PSLE 2020 Paper 1 Q28 Worked Solution

Step-by-step solution

Tape of stars and hearts with the repeating unit bracketed as "3 stars" and "2 hearts" and red cut lines marked on the tape — GPA worked solution: the repeating unit bracketed on the tape (3 stars, 2 hearts) with cut positions marked.

The repeating unit is ☆ ☆ ♡ ☆ ♡ (3 stars, 2 hearts). \(135\) stars \(= 45\) complete star-groups, giving \(45 \times 2 = 90\) hearts if the piece ends after the final heart, or \(90 - 1 = 89\) if it is cut before the last heart.

FLAG (recorded in full): All GPA sources (handwritten key, docx key, worked-on paper) give "89, 90" only. Independent brute-force enumeration over the repeating pattern shows the possible heart-counts for a contiguous piece containing exactly 135 stars are 89, 90 or 91, the 91 case arises when the piece both begins and ends with a heart (…cut just before a heart that precedes the first star, and just after the heart that follows the last star: ♡☆☆♡☆♡…☆♡). No official SEAB answer was available among the sources to adjudicate; GPA's published answer is 89/90.

Answer: 89 or 90 (GPA key), see flag: 91 is also mathematically possible

A question is hard because of its structure, not its story.

Change egg tarts to badges, a tank to two tanks, a ring of card to a folded sheet, and a child sees a brand new problem. The lock underneath is the same, and so is the key. Once a student can name the structure, a whole row of questions that look different start to open the same way.

It is also where marks really leak. Across fourteen years of papers, the marks lost in PSLE math leak at the reading far more than at the arithmetic, which is exactly why recognising the structure fixes them. We call this Lock and Key: name the lock, then the key follows.

Questions students ask

What does PSLE 2020 Paper 1 Question 28 test?

It is a number patterns question from the Number & Algebra strand, worth 2 marks.

Is there a video solution?

Not yet for this question. The full written solution is above, and we are filming Paper 2 walkthroughs steadily.

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PSLE 2020 Paper 1, Question 28: Number patterns

Step-by-step solution

A question is hard because of its structure, not its story.

More number patterns questions, worked the same way

Read a question, know the method.

Questions students ask

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