text{ km/h}$
C.$70\text{ km/h}$
D.$80\text{ km/h}$
Explanation: Average speed is total distance divided by total time: $\bar{v} = \frac{d_{\text{total}}}{t_{\text{total}}}$. The outbound trip takes $t_1 = \frac{180}{60} = 3\text{ hours}$, and the return trip takes $t_2 = \frac{180}{90} = 2\text{ hours}$. Total distance is $180 + 180 = 360\text{ km}$, and total time is $3 + 2 = 5\text{ hours}$. Thus, $\bar{v} = \frac{360}{5} = 72\text{ km/h}$ (the harmonic mean of 60 and 90).
10Two pipes running simultaneously can fill a water reservoir in $6\text{ hours}$. Working alone, the first pipe takes $5\text{ hours}$ less than the second pipe to fill the same reservoir. How many hours does the first pipe take to fill the reservoir alone?
A.15 hours
B.10 hours
C.12 hours
D.8 hours
Explanation: Let $t$ be the time taken by the first pipe alone; then the second pipe takes $t + 5$ hours. The combined rate is $\frac{1}{t} + \frac{1}{t + 5} = \frac{1}{6}$. Multiplying through by $6t(t + 5)$ yields $6(t + 5) + 6t = t(t + 5)$, which simplifies to $12t + 30 = t^2 + 5t$, or $t^2 - 7t - 30 = 0$. Factoring gives $(t - 10)(t + 3) = 0$. Since time must be positive, $t = 10\text{ hours}$.

About the GVE-11 Exam

Independent practice for Russia's State Graduation Exam for Grade 11 (ГВЭ-11), the GIA-11 route for specified groups of students. This is an English-language MCQ study adaptation, not an official translation, an official paper or a simulation of the written exams. Its 100 reviewed questions cover basic mathematics, Russian spelling, punctuation and speech norms, and the 2026 essay criteria.

Exam sponsor: Rosobrnadzor (Federal Service for Supervision in Education and Science) / FIPI. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Compulsory subjects are Russian and mathematics, each 235 minutes in written form. Mathematics has 14 short-answer tasks (maximum 14 points; recommended grade «3» from 5). Russian is a free-topic essay on one of five topics (maximum 17 points: content ССК1–ССК3 plus literacy ГК1–ГК4 and ФК1; grade «3» from 5) or a 400-series dictation. Oral forms are also provided.

Time Limit

235 minutes per written examination; standard accommodation adds 1.5 hours

Passing Score

Grade 3 (satisfactory / удовлетворительно): In mathematics, minimum 5 out of 14 points; in Russian essay variant, minimum 5 out of 17 points, under federal recommended conversion scales.

Exam / Certification Fees

No examination fee: Part 8 of Article 59 of Federal Law No. 273-FZ prohibits charging students for state final certification (ГИА).

Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

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.

29%

Mathematics: Arithmetic, Algebra & Equations

Calculations with fractions and decimals, percentage models, powers and roots, solving linear/quadratic equations and inequalities.

21%

Mathematics: Geometry, Functions & Probability

Triangles, quadrilaterals, circles, solids, reading graphs, the derivative, logical statements and elementary probability.

25%

Russian Language: Orthography & Punctuation

Literary spelling standards, prefixes, suffixes, parts of speech, and comma placement in simple, compound, and complex sentences.

15%

Russian Language: Text Composition & Speech Norms

Text structure, thematic development, paragraph cohesion, vocabulary suitability, and avoiding grammatical mistakes.

10%

GVE-11 Regulations, Rubrics & Scoring

Administrative rules, candidate eligibility routes, 5-point grade boundaries, and timing arrangements.

Preparing for the GVE-11 Exam

What You Need to Know

  • Passing score: Grade 3 (satisfactory / удовлетворительно): In mathematics, minimum 5 out of 14 points; in Russian essay variant, minimum 5 out of 17 points, under federal recommended conversion scales.
  • Assessment: Compulsory subjects are Russian and mathematics, each 235 minutes in written form. Mathematics has 14 short-answer tasks (maximum 14 points; recommended grade «3» from 5). Russian is a free-topic essay on one of five topics (maximum 17 points: content ССК1–ССК3 plus literacy ГК1–ГК4 and ФК1; grade «3» from 5) or a 400-series dictation. Oral forms are also provided.
  • Time limit: 235 minutes per written examination; standard accommodation adds 1.5 hours
  • Exam / certification fees: No examination fee: Part 8 of Article 59 of Federal Law No. 273-FZ prohibits charging students for state final certification (ГИА). 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

GVE-11: Suggested Study Strategy

1Secure the basic tasks first: under the recommended 2026 scale, 5 correct answers out of 14 reach grade «3» in written mathematics.
2Review official geometric formulas for areas and perimeters of basic shapes (triangles, rectangles, trapezoids, circles).
3For the Russian essay, state your own opinion on the topic and support it with at least two arguments from reading or life experience; aim for 300+ words.

Frequently Asked Questions

Who is eligible to take GVE-11 instead of EGE?

The 2026 FIPI specifications list students in closed special educational and penal institutions, vocational (СПО) students receiving secondary general education, and students and external candidates with ОВЗ, children with disabilities and people with disabilities. Participation follows the GIA-11 procedure.

Can GVE-11 results be used for university admission?

GVE-11 provides the state secondary general education certificate (аттестат). However, unlike EGE scores, GVE scores cannot be used directly in national university ranking competitions; graduates who wish to enter university typically take internal entrance examinations set directly by the higher education institution.

What is the passing threshold for GVE-11 written mathematics?

The written mathematics paper has 14 tasks worth 1 primary point each (maximum 14 points). Under official 2026 federal conversion recommendations, a score of 0–4 points is grade '2' (fail), 5–7 points is grade '3' (satisfactory/pass), 8–10 points is grade '4' (good), and 11–14 points is grade '5' (excellent).