Selangor Trial 2025 Add Maths Paper 1, Question 4Differentiation

Solved on video in English · Form 5, Differentiation · 6:03 video

The question

(a)

The point R(1, −1) lies on the curve y = (3 − 4x)³.

(a) Find the gradient of the tangent to the curve at point R.

(b)

(b) Find the equation of the normal to the curve at point R.

Selangor Trial 2025 Add Maths Paper 1, Question 4: the question as drawn in Eduly's video6:03

Part (a)

Step 1

Differentiate using the chain rule: dy/dx = 3(3 − 4x)² × (−4) = −12(3 − 4x)².

Why this step

A bracket raised to a power needs the chain rule: differentiate the outside, then multiply by the derivative of the inside, −4. Forgetting −4 is the top mistake.

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

Final answer

gradient = −12

Where students lose marks

Watch out: multiply by the derivative of the bracket, −4, and substitute x = 1 only after differentiating.

Part (b)

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

Final answer

y = (1/12)x − 13/12

Where students lose marks

Watch out: the normal uses the negative reciprocal of −12, not −12 itself. Also mind the signs in y − (−1) and −1/12 − 1.

Watch every step of this question solved on video (6:03), with the reason behind each step and a box that checks your own answer.

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