Math Riddle (Proof that all triangles are equilateral)

Can you spot the subtle mistake in this video?

Very interesting and a good exercise in geometry proving! 🙂


Featured book:

Tutor in a Book’s Geometry

Need help with Geometry? Designed to replicate the services of a skilled private tutor, the new and improved Tutor in a Book’s Geometry is at your service! TIB’s Geometry is an extremely thorough, teen tested and effective geometry tutorial.

TIB’s Geometry includes more than 500 of the right, well-illustrated, carefully worked out and explained proofs and problems. Throughout TIB’s Geometry, there is ongoing, specific guidance as to the most effective solution and test taking strategies. Recurring patterns, which provide solutions to proofs, are pointed out, explained and illustrated using the visual aids that students find so helpful. Also included are dozens of graphic organizers, which help students understand, remember and recognize the connections between concepts.

TIB’s author Jo Greig intended this book to level the playing field between the students who have tutors and those that don’t. As a long time, very successful private mathematics tutor and teacher, Jo Greig knew exactly how best to accomplish this! TIB’s Geometry 294 pages are packed with every explanation, drawing, hint and memory tool possible! Not only does it have examples of the right proofs and problems, it also manages to impart every bit of the enthusiasm that great tutors impart to their private tutoring students. Ms. Greig holds a bachelors’ degree in mathematics. Dr. J. Shiletto, the book’s mathematics editor, holds a Ph.D in mathematics.

 

E Maths Group Tuition and Why E Maths is actually more difficult than A Maths

https://mathtuition88.com/group-tuition/

Come for E Maths Tuition at Bishan! Conveniently located at Block 230 Bishan Street 23 #B1-35 S(570230), near Catholic High School.

Schedule:

  • Monday 7pm-9pm (E Maths)

(Perfect for students who have CCA in the afternoon, or students who want to keep their weekends free.)

Do not underestimate E Maths!

Those who truly understand the Maths Syllabus at Secondary Level will know that E Maths is in some ways, more difficult than A Maths. Not to mention the infamous E Maths Bell Curve, which is definitely well above 75 marks to get a chance of A1. (Some sources say the Bell Curve for E Maths is 90 marks. See http://forums.sgclub.com/singapore/questions_about_o_378705.html )

“Amaths is good, like ditzy said, I tell you, if you practise amaths everyday and do past years papers, you can see amaths quite okay one. During my secondary school years i felt that emaths more difficult than amaths.”

Source: http://sgforums.com/forums/2297/topics/401226

“You can ask many people out there, which one is more tedious and require thinking more, they’ll say emaths.
Reason simple very simple:
Emaths:
They throw an entire paragraph at you which hidden clues here and there, slight errors is almost unavoidable.
Amaths:
Short and simple, they throw question at you. Just solve. End of story.”

Source: http://forums.sgclub.com/singapore/additional_maths_hard_336484.html

My year some speculated that E Maths A1 was as high as 90?”

Source: http://forums.sgclub.com/singapore/questions_about_o_378705.html

Kinematics

Distance = Speed x Time

Time = Distance / Speed

Speed = Distance / Time

Distance-time graph

Speed = gradient

Remember Formula Using Units E.g.

Units of speed = km/h

Units of gradient = km/h

Speed-time graph

Distance travelled = Area under graph

Acceleration = gradient

Remember Formula using Units: E.g.

Units of distance = m

Units of area under graph = (m/s)s=m

Units of acceleration = m/s^2

Units of gradient = (m/s)/s=m/s^2

Useful Formula:

Area of trapezium = 1/2 x height x (sum of parallel sides)

The formula rhymes! 🙂

Differentiation Rules

Today, we will recap the four basic rules of Differentiation:

  • Differentiating Powers of x

\displaystyle\frac{d}{dx}x^n=nx^{n-1}

(Power comes down, and the remaining power reduced by 1)

  • Chain Rule (i.e. times differentiate inside the bracket)
  • Product Rule

\displaystyle\frac{d}{dx}(uv)=u\frac{dv}{dx}+v\frac{du}{dx}

(Keep the first term X differentiate the second, PLUS keep the second term X differentiate the first)

  • Quotient Rule

\displaystyle\frac{d}{dx}(\frac{u}{v})=\frac{v\frac{du}{dx}-u\frac{dv}{dx}}{v^2}

(Keep the bottom term differentiate the top MINUS keep the top differentiate the bottom, whole thing over v^2)

JC Cut Off Points (Latest)

Joint Admissions Exercise 2014

Source: http://nanyangjc.org/index.php/joint-admissions-exercise-2014/

Cut Off & Bonus Points

Applicants applying to enter NYJC must meet the entry criteria based on the L1R5 aggregate.For JAE, this aggregate is calculated from results obtained in the previous year’s Singapore-Cambridge GCE ‘O’ Level Examinations.Please note that the entry criteria changes from year to year and the following table should only be used as a guide.

MINIMUM L1R5 AGGREGATE [after bonus points deduction]

FACULTY ARTS SCIENCE
JAE 2013 8 8

Source: http://www.ajc.edu.sg/admission/admission_jae.html

AJC Cut Off Points:

FACULTY ARTS SCIENCE
JAE 2013 8 10

100,000 views on WordPress

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Probability Formula

Formulae for Probability

Works for All Cases:

  1. P(A∪B)=P(A)+P(B)-P(A∩B)

  2. P(A|B)=\displaystyle\frac{P(A\cap B)}{P(B)}

  3. P(A’)=1-P(A)


For Mutually Exclusive Events Only:

  1. P(A∩B)=0

Mutually Exclusive
Mutually Exclusive


For Independent Events Only:

  1. P(A∩B)=P(A) P(B)

  2. P(A|B)=P(A)

  3. P(B|A)=P(B)

  4. P(A’∩B)=P(A’) P(B)

  5. P(A∩B’)=P(A) P(B’)

  6. P(A’∩B’)=P(A’) P(B’)

NUS Past Year Paper

This is a list of websites related to NUS Past Year Paper:

1) Official NUS Past Year Exam Paper website: http://libguides.nus.edu.sg/content.php?pid=227106&sid=1896904

2) NUS Physics Society Past Year Paper: http://physics.nus.edu.sg/~physoc/pyp.html

3) NUS Maths Society Past Year Paper: http://www.nusmathsociety.org/pyp.html

COE Quota: Math Formula

Applications of Math in Real Life: COE Quota

Source: http://en.wikipedia.org/wiki/Certificate_of_Entitlement

The Formula for COE Quota is:

\begin{align} (\text{Total COE Quota})_{qy} = &g.(\text{Motor vehicle population})_{y-1}  \\ &+ (\text{Projected de-registrations})_{y} \\&+ (\text{Unallocated quota})_{qy-1} \end{align}

Quote: In the formula above, the subscript y denotes calendar year and the subscript qy denotes quota year (May to April). Initially, projected deregistrations for (calendar) year y were simply taken to be equal to actual deregistrations in y-1 but from quota year 1999-2000 onwards, a projected number of deregistrations has been used.

Each year, the quota is set to allow for a targeted g percent growth in the total motor vehicle population, plus additional quota licenses to cover the number of motor vehicles that will be deregistered during the (calendar) year, plus any unallocated quota licenses from the previous quota year.

Read more at: http://en.wikipedia.org/wiki/Certificate_of_Entitlement

Logic puzzle: Which octopus is telling the truth?

Source: http://math.stackexchange.com/questions/677495/logic-puzzle-which-octopus-is-telling-the-truth?newsletter=1&nlcode=97485%7cd140

King Octopus has servants with six, seven, or eight legs. The servants with seven legs always lie, but the servants with either six or eight legs always tell the truth.

One day, four servants met. The blue one says, “Altogether, we have 28 legs.” The green one says, “Altogether, we have 27 legs.” The yellow one says, “Altogether, we have 26 legs.” The red one says, “Altogether, we have 25 legs.”

What is the colour of the servant who tells the truth?

Read the discussion at: http://math.stackexchange.com/questions/677495/logic-puzzle-which-octopus-is-telling-the-truth?newsletter=1&nlcode=97485%7cd140

Snooze button good or bad? (Education, Productivity Tip)

The snooze button – one of life’s luxuries. But is it really helping you out, or making you more tired?

Which Secondary school is the best in Singapore

Which Secondary school is the best in Singapore

Due to too many secondary schools, we can only list a few here at the start. There may be other secondary schools that can be the best in Singapore. Do feel free to add your own school and vote for it below!

Also feel free to leave any comments as to why the secondary school you choose is the best in Singapore. (We are not just looking at academic results, any valid reason like CCA, school atmosphere can be accepted.)

Also, check out: Which JC is the best in Singapore?

Which JC is the best in Singapore?

Which JC is the best in Singapore?

Feel free to leave any comments as to why you think your JC is the best in Singapore 🙂

Also, check out: Which Secondary school is the best in Singapore

Math games

Check out this site on Math games: http://www.coolmath-games.com/

It has a lot of free Math games to help you work on your arithmetic skills.

A recommended game is “Count Cubes”: http://www.coolmath-games.com/0-countcubes/index.html

This game really helps in visualisation skills, further more Counting Cubes is a legitimate question that can come out in PSLE.

Hope you have fun trying out the game.

 

JC Subject Combination

JC Subject Combination

Check out our posts related to JC Subject Combination:

1) What is the Difference between H1 Mathematics, H2 Mathematics and H3 Mathematics?

2) Maths Skills to be a Good Lawyer

3) Maths Skills to be a Doctor

4) The ideal Singapore JC subject combination for applying to Medicine

Logarithm rules and Indices rules

Two page helpsheet and formula list regarding Logarithm rules and Indices rules, with common mistakes to avoid:

Logarithm and Indices Rules

Foot of perpendicular from point to plane

Check out our posts on Foot of perpendicular from point to line / plane:

1) Foot of Perpendicular (from point to line)

2) Foot of Perpendicular (from point to plane)

Maths Group Tuition at Bishan: E Maths and A Maths

https://mathtuition88.com/group-tuition/ https://mathtuition88.com/

Maths Tuition @ Bishan starting in 2014.

Secondary 4 O Level E Maths and A Maths.

Patient and Dedicated Maths Tutor (NUS Maths Major 1st Class Honours, Dean’s List, RI Alumni)

Email: mathtuition88@gmail.com

 

Free Exam Papers: https://mathtuition88.com/free-exam-papers/

Valentine’s Day Math

Check out this site at: http://blog.wolframalpha.com/2010/02/12/computing-valentines-day-with-wolframalpha/#comment-103489

Computing Valentine’s Day with Wolfram|Alpha

Draw nice heart shape formulas with Math Equations at Wolfram Alpha!

Free Exam Papers (A Level) (A Level Maths)

http://www.a-levelmaths.com/

Personally crafted free Maths practice Question Sets for all students/educators (A Level Maths Resource Site)

Back to Main Free Exam Papers Page: https://mathtuition88.com/free-exam-papers/


Free Exam Papers (A Level) (Teach JC Math)

http://teachmejcmath-sg.webs.com/exampapers.htm

JC H2 Maths Prelim Free Exam Papers

Back to Main Free Exam Papers Page: https://mathtuition88.com/free-exam-papers/


Free Exam Papers (Secondary) (Recent papers)

https://sites.google.com/a/moe.edu.sg/2011sec3f/files/e-math-prelim-papers-other-schools

A treasure trove of E Math Prelim Papers (very recent papers)

 

Back to Main Free Exam Papers Page: https://mathtuition88.com/free-exam-papers/


Free Exam Papers (Secondary) (10 Sets)

http://mathprelimpapers.wordpress.com/

10 Sets of Prelim Free Exam Papers (A Maths)

Back to Main Free Exam Papers Page: https://mathtuition88.com/free-exam-papers/


Free Exam Papers (Secondary) (Siglap)

https://sites.google.com/a/moe.edu.sg/mathsdept-siglapsec/sec4e5ndownloads

Siglap Secondary Maths Free Exam Papers

Back to Main Free Exam Papers Page: https://mathtuition88.com/free-exam-papers/


Free Exam Papers (Primary) (Test paper info)

http://test-paper.info/

Click on “Test Paper Database ” on the Left Navigation Panel. Many exam papers in PDF format. Login is necessary though.

Back to Main Free Exam Papers Page: https://mathtuition88.com/free-exam-papers/


Free Exam Papers (Primary) (Java samples)

http://www.java-samples.com/testpapers/index.php

Excellent website for downloading free exam papers for primary level. Highly recommended.

Back to Main Free Exam Papers Page: https://mathtuition88.com/free-exam-papers/


Which Secondary School to Choose?

After receiving PSLE results, the next question would be: Which Secondary School to Choose?

Choosing the right secondary school is a big decision that will impact the next 4 (or more) years of life. And, the school with the highest PSLE Cut Off Points, may or may not be the best fit. Most important is to choose a school with a conducive learning environment so that the student can excel and perform to his/her fullest potential.

Read more information about that on the following websites:

1) PSLE: Top 3 things to remember when choosing a secondary school

(http://www.straitstimes.com/breaking-news/singapore/story/psle-top-3-things-remember-when-choosing-secondary-school-your-child-2)

2) Guide to Selecting a Secondary School for your child

(http://www.kiasuparents.com/kiasu/content/guide-selecting-secondary-school-your-child)

PSLE Cut Off Point

Also check out: Recommended Books for GEP

PSLE Cut Off Point

Check out the following websites to determine the PSLE Cut Off Point for various secondary schools.

1) Source 1: http://www.post1.net/biow/entry/2012_psle_cutoff_points_to_2013_secondary_1

2) Source 2: http://forums.sgclub.com/singapore/secondary_school_ranking_453171.html


Featured book:

Becoming a Problem Solving Genius: A Handbook of Math Strategies


 

S/N Planning Area PSLE cut-off for Non-Affiliated Schools Secondary School (Aggregate Range of 2012 Primary 6 pupils posted to 2013 Secondary 1) Type 2013 Sec1 Express (Lower) 2013 Sec1 Express (Upper) 2013 Sec1 Express (Median) 2013 Sec1 Normal (A) Lower 2013 Sec1 Normal (A) Upper
. 1 BUKIT TIMAH NANYANG GIRLS’ HIGH SCHOOL * GIRLS 265 280
. 2 CENTRAL RAFFLES GIRLS’ SCHOOL (SECONDARY) GIRLS 263 280
. 3 BISHAN RAFFLES INSTITUTION CO-ED 263 284 266
. 4 BUKIT TIMAH HWA CHONG INSTITUTION CO-ED 261 277 264
. 5 BUKIT TIMAH NATIONAL JUNIOR COLLEGE CO-ED 259 272 261
. 6 KALLANG DUNMAN HIGH SCHOOL CO-ED 256 278 260
. 7 JURONG WEST RIVER VALLEY HIGH SCHOOL CO-ED 256 282 259
. 8 ANG MO KIO CHIJ ST. NICHOLAS GIRLS’ SCHOOL * GIRLS 253 268 254
. 9 BUKIT TIMAH METHODIST GIRLS’ SCHOOL (SECONDARY) * GIRLS 252 267 255
. 10 TOA PAYOH CEDAR GIRLS’ SECONDARY SCHOOL GIRLS 251 272 253

No more aircon for independent schools

Read more at: Funding cuts for top independent schools in Singapore

Chinese word of the day: 心静自然凉 (“When the mind is still, you will be calm, cool and collected.”)

Source: http://baike.soso.com/v4170229.htm

科学根据

编辑本段

心静,指为人处世、待人接物、幽居独处时的一种自然、平和的心态。心静自然凉,本义是说心里平静,内心自然凉快。后用来指在遇到问题、困难、挫折时,放平心态,以一颗平常心去处理生活中的问题。俗话说“心静自然凉”,说明人的主观感觉有一定的作用。最近,日本兵库县西宫市协立脑神经外科医院医师小山哲男和美国学者通过实验,为这一现象找到了一定科学依据。   小山医师以10名美国男女为实验对象,为把灼热的痛苦传给大脑,用小金属片给接受实验者的腿肚子施以热的刺激。如果是15秒的间隔,开始信号之后用48摄氏度热刺激,如果是30秒的间隔,开始信号之后用50摄氏度的热刺激,如此反复多次,让接受实验者在大脑中记住刺激的类型。
然后,改变刺激类型,过15秒间隔让接受实验者接受50摄氏度的热刺激,同时,用磁共振成像装置调查大脑活动的情况。结果发现,和隔30秒时施以50摄氏度的热刺激相比,大脑中的感情区域活动低下。研究人员询问接受实验者的痛苦感并量化分析之后,发现痛苦感约减少30%。  小山医师说,这一实验结果在某种程度上证明了“心静自然凉”的感觉。注射前医生对患者说不疼,是一种有科学根据的止痛法。这一成果已发表在美国《全国科学院学报》上。

含义

编辑本段

天气燥热,人会产生一系列负面情绪,比如烦躁不安等等,正所谓天气会影响人的心情,研究表明,对人体最适宜的温度是15摄氏度左右。 大家都明白,吵架的人都是脸红脖子粗的,紧张不安的人会出汗也会感觉比较热,本来嘛,谁在炎热的天气下会感觉舒服呢,恐怕一个个都是眉头紧锁吧,但反过来,如果让自己有些烦躁的心平静下来呢,这样可以起到降低血压等等作用。 更重要的是,把自己的注意力从炎热的天气上转移到其他可以让人感到平静愉快的事物上来,注意力转移了,自然就没那么“热”了!类似于爱因斯坦的相对论,心里的微妙变化完全可以改变人对外界事物的感知。

JC Results Release

Source: http://www.moe.gov.sg/media/press/2014/01/posting-results-2014-jae-and-jpsae.php

Posting Results For The 2014 Joint Admissions Exercise (JAE) and Joint Polytechnic Special Admissions Exercise (JPSAE)

1The Ministry of Education (MOE) will release the posting results for the 2014 Joint Admissions Exercise (JAE) and the Joint Polytechnic Special Admissions Exercise (JPSAE) on Wednesday, 5 February 2014, at 8.00 am.Applicants can obtain their posting results via the following channels:

2JAE

  • The JAE-Internet System (JAE-IS) is accessible through the JAE website at http://www.moe.gov.sg/education/admissions/jae; and
  • Short Messaging System (SMS) text messages sent to the mobile phone number provided by the applicant during registration.

3JPSAE

4Applicants posted to a Junior College (JC) or the Millennia Institute (MI) should report to these institutions on Thursday, 6 February 2014, at 7.30 am. Applicants posted to a Polytechnic or Institute of Technical Education (ITE) course will receive further instructions via an enrolment package from the respective institutions by mail.

5Appeals

6Applicants who wish to appeal for a transfer to another JC or the MI should approach the institution of their choice directly.

Recommended Graphics Calculator for JC

Source: http://www.seab.gov.sg/calculatorList/GuidelinesCalculators.pdf

Personally, the calculator I like most is the TI-84 series. There is no big difference between the different TI-84 models, all are good to use.

graphical calculator

Where to buy:

Buying from school is the best option, as often there is a discount. Otherwise, you can buy from a distributor at Bras Basah Complex: Learning InterActive Pte Ltd The Resource Centre Blk 231 Bain Street #04-39 Bras Basah Complex Singapore 180231 (http://li.com.sg/html/li_contactus_details.html)

If your calculator is damaged, do not throw it away, as there is a chance of a trade in (pay around $90 to trade in the old calculator for a new one).

The Mathematics of Chinese New Year (How to calculate its date)

Source: http://www.math.nus.edu.sg/aslaksen/calendar/chinese.shtml

If you are curious about the Mathematics behind the Chinese Calendar, do check out this website by Professor Helmer Aslaksen.

Excerpt: One rule of thumb is that Chinese New Year should be the new Moon closest to the beginning of spring (立春, lìchūn). This rule is correct most of the time, but it can fail if Lìchūn falls close to halfway between two new Moons. It failed in 1985 and will fail again in 2015. Since Lìchūn falls around February 4, this helps explain why Chinese New Year will always fall between January 21 and February 21. It also helps explain why Chinese New Year is called the spring festival. If you have a Western calendar that indicates the phases of the Moon, this will give you an approximation of the date of Chinese New Year. But notice that the Chinese calendar uses the time of new Moon in China.

As explained above, Chinese New Year will always fall between January 21 and February 21. The tropical (or solar) year is about 365.25 days, while a synodic (or lunar) month is about 29.5 days. Hence a lunar year consisting of 12 months will be about 12 x 29.5 = 354 days. So a lunar year is about 11 days shorter than a solar year.

The second rule of thumb is therefore that most of the time Chinese New Year will fall 11 (or sometimes 10 or 12) days earlier than the previous year, but if that would take us outside of the Chinese New Year range of January 21 to February 21, we must add a leap month, so Chinese New Year jumps 19 (or sometimes 18) days later. If this rule takes you close to January 21, you can end up being one month wrong, otherwise you will be at most one day off.

Read more at: http://www.math.nus.edu.sg/aslaksen/calendar/chinese.shtml#CNY

Clash of Clans Mathematics: Arithmetic Progression & Geometric Progression

Clash of Clans Mathematics: Arithmetic Progression & Geometric Progression

CoC_titlescreen_2013

We can learn some mathematics from the popular game, Clash of Clans!

Lets look at the Building Cost and Production Rate of the Gold Mine.

Source: http://clashofclans.wikia.com/wiki/Gold_Mine

Gold Mine11clash of clans gold mine ap gp

We see that the Build cost actually follows a geometric progression(approximately) as each time, the build cost approximately doubles.

The formula for the n-th term of a geometric progression is \boxed{ar^{n-1}}, where a is the first term, and r is the common ratio.

The above formula works well for the first 2 terms, for example the second term is 300=150(2^{2-1}).

However, the Production Rate follows an arithmetic progression, as per level, the production rate increases by 200/hr.

The formula for the n-th term of an arithmetic progression is \boxed{a+(n-1)d}, where a is the first term, and d is the common difference. The formula works for all the 5 levels: for instance at level 5 the production rate is 1000=200+(5-1)(200).

Thanks for reading, and do “like” this post if you enjoy reading it! Hope you learnt some mathematics along the way.

JC School Posting Results 2014

Source: http://www.moe.gov.sg/media/press/2014/01/posting-results-2014-jae-and-jpsae.php

Posting Results For The 2014 Joint Admissions Exercise (JAE) and Joint Polytechnic Special Admissions Exercise (JPSAE)

1The Ministry of Education (MOE) will release the posting results for the 2014 Joint Admissions Exercise (JAE) and the Joint Polytechnic Special Admissions Exercise (JPSAE) on Wednesday, 5 February 2014, at 8.00 am.Applicants can obtain their posting results via the following channels:

2JAE

  • The JAE-Internet System (JAE-IS) is accessible through the JAE website at http://www.moe.gov.sg/education/admissions/jae; and
  • Short Messaging System (SMS) text messages sent to the mobile phone number provided by the applicant during registration.

3JPSAE

4Applicants posted to a Junior College (JC) or the Millennia Institute (MI) should report to these institutions on Thursday, 6 February 2014, at 7.30 am. Applicants posted to a Polytechnic or Institute of Technical Education (ITE) course will receive further instructions via an enrolment package from the respective institutions by mail.

Read more at: http://www.moe.gov.sg/media/press/2014/01/posting-results-2014-jae-and-jpsae.php

Secrets of Mental Math: The Mathemagician’s Guide to Lightning Calculation and Amazing Math Tricks

Is there a mathematical reason why chocolate chip cookies have 37% (1/e) chocolate in them?

Source: http://math.stackexchange.com/questions/651823/is-there-a-mathematical-reason-why-chocolate-chip-cookies-have-37-1-e-chocola?newsletter=1&nlcode=97485%7cd140
Someone once briefly explained to me why it is that chocolate chip cookies have 37% chocolate in them. To the best of my memory it has to do with the way trying to place dots in a circle in a random and scattered way behave, which turns out to be 1/e or ≈37.
Chocolate Chip Cookie 37% 1/e

Interesting article for chocolate lovers!

Source: http://math.stackexchange.com/questions/651823/is-there-a-mathematical-reason-why-chocolate-chip-cookies-have-37-1-e-chocola?newsletter=1&nlcode=97485%7cd140