Maths Challenge

Hi, do feel free to try out our Maths Challenge (Secondary 4 / age 16 difficulty):

Source: Anderson E Maths Prelim 2011

If you have solved the problem, please email your solution to mathtuition88@gmail.com .

(Include your name and school if you wish to be listed in the hall of fame below.)

Students who answer correctly (with workings) will be listed in the hall of fame. 🙂

Hall of Fame (Correct Solutions):

1) Ex Moe Sec Sch Maths teacher Mr Paul Siew

2) Queenstown Secondary School, Maths teacher Mr Desmond Tay

3) Tay Yong Qiang (Waiting to enter University)

The ideal Singapore JC subject combination for applying to Medicine

Why Additional Maths (A Maths) is important for entering Medicine:

Pathway: A Maths (O Level) –> H2 Maths (A Level) –> NUS Medicine

Source: http://sgforums.com/forums/2297/topics/439605

Quote: While NUS and NTU Medicine does not (officially) require H2 Maths (ie. ‘A’ level Maths), some other (overseas) Medical schools might. And not having H2 Maths might (unofficially) disadvantage your chances, even for NUS and NTU.

Therefore (assuming you intend to fight all the way for your ambition), your safest bet would be to (fight for the opportunity) to take both H2 Bio and H2 Math. The ideal Singapore JC subject combination for applying to Medicine (in any University) is :

H2 Chemistry, H2 Biology, H2 Mathematics

Source: http://www.kiasuparents.com/kiasu/forum/viewtopic.php?f=40&t=12228

Quote: pre-requisites for nus medicine will be H2 Chem and H2 bio or physics.

as for what’s best,
H2 math is almost a must since without it you’ll be ruling out a lot of ‘back-up courses’

You can reach for the stars with Jaws, Braille and determination, mathematics whiz Yeo Sze Ling tells HELLEN TAN

Maths Group Tuition starting in 2014!

Source: http://ww1.math.nus.edu.sg/News%20Archive/2005,%2024%20May%20-%20Counting%20on%20her%20mind%20-%20Yeo%20Sze%20Ling.htm

Counting on her mind

You can reach for the stars with Jaws, Braille and determination, mathematics whiz Yeo Sze Ling tells HELLEN TAN

Given that multiple degrees are common today, the fact that Miss Yeo Sze Ling has two degrees in mathematics, and is working on her doctorate in the same field, is probably not news.

Until you find out that she is blind.

The 27-year-old who earned her Bachelor’s degree (Honours) and a Master’s degree from National University of Singapore (NUS) is now into research on coding mathematics theories and cryptography.

These are used in computing algorithms to protect passwords or data from being stolen when they are zipped from computer to computer.

The field is an interest she shares with John Nash Jr, a mathematical genius who won a Nobel Prize, portrayed in the Oscar-winning movie, A Beautiful Mind.

Certainly, like Nash, her achievements should mean a lot.

He was a schizophrenic who thought he was doing secret cryptography work for the American government.

She has been blind from the age of about four when glaucoma struck. Glaucoma is a condition that increases pressure within the eyeball causing sight loss.

Technology has come in handy.

On campus, she totes a laptop.

At home in a four-room HDB flat in Bishan, her desktop Compaq PC holds today’s tech staples – e-mail and MSN Messenger for exchanging notes with friends.

The Internet is her source for research as well as for online newspapers or electronic books like A Beautiful Mind.

…

Continue reading at http://ww1.math.nus.edu.sg/News%20Archive/2005,%2024%20May%20-%20Counting%20on%20her%20mind%20-%20Yeo%20Sze%20Ling.htm

Featured Mathematician of the Day: Shing-Tung Yau

Maths Group Tuition starting in 2014!

Source: http://en.wikipedia.org/wiki/Shing-Tung_Yau

Shing-Tung Yau (Chinese: 丘成桐; pinyin: Qiū Chéngtóng; Cantonese Yale: Yāu Sìngtùng; born April 4, 1949) is a Chinese-born American mathematician. He won the Fields Medal in 1982.

Yau’s work is mainly in differential geometry, especially in geometric analysis. His contributions have had an influence on both physics and mathematics and he has been active at the interface between geometry and theoretical physics. His proof of the positive energy theorem in general relativity demonstrated—sixty years after its discovery—that Einstein‘s theory is consistent and stable. His proof of the Calabi conjecture allowed physicists—using Calabi–Yau compactification—to show that string theory is a viable candidate for a unified theory of nature. Calabi–Yau manifolds are among the ‘standard toolkit’ for string theorists today.

Yau was born in Shantou, Guangdong Province, China with an ancestry in Jiaoling (also in Guangdong) in a family of eight children. When he was only a few months old, his family emigrated to Hong Kong, where they lived first in Yuen Long and then 5 years later in Shatin. When Yau was fourteen, his father Chiou Chenying, a philosophy professor, died.

After graduating from Pui Ching Middle School, he studied mathematics at the Chinese University of Hong Kong from 1966 to 1969. Yau went to the University of California, Berkeley in the fall of 1969. At the age of 22, Yau was awarded the Ph.D. degree under the supervision of Shiing-Shen Chern at Berkeley in two years. He spent a year as a member of the Institute for Advanced Study, Princeton, New Jersey, and two years at the State University of New York at Stony Brook. Then he went to Stanford University.

Since 1987, he has been at Harvard University,^[1] where he has had numerous Ph.D. students. He is also involved in the activities of research institutes in Hong Kong and China. He takes an interest in the state of K-12 mathematics education in China, and his criticisms of the Chinese education system, corruption in the academic world in China, and the quality of mathematical research and education, have been widely publicized.

Shing-Tung Yau at Harvard Law School dining hall (Photo credit: Wikipedia)

Prime Minister Lee Hsien Loong Truly Outstanding Mathematics Student

Just to share an inspirational story about studying Mathematics, and our very own Prime Minister Lee Hsien Loong. 🙂

Source: http://www2.ims.nus.edu.sg/imprints/interviews/BelaBollobas.pdf

(page 8/8)

Interview of Professor Béla Bollobás, Professor and teacher of our Prime Minister Lee Hsien Loong

I: Interviewer Y.K. Leong

B: Professor Béla Bollobás

I: I understand that you have taught our present Prime
Minister Lee Hsien Loong.

B: I certainly taught him more than anybody else in
Cambridge. I can truthfully say that he was an exceptionally
good student. I’m not sure that this is really known in
Singapore. “Because he’s now the Prime Minister,” people
may say, “oh, you would say he was good.” No, he was truly
outstanding: he was head and shoulders above the rest of
the students. He was not only the first, but the gap between
him and the man who came second was huge.

I: I believe he did double honors in mathematics and computer science.

B: I think that he did computer science (after mathematics) mostly because his father didn’t want him to stay in pure mathematics. Loong was not only hardworking, conscientious and professional, but he was also very inventive. All the signs indicated that he would have been a world-class research mathematician. I’m sure his father never realized how exceptional Loong was. He thought Loong was very good. No, Loong was much better than that. When I tried to tell Lee Kuan Yew, “Look, your son is phenomenally good: you should encourage him to do mathematics,” then he implied that that was impossible, since as a top-flight professional mathematician Loong would leave Singapore for Princeton, Harvard or Cambridge, and that would send the wrong signal to the people in Singapore. And I have to agree that this was a very good point indeed. Now I am even more impressed by Lee Hsien Loong than I was all those years ago, and I am very proud that I taught him; he seems to be doing very well. I have come round to thinking that it was indeed good for him to go into politics; he can certainly make an awful lot of difference.

H2 Maths 2012 A Level Solution Paper 2 Q6; H2 Maths Group Tuition

6(i)

$H_0: \mu=14.0 cm$

$H_1: \mu\neq 14.0 cm$

(ii)

$\bar{x}\sim N(14,\frac{3.8^2}{20})$

For the null hypothesis not to be rejected,

$Z_{2.5\%}<\frac{\bar{x}-14}{3.8/\sqrt{20}}<Z_{97.5\%}$

$-1.95996<\frac{\bar{x}-14}{3.8/\sqrt{20}}<1.95996$ (use GC invNorm function!)

$12.3<\bar{x}<15.7$ (3 s.f.)

(iii) Since $\bar{x}=15.8$ is out of the set $12.3<\bar{x}<15.7$ , the null hypothesis would be rejected. There is sufficient evidence that the squirrels on the island do not have the same mean tail length as the species known to her.

(technique: put in words what $H_1$ says!)

H2 Maths A Level 2012 Solution, Paper 2 Q5; H2 Maths Tuition

5(i)(a)

$P(\text{patient has the disease and test positive})=0.001(0.995)=9.95\times 10^{-4}$

$P(\text{patient does not have the disease and he tests positive})=(1-0.001)(1-0.995)=4.995\times 10^{-3}$

$P(\text{result of the test is positive})=9.95\times 10^{-4}+4.995\times 10^{-3}=5.99\times 10^{-3}$

(b)

Let A=patient has disease

Let B=result of test is positive

$\displaystyle\begin{array}{rcl}P(A|B)&=&\frac{P(A\cap B)}{P(B)}\\ &=&\frac{(0.001)(0.995)}{5.99\times 10^{-3}}\\ &=&0.166 \end{array}$

Note that the probability is surprisingly quite low! (This is called the False positive paradox, a statistical result where false positive tests are more probable than true positive tests, occurring when the overall population has a low incidence of a condition and the incidence rate is lower than the false positive rate. See http://en.wikipedia.org/wiki/False_positive_paradox)

(ii)

$\displaystyle P(A|B)=\frac{(0.001)p}{(0.001)p+(1-0.001)(1-p)}=0.75$

By GC, $p=0.999666$ (6 d.p.)

JC Junior College H2 Maths Tuition

If you or a friend are looking for Maths tuition: O level, A level H2 JC (Junior College) Maths Tuition, IB, IP, Olympiad, GEP and any other form of mathematics you can think of.

Experienced, qualified (Raffles GEP, NUS Maths 1st Class Honours, NUS Deans List) and most importantly patient even with the most mathematically challenged.

So if you are in need of the solution to your mathematical woes, drop me a message!

Tutor: Mr Wu

Email: mathtuition88@gmail.com

Website: Singapore Maths Tuition | Patient and Dedicated Maths Tutor in Singapore