Melaka Trial 2025 Add Maths Paper 1, Question 8Differentiation

Solved on video in English · Form 5, Differentiation · 4:55 video

The question

(a)

(a) Determine the limit value for lim (x → 2) (2x² + 1).

(b)

(b) Find dy/dx for the function y = 2x² + 1 by using first principles.

Step 1

The function 2x² + 1 is a polynomial, so the limit is found by direct substitution of x = 2.

Why this step

A polynomial has no gaps or jumps, so its limit at any point is just its value there. No tricks needed.

1 more step, with the reason for it, in the full solution

Final answer

Where students lose marks

Watch out: square only the 2 first, then multiply by 2. (2·2)² = 16 is wrong; 2(2²) = 8.

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

Final answer

dy/dx = 4x

Where students lose marks

Watch out: keep the middle term 4xδx when expanding, and use first principles, not the differentiation rule.

Watch every step of this question solved on video (4:55), with the reason behind each step and a box that checks your own answer.

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