SPM 2023 Add Maths Paper 1, Question 10Differentiation

Solved on video in English and Bahasa Melayu · 4 marks · Form 5, Differentiation · 5:34 video

The question

(a)

Solutions using methods other than calculus are not accepted. On Sunday, Mus bought a number of spherical balls with radius 5 cm. Some of the balls will be arranged in a single line on a rack with length 2.5 m. On Monday, the volume of each ball decreased uniformly by 20π cm³. Determine the maximum number of these balls which can be arranged on the rack on Monday.

[4 marks]

(b)

It is given that h(x) = 3x² + 7x − 8. Determine the type of the turning point of h(x). Justify your answer.

(c)

The gradient function of a curve is (2x + 1)³. The curve passes through (1/2, 5). Find the equation of the curve. Give your answer in the form y = a(2x + 1)^b + c, such that a, b and c are constants.

SPM 2023 Add Maths Paper 1, Question 10: the question as drawn in Eduly's video5:34

Part (a)

Step 1

Volume of a sphere V = (4/3)πr³, so dV/dr = 4πr².

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

Final answer

26 balls

Where students lose marks

Watch out: the question says calculus only. Use δV ≈ (dV/dr)δr; computing the new volume and solving for r loses the marks.

Part (b)

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

Final answer

Minimum point, because h''(x) = 6 > 0

Where students lose marks

Watch out: justify with h''(x) = 6 > 0. Saying 'a = 3 > 0, so U-shaped' is not calculus and loses the mark.

Part (c)

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

Final answer

y = (1/8)(2x + 1)⁴ + 3

Where students lose marks

Watch out: divide by 4 × 2 = 8 and don't keep a 3 in front; that gives a wrong c.

Watch every step of this question solved on video (5:34), with the reason behind each step and a box that checks your own answer.

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