SPM 2018 Add Maths Paper 2, Question 4Systems of Equations

Solved on video in English and Bahasa Melayu · 7 marks · Form 4, Systems of Equations · 6:20 video

The question

Diagram 2 shows the plan of a rectangular garden PQRS. The garden consists of a semicircular pond PTS and grassy area PQRST. It is given that SR = 6y metre and QR = 7x metre, x ≠ y. The area of the rectangular garden PQRS is 168 metre² and the perimeter of the grassy area is 60 metre. The pond with uniform depth contains 15.4 metre³ of water. By using π = 22/7, find the depth, in metre, of water in the pond.

[7 marks]

SPM 2018 Add Maths Paper 2, Question 4: the question as drawn in Eduly's video6:20

Step 1

Opposite sides of the rectangle are equal, so PQ = SR = 6y and the left side PS = QR = 7x. Area of PQRS = SR × QR = (6y)(7x) = 42xy. Set equal to 168: 42xy = 168, so xy = 4. ... (1)

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

Final answer

d = 0.45 m

Where students lose marks

Watch out: the pond's curved edge is only a semicircle (πr = 11x), and y = 2 must be rejected because x ≠ y.

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