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PSLE 2015 · Paper 1 · Q25 Measurement & Geometry · Geometry (properties of shapes) 1 mark difficulty 2 of 5

PSLE 2015 Paper 1, Question 25: Geometry (properties of shapes)

The answer

drawing, choose a dot \(C\) such that \(AC = AB\), then draw \(AC\) and \(BC\)

PSLE 2015 Paper 1 Question 25 · Verified worked solution by the Genius Plus Academy teaching team

What this question tests

This is Question 25 of the PSLE 2015 Paper 1 Mathematics paper. It tests geometry (properties of shapes), in the Measurement & Geometry strand. It is worth 1 mark. Open your copy of the paper at this question, then follow our full worked solution below.

Step-by-step solution

GPA solution: two valid positions of C drawn on the dot grid — GPA solution: the semicircle's diameter \(AB\) with two valid choices of \(C\) (blue and red triangles), each with \(AC = AB\); note "2 possible answers, NOT \(AC = BC\)!".

Since \(AB\) is the diameter (a radius-pair of the semicircle through its centre), pick \(C\) on a dot with \(AC = AB\), e.g. rotate \(B\) about \(A\); two dot positions inside the box satisfy \(AB = AC\) exactly. (The required triangle is isosceles with the two equal sides meeting at \(A\).)

Answer: drawing, choose a dot \(C\) such that \(AC = AB\), then draw \(AC\) and \(BC\)

Same structure, different costume

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.

See what the paper rewards → The hardest questions, shown working →

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