The hardest PSLE Maths questions, and how they are built
The last three questions of Paper 2 decide most AL1s. They are not random hard questions. They are built the same few ways, and a child who can name the way is most of the way there.
What the last three look like
I read the last three Paper 2 questions of twelve 2025 P5 end-of-year papers and eight 2025 P6 prelims from top schools, every page and every answer key. They are remarkably alike.
| In the school papers | |
|---|---|
| Marks | 4 or 5 each, 13 to 15 together: more than a quarter of Paper 2 |
| Length | 40 to 120 words, most around 60 |
| Parts | Two or three, and a later part almost always uses an earlier answer |
| Figures | Most have a figure, a table or a graph; the money and fraction problems usually do not |
| Working | 4 to 8 steps, with two to four quantities held at once |
| Topics | Fractions before and after, composite area and circles, patterns, ratio, money, angles in figures |
The six things that make them hard
Every one of these questions is hard for a reason that has a name. These six cover almost all of them.
- A total that is never given. Three children have the same number of coins, but nobody says how many. The number cancels out, and a child who hunts for it is stuck.
- Fractions of two different wholes. 3/5 of one group equals 1/4 of another. The fractions cannot be compared until they share a numerator. See fractions of a remainder.
- A rule run backwards. A pattern is easy to extend. The hard part asks which figure has 311 squares, and the rule has to be undone.
- A search with no formula. Cupcakes come only in boxes of 4 or 6, one kind outnumbers the other by 10, and the total lies between 30 and 50. The only way in is to list the cases in order.
- An area found only by adding and taking away. A leaf in a square is two quarter circles minus the square. Nothing in the figure gives it directly. See composite circles.
- Information hidden in the figure. "Identical" rectangles fix a length that is never written down; an isosceles triangle is implied by two equal sides, never marked.
A worked example
Ali, Mei and Ravi each have the same number of coins. All of Ali's coins are 20-cent coins. Mei has 5 one-dollar coins and the rest are 20-cent coins. Ravi has 11 one-dollar coins and the rest are 20-cent coins.
(a) How much more money does Ravi have than Mei?
(b) Mei's coins are worth $9.60 altogether. How many coins does each child have?
What makes it hard: the number of coins is never given. Most children try to find it first and cannot.
(a) Swapping a 20-cent coin for a one-dollar coin adds $1 − $0.20 = $0.80, and keeps the number of coins the same. Ravi has 11 − 5 = 6 more one-dollar coins than Mei, so Ravi has 6 × $0.80 = $4.80 more. The total number of coins was never needed.
(b) Mei's 20-cent coins are worth $9.60 − $5 = $4.60, which is $4.60 ÷ $0.20 = 23 coins. With the 5 one-dollar coins, Mei has 23 + 5 = 28 coins, and so does each child.
How to prepare for them
- Practise them as a set, at the end of a full paper. Tired, with 25 minutes left, is how they are met in the exam.
- Name the design before starting. "The total cancels", "equal numerators", "run the rule backwards". Naming it is most of the solution.
- Write the working. It is what earns marks when the final answer slips.
- Know the format. Paper 2 is 15 questions in 80 minutes from 2026. See the 2026 PSLE Maths format.
Every paper in our courses ends with three questions built this way, marked before the lesson so the class time goes on the ones your child missed. See the course dates.
Common questions about the hardest PSLE questions
Which are the hardest questions in PSLE Maths?
Usually the last three questions of Paper 2. In recent school papers they are worth 4 or 5 marks each, run to 40 to 120 words in two or three parts, and are hard for a specific reason: a total that is never given, fractions of two different wholes, a rule run backwards, a search with no formula, or an area found only by adding and subtracting other areas.
How long should my child spend on the last questions of Paper 2?
About 25 minutes for the last three. Paper 2 is 80 minutes for 50 marks, and the last three are worth 13 to 15 marks together. A child who reaches them with 10 minutes left will lose marks they could have earned.
Can my child earn marks on a question they cannot finish?
Yes. The first part is usually the easiest, and working is what earns marks when a final answer slips. Attempt every part (a), write the working, and move on rather than leaving a question blank.
Practise it, free
Each is a full Paper 1 and Paper 2, marked the moment it is handed in, with a report on what went wrong.
Three of these in every paper.
Online P6 Maths crash courses in the school holidays: one full paper a day, marked before class, and the hardest questions worked through live.
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