## Matrices Notes

PDF: Matrices Notes

Includes Important Matrices Often Tested!

Do you know how to add up two numbers using Matrix Multiplication?
Read the above notes to find out how!

## Kinematics

Distance = Speed x Time

Time = Distance / Speed

Speed = Distance / Time

## Distance-time graph

Remember Formula Using Units E.g.

Units of speed = km/h

Units of gradient = km/h

## Speed-time graph

Distance travelled = Area under graph

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! 🙂

## 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?

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

## 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 $v^2$)

# 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

AJC Cut Off Points:

 FACULTY ARTS SCIENCE JAE 2013 8 10

## 100,000 views on WordPress

We have reached 100,000 views on our WordPress.com site: http://mathtuition88.com

Sincere thanks to all the viewers and supporters! We will continue to post information about Mathematics, Education and General Knowledge on this website.

# Formulae for Probability

## COE Quota: Math Formula

Applications of Math in Real Life: COE Quota

The Formula for COE Quota is:

Quote: In the formula above, the subscript denotes calendar year and the subscript denotes quota year (May to April). Initially, projected deregistrations for (calendar) year were simply taken to be equal to actual deregistrations in 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 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.

## Logic puzzle: Which octopus is telling the truth?

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?

# Trigonometry Identities

### Negative angles:

• $\sin (-x)=-\sin x$
• $\boxed{\cos (-x)=\cos x}$        (Still Positive!)
• $\tan (-x)=-\tan x$

Reason: $-x$ is in the “C” quadrant so Cosine is still positive.

### Supplementary angles:

• $\boxed{\sin (180^\circ -x)=\sin x}$        (Still positive!)
• $\cos (180^\circ -x)=-\cos x$
• $\tan (180^\circ -x)=-\tan x$

Reason: $180^\circ -x$ is in the “S” quadrant so Sine is still positive.

### Complementary angles:

• $\sin (90^\circ -x)=\cos x$
• $\cos (90^\circ -x)=\sin x$
• $\tan (90^\circ -x)=\cot x$

Reason:

• $\sin (90^\circ -x)=\cos x=a/c$
• $\cos (90^\circ -x)=\sin x=b/c$
• $\tan (90^\circ -x)=\cot x=a/b$

# 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?

## 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.

## How to Get First Class Honours

Check out this site on How to Get First Class Honours at:

http://anythingthatinterestsme.blogspot.sg/2010/05/how-to-get-first-class-honours-in.html

I agree with most of the points in the post. I actually read this post before I even graduated, and it motivated me a lot. Hope that you will find it motivational too.

Most importantly, do not be overly stressed out by your goals. Life is a marathon, not a sprint, university is just a small aspect of your entire life. Enjoy your studies while in university, and it is more useful to develop life long skills like independent learning, teamwork and time management skills.

Meanwhile, you may like to check out the following posts:

The Lesson of Grace in Teaching (Motivational Post about Learning and Teaching)

## 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.

## 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.

 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 – –

# 5 Tips on How to improve for Maths (Primary, O Level, A Level)

1. Firstly, make sure that you do sufficient practice, especially for past year papers. Sometimes, students may think that they fully understood a topic, but there may be some gaps in their knowledge, which would be overcome by sufficient practice. Check out our site on Free Exam Papers.
2. Improve accuracy and reduce careless mistakes. Some tips to reduce careless mistakes are double-checking, and write neatly to reduce transfer or reading error. Also, check out our article on reducing careless mistakes.
3. Ensure adequate understanding. Ensure that each step of the question is being understood, and not relying on “guessing” or pure luck. This will enable the student to solve all similar questions of the same type. Having a good tutor, a study group of friends, or a parent knowledgeable in mathematics helps a lot.
4. Have a positive attitude about Maths. 🙂 Liking Maths helps a lot in doing well for Maths. Treat Maths like a game or puzzle to be solved, and not as a chore. Congratulate yourself after solving a question correctly, no matter how easy or basic it is. Soon, you will be able to experience the joy of Mathematics.
5. Finally, try to have a healthy lifestyle. Reduce harmful activities like too much computer games, as these can cause addiction and affect dopamine receptors in the brain, which hamper learning. Exercise and listening to music are good activities for soothing and relaxing the brain.

## How to Remember Trigonometric Special Angles easily using Calculator

How to Remember Special Angles easily using Calculator

Step 1: Type the expression into calculator, eg. $\sin (\frac{\pi}{3})$ (in radian mode, for this case)

Step 2: You will get 0.8660254038. Square the Answer. (Ans^2)

Step 3: You will get 3/4. That means $\sin (\frac{\pi}{3})=\frac{\sqrt{3}}{2}$

## No more aircon for independent schools

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

# The Base Converter: Convert Base to any Base Program

Using this online javascript program (written by me a long time ago), we can convert a number to any base we desire.

Hope you have fun playing with this app!

For instance, let choose the number 88, and see what it is in different bases

In base 2: 1011000

Base 3: 10021

Base 4: 1120

Base 5: 323

Base 6: 224

Base 7: 154

Base 8: 130

Base 9: 107

Base 10: 88

Base 11: 80

Base 12: 74

Base 13: 6A

Base 14: 64

Base 15: 5D

Base 16: 58

Also, Learn how to convert bases manually

## 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

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.

### 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)

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.

## Singapore Tuition Agency Review: Startutor.sg

From a tutor’s point of view, my favourite tuition agency website is Startutor.sg (http://startutor.sg/)

Firstly, the website has a great design, the best I have ever seen. They even have dedicated queries regarding their design. (http://startutor.sg/design)

Secondly, they do check and verify all the tutor’s certificates. Hence, parents can be assured that the tutors do have the relevant certificates that they claim to have.

Thirdly, they do have SMS notifications for tutors, which is good since tutors may not check the website everyday.

I am listed as a tutor on Startutor.sg, however nowadays most of the students contact me through my website.

Overall, Startutor.sg is an excellent tuition agency, with good website interface, and stringent certification checking on tutors.

For other subjects besides Mathematics, request for a tutor at Startutor! Startutor is Singapore’s most popular online agency, providing tutors to your home. There are no extra costs for making a request. (Website: http://startutor.sg/request,wwcsmt)

# Clash of Clans Mathematics: Arithmetic Progression & Geometric Progression

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.

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.

## 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.

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

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.

Interesting article for chocolate lovers!

## Math Fun Facts

Check out this website by Professor Francis Su!

Math Fun Facts are ideas and puzzles that will change the way you think.

This archive is designed as a resource for enriching your math courses and nurturing your interest and talent in mathematics! Each Math Fun Fact is a math puzzle or short article that contains a cool mathematics idea.  You’ll can learn about the mathematics of things like card shuffling to poker to computer  vision to fractals to music, just to name a few.  This makes great enrichment material for gifted math students or problem-solving groups.

http://www.math.hmc.edu/funfacts/

Excerpt:

# The Lesson of Grace in Teaching

From weakness to wholeness, the struggle and the hope

Francis Edward Su MAA Haimo Teaching Award Lecture Joint Math Meetings, January 11, 2013 An audio file is available: bit.ly/W4gyD0.

“We know truth, not only by reason, but also by the heart.” —Blaise Pascal