Hardest questions
The hardest PSLE 2026 Maths questions
About these questions
SEAB hasn't released the 2026 paper yet, so these questions are as students remember them. We'll update the wording when the paper is out.
The five hardest questions from the PSLE 2026 Maths paper, sat on Friday 25 September, with the answers and the working.
MOE caps the challenging questions at 15 marks out of 100. So a paper that felt terrible is usually a normal paper with a few very hard questions inside it.
Question 1 of 5
The painted cube cut in two
Paper 2 · Question 13
Volume · 5 marks · As students recall it
A cube was cut into two pieces, X and Y. All the faces of X and Y were painted. The total area painted was 1152 cm².
- (a)What is the length of the cube?[2]
- (b)The volume of Y is 1008 cm³ more than the volume of X. What is the height of X?[3]
Why children lost marks. A cube has 6 faces, so many children did 1152 ÷ 6 = 192. But 192 isn't a square number. That's the clue: the cut made 2 new faces.
(a) 6 faces plus the 2 new ones make 8 equal squares.
- 1 face = 1152 ÷ 8 = 144 cm².
- 12 × 12 = 144, so the cube is 12 cm long.
(b) X and Y stand on the same 12 cm by 12 cm base, so Y's extra volume is extra height.
- 1 cm of height holds 12 × 12 = 144 cm³.
- 1008 ÷ 144 = 7 cm, so Y is 7 cm taller than X.
- 12 − 7 = 5 cm, which is two equal heights.
- Height of X = 5 ÷ 2 = 2.5 cm.
Answers
(a) 12 cm
(b) 2.5 cm
Question 2 of 5
The square: true, false or not possible to tell
Paper 1 · Question 29
Geometry · As students recall it
ABCD is a square. D, F and B lie on a straight line, and A, F and E lie on a straight line. AD = AE and ∠DFE = 103°.
For each statement, put a tick in the correct column.
| True | False | Not possible to tell | |
|---|---|---|---|
| AE = DC | |||
| ∠ABD = 47° | |||
| Triangle DEC is isosceles. |
Why children lost marks. On the drawing, triangle DEC looks isosceles, so "Not possible to tell" is tempting. Every statement can be decided.
AE = DC: True. AE = AD is given, and AD = DC because both are sides of the square.
∠ABD = 47°: False. The diagonal BD halves the 90° corner, so ∠ABD = 45°.
Triangle DEC: find the angles first.
- ∠AFD = 180° − 103° = 77°, so ∠DAE = 180° − 77° − 45° = 58°.
- AD = AE, so ∠ADE = ∠AED = (180° − 58°) ÷ 2 = 61°.
- AB = AE too. In triangle ABE, ∠BAE = 90° − 58° = 32°, so ∠ABE = (180° − 32°) ÷ 2 = 74°.
Now test each pair of sides in DEC:
- DE = DC would make ADE equilateral, with every angle 60°. But ∠DAE = 58°.
- EC = DC = BC would make ∠BEC = ∠EBC = 90° − 74° = 16°, leaving 148° at C, inside a 90° corner.
- DE = EC would put E on the square's middle line, making ABE equilateral. But ∠BAE = 32°.
No two sides are equal, so False. (Some students recall 102°, not 103°. The answers don't change.)
Answers
AE = DC: True
∠ABD = 47°: False
Triangle DEC is isosceles: False
Question 3 of 5
The shape made of semicircles
Paper 2
Circles · 4 marks · As students recall it
The radius of each semicircle is 20 cm. (Take π = 3.14)
- (a)Find the perimeter of the shape.[2]
- (b)Find the area of the shape.[2]
Why children lost marks. It looks like seven separate sums. It's really two ideas.
Each semicircle is 40 cm across. Three sit side by side along the bottom, so the shape is 120 cm long, and the straight edge on top is 120 − 40 − 40 = 40 cm.
(a) The 7 curved edges are all the same.
- One curved edge = 3.14 × 40 ÷ 2 = 62.8 cm.
- Perimeter = 7 × 62.8 + 40 = 479.6 cm.
(b) The shape sits on a 120 cm by 40 cm rectangle. 4 semicircles stick out and 3 are cut in, so the area is the rectangle plus one semicircle.
- Rectangle = 120 × 40 = 4800 cm².
- One semicircle = 3.14 × 20 × 20 ÷ 2 = 628 cm².
- Area = 4800 + 628 = 5428 cm².
Answers
(a) 479.6 cm
(b) 5428 cm²
Question 4 of 5
The three rectangles rearranged
Paper 1 · Question 30
Area and perimeter · As students recall it
Figure 1 is made up of 3 identical rectangles. The same 3 rectangles are rearranged to form Figure 2.
The area of Figure 1 is 486 cm². Find the perimeter of Figure 2.
Why children lost marks. Figure 2 has short edges with no length given. You don't need them.
One rectangle. In Figure 1, the top rectangle is as long as two short sides, so each rectangle is two squares.
- 1 rectangle = 486 ÷ 3 = 162 cm², so 1 square = 81 cm².
- Short side = 9 cm, long side = 18 cm.
Figure 2. Push every notch out to the edge. The perimeter doesn't change, and the outline becomes a square of side 18 + 9 = 27 cm.
Perimeter = 4 × 27 = 108 cm.
Answer
108 cm
Question 5 of 5
The stick pattern
Paper 2 · Question 15
Patterns · As students recall it
The figures below are made up of sticks. The table shows the number of sticks used in each figure.
| Figure | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Number of sticks | 8 | 10 | 13 | 15 |
- (a)Find the number of sticks in Figure 5 and Figure 6.[1]
- (b)How many sticks does Figure 45 have?
Why children lost marks. The table goes +2, +3, +2. There's no single step to add, so many children got stuck.
The pictures explain it. Each new row of boxes takes 2 upright sticks, then 3 flat ones: 5 sticks. Odd figures are full rows, even figures are halfway.
(a) Figure 5 = 15 + 3 = 18. Figure 6 = 18 + 2 = 20.
(b) An odd figure is 3 flat sticks at the bottom plus 5 per row. Figure 45 has (45 + 1) ÷ 2 = 23 rows.
| Figure | Rows of boxes | Sticks |
|---|---|---|
| 1 | 1 | 3 + 5 = 8 |
| 3 | 2 | 3 + 5 × 2 = 13 |
| 5 | 3 | 3 + 5 × 3 = 18 |
| 45 | 23 | 3 + 5 × 23 = 118 |
Figure 45 = 3 + 5 × 23 = 118 sticks.
Answers
(a) Figure 5: 18 · Figure 6: 20
(b) 118
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Sources
PSLE 2026 Mathematics, Paper 1 and Paper 2 (Singapore Examinations and Assessment Board, © MOE), as recalled by students after the exam on 25 September 2026 and cross-checked across published write-ups. SEAB had not released the paper when this page was written. Ministry of Education, “Is the PSLE Mathematics paper so difficult?”, 16 August 2024, for the 15% figure.
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