Practice questions
Original question sets written by Per Sir, modelled on past-paper style, with answers on every set. Free to use — no sign-up, nothing to download.
These are not reproductions of HKEAA or IBO examination questions.
Choose your syllabus
HKDSE Mathematics — Compulsory Part →
Topic-by-topic practice across the three syllabus strands, in standard and challenge tiers, for Paper 1 and Paper 2.
IB and IGCSE sets are planned — HKDSE is the only syllabus covered today.
How to use it
Pick one topic and time yourself on a single set, like a short test.
Before you check the answers, mark every question you were unsure of. This is the step most people skip, and it is worth more than the score — it separates what you knew from what you guessed.
For each one you got wrong, ask which of three things happened: the concept was not clear, the arithmetic slipped, or you misread a condition in the question. They need completely different fixes.
Then bring the ones you got wrong to a lesson. One wrong question is worth more than ten right ones.
Why the questions look like this
None of these questions are copied from past papers. They are written from scratch, modelled on how the real papers ask things — and then deliberately varied, so that working through a set is not the same as having seen the answer before.
The difference shows up in how a question opens. A drill question names its method: find the perpendicular bisector of AB. Ours tend to state a condition instead — P is equidistant from A and B — and leave you to notice what that means. That first step, deciding what the question is actually asking, is the part worth practising. It is also the part a formula sheet cannot do for you.
So you will find parts that ask you to justify or explain rather than only compute, and a few questions built around a condition that looks like it fits a standard formula until you check it properly. Being caught by one of those once is worth more than getting ten routine questions right.
This is also a response to a real shift in recent HKDSE papers: drilling a procedure now earns less credit than it used to. The students who can read an unfamiliar setup calmly and work out which tool applies are the ones who do that quickly and well under exam pressure — and that is what separates an ordinary pass from a 5**. Each topic has a standard set at ordinary paper difficulty, and a challenge set that pushes harder on exactly that skill.
The full courses behind these sets are on the Mathematics page.
If you are preparing for the DSE
It is a long year, and most of it is unglamorous. You will sit down to a set like this, get several wrong, and feel like you have gone backwards. You have not. A question you got wrong and then understood is the only kind that reliably stays with you — the ones you got right on autopilot tend not to.
Nothing here is locked, and there is nothing to sign up for. Take what is useful, ignore the rest, and come back when you want another topic.
Good luck. You can do more than you think you can right now.
If you get stuck on something and want a hand with it, you are welcome to get in touch — no obligation either way.