MRSM Trial 2025 Add Maths Paper 1, Question 10Differentiation

Solved on video in English · Form 5, Differentiation · 7:06 video

The question

(a)

It is given that the curve y = x(4 − x)³ with a gradient function 4(1 − x)(4 − x)² has two stationary points, P(1, 27) and Q(4, 0). Determine the nature of stationary point Q by using the tangent sketching method.

(b)

A composite solid consists of a cone placed on top of a cylinder, both with radius x cm. The total surface area of the solid is given by A = 4π(x² + 54/x). Using calculus, show that the percentage change in the surface area of the solid increases by 3.55% when the radius increases from 10.5 cm to 10.7 cm. [Use π = 3.142]

(c)

A curve with the gradient function dy/dx = 8x + 3 passes through the point (1, 6). Find the equation of the curve.

MRSM Trial 2025 Add Maths Paper 1, Question 10: the question as drawn in Eduly's video7:06

Part (a)

Step 1

Test the sign of dy/dx = 4(1 − x)(4 − x)² on both sides of x = 4 (e.g. x = 3 and x = 5).

Why this step

dy/dx = 0 only tells us Q is stationary. To see if the curve turns, we check the gradient's sign just before and just after x = 4.

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

Final answer

Point of inflection

Where students lose marks

Watch out: dy/dx = 0 alone does not make Q a maximum or minimum. Check the gradient's sign on both sides.

Part (b)

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

Final answer

Shown (3.55% increase)

Where students lose marks

Watch out: the term 216π/x differentiates to −216π/x². Keep the minus sign or every later number goes wrong.

Part (c)

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

Final answer

y = 4x² + 3x − 1

Where students lose marks

Watch out: never forget + c, and 8x integrates to 4x², not 8x². Use the given point to find c.

Watch every step of this question solved on video (7:06), with the reason behind each step and a box that checks your own answer.

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