To really challenge your students, MAT, STEP and AEA questions provide an excellent source of questions. Dr Jamie Frost has created such a useful resource with his STEP, MAT and AEA questions all aligned to new A Level chapters. This dcument is 156 pages of categorised questions (brief answers are given). Also available is a pdf file of just the STEP questions.
For mark schemes see:
- MAT (Maths Admissions Test), see right hand menu, question papers, followed by solutions as separate documents. For superb resources for these questions see these Underground Mathematics Review Questions where you will find not only the questions but suggestions and complete solutions.
- AEA questions and mark schemes.
- STEP mark schemes (under STEP past papers). See also this post which includes details of a superb site for STEP questions as well as further resources; the site described has free access to fully worked solutions for STEP papers.
For further sources try UKMT Senior Maths Challenge Questions.
…and also see MadAsMaths with its many papers and solutions increaisng in difficulty.