SPM 2022 Add Maths Paper 2, Question 7Differentiation

Solved on video in English and Bahasa Melayu · 4 marks · Form 5, Differentiation · 6:01 video

The question

(a)

A district council constructs a parabolic steel frame to hang a banner. Diagram 3 shows the front view of the steel frame. A rectangular banner ABCD will be hung at points C and D such that CD is horizontal. The height of AB from the ground level is 1 metre. The edges A and B are tied vertically to the points G and H respectively. It is given that the gradient function of the curve is 6 − 2x and the distance of GH is 2p metre.

(a) (i) Show that the distance of EH is (3 + p) metre. (ii) Hence, express the area, L, of the banner in terms of p.

(b)

Using L = 16p − 2p³:

(b) If the cost to make the banner is RM40/metre², calculate the total cost, to the nearest RM, to make the banner such that its area is maximum.

[4 marks]

SPM 2022 Add Maths Paper 2, Question 7: the question as drawn in Eduly's video6:01

Part (a)

Step 1

The gradient function is dy/dx = 6 − 2x. Integrate to find the curve: y = ∫(6 − 2x) dx = 6x − x² + c.

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

Final answer

(i) EH = 3 + p (shown); (ii) L = 16p − 2p³

Where students lose marks

Watch out: justify EH using dy/dx = 0 at the top of the arch, and subtract AB's 1 m from the curve's height.

Part (b)

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

Final answer

Total cost ≈ RM697

Where students lose marks

Watch out: the question says 'to the nearest RM', so round RM696.80 to RM697. Don't leave it as 696.80.

Watch every step of this question solved on video (6:01), with the reason behind each step and a box that checks your own answer.

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