SPM 2024 Add Maths Paper 2, Question 7Progressions

Solved on video in English and Bahasa Melayu · Form 4, Progressions · 4:32 video

The question

Diagram 3 shows a symmetrical tube such that points A and B are on the same level.

A marble is released from point A and moves through the tube towards point B until it stops instantaneously for the first time at point C.

The marble will move back and forth through the tube until it stops completely at point O.

The marble stops instantaneously for the second time at point D and stops instantaneously for the third time at point E.

The distance travelled by the marble from point A to point C, point C to point D and subsequent distances are in the same ratio.

The total distance travelled by the marble from point A to point C and then from point C to point D is 629/4 cm. The distance travelled from point D to point E is 4913/80 cm.

If the marble takes 1 minute to stop completely at point O, determine whether the average speed of the marble exceeds 10 cm s⁻¹ or not. Show your calculation.

Step 1

The distances AC, CD, DE, ... form a geometric progression (GP) with first term a and common ratio r.

18 more steps, each with the reason for it, in the full solution

Final answer

Average speed = 85/9 ≈ 9.44 cm s⁻¹ < 10, so it does not exceed 10 cm s⁻¹

Where students lose marks

Watch out: use S∞ = a/(1 − r), convert 1 minute to 60 seconds before dividing, then state clearly whether the speed exceeds 10.

Watch every step of this question solved on video (4:32), with the reason behind each step and a box that checks your own answer.

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