SPM 2021 Add Maths Paper 1, Question 4Differentiation

Solved on video in English and Bahasa Melayu · Form 5, Differentiation · 4:10 video

The question

(a)

It is given that the equation of the curve is y = x + 2x^(−2). Find the gradient function of the curve.

(b)

A straight line touches the curve y = x + 2x^(−2) at point P. The straight line is perpendicular to the straight line y + 2x = 0. Find the coordinates of P.

SPM 2021 Add Maths Paper 1, Question 4: the question as drawn in Eduly's video4:10

Part (a)

Step 1

Differentiate term by term: d/dx(x) = 1 and d/dx(2x^(−2)) = (−2)(2)x^(−3) = −4x^(−3).

Why this step

Multiply by the power, then drop the power by 1. And don't forget plain x: its derivative is 1, not 0, so the +1 stays.

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

Final answer

dy/dx = 1 − 4/x³

Where students lose marks

Watch out: differentiate the plain x term too. d/dx(x) = 1, not 0, so don't drop the +1.

Part (b)

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

Final answer

P = (2, 5/2)

Where students lose marks

Watch out: substitute x = 2 into the curve, not the line y = −2x, or you get the wrong point (2, −4).

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