Free Practice Questions for EGE Math Profile
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Key Facts: EGE Math Profile Exam
The EGE Mathematics Profile has 19 tasks across two parts (FIPI 2026 specification).
Part 1 contains 12 short-answer tasks; Part 2 contains 7 extended-answer tasks (tasks 13-19).
The maximum primary score in 2026 is 32, raised after a new vector task (task 2) was added.
The exam lasts 3 hours 55 minutes (235 minutes).
The minimum threshold for university admission is 27 test points on the 100-point scale.
The EGE is administered free of charge by Rosobrnadzor, with content developed by FIPI.
Extended tasks 18 (parameters) and 19 (number theory) are each worth 4 primary points, the highest value.
The Profile exam is required for admission to technical and STEM university programmes in Russia.
The EGE Mathematics Profile is a 235-minute, 19-task advanced maths exam (12 short-answer + 7 extended-answer tasks, max 32 primary points) required for STEM university admission in Russia.
Sample EGE Math Profile Practice Questions
Try these sample questions to review concepts for the EGE Math Profile exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 100+ question experience with AI tutoring.
1On squared paper with cells 1 cm by 1 cm, a right triangle has legs of length 6 cm and 8 cm lying along the grid lines. What is the area of the triangle (Task 1, planimetry)?
2Vectors a = (3, 4) and b = (1, 0) are given in the coordinate plane. What is the dot (scalar) product a · b (Task 2, vectors, added in 2026)?
3A rectangular box (cuboid) has edges 2, 3 and 4. What is its volume (Task 3, stereometry)?
4A fair six-sided die is rolled once. What is the probability that the number rolled is greater than 4 (Task 4, classical probability)?
5Events A and B are independent with P(A) = 0.6 and P(B) = 0.5. What is P(A and B) (Task 5, probability theorems)?
6Solve the equation 3^(x-2) = 27 (Task 6, simplest equations).
7Find the value of log_2(8) + log_3(9) (Task 7, value of an expression).
8A point moves along a line so that its coordinate is x(t) = t^3 - 3t^2 + 5 (metres). Find its instantaneous velocity at t = 2 s (Task 8, derivative as rate).
9The line y = 4x - 7 is tangent to the graph of y = x^2 + bx + 3. Using the geometric meaning of the derivative, what is the slope of the tangent at the point of tangency (Task 8/9, tangent line)?
10A body is thrown upward and its height (metres) is h(t) = 20t - 5t^2. Using calculus, at what time does it reach maximum height (Task 9, applied/derivative problem)?
About the EGE Math Profile Exam
The EGE Mathematics Profile Level (Математика профильного уровня) is the advanced mathematics paper of Russia's Unified State Exam, required for admission to technical and STEM university programmes. The 2026 paper has 19 tasks in two parts: Part 1 (tasks 1-12) requires short numeric answers, and Part 2 (tasks 13-19) requires full written solutions graded by expert examiners. Content spans algebra, equations and inequalities (logarithmic, exponential, trigonometric), functions and the beginnings of analysis (derivatives, antiderivatives, extrema, tangents), planimetry, vectors and stereometry, probability and statistics, applied word problems, financial mathematics, parameters and number theory. The maximum primary score in 2026 is 32, converted to a 100-point test scale, with a minimum threshold of 27 test points for university entry. The exam lasts 3 hours 55 minutes and is administered free of charge by Rosobrnadzor.
Exam sponsor: Rosobrnadzor; content materials (KIMs) developed by FIPI. The requirements and fees below concern the certification or admission exam, separate from our free practice resources.
Questions
100 questions
Time Limit
3 hours 55 minutes (235 minutes)
Passing Score
Minimum 27 test points (out of 100) for university admission; grades 27-49 = '3', 50-63 = '4', 64+ = '5'
Exam / Certification Fees
Free for Russian school graduates (state-funded final certification, no fee)
Exam sponsor websiteFees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.
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.
Algebra: equations & inequalities
Exponential, logarithmic, trigonometric, rational and irrational equations and inequalities, and systems (Tasks 6, 13, 15)
Calculus & analysis
Derivatives, antiderivatives/integrals, tangents, rates of change, extrema and applied optimization (Tasks 8-9)
Functions & function investigation
Graphs, properties, monotonicity, max/min on intervals (Tasks 11-12)
Planimetry, vectors & stereometry
Areas, volumes, angles, triangles, circles, vectors and 3-D solids (Tasks 1-3, 14, 17)
Probability & statistics
Classical probability, addition and multiplication rules, conditional probability (Tasks 4-5)
Word & financial problems
Motion, work-rate, percentage and loan/deposit financial-math problems (Tasks 10, 16)
Parameters & number theory
Equations with parameters and properties of integers (Tasks 18-19)
Preparing for the EGE Math Profile Exam
What You Need to Know
- Passing score: Minimum 27 test points (out of 100) for university admission; grades 27-49 = '3', 50-63 = '4', 64+ = '5'
- Exam length: 100 questions
- Time limit: 3 hours 55 minutes (235 minutes)
- Exam / certification fees: Free for Russian school graduates (state-funded final certification, no fee) 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
EGE Math Profile: Suggested Study Strategy
Frequently Asked Questions
How many tasks are on the EGE Mathematics Profile exam in 2026?
There are 19 tasks: Part 1 has 12 short-answer tasks (1-12) and Part 2 has 7 extended-answer tasks (13-19) requiring full written solutions. A new vector task (task 2) was added in 2026.
What is the passing score for the EGE Mathematics Profile?
The minimum threshold for university admission is 27 test points out of 100 (about 6 primary points). Competitive STEM programmes typically require far higher scores, often 70+.
How long is the EGE Mathematics Profile exam?
The exam lasts 3 hours 55 minutes (235 minutes), enough time for the 12 short-answer and 7 extended-answer tasks.
Is the EGE Mathematics Profile free?
Yes. The EGE is a state final certification exam taken free of charge by Russian secondary-school graduates; the government funds its administration.
Who administers the EGE?
The EGE is overseen by Rosobrnadzor (the Federal Service for Supervision in Education and Science), with exam materials (KIMs) developed by FIPI, the Federal Institute of Pedagogical Measurements.
What topics does the Profile exam cover?
Algebra and equations, functions and beginnings of analysis (derivatives and integrals), planimetry, vectors and stereometry, probability and statistics, word and financial problems, parameters and number theory.