SPM 2022 Add Maths Paper 2, Question 10Differentiation

Solved on video in English and Bahasa Melayu · 5 marks · Form 5, Differentiation · 7:36 video

The question

(a)

Diagram 5 shows the straight line AB intersecting the curve y² = x + 9 at point A(−5, h), where B is (0, 3/2).

Find (a) the gradient of the tangent to the curve at point A.

[2 marks]

(b)

Using the curve y² = x + 9, the line AB and A(−5, 2), B(0, 3/2):

(b) Find the area of the shaded region.

(c)

Using the curve y² = x + 9 and h = 2:

(c) Find the volume generated, in terms of π, when the region bounded by the curve, the straight line y = h, the y-axis and the x-axis is revolved through 360° about the y-axis.

[3 marks]

SPM 2022 Add Maths Paper 2, Question 10: the question as drawn in Eduly's video7:36

Part (a)

Step 1

Write the curve as y = (x + 9)¹/2).

Why this step

Writing the root as a power lets us use the power rule and chain rule to differentiate.

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

Final answer

Gradient = 1/4

Where students lose marks

Watch out: write the × 1 from the inner (x + 9) in the chain rule. Skipping it can lose marks.

Part (b)

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

Final answer

169/12 unit²

Where students lose marks

Watch out: the triangle's height is 2 − 3/2 = 1/2, not 2. Using 2 gives 31/3 instead of 169/12.

Part (c)

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

Final answer

(602/5)π unit³

Where students lose marks

Watch out: write out the substitution of the limits y = 2 and y = 0 before simplifying. Skipping it loses working marks.

Watch every step of this question solved on video (7:36), with the reason behind each step and a box that checks your own answer.

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