SPM 2022 Add Maths Paper 1, Question 4Differentiation

Solved on video in English and Bahasa Melayu · Form 5, Differentiation · 5:42 video

The question

(a)

4 (a) Fei buys a block of ice in the shape of a cube. On the journey back home, the ice melts at the rate of 5.5 cm³ per minute. Determine the rate of change of the side length, in cm s^(−1), of the ice at the instant when the side length is 15 cm.

(b)

4 (b) Given that d/dx [5/(1 − x²] = g(x), find ∫ [2g(x) + 3] dx.

SPM 2022 Add Maths Paper 1, Question 4: the question as drawn in Eduly's video5:42

Part (a)

Step 1

Let V be the volume and x be the side length of the cube. Then V = x³.

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

Final answer

dx/dt = −11/81000 cm s⁻¹ (≈ −0.0001358)

Where students lose marks

Watch out: melting means dV/dt is negative, and convert 5.5 cm³ per minute to per second by dividing by 60.

Part (b)

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

Final answer

10/(1 − x²) + 3x + c

Where students lose marks

Watch out: integration undoes differentiation, so ∫ g(x) dx = 5/(1 − x²) straight away. Don't work out g(x) first.

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