SPM 2024 Add Maths Paper 2, Question 10Differentiation

Solved on video in English and Bahasa Melayu · 2 marks · Form 5, Differentiation · 4:59 video

The question

Diagram 4 shows the curve y = px³, such that p is a constant. The tangent to the curve at point A intersects the y-axis at B(0, −4).

Calculate (a) the value of p, (b) the area of the shaded region.

(b)

]

(b) the area of the shaded region,

the area of the shaded region.

(c)

(c) the volume generated, in terms of π, when the region bounded by the curve and the straight line x = 1 is revolved through 90° about the x-axis. [2 marks]

the volume generated, in terms of π, when the region bounded by the curve and the straight line x = 1 is revolved through 90° about the x-axis. [2 marks]

[2 marks]

Step 1

Point A lies on y = px³ at x = 1, so A = (1, p × 1³) = (1, p).

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

Final answer

p = 2; area = 3/2 unit²

Where students lose marks

Watch out: equate 3p with the gradient of AB (p + 4). For area, curve minus tangent, limits 0 to 1.

Part (b)

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

Final answer

3/2 unit² (or 1.5 unit²)

Where students lose marks

Watch out: integrate the correct curve, y = 2x³ (not y = (2/3)x²), before combining with the triangle areas.

Part (c)

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

Final answer

π/7 unit³

Where students lose marks

Watch out: take 1/4 of π∫y² dx for 90°, and add nothing else. Extra terms such as 4π are wrong.

Watch every step of this question solved on video (4:59), with the reason behind each step and a box that checks your own answer.

Start 7 days free Already a member? Watch it now

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

All questions in SPM 2024 Paper 2

Differentiation: lessons and every past-year question

Baca dalam Bahasa Melayu

More Differentiation questions

Questions are re-typeset by Eduly for study and commentary. Eduly is not affiliated with Lembaga Peperiksaan Malaysia or the Ministry of Education.