2011 A-level H2 Mathematics (9740) Paper 2 Question 11 Suggested Solutions

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

(i)
$\mathrm{P}(R = 4) = \frac{{^{18}\!C_{4}}{^{12}\!C_{6}}}{{^{30}\!C_{10}}} \approx 0.0941$

(ii)
$\mathrm{P}(R = r) > \mathrm{P}(R = r+1)$

$\Rightarrow \frac{{^{18}\!C_r}{^{12}\!C_{10-r}}}{{^{30}\!C_{10}}} > \frac{{^{18}\!C_{r+1}}{^{12}\!C_{9-r}}}{{^{30}\!C_{10}}}$

$(\frac{18!}{r!(18-r)!})(\frac{12!}{(10-r)!(2+r)!}) > (\frac{18!}{(r+1)!(17-r)!})(\frac{12!}{(9-r)!(3+r)!})$

$(r+1)! (17-r)! (9-r)! (r+3)! > r! (18-r)! (10-r)! (r+2)!$

$\frac{(r+1)!(r+3)!}{r!(r+2)!} > \frac{(18-r)!(10-r)!}{(17-r)!(9-r)!}$

$(r+1)(r+3) > (18-r)(10-r)$

$r^2 + 4r +3 > 180 -28 +r^2$

$r > 5.53$

Since r is an integer, $r = 6$

KS Comments:

(ii) is honestly not easy. Some students didn’t know the formula which is puzzling as the formal is given in MF15. I think it is important that students knows what formulas they are given in exams so they can utilise they properly.

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.

Comments

pingbacks / trackbacks

2011 A-level H2 Mathematics (9740) Suggested Solutions | The Culture
[…] Question 11 (Note Worthy) […]
October 10th, 2015 01:19 PM

Cart

2011 A-level H2 Mathematics (9740) Paper 2 Question 11 Suggested Solutions

KS Comments:

Leave a Reply to 2011 A-level H2 Mathematics (9740) Suggested Solutions | The Culture Cancel reply