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Exam Review

Key Facts: OGE Mathematics Exam

2026 official task count: 25; primary-score maximum: 31.

Duration: 235 minutes.

Official format: 19 short-answer tasks and six developed mathematical solutions.

Assessment language: Russian.

2026 federal recommendation: grade 3 begins at 8 of 31 primary points; regional authorities approve the final conversion scale. The recommended minimum also requires at least two geometry points.

This is independent practice and an English-language MCQ study adaptation, not an official translation, an official paper or a simulation of the exam language environment. MCQs do not replace the official short answers, developed responses or practical application tasks.

25 tasks; 235 minutes; maximum 31 primary points. This is independent practice and an English-language MCQ study adaptation, not an official translation, an official paper or a simulation of the exam language environment. MCQs do not replace the official short answers, developed responses or practical application tasks.

Sample OGE Mathematics Practice Questions

Try these sample questions to review concepts for the OGE Mathematics exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 25+ question experience with AI tutoring.

1Calculate −7 + 12.
A.−19
B.−5
C.5
D.19
Explanation: Adding twelve moves twelve units right from negative seven. The result is five.
2Calculate 7/8 − 1/3.
A.6/5
B.1/2
C.17/24
D.13/24
Explanation: Use the common denominator twenty-four: 7/8 = 21/24 and 1/3 = 8/24. Their difference is 13/24.
3An arithmetic progression starts 3, 7, 11, … . What is its nineteenth term?
A.75
B.79
C.72
D.76
Explanation: The common difference is four. The nineteenth term is eighteen steps after the first, so a₁₉ = 3 + 18 × 4 = 75.
4Simplify √72 − 2√8.
A.4√2
B.2√2
C.√56
D.2
Explanation: √72 = 6√2 and √8 = 2√2. Therefore 6√2 − 4√2 = 2√2.
5A jacket costs 640 rubles after a 20% discount. What was its original price?
A.768 rubles
B.512 rubles
C.800 rubles
D.3,200 rubles
Explanation: The discounted price is 80% of the original. Dividing 640 by 0.8 gives 800 rubles.
6Solve 3(2x − 1) = 4x + 9.
A.3
B.4
C.−6
D.6
Explanation: Expansion gives 6x − 3 = 4x + 9. Thus 2x = 12 and x = 6.
7Find both roots of x² − 5x + 6 = 0.
A.2 and 3
B.−2 and −3
C.1 and 6
D.−1 and −6
Explanation: The quadratic factors as (x − 2)(x − 3). Either factor can be zero, so the roots are 2 and 3.
8Solve (x − 1)(x + 3) ≤ 0 over the real numbers.
A.x ≤ −3 or x ≥ 1
B.−3 ≤ x ≤ 1
C.−3 < x < 1 only
D.x ≥ 3
Explanation: The product changes sign at −3 and 1 and is negative between them. The non-strict inequality includes both roots.
9Solve 1/(x − 2) + 1/(x + 2) = 1, respecting the domain restrictions.
A.x = 2 or x = −2
B.x = 1 only
C.x = 1 − √5 or x = 1 + √5
D.x = −1 − √5 or x = −1 + √5
Explanation: For x ≠ ±2, combining fractions gives 2x/(x² − 4) = 1, hence x² − 2x − 4 = 0. The two roots 1 ± √5 both satisfy the domain restriction.
10Real numbers x and y satisfy x + y = 7 and xy = 10. Find x² + y².
A.49
B.39
C.69
D.29
Explanation: Use x² + y² = (x + y)² − 2xy. This gives 49 − 20 = 29 without solving for x and y separately.

About the OGE Mathematics Exam

Main State Exam (ОГЭ) in Mathematics is a current 2026 subject assessment within Russian state final certification. 19 short-answer tasks and six developed mathematical solutions. The maximum primary score is 31. Assessment language: Russian. This is independent practice and an English-language MCQ study adaptation, not an official translation, an official paper or a simulation of the exam language environment. MCQs do not replace the official short answers, developed responses or practical application tasks. This bank contains 25 reviewed study questions. It is a selective learning resource, not complete coverage of every official topic or a replica of an examination paper.

Exam sponsor: Rosobrnadzor / FIPI. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Questions

25 questions

Time Limit

235 minutes

Passing Score

2026 federal recommendation: grade 3 begins at 8 of 31 primary points; regional authorities approve the final conversion scale. The recommended minimum also requires at least two geometry points.

Exam / Certification Fees

A current official fee statement was not confirmed in the sources checked; ask the regional examination authority.

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.

20/31 primary points (64.5%)

Arithmetic, algebra, functions, probability and applied work

Part 1 has fourteen non-geometry tasks; part 2 has three developed algebra or function problems.

11/31 (35.5%)

Geometry

Five short-answer and three developed geometry tasks; practise complete proofs and solutions separately.

Preparing for the OGE Mathematics Exam

What You Need to Know

  • Passing score: 2026 federal recommendation: grade 3 begins at 8 of 31 primary points; regional authorities approve the final conversion scale. The recommended minimum also requires at least two geometry points.
  • Exam length: 25 questions
  • Time limit: 235 minutes
  • Exam / certification fees: A current official fee statement was not confirmed in the sources checked; ask the regional examination authority. Official sources

Using Our Practice Resources

  • Work through all 25 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

OGE Mathematics: Suggested Study Strategy

1Use the approved 2026 FIPI specification and codifier to check the full assessed scope.
2Review the worked feedback here, then explain your reasoning without looking at the choices.
3Practise the official response methods separately, including complete written, spoken, laboratory, or computer work where required.

Frequently Asked Questions

What is the official 2026 assessment format?

19 short-answer tasks and six developed mathematical solutions. Assessment language: Russian.

How is the result assessed?

2026 federal recommendation: grade 3 begins at 8 of 31 primary points; regional authorities approve the final conversion scale. The recommended minimum also requires at least two geometry points.

Does this bank reproduce the official assessment?

This is independent practice and an English-language MCQ study adaptation, not an official translation, an official paper or a simulation of the exam language environment. MCQs do not replace the official short answers, developed responses or practical application tasks.

Who can take the assessment?

The OGE is part of grade 9 state final certification. Confirm admission requirements, the final oral-interview result and any permitted accommodations with the school or regional authority.

What is the examination fee?

A current official fee statement was not confirmed in the sources checked; ask the regional examination authority.

How much of the exam does this bank cover?

This bank contains 25 reviewed study questions. It is a selective learning resource, not complete coverage of every official topic or a replica of an examination paper. Use the official codifier and complete original-response practice to address the full assessment.