Kuala Lumpur Trial 2025 Add Maths Paper 1, Question 12
Solved on video in English · 6:04 video
The question
Diagram 7 shows four decreasing semicircles touching each other on the inside at E. B is the midpoint of AE, C is the midpoint of BE, and D is the midpoint of CE.
(a) Show that the areas of the semicircles centred at B, C and D form a Geometric Progression.
(b) State the common ratio.
(c) Hence, calculate the sum of the area of six semicircles in terms of πj.
6:04Part (a)
Step 1
Let the largest semicircle (on diameter AE, centred at B) have radius j, so its area is L₁ = ½π j².
3 more steps, each with the reason for it, in the full solution
Final answer
Shown: both ratios = 1/4
Where students lose marks
Watch out: compare areas, not radii, and show the ratio is the same for both consecutive pairs. That is what proves a GP.
Part (b)
2 more steps, each with the reason for it, in the full solution
Final answer
r = 1/4
Where students lose marks
Watch out: r is the ratio of areas (1/4), not the ratio of radii (1/2).
Part (c)
4 more steps, each with the reason for it, in the full solution
Final answer
S₆ = (1365/2048)πj² ≈ 0.6665πj²
Where students lose marks
Watch out: use n = 6 with the finite sum formula, not n = 4 or the sum to infinity. Check (1/4)⁶ = 1/4096.
Watch every step of this question solved on video (6:04), with the reason behind each step and a box that checks your own answer.
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