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International Mathematical Olympiad Association50 Questions
Mathematics MCQs
Practice Mathematics multiple-choice questions for International Mathematical Olympiad Association competitive exams. Each question includes the correct answer and a short explanation, and past-paper questions are marked so you can revise both repeated and fresh material in one place.
1 problem
3 problems
6 problems
4 problems
ExplanationThe competition format specifies 3 problems per day over two days.
3 hours
4 hours
4.5 hours
6 hours
ExplanationContestants are given four and a half hours for each of the two examination days.
Yes, basic calculators only
Yes, scientific calculators only
No electronic aids are permitted
Only for specific problems
ExplanationIMO regulations state that no calculators or electronic aids are permitted during the exam.
5 points
7 points
10 points
42 points
ExplanationEach problem is marked on a 0-7 scale, meaning the maximum for one problem is 7.
1, 2, 3, 4, 5, 6 in order
1, 4, 2, 5, 3, 6
Randomized difficulty
6, 5, 4, 3, 2, 1
ExplanationThe difficulty progression used by the Jury follows the order 1, 4, 2, 5, 3, 6.
3
4
6
8
ExplanationThe competition format consists of two days, with 3 problems to be solved on each day.
3 hours
4 hours
4.5 hours
5 hours
ExplanationContestants are given 4.5 hours on each of the two days to work on the three problems.
Yes, if they are non-graphing
Yes, all models are allowed
No, no electronic aids are permitted
Only simple arithmetic calculators
ExplanationThe IMO regulations strictly prohibit the use of calculators or any other electronic aids.
6
7
10
42
ExplanationEach problem is scored on a scale of 0 to 7 points.
Calculus, Linear Algebra, and Logic
Algebra, Combinatorics, Geometry, and Number Theory
Statistics, Trigonometry, and Probability
Physics, Chemistry, and Math
ExplanationIMO problems are chosen from these four core areas of secondary school mathematics.
Yes, they cover three additional, distinct problems
No, the same problems are given
Only one problem is different
They contain similar problems but with different numbers
ExplanationThe exam takes place over two consecutive days, with three unique problems provided on each day, totaling six problems.
21
36
42
60
ExplanationWith 6 problems worth 7 points each, the maximum possible total score is 6 * 7 = 42.
Multiple-choice answers only
Numerical answers only
Complete, written-out mathematical proofs
Short-answer paragraphs
ExplanationFull marks require a complete, correct, and well-justified mathematical argument or proof.
The IMO Board
The Host Country coordinators
Each team's own Leader
The Ethics Committee
ExplanationThe host organization provides coordinators who work with team leaders to finalize scores for each student.
Only English is used
English and French only
English, French, German, Russian, and Spanish
Only the host country's language
ExplanationThese five languages are recognized as the official languages of the International Mathematical Olympiad.
Randomly assigned
Increasing difficulty from 1 to 6
1-3 are easy, 4-6 are hard
Alternating difficulty based on topic
ExplanationThe IMO follows a planned difficulty progression, generally moving from more accessible to more challenging problems.
They can return at any time
They must be supervised by an invigilator
They are disqualified immediately
They can leave only during the final 15 minutes
ExplanationExam security protocols require constant supervision of contestants whenever they are out of the room.
Contestants
Team Leaders
Host Country Coordinators
The Ethics Committee
ExplanationThe Jury consists of the team leaders from all participating countries.
The IMO Office
The IMO Board
The Curriculum Committee
The Ethics Committee
ExplanationThe IMO Board is the body responsible for setting the overall policy and direction of the competition.
Up to 3
Up to 6
Up to 10
Exactly 1
ExplanationEach participating country is invited to send a team consisting of up to six contestants.
1950
1959
1965
1970
ExplanationThe inaugural IMO took place in Romania in 1959.
Based on fixed score cutoffs
Top 50% receive medals in a 1:2:3 ratio
Top 100 students receive gold
Based on random selection
ExplanationMedals are given to approximately half the contestants in a 1:2:3 ratio for gold, silver, and bronze.
Scoring 1 point on any problem
Scoring 7 points on at least one problem
Being in the top 50%
Solving every problem partially
ExplanationHonourable mentions are awarded to those who don't get a medal but achieve a perfect score on at least one problem.
Yes, with permission
No, they must not be enrolled in post-secondary education
Yes, if they are under 20
Only during their first year
ExplanationContestants must not be enrolled in any post-secondary educational institution to be eligible.
The IMO Board
The Host Organisation
The Jury
The Ethics Committee
ExplanationThe host organization is responsible for appointing the committee that reviews submitted problems.
Yes, they contain 3 different problems
No, the problems are the same
The problems are a continuation of day 1
Only one problem is new
ExplanationThe competition consists of 6 problems total, 3 on each day.
21
28
35
42
ExplanationWith 6 problems each worth 7 points, the maximum total is 6 * 7 = 42.
Final answers only
Complete proofs and justifications
Sketches and diagrams only
Notes and rough work
ExplanationIMO solutions must include complete, rigorous mathematical proofs and justifications to receive full credit.
They are encouraged to do so
They are not permitted to do so
They must finish all problems first
They receive extra credit
ExplanationRegulations state that students are not allowed to leave the examination room in the final 15 minutes.
Only the host country's coordinators
The team leaders and host country coordinators together
The students themselves
Only the IMO board
ExplanationThe coordination process involves collaboration between the team leaders and the host country's coordinators to ensure fairness.
To rank students by speed
To determine official scores fairly and transparently
To select new problems
To verify student identity
ExplanationCoordination ensures that all scores are assessed in a homogeneous, fair, and consistent manner.
The coordinator's score is final
The problem captain is consulted, then the Chief Coordinator, and finally the Jury
The score is automatically set to 0
The student is re-tested
ExplanationDisputes follow a specific escalation process through the problem captain, Chief Coordinator, and the Jury.
Yes, always
Only for geometry problems
No, only rulers and compasses
Yes, if provided by the host
ExplanationProtractors are explicitly banned; only basic writing and drawing instruments like rulers and compasses are permitted.
The Curriculum Committee
The Ethics Committee
The IMO Foundation
The ICT Group
ExplanationThe Ethics Committee is tasked with ensuring integrity and proper behavior across all IMO events.
A list of students who passed
A list of problems selected for final review before the contest
A list of rules for the exam
The list of previous gold medalists
ExplanationThe Problem Selection Committee prepares a shortlist of proposed problems from which the Jury selects the contest problems.
Yes, with Jury approval
No, never
Yes, automatically
Only if the deputy leader is sick
ExplanationRegulations allow for a leader to be replaced in an emergency, subject to the prior approval and consent of the Jury Chair.
Awards are given
Contestants take the exam
Attendees are transported to official departure sites
The jury meets for the last time
ExplanationThe host organization provides transport between accommodation sites and official arrival/departure points.
The IMO President
The Leader or Deputy Leader
The host country's police
No one
ExplanationLeaders and Deputy Leaders are officially acting in loco parentis for their team members during the competition.
Yes, if they are visually impaired
No, only provided answer forms are used
Yes, for the final hour
Only if they have internet access
ExplanationSolutions must be submitted on the physical answer forms provided by the host organization.
Yes, always
Never
Only in cases of Force Majeure
Only for students with medical issues
ExplanationRemote sitting is only an option in extreme situations such as war or natural disasters.
Managing the medals
Supporting technical systems and digital operations
Selecting the math problems
Funding the IMO foundation
ExplanationThe ICT group manages the website and other digital systems required for the IMO operation.
They receive a warning
They are liable to disqualification
They are given a lower score
Nothing
ExplanationViolation of regulations can lead to disqualification from the exam or competition.
The students
The Jury
The IMO Association
The local school
ExplanationThe host organization must follow the IMO Association's guidelines and regulations.
By random draw
By a vote of the Jury, based on Board recommendations
By the President's choice
By who has the most medals
ExplanationThe Board makes recommendations to the Jury, which ultimately decides the host for future Olympiads.
Yes, they always stay together
Only Observers C stay with the contestants
No, they stay in separate locations
They sleep in the exam room
ExplanationObserver C category is specifically for those residing at the same site as the contestants.
A phone call to the President
Online confirmation by the date specified in the Annual Regulations
An in-person meeting
A letter to the host's school
ExplanationRegistration must be done through the official online portal by the stated deadline.
The IMO Board
The Ethics Committee
The Curriculum Committee
The host country's government
ExplanationThe Annual Regulations for any given IMO must be formally approved by the IMO Board.
Yes, with a two-thirds majority vote
No, it is strictly forbidden
Yes, with a simple majority
Only if the host agrees
ExplanationA two-thirds majority is required to exceed the standard medal limit of 50%.
To select students
To provide long-term support and funding for the IMO
To write the exam problems
To coordinate the marking
ExplanationThe Foundation exists to support the mission and infrastructure of the IMO long-term.
Only the Leader and Deputy Leader can see them
Only participants and invited people can see them
They are made public on the website
Only the host's staff can see them
ExplanationBefore results are finalized, access to scripts is restricted to authorized participants and invited individuals.
Frequently Asked Questions
Are these Mathematics MCQs free?
Yes. Every Mathematics MCQ on this page is free to practice, including the correct answer and explanation.
Do these include past-paper questions?
Yes — questions sourced from past papers are clearly marked with a "Past Paper" badge, alongside fresh practice questions.
Which exams do these Mathematics MCQs help with?
They are aimed at International Mathematical Olympiad Association and related Pakistani competitive exams that test Mathematics.
How should I practice subject-wise MCQs?
Attempt each question first, then reveal the answer and read the explanation. Short, focused sessions on one subject work better than long unstructured reading.