For parents · Primary & PSLE math
The hardest PSLE questions are a small, knowable set
The word that frightens parents most is "impossible". But when you count, the hardest questions are not a flood. They are a small, knowable set, and most of them sit in territory we already understand.
Mrs Eileen Toh
Founder & Curriculum Architect · ex-MOE · 5 min read · Updated 22 Jun 2026
There is a word I hear from worried parents more than any other: impossible. The last questions in Paper 2 are described as impossible, unpredictable, the kind of thing no child could prepare for. I understand why. When a confident child comes home shaken by the tail end of a paper, "impossible" is exactly how it feels.
But I want to gently replace that word with a number, because the number is far calmer than the rumour. When we counted, the hardest questions turned out to be small in number and familiar in shape. Not impossible: knowable.
Thirty-one, in known territory
Across the 664 questions sat from 2012 to 2025, only 31 carry the top difficulty rating. That is the whole of the hardest band, across fourteen years of papers. And almost all of those 31 sit in the back third of Paper 2, exactly where a child would expect the toughest questions to live. They do not jump out at you from the easy stretch; they sit where the paper signals they will be.
Thirty-one over fourteen years is roughly two or so per paper. That is not a flood. It is a small, identifiable tail, and a tail you can look at squarely rather than fear.
Top-difficulty questions
the whole hardest band across fourteen years of papers
Structures
area and perimeter, volume and rate, fractions or part-whole
Where they sit
almost all of them in the back third, where you would expect
They cluster in three structures
This is the part that turns worry into a plan. Those 31 questions do not scatter randomly across the syllabus. They cluster in three structures your child already meets all year:
- Area and Perimeter. A composite figure to break into pieces, where the difficulty is in seeing the parts rather than in the arithmetic.
- Volume and Rate. A container, a flow, a before and after. The hardest versions add a twist, but the structure is one your child has seen.
- Fractions or Part-Whole. A quantity split into parts where the relationship has to be tracked carefully through several steps.
None of these is exotic. They are the same structures the paper tests at every level of difficulty, only stretched. That is precisely why they are learnable: the territory is familiar, even when the question is demanding.
Is the paper getting harder?
This is the question behind most of the worry, so let me answer it plainly. The very hardest band grew from 2019 to 2023, then eased again in 2024 and 2025. So there was a stretch where the toughest tail thickened, and then it relaxed. Across the whole period, the average barely moved; it was the top tail that rose and then settled, not the paper as a whole.
I would not turn that into a prediction either way. This is analysis of past papers, not a forecast. But the honest, calming point stands: the hardest tail is small and knowable, not a flood, and it has not run away from us.
You can see them solved
The surest antidote to "impossible" is to look the questions in the eye. We have gathered them in one place. Our hardest-questions hub has all twelve, solved, with videos, so your child can watch how each one is unpacked step by step rather than imagining a monster. If you would like the wider picture of what the paper tests and how often, the count lives in our pillar guide on the most-tested PSLE math topics.
These figures come from our tagged index of 709 PSLE questions, with the difficulty count here based on the 664 questions from the sat papers; the MOE Specimen paper we keep reported separately. The honest takeaway is the same one I give parents in the room: "impossible" is a feeling, and "31, in known territory" is the fact underneath it.