SPM 2017 Add Maths Paper 2, Question 11Integration

Solved on video in English · 10 marks · Form 5, Integration · 7:45 video

The question

Diagram 6 shows a curve y = 2x² - 18 and the straight line AB which is a tangent to the curve at point Q. It is given that the gradient of the straight line AB is 4. (a) Find the coordinates of point Q. (b) Calculate the area of the shaded region. (c) When the region bounded by the curve, the x-axis and the straight line y = h is rotated through 180° about the y-axis, the volume generated is 65π unit³. Find the value of h.

[10 marks]

SPM 2017 Add Maths Paper 2, Question 11: the question as drawn in Eduly's video7:45

Step 1

dy/dx = 4x. Since the gradient of tangent AB = 4: 4x = 4 => x = 1

Why this step

Because the line is a tangent, the curve's gradient at Q must equal the line's gradient, 4. So we differentiate the curve and set dy/dx = 4.

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

Final answer

(a) Q = (1, −16); (b) 13⅓ unit²; (c) h = −10

Where students lose marks

Watch out: integrate from 1 to 3, not the curve's own x-intercepts, and reject h = −26 (below the curve's lowest point).

Watch every step of this question solved on video (7:45), with the reason behind each step and a box that checks your own answer.

Start 7 days freeAlready a member? Watch it now

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

All questions in SPM 2017 Paper 2

Integration: lessons and every past-year question

More Integration questions

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