SPM 2020 Add Maths Paper 1, Question 16Integration

Solved on video in English and Bahasa Melayu · 4 marks · Form 5, Integration · 3:53 video

The question

(a)

It is given the integral from k to (m + 1) of (px³ dx = the integral from -4 to 4 of (-px³ dx, where p is a constant. State the value of m and of k.

[2 marks]

(b)

On Diagram 7, sketch and shade the region which represents the integral from -4 to 4 of (-p*x³ dx = 0.

[2 marks]

Step 1

Rewrite the right side: integral from -4 to 4 of (-px³ dx = -(integral from -4 to 4 of px³ dx).

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

Final answer

m = −5, k = 4

Where students lose marks

Watch out: don't match limits straight away. The minus sign means swap the limits first, so k = 4, not −4.

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

Final answer

Sketch and shading (see video)

Where students lose marks

Watch out: with p > 0, y = −px³ is a cubic, not a parabola. It goes through O and falls left to right.

Watch every step of this question solved on video (3:53), 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.