2011 A-level H2 Mathematics (9740) Paper 1 Question 9 Suggested Solutions

All solutions here are SUGGESTED. Mr. Teng will hold no liability for any errors. Comments are entirely personal opinions.

(i)
Depth drilled on the 10th day $= 256 +9(-7) = 193$

$T_n \textless 10$

$256 + (n-1)(-7) \textless 10$

$n > 36.1$

Total depth $= S_{37} = \frac{37}{2}[2(256) + 36(-7))] = 4810$

(ii)
$S_n > 0.99 s_{\infty}$

$\frac{256(1-(\frac{8}{9})^n)}{1-\frac{8}{9}} > 0.99 (\frac{256}{1-\frac{8}{9}})$

$(\frac{8}{9})^n \textless 0.01$

$n \mathrm{ln}(\frac{8}{9}) \textless \mathrm{ln} 0.01$

$n > \frac{\mathrm{ln} 0.01}{\mathrm{ln}(\frac{8}{9})} = 39.1$

Thus, it takes 40 days

KS Comments:

I feel that (i) is fine, student just needs to read really carefully and beware if they are using the term or sum formulas.
For (ii), it is worth noting that some students still have no clue how to deal with inequalities when there is $\mathrm{ln}$ involved.

About

KS Teng

KS has been teaching H2/H1 Mathematics and IB mathematics for the more than 10 years. Having taught students from all various Junior Colleges, KS adapts to students' abilities and help them better understand the topics. As someone who loves to teach mathematics and sees it as a truly useful tool in life, KS seeks to enable students to appreciate math. Therefore, his tuition mission is to motivate and cultivate students to be independent and confident thinkers.

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2011 A-level H2 Mathematics (9740) Paper 1 Question 9 Suggested Solutions

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