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2010-02-02T23:32:00.004+08:00

Multiples, Common Multiples and Lowest Common Multiples

Resourses:

http://www.mathgoodies.com/Lessons/vol3/lcm.html

http://www.mathsteacher.com.au/year8/ch01_arithmetic/03_mult/mult.htm

2010-02-02T23:07:00.002+08:00

Multiples
The multiples of a number are its products with the natural numbers 1, 2, 3, 4, 5, ....
Example 1
1 x 8 = 8
2 x 8 =16
3 x 8 =24
4 x 8 =32
5 x 8 =40
So, the multiples of 8 are 8, 16, 24, 32, 40 and so on.
Note:
The multiples of a number are obtained by multiplying the number by each of the natural numbers.

Example 2
Write down the first five multiples of 9.
Solution:
1 x 9 = 9
2 x 9 =18
3 x 9 =27
4 x 9 =36
5 x 9 =45
The multiples of 9 are obtained by multiplying 9 with the natural numbers 1, 2, 3, 4, 5 …
So, the first five multiples of 9 are 9, 18, 27, 36 and 45.

Common Multiples
Common multiples are multiples that are common to two or more numbers.

Example 3
Multiples of 2 are 2, 4, 6, 8, 10, 12, 14, 16, 18, …
Multiples of 3 are 3, 6, 9, 12, 15, 18, …
So, common multiples of 2 and 3 are 6, 12, 18, …
Example 4
Find the common multiples of 3 and 4.
Solution:
Multiples of 3 are 3, 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, …Multiples of 4 are 4, 8, 12, 16, 20, 24, 28, 32, 36, …
So, the common multiples of 3 and 4 are 12, 24, 36, …

Lowest Common Multiple
The lowest common multiple (LCM) of two or more numbers is the smallest common multiple.
Example 5
Multiples of 8 are 8, 16, 24, 32, …
Multiples of 6 are 6, 12, 18, 24, …
The LCM of 6 and 8 is 24
.
Example 6
Find the lowest common multiple of 2 and 5.
List the multiples of 5 and stop when you find a multiple of 2.
Multiples of 5 are 5, 10, …
Multiples of 2 are 2, 4, 6, 8, 10, …
The LCM of 2 and 5 is 10

2010-01-29T12:34:00.003+08:00

NUMBER PATTERNS AND SEQUENCES
Real-Life Examples
Try to discover geometric patterns in nature (shells, flowers, animals, pine cones, rocks); in architecture (archways, doorways, stairways, floor tiles, windows); in clothing and home fashion (designer labels, t-shirt logos, neckties, quilts, wallpaper, and floor tile); and in technology (computer-generated graphics and logos).

Create, Extend and Explain Number Patterns
Have fun with your family by making up number patterns. Encourage other family members to discover each pattern, predict the next three numbers in the pattern, and explain how the pattern works.
5, 10, 15, 20, 25, 30 … (35, 40, 45)
Add 5 to the previous number.
Count by five’s.

2, 4, 6, 8, 10, 12 … (14, 16, 18)
Add 2 to the previous number.
List the even numbers.
Count by 2.

1, 3, 5, 7, 9, 11 … (13, 15, 17)
Add 2 to the previous number.
List the odd numbers.

1, 2, 4, 8, 16 … (32, 64, 128)
Double the previous number.
Multiply the previous number by 2.
Add 1 to the first number, then 2 to the next number, then 4, then 8, etc.

1, 4, 9, 16, 25, 36, 49 … (64, 81, 100)
Multiply each number by itself (1 x 1 = 1, 2 x 2 = 4, 3 x 3 = 9, 4 x 4 = 16).
Find the perfect squares of the counting numbers.
Add 3 to the first number, then 5 to the next number, then 7, then 9, then 11, etc.

2010-01-15T23:34:00.003+08:00

Write Words on Calculators?

This is a fun activity to do when you are bored in your Math class!

Calculator Words. Type 200 Words Using A Simple Calculator - These bloopers are hilarious
CALCULATOR WORDS
Use a calculator to find these words by doing the following calculations and then turning your calculator upside down.
a. 3357 -2223 to get a place you wouldn’t go to. (………………..…….)
b. 300 000 + 18 830 to get a girl’s name. (…………………..….)
c. 85 423 + 294 496 to get something you might do if you’re happy or embarrassed about something. (…………………..….)
d. 6411 − 897 to get a noise you wouldn’t want to hear while bushwalking. (………..…………….)
e. 63 552 ÷ 64 to get something you eat. (…………………..….)
f. 203 × 15 to get something you wear. (……………..……….)
g. 52 043 ÷ 71 to get an animal. (………………..…….)
h. 52 360 ÷ 17 to get a musical instrument. (…..………………….)
i. 4417 x 8 to get some animals. (………………..…….)
j. 923 x 5 to get something you need your breath to do. (……..……………….)
k. 23 x 19 + 7301 to get something you often hear at school. (……..……………….)
l. 888 888 ÷ 2 – 65 638 to get something you shouldn’t do when you eat. (……..……..………..)
m. 4536 ÷ 81 + 261 to get something you should never do. (……………….……..)
n. 237 023 x 2 ÷ 421 x 2 + 4853 to get something you find in the garden. (……….……………..)
o. 6716 ÷ 73 x 125 136 ÷ 16 – 642 187 to get something you may find on the beach. (………………….…..)
p. 7 + 700 + 7000 + 10 000 + 300 000 + 5 000 000 to get something that you shouldn’t eat too much of. (……..……………....)

2010-01-14T23:08:00.003+08:00

The following videos show more examples of the application of PEMDAS

2010-01-14T22:59:00.002+08:00

COMBINED OPERATIONS
If the expression consists of parenthesis, exponents, +, –, × and ÷, then the operations MUST be performed in the following order.
Always work on the calculations within parenthesis first if any.
Next, calculate the exponents.
Then, carry out multiplication or division, working from left to right.
Lastly, do addition or subtraction, working from left to right.

The order to perform combined operations is called the PEMDAS rule.
Note: A common mnemonic for PEMDAS is Please Excuse My Dear Aunt Sally.
Example:
Evaluate 10 ÷ 2 + 12 ÷ 2 × 3
Using the PEMDAS rule, we need to evaluate the division and multiplication before subtraction and addition. It is recommended that you put in parenthesis to remind yourself the order of operation.
Solution:
10 ÷ 2 + 12 ÷ 2 × 3
= ( 10 ÷ 2) + (12 ÷ 2 × 3)
= 5 + 18
= 23

2010-01-03T21:04:00.004+08:00

HAPPY NEW YEAR.

WELCOME BACK TO SCHOOL.

........................................................................

WHOLE NUMBERS
Divisibility Tests

Divisibility by 2
A whole number is divisible by 2 if the digit in its units position is even, (either 0, 2, 4, 6, or 8).
Examples:
The number 84 is divisible by 2 since the digit in the units position is 4, which is even.The number 333336 is divisible by 2 since the digit in the units position is 6, which is even.The number 1297000 is divisible by 2 since the digit in the units position is 0, which is even.

Divisibility by 3
A whole number is divisible by 3 if the sum of all its digits is divisible by 3.
Examples:
The number 177 is divisible by three, since the sum of its digits is 15, which is divisible by 3.The number 8882151 is divisible by three, since the sum of its digits is 33, which is divisible by 3.The number 162345 is divisible by three, since the sum of its digits is 21, which is divisible by 3.
If a number is not divisible by 3, the remainder when it is divided by 3 is the same as the remainder when the sum of its digits is divided by 3.
Examples:
The number 3248 is not divisible by 3, since the sum of its digits is 17, which is not divisible by 3. When 3248 is divided by 3, the remainder is 2, since when 17, the sum of its digits, is divided by three, the remainder is 2.
The number 172345 is not divisible by 3, since the sum of its digits is 22, which is not divisible by 3. When 172345 is divided by 3, the remainder is 1, since when 22, the sum of its digits, is divided by three, the remainder is 1.

Divisibility by 4
A whole number is divisible by 4 if the number formed by the last two digits is divisible by 4.
Examples:
The number 3124 is divisible by 4 since the number formed by its last two digits, 24, is divisible by 4.The number 1333336 is divisible by 4 since the number formed by its last two digits, 36, is divisible by 4.The number 1297000 is divisible by 4 since the number formed by its last two digits, 0, is divisible by 4.
If a number is not divisible by 4, the remainder when the number is divided by 4 is the same as the remainder when the last two digits are divided by 4.
Example:
The number 172345 is not divisible by 4, since the number formed by its last two digits, 45, is not divisible by 4. When 172345 is divided by 4, the remainder is 1, since when 45 is divided by 4, the remainder is 1.

Divisibility by 5
A whole number is divisible by 5 if the digit in its units position is 0 or 5.
Examples:
The number 95 is divisible by 5 since the last digit is 5.The number 343370 is divisible by 5 since the last digit is 0. The number 129700195 is divisible by 5 since the last digit is 5.
If a number is not divisible by 5, the remainder when it is divided by 5 is the same as the remainder when the last digit is divided by 5.
Example:
The number 145632 is not divisible by 5, since the last digit is 2. When 145632 is divided by 5, the remainder is 2, since 2 divided by 5 is 0 with a remainder of 2.
The number 7332899 is not divisible by 5, since the last digit is 9. When 7332899 is divided by 5, the remainder is 4, since 9 divided by 5 is 1 with a remainder of 4.

Divisibility by 6
A number is divisible by 6 if it is divisible by 2 and divisible by 3. We can use each of the divisibility tests to check if a number is divisible by 6: its units digit is even and the sum of its digits is divisible by 3.
Examples:
The number 714558 is divisible by 6, since its units digit is even, and the sum of its digits is 30, which is divisible by 3. The number 297663 is not divisible by 6, since its units digit is not even.The number 367942 is not divisible by 6, since it is not divisible by 3. The sum of its digits is 31, which is not divisible by 3, so the number 367942 is not divisible by 3.

Divisibility by 8
A whole number is divisible by 8 if the number formed by the last three digits is divisible by 8.
Examples:
The number 88863024 is divisible by 8 since the number formed by its last three digits, 24, is divisible by 8.The number 17723000 is divisible by 8 since the number formed by its last three digits, 0, is divisible by 8.The number 339122483984 is divisible by 8 since the number formed by its last three digits, 984, is divisible by 8.
If a number is not divisible by 8, the remainder when the number is divided by 8 is the same as the remainder when the last three digits are divided by 8.
Example:
The number 172045 is not divisible by 8, since the number formed by its last three digits, 45, is not divisible by 8. When 172345 is divided by 8, the remainder is 5, since when 45 is divided by 8, the remainder is 5.

Divisibility by 9
A whole number is divisible by 9 if the sum of all its digits is divisible by 9.
Examples:
The number 1737 is divisible by nine, since the sum of its digits is 18, which is divisible by 9.The number 8882451 is divisible by nine, since the sum of its digits is 36, which is divisible by 9.The number 762345 is divisible by nine, since the sum of its digits is 27, which is divisible by 9.
If a number is not divisible by 9, the remainder when it is divided by 9 is the same as the remainder when the sum of its digits is divided by 9.
Examples:
The number 3248 is not divisible by 9, since the sum of its digits is 17, which is not divisible by 9. When 3248 is divided by 9, the remainder is 8, since when 17, the sum of its digits, is divided by 9, the remainder is 8.
The number 172345 is not divisible by 9, since the sum of its digits is 22, which is not divisible by 9. When 172345 is divided by 9, the remainder is 4, since when 22, the sum of its digits, is divided by 9, the remainder is 4.

Divisibility by 10
A whole number is divisible by 10 if the digit in its units position is 0.
Examples:
The number 1229570 is divisible by 10 since the last digit is 0.The number 676767000 is divisible by 10 since the last digit is 0.The number 129700190 is divisible by 10 since the last digit is 0.
If a number is not divisible by 10, the remainder when it is divided by 10 is the same as the units digit.
Examples:
The number 145632 is not divisible by 10, since the last digit is 2. When 145632 is divided by 10, the remainder is 2, since the units digit is 2.The number 7332899 is not divisible by 10, since the last digit is 9. When 7332899 is divided by 10, the remainder is 4, since the units digit is 9.

Divisibility by 11
Starting with the units digit, add every other digit and remember this number. Form a new number by adding the digits that remain. If the difference between these two numbers is divisible by 11, then the original number is divisible by 11.
Examples:
Is the number 824472 divisible by 11? Starting with the units digit, add every other number:2 + 4 + 2 = 8. Then add the remaining numbers: 7 + 4 + 8 = 19. Since the difference between these two sums is 11, which is divisible by 11, 824472 is divisible by 11.
Is the number 49137 divisible by 11? Starting with the units digit, add every other number:7 + 1 + 4 = 12. Then add the remaining numbers: 3 + 9 = 12. Since the difference between these two sums is 0, which is divisible by 11, 49137 is divisible by 11.
Is the number 16370706 divisible by 11? Starting with the units digit, add every other number:6 + 7 + 7 + 6 = 26. Then add the remaining numbers: 0 + 0 + 3 + 1=4. Since the difference between these two sums is 22, which is divisible by 11, 16370706 is divisible by 11.

Divisibility by 12
A number is divisible by 12 if it is divisible by 4 and divisible by 3. We can use each of the divisibility tests to check if a number is divisible by 12: its last two digits are divisible by 4 and the sum of its digits is divisible by 3.
Examples:
The number 724560 is divisible by 12, since the number formed by its last two digits, 60, is divisible by 4, and the sum of its digits is 30, which is divisible by 3.The number 36297414 is not divisible by 12, since the number formed by its last two digits, 14, is not divisible by 4.The number 367744 is not divisible by 12, since it is not divisible by 3. The sum of its digits is 29, which is not divisible by 3, so the number 367942 is not divisible by 3.

Divisibility by 15
A number is divisible by 15 if it is divisible by 3 and divisible by 5. We can use each of the divisibility tests to check if a number is divisible by 15: its units digit is 0 or 5, and the sum of its digits is divisible by 3.
Example:
The number 7145580 is divisible by 15, since its units digit is even, and the sum of its digits is 30, which is divisible by 3.

Divisibility by 16
A whole number is divisible by 16 if the number formed by the last four digits is divisible by 16.
Examples:
The number 898630032 is divisible by 16 since the number formed by its last four digits, 32, is divisible by 16.The number 1772300000 is divisible by 16 since the number formed by its last four digits, 0, is divisible by 16.The number 339122481296 is divisible by 16 since the number formed by its last four digits, 1296, is divisible by 16.
If a number is not divisible by 16, the remainder when the number is divided by 16 is the same as the remainder when the last four digits are divided by 16.
Example:
The number 172411045 is not divisible by 16, since the number formed by its last four digits, 1045, is not divisible by 16. When 172411045 is divided by 16, the remainder is 5, since when 1045 is divided by 16, the remainder is 5.

Divisibility by 18
A number is divisible by 18 if it is divisible by 2 and divisible by 9. We can use each of the divisibility tests to check if a number is divisible by 18: its units digit is even and the sum of its digits is divisible by 9.
Examples:
The number 7145586 is divisible by 18, since its units digit is even, and the sum of its digits is 36, which is divisible by 9. The number 2976633 is not divisible by 18, since its units digit is not even.The number 367942 is not divisible by 18, since it is not divisible by 9. The sum of its digits is 31, which is not divisible by 9, so the number 367942 is not divisible by 9.

Divisibility by 20
A number is divisible by 20 if its units digit is 0, and its tens digit is even. In other words, the last two digits form one of the numbers 0, 20, 40, 60, or 80.
Examples:
The number 3351002760 is divisible by 20, since the number formed by its last two digits is 60.The number 802199730000 is divisible by 20, since the number formed by its last two digits is 0.

Divisibility by 22
A number is divisible by 22 if it is divisible by the numbers 2 and 11. We can use each of the divisibility tests to check if a number is divisible by 22: its units digit is even, and the difference between the sums of every other digit is divisible by 11.
Example:
Is the number 117524 divisible by 22? The units digit is even, so it is divisible by 2. The two sums of every other digit are 4 + 5 + 1 = 10 and 2 + 7 + 1 = 10, which have a difference of 0. Since 0 is divisible by 11, 117524 is divisible by 11. Thus, 117524 is divisible by 22, since it is divisible by both 2 and 11.

Divisibility by 25
A number is divisible by 25 if the number formed by the last two digits is any of 0, 25, 50, or 75 (the number formed by its last two digits is divisible by 25).
Examples:
The number 73224050 is divisible by 25, since its last two digits form the number 50.The number 1008922200 is divisible by 25, since its last two digits form the number 0.

2009-11-17T07:30:00.001+08:00

Who Owns The fish?
Albert Einstein [allegedly] wrote this riddle early on in his career. He said that 98% of the world's population would not be able to solve it (there are no tricks, just pure logic). The question is: Who owns the fish? Here's the riddle:
In a street, there are five houses, painted five different colors. In each house live a person of different nationality. The five homeowners each drink a different kind of beverage, smoke a different brand of cigarette and keep a different pet.
1. The Brit [Englishman] lives in the red house.
2. The Swede has a dog.
3. The Dane drinks tea.
4. The green house is on the left of the white house.
5. The owner of the green house drinks coffee.
6. The person who smokes Pall Mall has birds.
7. In the yellow house, they smoke Dunhill.
8. The man living in the middle house drinks milk.
9. The Norwegian lives in the first house.
10. The man who smokes Blend lives next to the house with cats.
11. The horseman lives next to the man who smokes Dunhill.
12. The man who smokes Blue Master drinks beer.
13. The German smokes Prince.
14. The Norwegian lives next door to the blue house.
15. The man who smokes Blend has a neighbor who drinks water.

2009-11-01T07:51:00.001+08:00

AFTER END OF YEAR EXAM

2009-10-24T15:10:00.004+08:00

Online Crossword Puzzles

Please visit:
http://www.eduplace.com/kids/hmsc/content/crossword/

Contents:

Continuity of Life

Classifying Organisms

Cell Structure and Function

Reproduction and Heredity

Change Over Time

The Changing Environment

Cycles in the Biosphere

Earth’s Ecosystems

Populations

The Dynamic Earth

The Rock Cycle The Dynamic Earth

Earth’s Energy Resources

Earth in the Universe

Global Weather Systems

Earth, Moon, and Sun

The Solar System and Beyond

Matter and Its Properties

Composition of Matter

Physical and Chemical Changes

Energy, Forces, and Motion

Energy Light and Its Properties

Electricity and Magnetism Motion, Gravity, and Work

2009-10-24T14:46:00.004+08:00

Using Games in Education
Games provide an excellent environment to explore ideas of computational thinking. The fact that many games are available both in a non-computerized form and in a computerized form helps to create this excellent learning environment. A modern education prepares students to be productive and responsible adult citizens in a world in which mind/brain and computer working
together is a common approach to solving problems and accomplishing tasks.

Puzzles
A puzzle is a type of game. To better under the purpose, think about some popular puzzles such as crossword puzzles, jigsaw puzzles, and logic puzzles (often called brain teasers). In every case, the puzzle-solver’s goal is to solve a particular mentally challenging problem or accomplish a particular mentally challenging task.

Many people are hooked on certain types of puzzles. For example, some people routinely start the day by spending time on the crossword puzzle in their morning newspaper. In some sense, they have a type of addiction to crossword puzzles. The fun is in meeting the challenge of the puzzle—making some or a lot of progress in completing the puzzle.

Crossword puzzles draw upon one’s general knowledge, recall of words defined or suggested by short definitions or pieces of information, and spelling ability. Through study and practice, a person learns some useful strategies and can make considerable gains in crossword puzzlesolving expertise. Doing a crossword puzzle is like doing a certain type of brain exercise. In recent years, research has provided evidence that such brain exercises help stave of the dementia and Alzheimer’s disease that are so common in old people.

From an educational point of view, it is clear that solving crossword puzzles helps to maintain and improve one’s vocabulary, spelling skills, and knowledge of many miscellaneous tidbits of information. Solving crossword puzzles tends to contribute to one’s self esteem. For many people, their expertise in solving crossword puzzles plays a role in their social interaction with other people.

Want to read more about Using Game In Education, visit:
http://darkwing.uoregon.edu/~moursund/Books/Games/Games.pdf

2009-09-09T02:41:00.004+08:00

Why 09/09/09 Is So Special?

Numerologists aren't the only ones excited about Wednesday's date.

Not only does the date look good in marketing promotions, but it also represents the last set of repeating, single-digit dates that we'll see for almost a century (until January 1, 2101), or a millennium (mark your calendars for January 1, 3001), depending on how you want to count it.
Though technically there's nothing special about the symmetrical date, some concerned with the history and meaning of numbers ascribe powerful significance to 09/09/09. For cultures in which the number nine is lucky, Sept. 9 is anticipated - while others might see the date as an ominous warning.

Math magic

Modern numerologists - who operate outside the realm of real science - believe that mystical significance or vibrations can be assigned to each numeral one through nine, and different combinations of the digits produce tangible results in life depending on their application.
As the final numeral, the number nine holds special rank. It is associated with forgiveness, compassion and success on the positive side as well as arrogance and self-righteousness on the negative, according to numerologists.

Though usually discredited as bogus, numerologists do have a famous predecessor to look to. Pythagoras, the Greek mathematician and father of the famous theorem, is also credited with popularizing numerology in ancient times.

"Pythagoras most of all seems to have honored and advanced the study concerned with numbers, having taken it away from the use of merchants and likening all things to numbers," wrote Aristoxenus, an ancient Greek historian, in the 4th century B.C.As part of his obsession with numbers both mathematically and divine, and like many mathematicians before and since, Pythagoras noted that nine in particular had many unique properties. Any grade-schooler could tell you, for example, that the sum of the two-digits resulting from nine multiplied by any other single-digit number will equal nine. So 9x3=27, and 2+7=9.

Multiply nine by any two, three or four-digit number and the sums of those will also break down to nine. For example: 9x62 = 558; 5+5+8=18; 1+8=9.
Sept. 9 also happens to be the 252nd day of the year (2 + 5 +2)...

Loving 9

Both China and Japan have strong feelings about the number nine. Those feelings just happen to be on opposite ends of the spectrum. The Chinese pulled out all the stops to celebrate their lucky number eight during last year's Summer Olympics, ringing the games in at 8 p.m. on 08/08/08. What many might not realize is that nine comes in second on their list of auspicious digits and is associated with long life, due to how similar its pronunciation is to the local word for long-lasting (eight sounds like wealth).

Historically, ancient Chinese emperors associated themselves closely with the number nine, which appeared prominently in architecture and royal dress, often in the form of nine fearsome dragons. The imperial dynasties were so convinced of the power of the number nine that the palace complex at Beijing's Forbidden City is rumored to have been built with 9,999 rooms.

Japanese emperors would have never worn a robe with nine dragons, however.
In Japanese, the word for nine is a homophone for the word for suffering, so the number is considered highly unlucky - second only to four, which sounds like death.

Many Japanese will go so far as to avoid room numbers including nine at hotels or hospitals, if the building planners haven't already eliminated them altogether.

Original Story: Why 09/09/09 Is So Special LiveScience.com

2009-08-29T06:05:00.005+08:00

Menjelang Sambutan Ulangtahun Kemerdekaan

2009-08-28T00:52:00.002+08:00

Effective Study Skills
Students often fail to secure good grades despite studying for hours. This is because they have never studied effectively. Unless you know how to make your study hours effective, you cannot get the expected results. Here we will give you some glimpses of effective study skills.

A study is called effective if you can remember and recall the major segments of the syllabus that you have read. Do not try to cram chapters that you fail to understand. You will never be able to remember them. The easiest thing to do is to seek the assistance of your classmates or the teachers to understand the confusing portions.
You have to decide what is most important to you. Make your schedule to address those important needs. You should never compromise with your priorities. Never try to finish too many things at a time. Study all the subjects on a regular basis while allotting some time for revisions. Keep yourself motivated. It is better to know the theme of the chapter that you are planning to study. Reading it line by line will then help you understand it better.
Effective study skills also stress on reading methods. You will see that there are some words that have fonts in bold or italics; you should pay special attention to these. You can also try to find whether the current text refers to any other works of the author that you have read earlier.
Effective study skills include listening to the explanations given by teachers. You should read and understand the notes that you have taken in the classroom. Following these aforesaid effective study skills will save you disappointments and help you get the desired results.

2009-08-09T11:13:00.015+08:00

Solid Geometry

Solid geometry is concerned with three-dimensional shapes. Some examples of three-dimensional shapes are cubes, rectangular solids, prisms, cylinders, spheres, cones and pyramids.

Cubes
A cube is a three-dimensional figure with six matching square sides.

The figure above shows a cube.

The dotted lines indicate edges hidden from your view.

If s is the length of one of its sides,

the Volume of the cube = s x s x s.

Since the cube has six square-shape sides,

the Surface area of a cube = 6 x s x s

Cuboid

In a cuboid, the length, width and height may be of different lengths.

The volume of the above cuboid would be the product of the length, width and height that is
Volume of rectangular solid = lwh
Surface area of rectangular solid = 2(lw + wh + lh)

Prisms
A prism is a solid that has two congruent parallel bases that are polygons. The polygons form the bases of the prism and the length of the edge joining the two bases is called the height.

A rectangular solid is a prism with a rectangle-shaped base.
The volume of a prism is given by the product of the area of its base and its height.

Cylinders
A cylinder is a solid with two congruent circles joined by a curved surface.
In the above figure, the radius of the circular base is r and the height is h.

The volume of the cylinder is the area of the base × height.

Spheres
A sphere is a solid with all its points the same distance from the center.

Cones

A circular cone has a circular base, which is connected by a curved surface to its vertex. A cone is called a right circular cone, if the line from the vertex of the cone to the center of its base is perpendicular to the base.

Pyramids
A pyramid is a solid with a polygon base and connected by triangular faces to its vertex. A pyramid is a regular pyramid if its base is a regular polygon and the triangular faces are all congruent isosceles triangles.

2009-08-05T11:03:00.007+08:00

Symmetry / Reflection

A plane figure is symmetrical about a line if it is divided into two identical (coincident) parts by that line. The line is called its line (or axis) of symmetry.
A plane figure is symmetrical about a point if every line segment joining two points of the figure and passing through the point is bisected at that point. The point is called its point (or center) of symmetry.
A plane figure has a rotational symmetry if on rotation through some angle ( 180°) about a point it looks the same as it did in its starting position.
If A° ( 180°) is the smallest angle through which a figure can be rotated and still looks the same, then it has a rotational symmetry of order 360/A.
The reflection (or image) of a point P in a line AB is a point P' such that AB is the perpendicular bisector of the line segment PP'.
To find the reflection (or image) of a point P in a line ABFrom P, draw PM perpendicular to AB and produce PM to P' such that MP'= MP, then P' is the reflection (or image) of P in the line AB.
The reflection of the point P (x, y) in the x-axis is the point P'(x, -y).
The reflection of the point P (x, y) in the y-axis is the point P'(-x, y).
If a point P (x, y) is rotated through 180° (clockwise or anti-clockwise) about the origin to the point P', then co-ordinates of P' are (-x,-y).
If a point P (x, y) is rotated through 90° clockwise about the origin to the point P', then co-ordinates of P' are (y,-x).
If a point P (x, y) is rotated through 90° anti-clockwise about the origin to the point P', then co-ordinates of P' are (-y,x).

2009-07-29T08:03:00.000+08:00

RIDDLE

2009-07-29T07:33:00.000+08:00

2009-07-29T07:27:00.001+08:00

2009-07-29T07:23:00.002+08:00

Brain Teaser

2009-07-29T06:46:00.006+08:00

CIRCLES

A circle is the set of all those points, say P, in a plane, each of which is at a constant distance from a fixed point in that plane.
The fixed point is called the center and the constant distance is called the radius.
All radii of a circle are equal.

A line segment joining any two points of a circle is called a chord of the circle.
A chord of a circle passing through its center is called a diameter of the circle

Length of diameter = 2 × radius

Exercise.
1. Fill in the blanks with correct word(s) to make the statement true:

(i) Radius of a circle is one-half of its.....

(ii) A radius of a circle is a line segment with one end point at..... and the other end on.....

(iii) A chord of a circle is a line segment with its end points....

(iv) A diameter of a circle is a chord that..... the center of the circle.

(v) All radii of a circle are.....

2. State which of the following statements are true and which are false:

(i) A line segment with its end-points lying on a circle is called a diameter of the circle.

(ii) Diameter is the longest chord of the circle.

(iii) The end-points of a diameter of a circle divide the circle into two parts; each part is called a semi-circle.

(iv) A diameter of a circle divides the circular region into two parts; each part is called a semi-circular region.

(v) The diameters of a circle are concurrent. The center of the circle is the point common to all diameters.

(vi) Every circle has unique center and it lies inside the circle.

(vii) Every circle has unique diameter.

2009-07-07T09:56:00.002+08:00

Maths Challenge 2

7th July- 17th July

Each letter stands for a digit from 0 to 9. No two digits have the same letter code and each letter corresponds to a distinct digit. Discover the code so that the problems become true.

1. T H R E E + T H R E E + F O U R = E L E V E N

2. A B C D E x 4 = E D C B A

3. WRONG + WRONG = R I G H T

2009-07-07T09:23:00.003+08:00

Maths Challenge 1

Answers:

2. 58 years

3. 179

2009-07-03T22:42:00.010+08:00

Maths Jokes

Teacher: What is 2k + k?
Student: 3000!
____________________________________________________

Teacher: "Who can tell me what 7 times 6 is?"
Student: "It's 42!"
Teacher: "Very good! - And who can tell me what 6 times 7 is?"
Same student: "It's 24!"

-------------------------------------------------------------
What is "pi"?

Mathematician: Pi is the ratio of the circumference of a circle to its diameter.

Engineer: Pi is about 22/7.

Physicist: Pi is 3.14159 plus or minus 0.000005

Computer Programmer: Pi is 3.141592653589 in double precision.

Nutritionist: You one track math-minded fellows, Pie is a healthy and delicious dessert!

2009-06-30T21:15:00.009+08:00

Preparation For Ujian Cermin Diri 2

Loci In Two Dimension
EXPRESS NOTES

1. The locus of a point is the path traced out by the moving point under given geometrical condition (or conditions). Alternatively, the locus is the set of all those points which satisfy the given geometrical condition (or conditions).

2. TYPES OF LOCUS
The locus of a point, which is equidistant from two fixed points, is the perpendicular bisector of the straight line joining the two fixed points.
The locus of a point, which is equidistant from two intersecting straight lines, consists of a pair of straight lines which bisect the angles between the two given lines.

EXERCISE

1. Draw and describe the locus in each of the following cases:

(i) The locus of points at a distance 2 cm from a fixed line.

(ii) The locus of points (in a plane) at a constant distance 2 cm from a fixed point in the plane.

(iii) The locus of points (in space) at a constant distance 2 cm from a fixed point.

(iv) The locus of centers of all circles passing through two fixed points.

(v) The locus of a point in the rhombus ABCD which is equidistant from the sides AB and AD.

(vi) The locus of a point in the rhombus which is equidistant from the points A and C.

(vii) The locus of center of a circle of varying radius and touching two arms of ABC.

(viii) The locus of center of a circle of varying radius and touching a fixed circle, center O, at a fixed point A on it.

(ix) The locus of center of a circle of radius 2 cm and touching a fixed circle of radius 3 cm with center O.

2. A, B and C are three collinear points.

(i) Construct the locus of point equidistant from A and B.

(ii) Construct the locus of point equidistant from B and C.

(iii) Is it possible to locate a point equidistant from A, B and C.

3. Take PQ = 6 cm. Construct

(i) the locus of points equidistant from P and Q.

(ii) the locus of points 5 cm from P.Mark the two points which lie on both loci and measure the distance between them.

4. In a triangle ABC, the right bisectors of AB and BC meet at P.

(i) Assign the special name to the point P.

(ii) Prove that PA = PB = PC.

(iii) If ABC = 90°, find the exact location of the point P with respect to the side AC.

5. Construct a triangle PQR with PQ = 5 cm, QR = 4 cm and RP = 3·6 cm. Find by construction a point P which is equidistant from the three vertices P, Q and R.

6. Construct a triangle ABC in which BC = 3·8 cm, CA = 4 cm and AB = 5·1 cm. Find by construction a point P which is equidistant from BC and AB, and also equidistant from B and C.

7. Construct a triangle ABC, in which AC = BC = 5 cm and AB = 6 cm. Locate the points equidistant from AB, AC and at a distance 2 cm from BC. Measure the distance between the two points obtained.

8. Construct a triangle ABC, in which AC = BC = 5 cm and AB = 6 cm. Locate the points equidistant from B, C and at a distance 2 cm from A. Measure the distance between the two points obtained.

9. Construct ABC = 75°. Mark a point P equidistant from AB and BC such that its distance from another line DE is 2·3 cm.

10. Draw two intersecting straight lines to include an angle of 135°. Also locate points which are equidistant from these lines and also 1·8 cm away from their point of intersection. How many such points exist?

11. AB and CD are two intersecting st. lines. Locate points which are at distances 2·5 cm and 1·8 cm from AB and CD respectively. How many such points are there?

12. Without using set square or protractor, construct the quadrilateral ABCD in which BAD = 45°, AD = AB = 6 cm, BC = 3·6 cm and CD = 5 cm.

(i) Measure BCD.

(ii) Locate the point P on BD which is equidistant from BC and CD.

13. Without using set square or protractor, construct rhombus ABCD with sides of length 4 cm and diagonal AC of length 5 cm. Measure ABC. Find the point P on AD such that PB = PC. Measure the length AP.

14. ABCD is a rhombus with side 4 cm and ABC = 120°.

Construct the locus of points inside the rhombus

(i) equidistant from A and C.

(ii) equidistant from B and D.

(iii) equidistant from A and B.

15. Draw a line segment AB of length 6 cm, M is mid point of AB. Construct:

(i) the locus of points 3 cm from AB

(ii) the locus of points 5 cm from M.

Mark two points P and Q on the same side of AB satisfying the above loci. Measure the distance between P and Q.

16. AB is a fixed line. Draw and describe the locus of the center of a circle of radius 2·5 cm and touching the line AB.

17. If the diagonals of a quadrilateral bisect each other, prove that the quadrilateral is a rhombus.

18. Using ruler and compasses only, construct a quadrilateral ABCD in which AB = 6 cm, BC = 5 cm, B = 60°, AD = 5 cm and D is equidistant from AB and BC. Measure CD.

19. Use ruler and compasses only for this question. Draw a circle of radius 4 cm and mark two chords AB and AC of the circle of length 6 cm and 5 cm respectively.

(i) Construct the locus of points, inside the circle, that are equidistant from A and C. Prove your construction.

(ii) Construct the locus of points, inside the circle, that are equidistant from AB and AC.

20. Use ruler and compasses only for the following question:Construct triangle BCP, where CB = 5 cm, BP = 4 cm, PBC = 45°.

Complete the rectangle ABCD such that

(i) P is equidistant from AB and BC, and

(ii) P is equidistant from C and D.Measure and write down the length of AB.

Answers

1. (i) A pair of straight lines parallel to the given line.

(ii) A circle with fixed point as center and radius 2 cm.

(iii) A sphere with fixed point as center and radius 2 cm.

(iv) Perpendicular bisector of the line segment joining given points.

(v) Diagonal AC of the rhombus ABCD.

(vi) Diagonal BD of the rhombus ABCD.

vii) The bisector of ABC.

(viii) The straight line passing through O and A.

(ix) Concentric circle of radius 1 cm if circles touch internally; and concentric circle of radius 5 cm if circles touch externally.

2. (iii) No

3. 8 cm

4. (i) circumcenter

(iii) Mid-point of AC

7. 4·1 cm (app.)

8. 3·4 cm (app.)

10. Four

11. Four

12. (i) 65°.

13. 78°; 1·2 cm

14. (i) Diagonal BD (ii) diagonal AC (iii) right bisector of AB

15. (i) Pair of straight lines parallel to AB and at distance 3 units on either side of AB (ii) Circle with center M and radius 5 cm; 8 cm

16. Pair of straight lines parallel to AB and at distance 2·5 cm on either side of AB18. 5·25 cm approximately

19. (i) The diameter of the circle right bisecting AC (ii) The segment of the circle bisecting BAC.

20. 5·5 cm (app.)

2009-06-30T16:42:00.004+08:00

Peeling Potatoes

2009-06-30T00:04:00.002+08:00

Loci In two Dimension
Loci 1

Loci 2

2009-06-29T23:55:00.005+08:00

Cartesian Coordinate
Revision Exercise

1 . Diagram 1 shows a Cartesian plane.

Diagram 1
Based on the Cartesian plane in diagram 1;

a. state the coordinates of A, B and C

b. find the distance from A to the y-axis

c. find the midpoint of AC

d. if the midpoint of BD is (-2,0), what is the coordinate of D

2. In diagram 2, PQ = QR.

Diagram 2
Find

a) the length of PQ.

b) the coordinates of point R.

c) the midpoint between points Q and R.

3. In diagram 3, points A, B and D are three of the vertices of a rectangle.

Diagram 3

State the coordinates of the fourth vertex of the rectangle.

2009-06-29T23:02:00.003+08:00

Coordinate System

Distance Between Two Points

Finding The Midpoint

2009-06-26T22:37:00.015+08:00

Math Challenge 1
27th June - 3rd July
Three challenges to set you thinking: How many can you solve...........?

No. 1: "A Perfect Match"

In the diagram below, 11 matches make 3 squares:
Your challenge is to move 3 matches to show 2 squares.

No. 2: "Nenek’s age"

Mamat asked his nenek how old she was. Rather than giving him a straight answer, she replied: "I have 6 children, and there are 4 years between each one and the next. I had my first child (Pak Long Husin) when I was 19. Now the youngest one (Mak Su Jamilah) is 19 herself. That's all I'm telling you!". How old is Mamat's nenek?

No. 3: "Peas Galore"

At a school fete people were asked to guess how many peas there were in a jar. No one guessed correctly, but the nearest guesses were 163, 169, 178 and 182. One of the numbers was one out, one was three out, one was ten out and the other sixteen out.
How many peas were there in the jar?

e-mail your answers to your teacher before 4th July 2009

2009-06-26T12:49:00.005+08:00

Baking By Numbers
Not all people are chefs, but we are all eaters. Most of us need to learn how to follow a recipe at some point. To create dishes with good flavor, consistency, and texture, the various ingredients must have a kind of relationship to one another. For instance, to make cookies that both look and taste like cookies, you need to make sure you use the right amount of each ingredient. Add too much flour and your cookies will be solid as rocks. Add too much salt and they'll taste terrible.

Ratios: Relationships between quantities
That ingredients have relationships to each other in a recipe is an important concept in cooking. It's also an important math concept. In math, this relationship between 2 quantities is called a ratio. If a recipe calls for 1 egg and 2 cups of flour, the relationship of eggs to cups of flour is 1 to 2. In mathematical language, that relationship can be written in two ways:
1/2 or 1:2
Both of these express the ratio of eggs to cups of flour: 1 to 2. If you mistakenly alter that ratio, the results may not be edible.

Working with proportion
All recipes are written to serve a certain number of people or yield a certain amount of food. You might come across a cookie recipe that makes 2 dozen cookies, for example. What if you only want 1 dozen cookies? What if you want 4 dozen cookies? Understanding how to increase or decrease the yield without spoiling the ratio of ingredients is a valuable skill for any cook.

Let's say you have a mouth-watering cookie recipe:

1 cup flour

1/2 tsp. baking soda

1/2 tsp. salt

1/2 cup butter

1/3 cup brown sugar

1/3 cup sugar1 egg

1/2 tsp. vanilla1 cup chocolate chips

This recipe will yield 3 dozen cookies. If you want to make 9 dozen cookies, you'll have to increase the amount of each ingredient listed in the recipe. You'll also need to make sure that the relationship between the ingredients stays the same. To do this, you'll need to understand proportion. A proportion exists when you have 2 equal ratios, such as 2:4 and 4:8. Two unequal ratios, such as 3:16 and 1:3, don't result in a proportion. The ratios must be equal.

Going back to the cookie recipe, how will you calculate how much more of each ingredient you'll need if you want to make 9 dozen cookies instead of 3 dozen? How many cups of flour will you need? How many eggs? You'll need to set up a proportion to make sure you get the ratios right.
Start by figuring out how much flour you will need if you want to make 9 dozen cookies. When you're done, you can calculate the other ingredients. You'll set up the proportion like this:

(1 cup flour /x cups flour ) x 3 dozen/9 dozen

You would read this proportion as "1 cup of flour is to 3 dozen as X cups of flour is to 9 dozen." To figure out what x is (or how many cups of flour you'll need in the new recipe), you'll multiply the numbers like this:

x times 3 = 1 times 9,

Therefore 3x = 9

Now all you have to do is find out the value of x. To do that, divide both sides of the equation by 3. The result is X = 3. To extend the recipe to make 9 dozen cookies, you will need 3 cups of flour. What if you had to make 12 dozen cookies? Four dozen? Seven-and-a-half dozen? You'd set up the proportion just as you did above, regardless of how much you wanted to increase the recipe.
What if your recipe has metric measurements? Find out more about the metric system in

"Meters and Liters: Converting to the Metric System of Measurements."

Source:http://www.learner.org/interactives/dailymath/cooking.html

2009-06-24T12:48:00.006+08:00

All About Patterns
Mathematics has been called 'science of patterns'. Recognizing and describing patterns and using patterns are important mathematical skills.

A Bee Tree
Although a female honeybee has two parents, a male honeybee's ancestors reveals an interesting pattern of numbers.

1 bee

1 parent

2 grandparent

3 great-grandparent

5 greatt-great-grandparent

8 great-graet-great-grandparent

The numbers of bees in the generation: 1,1,2,3,5,8.......form a famous list of numbers knowns as the Fibonacci sequence. This number sequence has fascinated peoples for centuries because it appears so often in nature.

You can find numbers from the Fibonacci sequence in the patterns of leaves on plants, in the arrangement of scales pineapples and in the spirals of nautilus shells

The surface of a honeycomb is made up of a pattern of hexagons that fit together with no overlaps

About Fibonacci
Leonardo Fibonacci was born in Pisa, Italy, around 1175. His father was Guilielmo Bonacci, a secretary of the Republic of Pisa.His father was also a customs officer for the North African city of Bugia. Some time after 1192. Bonacci brought his son with him to Bugia.Guilielmo wanted for Leonardo to become a merchant and so arranged for his instruction in calculational techniques, escpecially those involving the Hindu - Arabic numerals which had not yet been introduced into Europe.Since Fibonacci was the son of a merchant, he was able go travel freely all over the Byzantine Empire. Merchants at the time were immuned, so they were allowed to move about freely. This allowed him to visit many of the area's centers of trade. While he was there, he was able to learn both the mathematics of the scholars and the calculating schemes in popular use, at the time.

2009-06-18T20:39:00.005+08:00

MATHS IN HOME DECORATING

What does math have to do with home decorating? Most home decorators need to work within a budget. But in order to figure out what you'll spend, you first have to know what you need. How will you know how many rolls of wallpaper to buy if you don't calculate how much wall space you have to cover? Understanding some basic geometry can help you stick to your budget.

The word geometry literally means "to measure the Earth." Geometry is the branch of math that is concerned with studying area, distance, volume, and other properties of shapes and lines. If you need to know the distance between two points, the volume of water in a pool, the angle of a tennis serve, or how much wallpaper it will take to cover a wall, geometry holds the answers.

Figuring area: Squares and rectangles

Imagine you're planning to buy new carpeting for your home. You're going to put down carpeting in the living room, bedroom, and hallway, but not in the bathroom. You could try to guess at how much carpet you might need to cover these rooms, but you're better off figuring out exactly what you need. To determine how much carpet you'll need, you'll use this simple formula:

Area = Length x Width

This formula is used to determine the area of a rectangle or square. In the floor plan below, all of the floor space (as well as the walls and ceilings) is made up of squares or rectangles, so this formula will work for figuring the area you need to carpet.

Start by figuring the total area of the floor plan. When you're done, you can deduct the area of the bathroom, since you don't want to carpet that room. To figure out the total area of the floor plan, you'll need to know the total length and width. The total length of the floor plan shown above is 12 feet plus 10 feet, or 22 feet. The total width is 7 feet plus 5 feet, or 12 feet. Plug these numbers into your equation to get the total area of the floor plan:

A = 22feet x 12 feet = 264 sq feet

The total area of your floor plan is 264 square feet. Now you need to figure out the area of the bathroom so you can deduct it from the total area. The bathroom is 7 feet long and 5 feet wide, so it has an area of 35 square feet. Deducting the area of the bathroom from the total area (264 minus 35) leaves you with 229 square feet to carpet.

Figuring Area : Circles

Calculating how much carpet you'll need is a fairly simple task if your home has only square or rectangular rooms. But what if you have a circular alcove at the end of one room? How do you figure the area of a circle? Use this formula:

A = pi x r²

In English, this formula means "area equals pi times the radius squared." A circle's radius is one half of its diameter, or one half of what you get if you measure all the way across its widest part. "Squaring" something means you multiply it by itself. Pi is a number that roughly equals 3.14159.

If your living room has a semi-circular alcove as shown in the floor plan above, you'll need to use this additional equation to figure out its area. To figure the radius of your alcove, the number you'll need to plug into the equation, you'll divide its diameter in half. Its diameter is the same as the width of the living room: 12 feet. Half of that is its radius: 6 feet.
Let's plug in the numbers:

A = 3.14159 x (6 feet x 6 feet)

A = 113 square feet (rounded to the closest square foot)

If your alcove were a complete circle, it would have an area of 113 square feet. Because it's a half circle, its area is half of that, or 56.5 square feet. Adding 56.5 square feet to the rest of your floor plan's area of 229 square feet gives you the total area you want to carpet: 285.5 square feet. Using geometry, you can buy exactly the amount of carpet you need.

http://www.learner.org/interactives/dailymath/decorating.html

2009-06-15T23:55:00.007+08:00

How To Study Mathematics
You can learn mathematics better if you do certain things. A lot of people never learn these basic approaches that can open up the world of math.

Steps
1. Learn the vocabulary!
Every area of Math has its own vocabulary. You should memorize every definition, word for word. (Don't leave anything out.) You should be able to recite them. If you can recite them, and if you can write them all out, then you know them. If you can't do that, then you don't know them. This might sound like a lot of work, but it is nothing compared to the memorizing in history or geography.

2. Try to work the problems and do the exercises, at least some of them.

If there is a sample problem in your book, or an example problem, work through it yourself,

and use the sample in your book to guide you.

3. Identify the error.

If you make a mistake in a problem, or in a proof, or take a wrong turn, figure out why! Figure

out what it was, or what it was that you were thinking, that led you down the wrong path

4. Avoid the risk of frustration.

Don't go on in your book until you have learned the material where you are now. The later stuff builds on the earlier stuff. A math book is like a novel, it doesn't make sense unless you start at the beginning.

5. Write down your question, if you don't understand a specific concept.

By identifying what you need to learn, you'll speed up the learning process.

6. Be able to explain it to somebody else.

This is a sure way to find out what you don't understand.

WARNING!!!!!!!!

Don't be afraid to ask for help from someone who has been doing math for a long time or is further along.

Don't be too hard on yourself. Realize that many have struggled with the same areas you are learning. Some people just take longer to understand math. Eventually, with enough, perserverance, you can succeed in math.

2009-06-15T23:16:00.004+08:00

CARTESIAN COORDINATES

The Cartesian coordinate system was developed by the mathematician Descartes during an illness. As he lay in bed sick, he saw a fly buzzing around on the ceiling, which was made of square tiles. As he watched he realized that he could describe the position of the fly by the ceiling tile he was on. After this experience he developed the coordinate plane to make it easier to describe the position of objects.

Cartesian Coordinate System consists of two axes, X and Y, which intersect each other at a point called `origin`, and is used to define the position of any point by using ordered pairs. In two-dimensional coordinate system, the reference of a point is given by using two coordinates, X and Y.

Who Uses Coordinates?

The system of coordinates that Descartes invented is used in many modern applications. For example, on any map the location of a country or a city is usually given as a set of coordinates. The location of a ship at sea is determined by longitude and latitude, which is an application of the coordinate system to the curved surface of Earth. Computer graphic artists create figures and computer animation by referencing coordinates on the screen.

2009-05-04T10:00:00.009+08:00

GEOMETRICAL CONSTRUCTIONS

.........................................................................................

Geometry and its construction have a long history starting fron Ancient Egypt and Ancient Greece. Rhind Papyrus, Thales and Euclid were among the mathematicians who played important roles in the foundations of geometry and its construction.

In 1858, A. Henry Rhind bought a scroll that was 18 feet long and 13 inches high, which is now called the Rhind Mathematical Papyrus. A scribe named Ahmes made this copy around 1650 or 1700 BCE (different sources are inconsistent with the date), and he copied it from a document that dated 200 years before that, making the original from around 1850 BCE. The Rhind, also called the Ahmes Papyrus, is the greatest source of information on Egyptian mathematics from that time.
Although scholars are not exactly sure what the purpose of the Rhind originally was, it seems to be a sort of guide to Ancient Egyptian mathematics. It contains 87 math problems, including equations, volumes of cylinders and prisms, and areas of triangles, rectangles, circles and trapezoids, and fractions. The Egyptians used unit fractions, which are fractions with one in the numerator, in the Rhind Papyrus. In order to simplify things, the Egyptians included an important table in the papyrus, so they could look up the answers to arithmetic problems. This table showed the number 2 divided by all the odd numbers from 3 to 101. The answers to these division problems were stated in the table as several fractions added together, although the plus signs were omitted. For example, the fraction 5/8 would have been written like this: 1/2 1/8. Addition and subtraction were accomplished in this way, but multiplication and division were a different matter. In fact, the only multiplication that the Egyptians used was with the number 2. If they wanted to multiply 17 by 4, they would have doubled 17 to get 34, and then they would have doubled 34 to get a final answer of 68. Although this method was effective it was also time consuming! Division was accomplished by successively doubling the denominator of a fraction.
The Egyptians did not know as many mathematical facts and were not as adept at performing mathematical functions as the Greeks who came a thousand years after them. However, the Rhind was used as a model for mathematics in Ancient Greece. It is clear that the civilizations that came after the Egyptians built upon the strong framework of information and mathematical processes contained in the Rhind Papyrus to develop their more advanced systems of mathematics.
A. Henry Rhind died five years after purchasing the Rhind Papyrus, and it was obtained by the British Museum. Fortunately enough for historians and mathematicians alike, large missing pieces of the Rhind were found in New York's Historical society and reunited with the other part of the papyrus. The British Museum now holds the Rhind Papyrus, with all the mysteries and answers of the ancient Egyptians, within their walls.

The Equations Found on the Rhind Papyrus

2009-04-28T09:59:00.003+08:00

PRIMITIVE PYTHAGOREAN TRIPLES

Every primitive Pythagorean triple (a, b, c) is of the form a = m^2 − n^2, b= 2mn, c = m^2 + n^2. If m is even then n must be odd or the other way round.

Some basic properties of Pythagorean triples:
1. Exactly one leg is even.
2. Exactly one leg is divisible by 3.
3. Exactly one side is divisible by 5.
4. The area is divisible by 6.
5. The area of a Pythagorean triangle can never be a square number. Indeed, there is no Pythagorean triangle with two sides whose lengths are square
numbers.

2009-04-20T22:53:00.004+08:00

MATHEMATICS BRAIN TEASER

HOW MANY CAMPERS?

Kem Bestari's cook, Puan Asiah, was just about to begin preparing the picnic lunch for all the campers. She already knew she needed to fill 55 bowls of the same size and capacity with the same amount of food. When she was done, she decided to read the guidelines for the picnic, just out of curiosity.

The guidelines said:
1. Every camper gets their own bowl of soup.
2. Every two campers will get one bowl of mee to share.
3. Every three campers will get one bowl of salad to share.
4. All campers are required to have their own helping of salad, mee, and soup.

After some rapid calculations, Puan Asiah was able to figure out how many campers were going to the picnic. Can you?

GOOD LUCK
Submit your solution to your Maths's teacher...

2009-04-20T22:44:00.003+08:00

RIDDLE

Five Of A Kind

The first is needed to make quotes you see,
And it often sticks up when it's time for noon tea.

The second's biggest distinction is found
Bearing the symbol of love that is bound.

The third should be biggest but that can depend,
Never standing alone or it may offend.

The fourth is oft used when making a selection
Or if you should need a gun for protection.

The fifth is the fattest and oddest by far,
And can sometimes be found in a wrestling war.
What are they?

2009-04-17T07:07:00.005+08:00

MATHS GIGGLES

TABLE 1

TEACHER : Why are you doing your math sums on the floor?

STUDENT : You told me to do it without using tables!

TABLE 2

TEACHER : Please refer to the table. Circle number two and all the multiples of two.

STUDENT : Teacher I can't see anything on my table.

2009-04-16T23:18:00.006+08:00

PYTHAGOREAN TRIPLE

It is surprising that there are some right-angled triangles where all three sides are whole numbers. The three whole number side-lengths are called a Pythagorean triple.

An example is a = 3, b = 4 and c = 5, called "the 3-4-5 triangle". 3²+4² = 9 + 16 = 25 = 5² so a² + b² = c².

Notice that the greatest common divisor of the three numbers 3, 4, and 5 is 1.

Pythagorean triples with this property are called primitive. From primitive Pythagorean triples, you can get other, imprimitive ones, by multiplying each of a, b, and c by any positive whole number d > 1. This is because

a² + b² = c² if and only if (da)² + (db)² = (dc)².

Thus (a,b,c) is a Pythagorean triple if and only examples if (da,db,dc) is. For example, (6,8,10) and (9,12,15) are imprimitive Pythagorean triples.

Here are the of the first few primitive Pythagorean triples

a	b	c	a	b	c	a	b	c
3	4	5	5	12	13	7	24	25
8	15	17	9	40	41	11	60	61
12	35	37	13	84	85	16	63	65
36	77	85	39	80	89	48	55	73

CHALLENGE YOURSELF

1. Find the only Pythagorean triangles with an area equal to their perimeter.

2. Ahmad has a triangular orchard with sides measuring 560 m, 420 m and 300 m. Determine whether the shape of his orchard is a right-angled, obtuse-angled or acute-angled triangle.