Math Blog

When Math Doesn’t Add Up

Christian Math post

Donna's avatarEvident Grace

Here are some amazing spiritual math and science facts:

1 + 1 + 1 = 3 when it’s the Trinity. God is three in one! No, we can’t figure it out but God is not limited by the math He invented for us to make sense of our little world. I delight in worshiping a God who is great beyond my understanding Smile.

2 wrongs don’t make 1 right. It’s not like multiplying two negative numbers which gives us a positive.
For example, 1 unintended pregnancy + 1 abortion does NOT equal one “right.” (No one has the “right” to kill a baby—including his/her mother!)

Gravity (physical law) always pulls us down. But glory lifts us upward. Our body is temporal; it has to stay on this earth whether we’re alive or dead. Our spirit can receive God’s never-ending life that give us supernatural power during this life and eternal…

View original post 114 more words

Methodology for Checking for Careless Mistakes

Checking for careless mistakes using the Substitution Method

  • Normal method of checking (i.e. check your working from front to back again), may or may not find the error
  • Using Substitution Method of checking guarantees that your answer is correct, and will find an error if there is one.
  • Use  Substitution Method of checking for all algebra/solving/simplify questions worth 2 marks or more. You will be able to save many many marks using this method!
  • Only takes 10 seconds with practice. (use calculator)

Example (using substitution method)

Express \displaystyle\frac{2x-3}{x^2+4x+3}-\frac{1}{x+3} as a single fraction in its simplest form. [2 marks]

After getting your answer (\displaystyle\frac{x-4}{(x+3)(x+1)}), you can substitute in the value \boxed{x=9}.

When, x=9, \displaystyle\frac{2x-3}{x^2+4x+3}-\frac{1}{x+3}=\frac{1}{24}, and \displaystyle\frac{x-4}{(x+3)(x+1)}=\frac{1}{24}

Since both expressions give the same value, you have just checked that your answer is correct!

Humorous cartoon featuring Jackie Chan.
Sincerely wishing all students to reduce their careless mistakes to as low as possible!

Our Daily Story #7: Algebraic Equation Owed to the Mathematical Thief

tomcircle's avatarMath Online Tom Circle

From the previous O.D.S. stories (#3, #4) on Quintic equations (degree 5) by Galois and Abel in the 19th century, we now trace back to the first breakthrough in the 16th century of the Cubic (degree 3) & Quartic (degree 4) equations with radical solution, i.e. expressed by 4 operations (+ – × /) and radicalroots {$latex sqrt{x} , : sqrt [n]{x} $ }.

Example: Since Babylonian time, and in 220 AD China’s Three Kingdoms Period by 趙爽 Zhao Shuang of the state of Wu 吳, we knew the radical solution of Quadratic equations of degree 2 :
$latex ax^2 + bx + c = 0 $

can be expressed in radical form with the coefficients a, b, c:

$latex boxed{x= frac{-b pm sqrt{b^{2}-4ac} }{2a}}$

Are there radical solutions for Cubic equation (degree 3) and Quartic equations (degree 4) ? We had to wait till the European Renaissance…

View original post 138 more words

Our Daily Story #6: A Subway Sandwich Mathematician Zhang Yitang 张益唐

tomcircle's avatarMath Online Tom Circle

Zhang is the typical demonstration of pure perseverance of traditional Chinese mathematicians: knock harder and harder until the truth is finally cracked.

His work is based on the prior half-way proof by 3 other mathematicians “GPY”:

image

Gap between Primes:

Let p1 and p2 be two adjacent primes separated by gaps of 2N:

p1 – p2 = 2 (twin primes)
eg. (3, 5), (5, 7)… (11, 13) and the highest twin primes found so far (the pair below: +1 and -1)
image

p1 – p2 = 4 (cousin primes)
eg. (7, 11)

p1 – p2 = 6 (sexy primes)
eg. (23, 29)
…
p1 – p2 = 2N

Euclid proved 2,500 years ago there are infinite many primes, but until today nobody knows are these primes bounded by a gap (2N) ?

Zhang, while working as a sandwich delivery man in a Subway shop…

View original post 97 more words

Our Daily Story #5: The Prince of Math

tomcircle's avatarMath Online Tom Circle

Carl Friedrich Gauss is named the “Prince of Math” for his great contributions in almost every branch of Math.

As a child of a bricklayer father, Gauss used to follow his father to construction site to help counting the bricks. He learned how to stack the bricks in a pile of ten, add them up to obtain the total. If a pile has only 3, for example, he would top up 7 to make it 10 in a pile. Then 15 piles of 10 bricks would give a total of 150 bricks.

One day in school, his teacher wanted to occupy the 9-year-old children from talking in class, made them add the sum:
1 + 2 + 3+ ….+ 98 + 99 + 100 = ?

Gauss was the first child to submit the sum within few seconds = 5,050.

He used his brick piling technique: add

1 + 100…

View original post 82 more words

Our Daily Story #3: The Math Genius Who Failed Math Exams Twice

tomcircle's avatarMath Online Tom Circle

To prove the FLT, Prof Andrews Wiles used all the math tools developed from the past centuries till today. One of the key tool is the Galois Group,  invented by a 19-year-old French boy in 19th century, Evariste Galois. His story is a tragedy – thanks to the 2 ‘incompetent’ examiners of the Ecole Polytechnique (a.k.a. “X”), the Math genius failed in the Concours (Entrance Exams) not only once, but twice in consecutive years.
Rejected by universities and the ugly French politics and academic world, Galois suffered set back one after another, finally ended his life in a ‘meaningless’ duel at 20.

He wrote down his Math findings the eve before he died – “Je n’ai pas le temps” (I have no more time) – begged his friend to send them to two foreigners (Gauss and Jacobi) for review of its importance. “Group Theory”…

View original post 24 more words

Our Daily Story #9: The Indian Clerk Mathematician

tomcircle's avatarMath Online Tom Circle

The story of Ramanujian:

http://en.m.wikipedia.org/wiki/Srinivasa_Ramanujan

image

image
http://mathworld.wolfram.com/Hardy-RamanujanNumber.html

We have seen how two 19th century greatest mathematicians Cauchy and Gauss who were not helpful to two young unknown mathematicians Galois and Abel, now let’s see an opposite example — the discovery of an unknown math genius Ramanujian by the greatest Pure Mathematician in 20th century Prof G.H. Hardy.

References:
1.
http://tomcircle.wordpress.com/2013/11/27/163-and-ramanujan-constant/

2.
http://tomcircle.wordpress.com/2013/07/04/ramanujian/

View original post

Our Daily Story #10: A Shop Assistant Math Professor

tomcircle's avatarMath Online Tom Circle

In the previous story (#9) we mentioned Ramanujan having the luck of being spotted by Prof G.H. Hardy as the treasure of mathematics, another Chinese Hua Luogeng 华罗庚, 20 years younger than Ramanujan,  was also coached by Prof Hardy, although Prof Hardy did not realize Hua’s potential later to the modern mathematics in China.

Hua dropped out of secondary school due to poverty, he worked in his father’s little grocery shop as the shop assistant. His talent was spotted by the French-educated mathematician Prof Xiong Qinlai ( 熊庆来) in Tsinghua University 清华大学 from a paper the young boy published – on Quantic Equation Solvability error made by a Math Professor Su. Hua was admitted to Tsinghua University as assistant math lecturer on exception. Later he was sent to Cambridge on 庚子赔款 Boxer Indemnity scholarship.

When Prof Hardy met Hua, he let Hua choose between:
1) Work on a PhD…

View original post 168 more words

Are Math competitions good?

Are Math competitions good?

Source: http://www.dnaindia.com/academy/report-do-math-competitions-inspire-students-to-gain-proficiency-in-the-subject-1966588

Check out the above website to see the pros and cons of Math competitions, and whether they inspire students to be better at Math.

The most important is to enjoy doing Math, as Math is fun!


Math Olympiad Contest Problems for Elementary and Middle Schools, Vol. 1

Our Daily Story #8: The Rigorous Mathematician with epsilon-delta

The story of Cauchy and mathematical analysis

tomcircle's avatarMath Online Tom Circle

image

http://en.m.wikipedia.org/wiki/Augustin-Louis_Cauchy

We mentioned Augustin Louis Cauchy in the tragic stories of Galois and Abel. Had Cauchy been more generous and kind enough to submit the two young mathematicians’ papers to the French Academy of Sciences, their fates would have been different and they would not have died so young.

Cauchy was excellent in language. He was the 2nd most prolific writer (of Math papers) after Euler in history. When he was a math prodigy, his neighbor — the great French mathematician and scientist Pierre-Simon Laplace — advised Cauchy’s father to focus the boy on language before touching mathematics. (Teachers / Parents take note of the importance of language in Math education.)

Cauchy’s language education made him very rigorous in micro-details. This was the man who developed the most rigorous epsilon-delta Advanced Calculus (called Analysis) after Newton / Lebniz had invented the non-rigorous Calculus (why?).

Rigorous epsilon-delta…

View original post 172 more words

RE:FRAMED: How do I get homework done?

Motivational post on “How to get homework done”
Useful for students taking O Levels

aboveandbeyondtheworld's avatarBeyond the Status Quo

We all know how terrible homework is and how long it takes and how you could be doing SOOO many other things that are not homework. Like nothing productive. That kind of stuff. And once we actually get started, it’s so difficult to keep on track. Sometimes we hit a brick wall and so we just stop and do something else. And then there are those moments where you have so much work to do that you take a nap. Or the infamous “due tomorrow do tomorrow” mentality. When teachers assign a certain portion of reading you think, “Sweet! No homework!” just because you don’t get credit for actually reading it. This affects almost every single person and extends beyond schooling and even into your real life work. What should you do? Well I can’t tell you, but I can confide in the type of mentality I have and what…

View original post 511 more words

O level fail maths

O level fail maths

Students should try their best to pass O Level Maths, as it is absolutely essential to enter JC and Poly. Passing O Level Maths is not as difficult as it seems, sufficient practice usually can enable a student to pass.

Do check out the following forums on what next steps to do, in the unfortunate event that O level Maths is failed. Do not despair though, there are always alternative options, which are explored in the following forums:

1) Failed O’Level maths can’t go into poly?

2) O level results fail maths Poly how??

Remember it is never too late to start improving your studies now. Learning is a lifelong process; it is a journey, not a destination.

Singapore starting salary

Singapore starting salary (Education News)

The ‘A’ Levels results have just been released! Thinking of what course to pursue in university? Check out this list of Singapore starting salaries organised by faculty.

However, do not base your choice based on salary alone, do consider where your interest and passion lies! Also check out this post on NUS Cut Off Points for various faculties.

Source: http://www.moe.gov.sg/education/post-secondary/files/ges-nus.pdf

GRADUATE EMPLOYMENT SURVEY

If the table doesn’t display properly on your browser, check out the source above for clearer details!

NUS: 2013 GES Employment Rates1 and Salaries of Graduates by Bachelor Degree Degree Overall Employment Rate

 

2

(%)

 

 Full-time Permanent Employment Rate

 

3

(%)

 

 Basic Monthly Salary

 

4

($)

 

 Gross Monthly Salary

 

5

($)

 
Mean

 

 Median

 

 Mean

 

 Median

 

 25

 

th Percentile

 

 75

 

th Percentile

 
Faculty of Arts & Social Sciences

 
Bachelor of Arts

 

 

 84.8

 

 

 70.1

 

 

 2,741

 

 

 2,730

 

 

 2,888

 

 

 2,800

 

 

 2,500

 

 

 3,080

 

 
Bachelor of Arts (Hons)

 

 

 86.6

 

 

 74.6

 

 

 3,057

 

 

 3,200

 

 

 3,154

 

 

 3,200

 

 

 2,800

 

 

 3,500

 

 
Bachelor of Social Sciences

 

 

 88.1

 

 

 76.8

 

 

 3,098

 

 

 3,100

 

 

 3,210

 

 

 3,200

 

 

 2,800

 

 

 3,500

 

 
NUS Business School

 
Bachelor of Business Administration

 

 

 88.7

 

 

 81.7

 

 

 2,960

 

 

 2,868

 

 

 3,062

 

 

 3,000

 

 

 2,700

 

 

 3,370

 

 
Bachelor of Business Administration (Hons)

 

 

 94.6

 

 

 90.3

 

 

 3,404

 

 

 3,050

 

 

 3,512

 

 

 3,200

 

 

 2,800

 

 

 3,800

 

 
Bachelor of Business Administration (Accountancy)

 

 

 93.3

 

 

 88.9

 

 

 2,740

 

 

 2,700

 

 

 2,922

 

 

 2,700

 

 

 2,700

 

 

 3,018

 

 
Bachelor of Business Administration (Accountancy) (Hons)

 

 

 97.2

 

 

 94.4

 

 

 3,065

 

 

 2,800

 

 

 3,143

 

 

 2,800

 

 

 2,700

 

 

 3,200

 

 
School of Computing

 
Bachelor of Computing (Communications and Media)

 

 

 88.9

 

 

 77.8

 

 

 3,350

 

 

 3,000

 

 

 3,377

 

 

 3,050

 

 

 2,825

 

 

 3,425

 

 
Bachelor of Computing (Computational Biology)**

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 
Bachelor of Computing (Computer Engineering)**

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 
Bachelor of Computing (Computer Science)

 

 

 92.4

 

 

 83.3

 

 

 3,933

 

 

 3,400

 

 

 3,953

 

 

 3,425

 

 

 3,000

 

 

 4,000

 

 
Bachelor of Computing (Electronic Commerce)

 

 

 88.9

 

 

 83.3

 

 

 3,277

 

 

 3,050

 

 

 3,320

 

 

 3,080

 

 

 2,800

 

 

 3,553

 

 
Bachelor of Computing (Information Systems)

 

 

 89.2

 

 

 83.9

 

 

 3,266

 

 

 3,000

 

 

 3,322

 

 

 3,005

 

 

 3,000

 

 

 3,800

 

 
Faculty of Dentistry

 
Bachelor of Dental Surgery

 

 

 100.0

 

 

 100.0

 

 

 4,106

 

 

 4,000

 

 

 4,106

 

 

 4,000

 

 

 4,000

 

 

 4,400

 

 
School of Design & Environment

 
Bachelor of Arts (Architecture)**6

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 
Bachelor of Arts (Industrial Design)

 

 

 82.1

 

 

 53.6

 

 

 3,007

 

 

 2,650

 

 

 3,023

 

 

 2,650

 

 

 2,400

 

 

 3,000

 

 
Bachelor of Science (Project and Facilities Management)

 

 

 96.8

 

 

 96.8

 

 

 2,961

 

 

 2,980

 

 

 3,025

 

 

 3,000

 

 

 2,800

 

 

 3,200

 

 
Bachelor of Science (Real Estate)

 

 

 89.2

 

 

 89.2

 

 

 2,839

 

 

 2,800

 

 

 2,988

 

 

 2,900

 

 

 2,600

 

 

 3,179

 

 
Faculty of Engineering

 
Bachelor of Engineering (Bioengineering)

 

 

 74.0

 

 

 60.0

 

 

 2,823

 

 

 3,000

 

 

 3,068

 

 

 3,000

 

 

 2,720

 

 

 3,250

 

 
Bachelor of Engineering (Chemical Engineering)

 

 

 93.2

 

 

 90.0

 

 

 3,245

 

 

 3,000

 

 

 3,359

 

 

 3,175

 

 

 3,000

 

 

 3,644

 

 
Bachelor of Engineering (Civil Engineering)

 

 

 96.1

 

 

 94.1

 

 

 3,140

 

 

 3,000

 

 

 3,154

 

 

 3,050

 

 

 3,000

 

 

 3,300

 

 
Bachelor of Engineering (Computer Engineering)

 

 

 88.9

 

 

 85.6

 

 

 3,592

 

 

 3,200

 

 

 3,653

 

 

 3,200

 

 

 3,000

 

 

 3,970

 

 
Bachelor of Engineering (Electrical Engineering)

 

 

 88.5

 

 

 88.0

 

 

 3,286

 

 

 3,100

 

 

 3,334

 

 

 3,200

 

 

 3,000

 

 

 3,600

 

 
Bachelor of Engineering (Engineering Science)

 

 

 86.2

 

 

 75.9

 

 

 2,940

 

 

 3,000

 

 

 2,960

 

 

 3,000

 

 

 2,800

 

 

 3,150

 

 
Bachelor of Engineering (Environmental Engineering)

 

 

 93.8

 

 

 87.5

 

 

 3,153

 

 

 3,100

 

 

 3,208

 

 

 3,110

 

 

 3,000

 

 

 3,500

 

 
Bachelor of Engineering (Industrial and Systems Engineering)

 

 

 93.9

 

 

 92.4

 

 

 3,330

 

 

 3,200

 

 

 3,397

 

 

 3,200

 

 

 3,000

 

 

 3,800

 

 
Bachelor of Engineering (Materials Science and Engineering)

 

 

 90.9

 

 

 87.9

 

 

 3,036

 

 

 3,000

 

 

 3,169

 

 

 3,000

 

 

 3,000

 

 

 3,260

 

 
Bachelor of Engineering (Mechanical Engineering)

 

 

 89.1

 

 

 87.2

 

 

 3,155

 

 

 3,000

 

 

 3,319

 

 

 3,225

 

 

 3,000

 

 

 3,500

 

 
Faculty of Law

 
Bachelor of Laws (LLB) (Hons)6

 

 

 98.8

 

 

 98.2

 

 

 4,922

 

 

 4,800

 

 

 5,099

 

 

 5,000

 

 

 4,500

 

 

 5,800

 

 
YLL School of Medicine

 
Bachelor of Medicine and Bachelor of Surgery (MBBS)6

 

 

 100.0

 

 

 100.0

 

 

 4,406

 

 

 4,500

 

 

 4,741

 

 

 4,500

 

 

 4,500

 

 

 5,200

 

 
Bachelor of Science (Nursing)

 

 

 97.5

 

 

 97.5

 

 

 2,687

 

 

 2,750

 

 

 2,886

 

 

 2,950

 

 

 2,700

 

 

 3,050

 

 
Bachelor of Science (Nursing) (Hons)

 

 

 100.0

 

 

 100.0

 

 

 2,896

 

 

 3,000

 

 

 3,042

 

 

 3,025

 

 

 3,000

 

 

 3,200

 

 
Yong Siew Toh Conservatory of Music

 
Bachelor of Music**

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 
Faculty of Science

 
Bachelor of Applied Science**

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 
Bachelor of Applied Science (Hons)

 

 

 97.3

 

 

 97.3

 

 

 2,850

 

 

 2,750

 

 

 2,925

 

 

 2,900

 

 

 2,600

 

 

 3,255

 

 
Bachelor of Science

 

 

 80.9

 

 

 65.1

 

 

 2,726

 

 

 2,700

 

 

 2,804

 

 

 2,800

 

 

 2,600

 

 

 3,000

 

 
Bachelor of Science (Hons)

 

 

 83.6

 

 

 74.0

 

 

 3,101

 

 

 3,000

 

 

 3,217

 

 

 3,100

 

 

 2,868

 

 

 3,500

 

 
Bachelor of Science (Computational Biology)**

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 

 N.A.

 

 
Bachelor of Science (Pharmacy) (Hons)6

 

 

 96.4

 

 

 96.4

 

 

 3,473

 

 

 3,500

 

 

 3,540

 

 

 3,500

 

 

 3,350

 

 

 3,750

 

 

How do the power-series definitions of sin and cos relate to their geometrical interpretations?

gowers's avatarGowers's Weblog

I hope that most of you have either asked yourselves this question explicitly, or at least felt a vague sense of unease about how the definitions I gave in lectures, namely

$latex displaystyle cos x = 1 – frac{x^2}{2!}+frac{x^4}{4!}-dots$

and

$latex displaystyle sin x = x – frac{x^3}{3!}+frac{x^5}{5!}-dots,$

relate to things like the opposite, adjacent and hypotenuse. Using the power-series definitions, we proved several facts about trigonometric functions, such as the addition formulae, their derivatives, and the fact that they are periodic. But we didn’t quite get to the stage of proving that if $latex x^2+y^2=1$ and $latex theta$ is the angle that the line from $latex (0,0)$ to $latex (x,y)$ makes with the line from $latex (0,0)$ to $latex (1,0)$, then $latex x=costheta$ and $latex y=sintheta$. So how does one establish that? How does one even define the angle? In this post, I will give one possible answer to…

View original post 2,166 more words

‘A’ level results release next Monday

2013 GCE ‘A’ Level exam results release next Monday

Read more at: http://www.moe.gov.sg/media/press/2014/02/release-of-2013-gce-a-level-results.php

Release of 2013 GCE ‘A’ Level Examination Results on 3 March 2014

1The results of the 2013 Singapore-Cambridge GCE Advanced Level Examination will be released on Monday, 3 March 2014.

 

Proof of Fermat’s Last Theorem by our reader

One of our readers has posted an attempted proof of Fermat’s Last Theorem at:

https://mathtuition88.com/2013/08/31/fermats-last-theorem-2/comment-page-1/

(Scroll down to the comments)

Do check it out and feel free to discuss in the comments!

Astronomy Talk by Henry Lin

Source: http://www.ted.com/talks/henry_lin_what_we_can_learn_from_galaxies_far_far_away.html?utm_source=newsletter_weekly_2014-03-01&utm_campaign=newsletter_weekly&utm_medium=email&utm_content=talk_of_the_week_button

In a fun, exciting talk, teenager Henry Lin looks at something unexpected in the sky: distant galaxy clusters. By studying the properties of the universe’s largest pieces, says the Intel Science Fair award winner, we can learn quite a lot about scientific mysteries in our own world and galaxy.

 

[Math is Fun] Why 0 cannot be divisor?

zkchong's avatarZan-Kai

I remember my secondary teacher told me that 1 cannot be divided by 0.

Why 0 cannot be divisor?

“Because it is just not permitted in arithmetic”, he said.

Well. It is not permitted because it is not permitted. A kid shouldn’t ask much…

Throughout my N years of learning and teaching, I know that 0 cannot be a divisor because if it does, something will go wrong in mathematics. But how things can go wrong other than the calculator showing some error messages?

Here is a simple example.

Let say

  1 / 0 = SOMETHING,

is valid.

If so, I can multiply both left hand and right hand sides by 0.  And, it becomes

1 = SOMETHING * 0.
1 = 0.

Oops, something is wrong with the arithmetic. That’s why we can’t have 0 as the divisor.

Well. Perhaps you are not yet convinced and ask “how about…

View original post 83 more words

When is PSLE 2014

When is PSLE?

Please double confirm with the source at: http://www.seab.gov.sg/examTimeTable/2014PSLEExamTimetable.pdf

PSLE Exam Dates/Schedule/Timetable

A. Oral Examination

Date Paper Time
Thursday, 14 August&Friday, 15 August

 

 English Language / Foundation EnglishChinese / Malay / TamilFoundation Chinese / Foundation Malay / Foundation Tamil

 

 0800 – 1300 h
Friday, 15 August Bengali / Gujarati / Hindi / Panjabi / UrduFoundation Bengali / Foundation Gujarati / Foundation Hindi / Foundation Panjabi / Foundation Urdu 0800 – 1300 h
C. Written Examination Date

 

 Paper

 

 Time

 

 Duration

 
Thursday,

25 September

 

 

 English Language Paper 1

English Language Paper 2

Foundation English Paper 1

Foundation English Paper 2

 

 

 0815 – 0925 h

1030 – 1220 h

0815 – 0925 h

1030 – 1150 h

 

 

 1 h 10 min

1 h 50 min

1 h 10 min

1 h 20 min

 

 
Friday,

26 September

 

 

 Mathematics Paper 1

Mathematics Paper 2

Foundation Mathematics Paper 1

Foundation Mathematics Paper 2

 

 

 0815 – 0905 h

1015 – 1155 h

0815 – 0915 h

1015 – 1130 h

 

 

 50 min

1 h 40 min

1 h

1 h 15 min

 

 
Monday,

29 September

 

 

 Chinese / Malay / Tamil

Bengali / Gujarati / Hindi / Panjabi / Urdu

Paper 1

Chinese / Malay / Tamil

Bengali / Gujarati / Hindi / Panjabi / Urdu

Paper 2

Foundation Chinese/ Foundation Malay/ Foundation Tamil Paper 1

 

 

 0815 – 0905 h

1015 – 1155 h

0815– 0845 h

 

 

 50 min

1 h 40 min

30 min

 

 
Tuesday,

30 September

 

 

 Science

Foundation Science

 

 

 0815 – 1000 h

0815 – 0930 h

 

 

 1 h 45 min

1 h 15 min

 

 
Wednesday,

1 October

 

 

 Higher Chinese / Higher Malay / Higher Tamil Paper 1

Higher Chinese / Higher Malay / Higher Tamil Paper 2

 

 

 0815 – 0905 h

1015 – 1135 h

 

 

 50 min

1 h 20 min

 

 

Our Daily Story #4: Niels Henrik Abel, a poor Math genius

tomcircle's avatarMath Online Tom Circle

Galois and Abel had many things in common: both worked on the Quintic equation (of degree 5). Abel first proved there was NO radical solution; Galois, who was 9 years younger, went one step further to explain WHY no solution (with Group theory).

Both were young Math genius not recognized by the world of mathematics. Their fates were ruined by the same French mathematician Cauchy, who hid their Math papers from the recognition of the French Academy of Science.

Both died young: Abel at 26,  Galois 20.
Abel was poor and weak in health. His dream job of professorship came 2 days (too late) after his death.

Ironically, today the top Math award in monetary term (US$ 1 million) for the world’s top mathematician is named after this extremely poor mathematician – the Abel Prize.

http://scienceworld.wolfram.com/biography/Abel.html

(Go to YouTube “Niels Henrik Abel” to read the English sub-title)

View original post

A series of tubes…uh….numbers

danielg421's avatarMathematically Inclined

Image

 

If you want to feel comfortable with math, you have to understand that the world exists through a series of complex patterns. Admittedly, we can’t say this for sure. The universe is so infinitely large (and by the time you finish reading this blog post it will have already grown by an immeasurable amount), and our grasp on math is so tentative as humans that it’s impossible to notice or even understand the pattern at work on a large scale. However, the belief in patterns can be thought of more as a philosophy rather than an explanation for the world.

 

One of the most fundamental patterns in Algebra and number theory is the Fibonacci sequence. Now, this can get pretty dense, so bear with me.

 

The Fibonacci sequence was first introduced in 1202 by an (you guessed it) Italian mathematician Leonardo Fibonacci. Though, as we’ll soon see…

View original post 324 more words

Our Daily Story #2: The man who cracked FLT

tomcircle's avatarMath Online Tom Circle

Follow up with the story #1 on FLT (Fermat’s Last Theorem),  it was finally cracked 358 years later in 1994 by a British mathematician Professor Andrew Wiles in Cambridge.
The proof of FLT is itself another exciting story, a 7-year lonely task on the attic top of his Cambridge house, nobody in the world knew anything about it, until the very day when Prof Wiles gave a seemingly unrelated lecture which ended with his announcement: FLT is finally proved. The whole world was shocked!

http://en.m.wikipedia.org/wiki/Wiles%27_proof_of_Fermat%27s_Last_Theorem

Part 1/5 Andrew Wiles and FLT Proof:

(Part 2 – 5 to follow from YouTube)

Speech at IMO by Andrew Wiles:

View original post

Our Daily Story #1 : The Fermat’s Last Theorem

tomcircle's avatarMath Online Tom Circle

While reading “Our Daily Bread” during my daily Bible reading time, it strikes me an idea to create a series of “Our Daily Story” for our Math studying time.
The former makes the Bible alive, connected to our daily life in the context of scriptures; the later will make Math alive, motivate the interest and curiosity of the students to the otherwise cold (and scary, boring) subject, connecting Math to their familiar world.

It is encouraged by Math educationists that a10-minute math story time before class will enthuse the students, to want to know more about the Math topic relating to the mathematician in the story.

My first story will start from The Fermat’s Last Theorem (or FLT), simply because I admire the amateur mathematicians who, for all better choices to spend their spare times, are attracted by the beauty of Math and to become great mathematician…

View original post 156 more words

Our Daily Story #3: The Math Genius Who Failed Math Exams Twice

tomcircle's avatarMath Online Tom Circle

To prove the FLT, Prof Andrews Wiles used all the math tools developed from the past centuries till today. One of the key tool is the Galois Group,  invented by a 19-year-old French boy in 19th century, Evariste Galois. His story is a tragedy – thanks to the 2 ‘incompetent’ examiners of the Ecole Polytechnique (a.k.a. “X”), the Math genius failed in the Concours (Entrance Exams) not only once, but twice in consecutive years.
Rejected by universities and the ugly French politics and academic world, Galois suffered set back one after another, finally ended his life in a ‘meaningless’ duel at 20.

He wrote down his Math findings the eve before he died – “Je n’ai pas le temps” (I have no more time) – begged his friend to send them to two foreigners (Gauss and Jacobi) for review of its importance. “Group Theory”…

View original post 24 more words

Creating Computer Games with Maths

makingpi's avatarmakingpi

Computer games – some people like them and some people hate them (usually parents).  However at Gastrells Primary School the students  make computer games.  These computer games  have a difference, the student design them to teach Maths.  The first project they undertook was the development of their own coordinate game. This was so successful that the students have volunteered to teach the whole class how to develop coordinate games.  Furthermore, the school has gained some great homegrown resources.

View original post

(Finite) Fields — A Primer

Jeremy Kun's avatarMath ∩ Programming

So far on this blog we’ve given some introductory notes on a few kinds of algebraic structures in mathematics (most notably groups and rings, but also monoids). Fields are the next natural step in the progression.

If the reader is comfortable with rings, then a field is extremely simple to describe: they’re just commutative rings with 0 and 1, where every nonzero element has a multiplicative inverse. We’ll give a list of all of the properties that go into this “simple” definition in a moment, but an even more simple way to describe a field is as a place where “arithmetic makes sense.” That is, you get operations for $latex +,-, cdot , /$ which satisfy the expected properties of addition, subtraction, multiplication, and division. So whatever the objects in your field are (and sometimes they are quite weird objects), they behave like usual numbers in a very…

View original post 2,648 more words

7. How are theorems in circles used? How are trigonometric functions embedded?

akkiara's avatarAkkiara Symonn May Sawali's

Ferris Wheel :)

In a Ferris wheel, the circle is used as the main shape of the ride and makes the ride continuous. A circle is special and useful in this situation in the aspect that all the carts are equally distant from the center point and the wheel rotates 360 degrees. The second picture shows a slide from one of the rides in Star City that when it was built, people calculated the right slope in order to give excitement to the riders but not that much for safety. The concept of slope was used then.

SUUUN SHADOW YEAHHH

Trigonometric Functions are used to “solve” or think of a solution to everyday life problems even though we don’t see them all. For example, the picture above shows a sketch that we can solve by using trigonometry. There are many other examples like:

a. Hula Hoop-concept of tangents is used. Every time it rotates one side…

View original post 42 more words

Clash of Clans Math: Mortar Damage Per Hit

Today, we will use Math to calculate the Mortar Damage (Per Hit) for the popular game Clash of Clans!

Mortar6Mortar7Mortar8

Reference: http://clashofclans.wikia.com/wiki/Mortar

The formula needed is Damage per second (DPS) = Damage / Time.

Hence, Damage = DPS x Time!

The Mortar takes 5 seconds to fire. Hence, take the DPS reading from the game, and multiply it by 5, and you will get the actual damage done by the Mortar!

For instance, Mortar Level 1 has 4 DPS. Hence, each shot does 4×5=20 damage.

The full stats are listed here:

Level Damage per Second Damage per Shot
1 4 20
2 5 25
3 6 30
4 7 35
5 8 40
6 9 45
7 11 55
8 13 65

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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! 🙂

100 Chicken and Rabbit Questions and Answers

Questions: (Answers Below)

Generated using: Chicken and Rabbit Question Generator

Q1) A farmer has 35 chickens and cows in total.
He counted 108 legs altogether.
How many chickens and how many cows are there?

Q2) A farmer has 45 ducks and horses in total.
He counted 140 legs altogether.
How many ducks and how many horses are there?

Q3) A farmer has 6 chickens and cows in total.
He counted 20 legs altogether.
How many chickens and how many cows are there?

Q4) A farmer has 24 chickens and horses in total.
He counted 70 legs altogether.
How many chickens and how many horses are there?

Q5) A farmer has 33 chickens and horses in total.
He counted 84 legs altogether.
How many chickens and how many horses are there?

Q6) A farmer has 23 ducks and rabbits in total.
He counted 86 legs altogether.
How many ducks and how many rabbits are there?

Q7) A farmer has 31 chickens and cows in total.
He counted 96 legs altogether.
How many chickens and how many cows are there?

Q8) A farmer has 26 ducks and cows in total.
He counted 98 legs altogether.
How many ducks and how many cows are there?

Q9) A farmer has 25 chickens and rabbits in total.
He counted 80 legs altogether.
How many chickens and how many rabbits are there?

Q10) A farmer has 29 ducks and horses in total.
He counted 84 legs altogether.
How many ducks and how many horses are there?

Q11) A farmer has 24 chickens and horses in total.
He counted 62 legs altogether.
How many chickens and how many horses are there?

Q12) A farmer has 28 ducks and cows in total.
He counted 76 legs altogether.
How many ducks and how many cows are there?

Q13) A farmer has 27 chickens and cows in total.
He counted 104 legs altogether.
How many chickens and how many cows are there?

Q14) A farmer has 34 chickens and cows in total.
He counted 112 legs altogether.
How many chickens and how many cows are there?

Q15) A farmer has 39 chickens and cows in total.
He counted 124 legs altogether.
How many chickens and how many cows are there?

Q16) A farmer has 35 ducks and rabbits in total.
He counted 84 legs altogether.
How many ducks and how many rabbits are there?

Q17) A farmer has 30 chickens and rabbits in total.
He counted 76 legs altogether.
How many chickens and how many rabbits are there?

Q18) A farmer has 33 chickens and rabbits in total.
He counted 96 legs altogether.
How many chickens and how many rabbits are there?

Q19) A farmer has 31 ducks and cows in total.
He counted 68 legs altogether.
How many ducks and how many cows are there?

Q20) A farmer has 30 ducks and cows in total.
He counted 106 legs altogether.
How many ducks and how many cows are there?

Q21) A farmer has 11 ducks and horses in total.
He counted 26 legs altogether.
How many ducks and how many horses are there?

Q22) A farmer has 31 chickens and cows in total.
He counted 120 legs altogether.
How many chickens and how many cows are there?

Q23) A farmer has 46 ducks and cows in total.
He counted 150 legs altogether.
How many ducks and how many cows are there?

Q24) A farmer has 21 chickens and horses in total.
He counted 66 legs altogether.
How many chickens and how many horses are there?

Q25) A farmer has 55 ducks and horses in total.
He counted 164 legs altogether.
How many ducks and how many horses are there?

Q26) A farmer has 44 ducks and rabbits in total.
He counted 120 legs altogether.
How many ducks and how many rabbits are there?

Q27) A farmer has 36 ducks and cows in total.
He counted 94 legs altogether.
How many ducks and how many cows are there?

Q28) A farmer has 20 chickens and rabbits in total.
He counted 48 legs altogether.
How many chickens and how many rabbits are there?

Q29) A farmer has 37 ducks and cows in total.
He counted 128 legs altogether.
How many ducks and how many cows are there?

Q30) A farmer has 15 ducks and rabbits in total.
He counted 34 legs altogether.
How many ducks and how many rabbits are there?

Q31) A farmer has 25 chickens and cows in total.
He counted 90 legs altogether.
How many chickens and how many cows are there?

Q32) A farmer has 12 ducks and rabbits in total.
He counted 46 legs altogether.
How many ducks and how many rabbits are there?

Q33) A farmer has 47 ducks and cows in total.
He counted 150 legs altogether.
How many ducks and how many cows are there?

Q34) A farmer has 20 ducks and cows in total.
He counted 54 legs altogether.
How many ducks and how many cows are there?

Q35) A farmer has 45 ducks and rabbits in total.
He counted 132 legs altogether.
How many ducks and how many rabbits are there?

Q36) A farmer has 18 ducks and horses in total.
He counted 48 legs altogether.
How many ducks and how many horses are there?

Q37) A farmer has 17 chickens and horses in total.
He counted 64 legs altogether.
How many chickens and how many horses are there?

Q38) A farmer has 48 ducks and rabbits in total.
He counted 154 legs altogether.
How many ducks and how many rabbits are there?

Q39) A farmer has 37 chickens and horses in total.
He counted 106 legs altogether.
How many chickens and how many horses are there?

Q40) A farmer has 23 ducks and horses in total.
He counted 46 legs altogether.
How many ducks and how many horses are there?

Q41) A farmer has 34 chickens and cows in total.
He counted 92 legs altogether.
How many chickens and how many cows are there?

Q42) A farmer has 20 chickens and rabbits in total.
He counted 58 legs altogether.
How many chickens and how many rabbits are there?

Q43) A farmer has 31 ducks and cows in total.
He counted 118 legs altogether.
How many ducks and how many cows are there?

Q44) A farmer has 26 ducks and rabbits in total.
He counted 96 legs altogether.
How many ducks and how many rabbits are there?

Q45) A farmer has 23 ducks and horses in total.
He counted 84 legs altogether.
How many ducks and how many horses are there?

Q46) A farmer has 34 chickens and horses in total.
He counted 80 legs altogether.
How many chickens and how many horses are there?

Q47) A farmer has 51 ducks and cows in total.
He counted 156 legs altogether.
How many ducks and how many cows are there?

Q48) A farmer has 18 chickens and horses in total.
He counted 50 legs altogether.
How many chickens and how many horses are there?

Q49) A farmer has 8 chickens and horses in total.
He counted 18 legs altogether.
How many chickens and how many horses are there?

Q50) A farmer has 45 ducks and cows in total.
He counted 124 legs altogether.
How many ducks and how many cows are there?

Q51) A farmer has 28 chickens and horses in total.
He counted 100 legs altogether.
How many chickens and how many horses are there?

Q52) A farmer has 21 ducks and cows in total.
He counted 66 legs altogether.
How many ducks and how many cows are there?

Q53) A farmer has 19 ducks and rabbits in total.
He counted 70 legs altogether.
How many ducks and how many rabbits are there?

Q54) A farmer has 45 ducks and cows in total.
He counted 132 legs altogether.
How many ducks and how many cows are there?

Q55) A farmer has 17 chickens and rabbits in total.
He counted 48 legs altogether.
How many chickens and how many rabbits are there?

Q56) A farmer has 28 chickens and cows in total.
He counted 86 legs altogether.
How many chickens and how many cows are there?

Q57) A farmer has 41 chickens and cows in total.
He counted 122 legs altogether.
How many chickens and how many cows are there?

Q58) A farmer has 21 ducks and rabbits in total.
He counted 68 legs altogether.
How many ducks and how many rabbits are there?

Q59) A farmer has 11 chickens and rabbits in total.
He counted 30 legs altogether.
How many chickens and how many rabbits are there?

Q60) A farmer has 29 chickens and horses in total.
He counted 116 legs altogether.
How many chickens and how many horses are there?

Q61) A farmer has 24 chickens and cows in total.
He counted 52 legs altogether.
How many chickens and how many cows are there?

Q62) A farmer has 39 chickens and rabbits in total.
He counted 130 legs altogether.
How many chickens and how many rabbits are there?

Q63) A farmer has 23 ducks and rabbits in total.
He counted 54 legs altogether.
How many ducks and how many rabbits are there?

Q64) A farmer has 30 ducks and cows in total.
He counted 104 legs altogether.
How many ducks and how many cows are there?

Q65) A farmer has 16 ducks and horses in total.
He counted 32 legs altogether.
How many ducks and how many horses are there?

Q66) A farmer has 19 chickens and rabbits in total.
He counted 50 legs altogether.
How many chickens and how many rabbits are there?

Q67) A farmer has 52 chickens and cows in total.
He counted 156 legs altogether.
How many chickens and how many cows are there?

Q68) A farmer has 33 chickens and rabbits in total.
He counted 108 legs altogether.
How many chickens and how many rabbits are there?

Q69) A farmer has 55 ducks and rabbits in total.
He counted 168 legs altogether.
How many ducks and how many rabbits are there?

Q70) A farmer has 38 chickens and horses in total.
He counted 112 legs altogether.
How many chickens and how many horses are there?

Q71) A farmer has 42 ducks and rabbits in total.
He counted 110 legs altogether.
How many ducks and how many rabbits are there?

Q72) A farmer has 26 ducks and horses in total.
He counted 60 legs altogether.
How many ducks and how many horses are there?

Q73) A farmer has 39 ducks and rabbits in total.
He counted 104 legs altogether.
How many ducks and how many rabbits are there?

Q74) A farmer has 36 chickens and rabbits in total.
He counted 86 legs altogether.
How many chickens and how many rabbits are there?

Q75) A farmer has 14 chickens and cows in total.
He counted 38 legs altogether.
How many chickens and how many cows are there?

Q76) A farmer has 37 chickens and cows in total.
He counted 128 legs altogether.
How many chickens and how many cows are there?

Q77) A farmer has 39 ducks and cows in total.
He counted 102 legs altogether.
How many ducks and how many cows are there?

Q78) A farmer has 54 ducks and cows in total.
He counted 158 legs altogether.
How many ducks and how many cows are there?

Q79) A farmer has 20 chickens and rabbits in total.
He counted 74 legs altogether.
How many chickens and how many rabbits are there?

Q80) A farmer has 47 ducks and rabbits in total.
He counted 134 legs altogether.
How many ducks and how many rabbits are there?

Q81) A farmer has 25 chickens and rabbits in total.
He counted 70 legs altogether.
How many chickens and how many rabbits are there?

Q82) A farmer has 42 ducks and horses in total.
He counted 136 legs altogether.
How many ducks and how many horses are there?

Q83) A farmer has 41 ducks and rabbits in total.
He counted 128 legs altogether.
How many ducks and how many rabbits are there?

Q84) A farmer has 10 ducks and cows in total.
He counted 20 legs altogether.
How many ducks and how many cows are there?

Q85) A farmer has 34 ducks and horses in total.
He counted 116 legs altogether.
How many ducks and how many horses are there?

Q86) A farmer has 28 chickens and cows in total.
He counted 78 legs altogether.
How many chickens and how many cows are there?

Q87) A farmer has 12 ducks and rabbits in total.
He counted 32 legs altogether.
How many ducks and how many rabbits are there?

Q88) A farmer has 26 chickens and horses in total.
He counted 82 legs altogether.
How many chickens and how many horses are there?

Q89) A farmer has 20 ducks and cows in total.
He counted 70 legs altogether.
How many ducks and how many cows are there?

Q90) A farmer has 42 ducks and cows in total.
He counted 128 legs altogether.
How many ducks and how many cows are there?

Q91) A farmer has 15 ducks and cows in total.
He counted 42 legs altogether.
How many ducks and how many cows are there?

Q92) A farmer has 46 chickens and horses in total.
He counted 132 legs altogether.
How many chickens and how many horses are there?

Q93) A farmer has 23 chickens and horses in total.
He counted 46 legs altogether.
How many chickens and how many horses are there?

Q94) A farmer has 27 ducks and cows in total.
He counted 98 legs altogether.
How many ducks and how many cows are there?

Q95) A farmer has 40 ducks and horses in total.
He counted 134 legs altogether.
How many ducks and how many horses are there?

Q96) A farmer has 35 chickens and horses in total.
He counted 122 legs altogether.
How many chickens and how many horses are there?

Q97) A farmer has 24 chickens and horses in total.
He counted 96 legs altogether.
How many chickens and how many horses are there?

Q98) A farmer has 22 ducks and rabbits in total.
He counted 80 legs altogether.
How many ducks and how many rabbits are there?

Q99) A farmer has 11 chickens and cows in total.
He counted 36 legs altogether.
How many chickens and how many cows are there?

Q100) A farmer has 26 chickens and horses in total.
He counted 60 legs altogether.
How many chickens and how many horses are there?

Answers:
Q1) chickens=16
cows=19

Q2) ducks=20
horses=25

Q3) chickens=2
cows=4

Q4) chickens=13
horses=11

Q5) chickens=24
horses=9

Q6) ducks=3
rabbits=20

Q7) chickens=14
cows=17

Q8) ducks=3
cows=23

Q9) chickens=10
rabbits=15

Q10) ducks=16
horses=13

Q11) chickens=17
horses=7

Q12) ducks=18
cows=10

Q13) chickens=2
cows=25

Q14) chickens=12
cows=22

Q15) chickens=16
cows=23

Q16) ducks=28
rabbits=7

Q17) chickens=22
rabbits=8

Q18) chickens=18
rabbits=15

Q19) ducks=28
cows=3

Q20) ducks=7
cows=23

Q21) ducks=9
horses=2

Q22) chickens=2
cows=29

Q23) ducks=17
cows=29

Q24) chickens=9
horses=12

Q25) ducks=28
horses=27

Q26) ducks=28
rabbits=16

Q27) ducks=25
cows=11

Q28) chickens=16
rabbits=4

Q29) ducks=10
cows=27

Q30) ducks=13
rabbits=2

Q31) chickens=5
cows=20

Q32) ducks=1
rabbits=11

Q33) ducks=19
cows=28

Q34) ducks=13
cows=7

Q35) ducks=24
rabbits=21

Q36) ducks=12
horses=6

Q37) chickens=2
horses=15

Q38) ducks=19
rabbits=29

Q39) chickens=21
horses=16

Q40) ducks=23
horses=0

Q41) chickens=22
cows=12

Q42) chickens=11
rabbits=9

Q43) ducks=3
cows=28

Q44) ducks=4
rabbits=22

Q45) ducks=4
horses=19

Q46) chickens=28
horses=6

Q47) ducks=24
cows=27

Q48) chickens=11
horses=7

Q49) chickens=7
horses=1

Q50) ducks=28
cows=17

Q51) chickens=6
horses=22

Q52) ducks=9
cows=12

Q53) ducks=3
rabbits=16

Q54) ducks=24
cows=21

Q55) chickens=10
rabbits=7

Q56) chickens=13
cows=15

Q57) chickens=21
cows=20

Q58) ducks=8
rabbits=13

Q59) chickens=7
rabbits=4

Q60) chickens=0
horses=29

Q61) chickens=22
cows=2

Q62) chickens=13
rabbits=26

Q63) ducks=19
rabbits=4

Q64) ducks=8
cows=22

Q65) ducks=16
horses=0

Q66) chickens=13
rabbits=6

Q67) chickens=26
cows=26

Q68) chickens=12
rabbits=21

Q69) ducks=26
rabbits=29

Q70) chickens=20
horses=18

Q71) ducks=29
rabbits=13

Q72) ducks=22
horses=4

Q73) ducks=26
rabbits=13

Q74) chickens=29
rabbits=7

Q75) chickens=9
cows=5

Q76) chickens=10
cows=27

Q77) ducks=27
cows=12

Q78) ducks=29
cows=25

Q79) chickens=3
rabbits=17

Q80) ducks=27
rabbits=20

Q81) chickens=15
rabbits=10

Q82) ducks=16
horses=26

Q83) ducks=18
rabbits=23

Q84) ducks=10
cows=0

Q85) ducks=10
horses=24

Q86) chickens=17
cows=11

Q87) ducks=8
rabbits=4

Q88) chickens=11
horses=15

Q89) ducks=5
cows=15

Q90) ducks=20
cows=22

Q91) ducks=9
cows=6

Q92) chickens=26
horses=20

Q93) chickens=23
horses=0

Q94) ducks=5
cows=22

Q95) ducks=13
horses=27

Q96) chickens=9
horses=26

Q97) chickens=0
horses=24

Q98) ducks=4
rabbits=18

Q99) chickens=4
cows=7

Q100) chickens=22
horses=4