2011 A-level H2 Mathematics (9740) Paper 2 Question 7 Suggested Solutions

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

(i)
Firstly, the number of different friends is a fixed constant.
Secondly, the probability of successfully contacting a friend is constant.

(ii)
The probability of contacting a friend will vary from friend to friend, as some friend might not be free or contactable during that evening.

(iii)
$\mathrm{R} \sim \mathrm{B}(8,0.7)$

$\mathrm{P}(R \ge 6) = 1 - \mathrm{P}(R \le 5) \approx 0.552$

(iv)
$\mathrm{R} \sim \mathrm{B}(40, 0.7)$

Since $n = 40 \mathrm{~is~large,~} np = 28 > 5 \mathrm{~and~} nq = 12 > 5 ~ \mathrm{R} \sim \mathrm{N}(28, 8.4) \mathrm{approximately}$

$\mathrm{P}(R \textless 25)$

$= \mathrm{P}(R \textless 24.5)$ by continuity correction

$\approx 0.114$

KS Comments:

Students should be careful to write all assumptions in the context of question. I cannot stress the importance of this. Conditions for Binomial Approximation have to be well stated and explained. Lastly, remember to do continuity correction.

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 2 Question 7 Suggested Solutions

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