SPM 2021 Add Maths Paper 2, Question 7Integration

Solved on video in English and Bahasa Melayu · Form 5, Integration · 6:08 video

The question

(a)

The gradient function of a curve is 2x − 2. The curve passes through the point (−2, −7). (a) Find the equation of the curve.

(b)

The curve y = x² − 2x − 15 is moved 1 unit to the left. (b) Find the new equation of the curve. Hence, find the volume generated, in terms of π, when the region bounded by the curve and the x-axis is revolved 180° about the y-axis.

SPM 2021 Add Maths Paper 2, Question 7: the question as drawn in Eduly's video6:08

Part (a)

Step 1

Integrate the gradient function: y = ∫(2x − 2) dx = x² − 2x + c.

Why this step

Integration reverses differentiation. Add 1 to the power, then divide by the new power, so 2x becomes x², not 2x². Don't forget + c.

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

Final answer

y = x² − 2x − 15

Where students lose marks

Watch out: 2x integrates to x², not 2x². Add 1 to the power, divide by the new power, and don't forget + c.

Part (b)

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

Final answer

y = x² − 16; V = 128π unit³

Where students lose marks

Watch out: keep π in the final volume. Writing 128 instead of 128π unit³ loses the mark.

Watch every step of this question solved on video (6:08), with the reason behind each step and a box that checks your own answer.

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