SPM 2023 Add Maths Paper 2, Question 8Differentiation

Solved on video in English and Bahasa Melayu · Form 5, Differentiation · 7:47 video

The question

(a)

Diagram 4 shows a curve y = x² − 9 and the tangent to the curve at point A. The tangent has equation x/5 − y/10 = 1. Find the value of p.

(b)

Diagram 4 shows the curve y = x² − 9 and the tangent at A with equation x/5 − y/10 = 1, where p = 1.

(b) Find the area of the coloured region.

(c)

Diagram 4 shows the curve y = x² − 9 and its tangent at A, equation x/5 − y/10 = 1.

Step 1

Rewrite the tangent line: x/5 − y/10 = 1 → multiply by 10 → 2x − y = 10 → y = 2x − 10.

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

Final answer

p = 1

Where students lose marks

Watch out: don't use the curve's x-intercepts (±3). Use the tangent condition: equal gradients, or a repeated root when solving simultaneously.

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

Final answer

28/3 unit² (≈ 9.33 unit²)

Where students lose marks

Watch out: the region is below the x-axis, so take the absolute value. Don't use the region between curve and tangent (20/3).

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

Final answer

257π/12 unit³

Where students lose marks

Watch out: 180° is only half a turn, so halve the 360° volume, and leave the answer in terms of π.

Watch every step of this question solved on video (7:47), with the reason behind each step and a box that checks your own answer.

No card. Every past-year question on video, in English and BM.