I still remember when I took my H2 Math exams in the hall and there used to be this group of students who would frequently visit the toilet during the exam. The frequency that they visited the toilet was an indication that they were already done with the paper and the exam was only halfway through. This were the kids that were deemed “too smart” for A level Math tuition and as they were probably on a whole other level as compared to the rest of us. That being said, we can also improve our skills to be as proficient as they are by finding questions that challenge us. Remember how you started learning a topic, before all the H2 Math tuition and many rounds of practice; the struggle that you had made you who you are today. It is the same feel that would push you even further, by seeking questions that challenge you. Let me share with you some places where you could find questions that pushes you.
One place where you could get this is at A level/ H2 math tuition centers. This is one of the places where students who are already getting good grades go if they are aiming to become the top few. At centres specializing in A Level/ H2 Mathematics tuition, the tutors actually do look through and attempt many questions and are able to judge how difficult they are for the students. They would also provide detailed solutions to the questions so that students would not be stuck for an eternity doing the questions. A level math tutors would also be able to explain to you the way to solve the question or further explain on the solutions. This would allow you to spend more time learning rather than struggling, thus your precious time would be spent more efficiently.
Apart from past year Cambridge A level papers, there are other papers which you can find to challenge yourself. A recommended place to look would be the Sixth Term Entrance Papers (STEP), and you might even come across such questions in your tutorials. STEP is the aptitude test that applicants to Cambridge and other UK universities would take for certain courses like Mathematics. The questions are based on the content from the UK GCSEs and A levels, which is equivalent to out O levels and A levels respectively. There are three levels, where level 1 is the easiest and level 3 is the hardest. There are also questions from H2 further Math. I feel that by the level 1 papers are still doable as they cover mainly H2 Math content. However, the questions are not the typical questions that you see in exam papers and probably most H2 Math tuition centers. This is where you can attempt questions on a topic from different angles. Moreover, as the H2 math A Levels exam questions are becoming more “random”, it would be good practice to think on the spot.
H2 / A level Physics tuition classes are definitely where you can find challenging questions for physics for the same reasons I mention above. However, there are also papers out there that are similar to the H2 physics examinations that is based on the H2 Physics curriculum in Singapore. You can also attempt the Physics Admission test by Oxford university, which is taken by those applying to study physics at Oxford, or you could also attempt the British Physics Olympiad. Both of which are testing you on the content that you have learnt in school and/or H2 Physics tuition but from different angles. These questions definitely are more mathematical in nature and require less explanation. For explanation questions, you could look towards the Cambridge Natural sciences admission exams where there are some explanation type questions that would challenge you.
If what you are looking for is closer to home, you might want to try past year H2 Math/ H2 Physics past year papers from the JCs that are known to set harder papers. These schools already have very smart students and would want to challenge them, so they are likely to set papers that are harder. That being said, some H2 Math and A level physics tuition centres also look through these papers and the tutors have already sieved the harder questions out. You can simply approach your tutor for some of such questions.
My believe is that attempting tougher questions will help you improve rather than stagnate at the same level, thus I find it worthwhile to do some of such questions. Moreover, some of them are in fact quite interesting and will keep your interest in the subject afloat.