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### MATHEMATICS 9709

#### Cambridge International AS and A Level

 Name of student Date Adm. number Year/grade Stream Subject Pure Mathematics 1 (P1) Variant(s) P11, P12, P13 Start time Duration Stop time

Qtn No. 1 Total
Marks 11 11
Score

Get Mathematics 9709 Topical Questions (2010-2021) for $14.5 per Subject. Attempt the 1 question Question 1 Code: 9709/13/M/J/18/11, Topic: Differentiation, Integration The diagram shows part of the curve$y=(x+1)^{2}+(x+1)^{-1}$and the line$x=1$. The point$A$is the minimum point on the curve.$\text{(i)}$Show that the$x$-coordinate of$A$satisfies the equation$2(x+1)^{3}=1$and find the exact value of$\displaystyle\frac{\mathrm{d}^{2} y}{\mathrm{~d} x^{2}}$at$A$.$[5]\text{(ii)}$Find, showing all necessary working, the volume obtained when the shaded region is rotated through$360^{\circ}$about the$x$-axis.$[6]\$

Worked solutions: P1, P3 & P6 (S1)

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