1. Junior Mathematics Challenge (JMC)
Exam Time:
60 minutes
Exam Format:
25 multiple-choice questions; total 135 points. The first 15 questions are worth 5 points each, and the last 10 questions are worth 6 points each. 1 point is deducted for each incorrect answer to questions 16-20, and 2 points are deducted for each incorrect answer to questions 21-25. Blank questions are worth 0 points.
Exam Requirements:
Blank paper is allowed for rough work; graph paper, calculators, and measuring instruments are prohibited.
Use a B or HB non-mechanical pencil.
Do not expect to complete the entire paper within the allotted time. The questions on this paper are arranged roughly by difficulty, with the more difficult questions at the end. You do not need to complete all the questions within the allotted time. Keep this in mind when deciding which questions to tackle.
The questions on this paper are designed to challenge your thinking, not guessing. Solving one question carefully will earn you a higher score and greater satisfaction than guessing many answers. This paper is about solving interesting problems, not about lucky guesses.
2. Junior Kangaroo
The Junior Kangaroo Challenge is a follow-up round to the Junior Mathematics Challenge (JMC), a 60-minute challenge consisting of 25 multiple-choice questions.
Eligibility:
Entry to the Junior Kangaroo Challenge is by invitation or self-determination based on a qualifying JMC score. Thousands of UK students qualify for the JMC each year. It is open only to UK schools.
Exam Duration:
60 minutes
Exam Components:
25 multiple-choice questions, totaling 135 points. The first 15 questions are worth 5 points each, and the last 10 are worth 6 points each. No points are deducted for incorrect answers.
Awards:
The top 25% receive a certificate of merit; the rest receive a participation certificate.
Exam Requirements:
Rough work on white paper is permitted; graph paper, calculators, and measuring instruments are prohibited.
Use a B or HB non-mechanical pencil. Choose only one option (A, B, C, D, E) on each answer sheet. Do not mark multiple options.
Do not expect to complete the entire paper within the allotted time. The questions in this paper are arranged in general order of difficulty, with the more difficult questions at the end. You do not need to complete all the questions within this time. Keep this in mind when deciding which questions to tackle.
The questions in this paper are designed to challenge your thinking, not guessing. Carefully solving one question will earn you more points and more satisfaction than guessing many answers. This paper is about solving interesting problems, not about lucky guesses.
3. Junior Mathematical Olympiad (JMO)
The Junior Mathematical Olympiad is a follow-up to the Junior Mathematical Challenge (JMC), a 2-hour challenge containing 16 questions; 10 questions in Part A and 6 Olympiad-style questions in Part B.
Eligibility:
Eligibility for the Junior Mathematical Olympiad is by invitation based on qualifying JMC scores, or by self-determination. Approximately 1,200 students qualify for the JMC each year.
Exam Duration:
120 minutes
Exam Components:
16 questions in total. Section A: 10 questions, 1 point each, full marks for a correct answer. Section B: 6 questions, 10 points each, requiring both work and answer.
Exam Requirements:
Rough work is allowed on blank paper; graph paper, calculators, and measuring instruments are prohibited.
Do not submit rough work; your answers should be completely simplified and accurate. If applicable, they may contain symbols such as π, fractions, or square roots, but not decimal approximations.
Only answer the questions in Section A. For the questions in Section B, you should provide a complete written solution, including an explanation of the mathematical reasons why your method is correct. Simply stating an answer, even a correct one, will only earn you a small number of marks; furthermore, incomplete or poorly worded solutions will not receive full marks.
4. Intermediate Mathematics Challenge (IMC)
Exam Duration:
60 minutes
Exam Components:
25 multiple-choice questions, totaling 135 points. The first 15 questions are worth 5 points each, and the last 10 questions are worth 6 points each. 1 point is deducted for each incorrect answer to questions 16-20, and 2 points are deducted for each incorrect answer to questions 21-25. Blank questions are worth 0 points.
Exam Requirements:
Blank paper is allowed for rough work; graph paper, calculators, and measuring instruments are prohibited.
Use a B or HB non-mechanical pencil.
Do not expect to complete the entire paper within the allotted time. The questions in this paper are arranged roughly by difficulty, with the more difficult questions at the end. You do not need to complete all the questions within the allotted time. Keep this in mind when deciding which questions to tackle.
The questions on this paper are designed to challenge your thinking, not guessing. Solving one question carefully will earn you a higher score and greater satisfaction than guessing many answers. This paper is about solving interesting problems, not about lucky guesses.
5. Grey/Pink Kangaroo
Eligibility:
Eligibility for Grey and Pink Kangaroo exams is by invitation or self-determination based on qualifying IMC scores. Thousands of UK students qualify for the IMC each year. Open only to UK schools.
Exam Duration:
60 minutes
Exam Components:
25 multiple-choice questions, totaling 135 points. The first 15 questions are worth 5 points each, and the last 10 are worth 6 points each. No points are deducted for incorrect answers.
Exam Requirements:
Blank paper is allowed for rough work; graph paper, calculators, and measuring instruments are prohibited.
Use a B or HB mechanical pencil. On the answer sheet, select only one option (A, B, C, D, E) for each question. Do not select multiple options.
Do not expect to complete the entire paper within the allotted time. The questions in this paper are arranged roughly by difficulty, with the more difficult questions at the end. You do not need to complete all questions within the allotted time. Keep this in mind when deciding which questions to tackle.
This exam is designed to challenge your thinking, not guessing. Solving a problem carefully will earn you a higher score and greater satisfaction than guessing many answers. This exam is about solving interesting problems, not about lucky guesses.
6. Cayley, Hamilton, and McLaughlin Mathematical Olympiad
Eligibility:
Eligibility for the Intermediate Mathematical Olympiad is by invitation or self-determination based on a qualifying IMC score. Approximately 1,800 students qualify for the IMC each year.
Exam Duration:
120 minutes
Exam Components:
6 Olympiad problems requiring fully simplified answers and complete solution processes. The clarity and accuracy of the presented solution process will affect the score.
Exam Requirements:
Blank paper is allowed for rough work; graph paper, calculators, and measuring instruments are prohibited.
Do not submit rough work.
Your answers should be fully simplified and accurate. They may contain symbols such as π, fractions, or square roots (if applicable), but decimal approximations are not allowed.
You should provide a complete written solution, including the correct mathematical justification for your approach. Simply stating the answer, even if correct, will only earn you a few points; moreover, incomplete or poorly expressed solutions will not receive full marks.
7. Advanced Mathematics Challenge (SMC)
Exam Duration:
90 minutes
Exam Components:
25 multiple-choice questions, 4 points for a correct answer, 1 point deducted for each incorrect answer, starting with an initial score of 25.
Exam Requirements:
Blank paper is allowed for rough work; graph paper, calculators, and measuring instruments are prohibited.
Use a B or HB non-mechanical pencil.
Do not expect to complete the entire paper within the allotted time. The questions on this paper are arranged roughly by difficulty, with the more difficult questions at the end. You do not need to complete all the questions within the allotted time. Keep this in mind when deciding which questions to tackle.
The questions on this paper are designed to challenge your thinking, not guessing. Solving one problem carefully will earn you a higher score and greater satisfaction than guessing many answers. This paper is about solving interesting problems, not about lucky guesses.
8. Andrew Jobbins, Advanced Kangaroo
Exam Duration:
60 minutes
Exam Components:
20 questions, 5 points each. The answer to each question is a positive integer less than 1000.
Exam Instructions:
Blank paper is allowed for rough work; graph paper, calculators, and measuring instruments are prohibited.
Use a B or HB non-mechanical pencil to write your answer to each question as a three-digit number from 000 to 999. Pay close attention to the example on the answer sheet, which shows how to code your answers.
Do not expect to complete the entire paper within the allotted time. The questions in this paper are arranged roughly by difficulty, with the more difficult questions at the end. You do not have to complete all the questions within the allotted time. Keep this in mind when deciding which questions to tackle.
The questions on this paper are designed to challenge your thinking, not guessing. Doing one question carefully will earn you a higher score and greater satisfaction than guessing many answers. This paper is about solving interesting questions, not about lucky guesses.
9. BMO1
Eligibility:
UK students must advance from SMC to participate in BMO Round 1, while Chinese students can participate directly in BMO.
Exam Duration:
210 minutes
Exam Components:
6 Olympiad math problems, 10 points each, requiring fully simplified answers and complete solution processes.
Exam Requirements:
A complete written solution (not just the answer) is required, fully justifying any assertions you may make. Draft a rough sketch first, then carefully draft the final version, and finally write down your best attempt.
A complete solution will convey more confidence than partial attempts at all four problems.
Rulers, set squares, and compasses are allowed, but calculators and protractors are prohibited. Using geometric instruments to construct large, precise diagrams for geometry problems is strongly encouraged.
You should use blue or black ink, but pencils and other colors are acceptable for diagrams.
You may submit drafts containing calculations, examples, or ideas not presented in your final attempt; write "ROUGH" at the top of each page of drafts.
10. BMO2
BMO2 is the next round after BMO1. Only students who achieve a certain high score in Round 1 qualify for Round 2. The top 24 students in BMO2 will go to Cambridge University for training to compete for a place representing the UK in the International Mathematical Olympiad.
Exam Duration:
210 minutes
Exam Components: 4 Olympiad problems, 10 points each. Complete simplified answers and full solution processes are required. Solving one or two problems completely will earn more points than solving all four problems incompletely.
Exam Requirements:
A complete written solution (not just the answer) is required, along with full proofs for any assertions you may make. Draft a rough sketch first, then carefully draft the final version, and finally write down your best attempt.
One or two complete solutions will convey more confidence than partial attempts at all four problems.
Rulers and compasses are allowed, but calculators and protractors are prohibited.
You should use blue or black ink, but pencil and other colors are acceptable for diagrams.
You may submit drafts containing calculations, examples, or ideas not included in the final assignment; write "ROUGH" at the top of each page of the draft.
Approximately 24 high-achieving students qualified to represent the UK at the International Mathematical Olympiad will be invited to a training course in Cambridge during the Easter holidays.
11. Girls' Mathematical Olympiad (MOG)
Exam Duration:
150 minutes
Exam Components:
5 questions, 10 points each, requiring fully simplified answers and complete solution processes.
Participation Information:
Each school can participate 4 times free of charge.
Exam Requirements:
Questions 2 and 3 only require a written answer. The answer sheet clearly indicates the location of the answers.
Questions 1, 4, and 5 require a complete written explanation. If your solution involves calculations, equations, tables, etc., explain the source of these and how you used them. Explain how the steps of your solution are connected and provide sufficient evidence for your assertions. A simple answer will earn very few points (if any).
Good ideas may be awarded partial credit, so please submit everything that shows your thoughts on the problem—the clearer the better. However, a complete solution will earn more points than several incomplete attempts.
The earlier questions are often simpler. Questions have multiple parts. The earlier parts usually introduce results or ideas that will help solve the later parts.
Rulers and compasses are allowed, but calculators and protractors are prohibited.
You may jot down your ideas on scratch paper, but you should write your solution on the answer sheet provided for each question.
