MRSM Trial 2025 Add Maths Paper 2, Question 3Differentiation

Solved on video in English · Form 5, Differentiation · 6:02 video

The question

(a)

Solutions using methods other than calculus are not accepted. Diagram 2 shows the base of a pool PQRST that will be built such that PQR is a semicircle and TP = SR. The top side TP = 6y m and the vertical side ST = x m. [Use π = 3.142]

(a) If the perimeter of the base of the pool is 120 m, show that the area, in m², of the pool's base is A = 60x − (4 + 3π)x²/8.

(b)

Diagram 2 shows the base of a pool PQRST (PQR a semicircle, TP = SR = 6y m, ST = x m) with base area A = 60x − (4 + 3π)x²/8. 142]

(b) If the pool has a depth of 10 m, determine whether it is capable of holding 5000 m³ of water.

MRSM Trial 2025 Add Maths Paper 2, Question 3: the question as drawn in Eduly's video6:02

Part (a)

Step 1

The semicircle PQR has diameter PR = x (the right side of the rectangle), so its radius = x/2 and its arc length = π(x/2) = πx/2.

Why this step

The diameter is the rectangle's right side, x. The arc is only half a circle, so use πr = πx/2, not the full 2πr.

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

Final answer

Shown

Where students lose marks

Watch out: the arc PQR is only half a circle, so use πx/2 (not 2πr), and subtract the semicircle's area from the rectangle.

Part (b)

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

Final answer

Yes (5362.7 m³ > 5000 m³)

Where students lose marks

Watch out: differentiate to find the maximum area, multiply it by the depth 10, then compare with 5000 and state your conclusion.

Watch every step of this question solved on video (6:02), with the reason behind each step and a box that checks your own answer.

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