SPM 2021 Add Maths Paper 2, Question 8Differentiation

Solved on video in English and Bahasa Melayu · Form 5, Differentiation · 7:11 video

The question

(a)

Diagram 4 shows a trapezium PQRT (with point S on the bottom side TR). QS is parallel to PT, and there is a right angle at T. It is given that TR = 26 cm, QS = x cm and SR = 2x cm. (a)(i) State the area, in cm², of PQST in terms of x. (a)(ii) Hence, find the maximum area, in cm², of PQST.

(b)

For the trapezium in Diagram 4, the area of PQST is A = 26x − 2x² cm². (b) Given that the rate of change of the area of PQST is 36 cm² s⁻¹ when x = √5 cm, calculate the length, in cm, of QS after 3 seconds.

(c)
SPM 2021 Add Maths Paper 2, Question 8: the question as drawn in Eduly's video7:11

Part (a)

Step 1

PQST is a rectangle: its height is QS = PT = x, and its width is TS = TR − SR = 26 − 2x.

Why this step

TR is the whole base, but the rectangle only uses TS. SR = 2x belongs to triangle QSR, so we subtract it.

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

Final answer

(i) A = 26x − 2x² cm²; (ii) maximum area = 84.5 cm²

Where students lose marks

Watch out: differentiate and set dA/dx = 0. Setting A = 0 only gives x = 0 or 13, not the maximum area.

Part (b)

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

Final answer

QS ≈ 8.57 cm

Where students lose marks

Watch out: after 3 seconds, QS = starting x + (dx/dt)(3). Don't forget the starting x = √5 or the ×3.

Part (c)

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

Final answer

δA ≈ −0.36 cm² (area decreases)

Where students lose marks

Watch out: 2x² differentiates to 4x, not 2x. Using 26 − 2x gives −0.44 instead of −0.36.

Watch every step of this question solved on video (7:11), 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 2021 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.