UKMT Challenges

Instructions 

1. Do not start the Challenge until the time your teacher has agreed with you.

2. The Challenge lasts 60 minutes. Your clock starts when you click on the start button. You can attempt the questions in any order and your answers will be saved immediately but you can always go back to change an answer. When you are done you can close your browser, logout or select the 'I have finished' option beneath question 25. No answers, or personal details, may be entered after the allowed time is over.

Please note that your answers are saved as you go along. Even if you run out of time and the system logs you out, all answers submitted up to that point will have been saved.

3. The use of blank or lined paper for rough working is allowed; squared paper, calculators and measuring instruments are forbidden. 

4. Do not expect to finish the whole paper in the time allowed. The questions in this paper have been arranged in approximate order of difficulty with the harder questions towards the end. You are not expected to complete all the questions during the time. You should bear this in mind when deciding which questions to tackle. 

6. Scoring rules: 

5 marks are awarded for each correct answer to Questions 1-15; 

6 marks are awarded for each correct answer to Questions 16-25; 

Each incorrect answer to Questions 16-20 loses 1 mark; 

Each incorrect answer to Questions 21-25 loses 2 marks. 

7. The questions on this paper are designed to challenge you to think, not to guess. You will gain more marks, and more satisfaction, by doing one question carefully than by guessing lots of answers. This paper is about solving interesting problems, not about lucky guessing.

Intermediate Mathematical Challenge 2023 - Northern Ireland Year 12

During this practice competition you will receive immediate feedback on your answer.

(During the official challenge you will not see whether you have answered a question correctly or not.)