The UK Maths Challenges provide a wonderful library of multiple choice problems; you can practice for the UK Maths Challenges with past papers for the Junior, Intermediate, or Senior Challenges. Questions and full solutions are provided.
As well as a full solution that does not use the multiple-choice answers further ideas are given for investigation.
Maths Challenge questions are an excellent resource at any time – not just for preparation for the competitions, particularly with the increased requirement for problem-solving skills at all levels. On the outstanding Diagnostic Questions site you can choose Junior Maths Challenge questions by topic by choosing the Themed Quizzes option. These quizzes consist of sets of four or five questions grouped by topic. (Log in to Diagnostic Questions to use the link.)
Another way to access Maths Challenge questions by topic for Junior, Intermediate and Senior is from Dr Frosts’s wonderful website full of outstanding resources.
Very conveniently it is possible to download zip files of questions by topic.
For an alternative way to search, search the UKMT database by curriculum topic, the database includes Junior Maths Olympiad.
Further outstanding resources from UKMT include the Team Challenge resources.
The UK Maths Challenges are included on the Problems & Activities page.
For more sources of multiple choice questions see this post.