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

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

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

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:

P(A∪B)=P(A)+P(B)-P(A∩B)
P(A|B)= $\displaystyle\frac{P(A\cap B)}{P(B)}$
P(A’)=1-P(A)

For Mutually Exclusive Events Only:

P(A∩B)=0

For Independent Events Only:

P(A∩B)=P(A) P(B)
P(A|B)=P(A)
P(B|A)=P(B)
P(A’∩B)=P(A’) P(B)
P(A∩B’)=P(A) P(B’)
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.

Technorati Blog Claim

HFHA4C8ZTVTE

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?

sin(180-x)

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?

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.

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)

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

Free exam papers 2012

Check out our post on Free exam papers 2012 at:

https://mathtuition88.com/free-exam-papers

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

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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)

O Level Probability

Check out this challenging O Level Probability question at:

https://mathtuition88.com/2013/06/28/xinmin-secondary-2010-prelim-paper-i-q24-solution/

Secondary Cut Off Point

Regarding Secondary Cut Off Point for PSLE Scores, please refer to our post at:

https://mathtuition88.com/2014/02/08/psle-cut-off-point/

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	–	–

NUS Cut Off Point

Check out our article about NUS Cut Off Point at https://mathtuition88.com/2013/11/13/a-level-marksgrade-required-to-enter-nus/

Group Tuition at Bishan

Maths Group Tuition at Bishan

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

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.
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.
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.
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.
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.”)

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。

Online Base Converter Program for all bases

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

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

The JPSAE portal can be accessed at https://www.polytechnic.edu.sg/applications/jpsae/Applicant/Login.aspx.

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.

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.

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.

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

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)

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

The JPSAE portal can be accessed at https://www.polytechnic.edu.sg/applications/jpsae/Applicant/Login.aspx.

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

Singapore Math Book – Best Seller on Amazon

Singapore Math Practice, Level 1A, Grade 2

Math Practice, Grade 3 (Singapore Math)

Math Fun Facts

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

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/

The Lesson of Grace in Teaching

Source: http://mathyawp.blogspot.sg/2013/01/the-lesson-of-grace-in-teaching.html

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

I’m honored but I’m also really humbled to be giving this talk to a room full of great teachers, because I know that each of you have a rich and unique perspective on teaching. I had to ask myself: could I really tell YOU anything significant about teaching? So I decided instead to talk about something else, that at first may appear to have nothing to do with teaching, and yet it has everything to do with teaching. I want to talk about the biggest life lesson that I have learned, and that I continue to learn over and over again. It is deep and profound. It has changed the way I relate with people. It has reshaped my academic life. And it continually renovates the way I approach my students. And perhaps it will help you frame your own thoughts about teaching. The beginning of that lesson is this:

Your accomplishments are NOT what make you a worthy human being.

It sounds easy for me to say, especially after having some measure of academic ‘success’ and winning this teaching award. But twenty years ago, I was a struggling grad student, seeking validation for my mathematical talent but flailing in my research, seeking my identity in my work but discouraged enough to quit. My advisor had even said to me:

“You don’t have what it takes to be a successful mathematician.”

It was my lowest point. Weak and weary, with my identity and my pride stripped away and my PhD nearly out of reach, I realized then that my identity and self-worth could NOT rest on whether I succeeded or failed to get my PhD. So *IF* I were to continue in mathematics, I could not do it for any acclaim that I might receive or for the trappings of what the academic world would call success. I should only do it because math is beautiful, and I feel drawn to it. In my quiet moments, with no one watching, I still found math fun to think about. So I was convinced it was my calling, despite the hurtful thing my advisor had said. So did I quit? No. I just changed advisors. This time, I chose differently. Persi Diaconis was an inspiring teacher. More than that, he had shown me a great kindness a couple of years before. The semester I took a class from him, my mother died and I needed an extension on my work. I’ll never forget his response: “I’m really sorry about your mother. Let me take you to coffee.” I remember thinking: “I’m just some random student and he’s taking me to coffee?” But I really needed that talk. We pondered life and its burdens, and he shared some of his own journey. For me, in a challenging academic environment, with enormous family struggles, to connect with my professor on a deeper level was a great comfort. Yes, Persi was an inspiring teacher, but this simple act of kindness—of authentic humanness—gave me a greater capacity and motivation to learn from him, because we had entered into authentic community with each other, as teacher and student, who were real people to each other.

Continue reading this inspirational article at: http://mathyawp.blogspot.sg/2013/01/the-lesson-of-grace-in-teaching.html

Distance-time graph

Speed-time graph

Questions: (Answers Below)

Joint Admissions Exercise 2014

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Formulae for Probability

Works for All Cases:

P(A∪B)=P(A)+P(B)-P(A∩B)

P(A|B)=

P(A’)=1-P(A)

For Mutually Exclusive Events Only:

P(A∩B)=0

For Independent Events Only:

P(A∩B)=P(A) P(B)

P(A|B)=P(A)

P(B|A)=P(B)

P(A’∩B)=P(A’) P(B)

P(A∩B’)=P(A) P(B’)

P(A’∩B’)=P(A’) P(B’)

Trigonometry Identities

Negative angles:

Supplementary angles:

Complementary angles:

Which Secondary school is the best in Singapore

Which JC is the best in Singapore?

JC Subject Combination

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PSLE Cut Off Point

NUS Cut Off Point

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

科学根据

含义

The Base Converter: Convert Base to any Base Program

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

Where to buy:

Clash of Clans Mathematics: Arithmetic Progression & Geometric Progression

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

The Lesson of Grace in Teaching

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