Math game 2

This is the link for the math game. Have fun and enjoy!

Link: http://api.ning.com/files/NGc*L6SXutyeOUCOgOZf9Q2v4D--5szTX8bKYUqStMTT9TDX-KOoBOUijGVagFQpV0LYC4EzRuj0ONBokgyWbDeDW6NfiHRQ/Math_Game_1.ppt

Lesson 3

Secondary One Mathematics

For today’s lesson, we all learn more about standard form, ratio, rate, uniform speed and average speed, decimals and fractions, *direct and inverse proportion. In addition, we will also be going through percentages and its applications such as changing the fractions to percentages and calculating % of quantity to find out the discount, taxation, increase and decrease, profits and losses.

Lesson time:

Standard form is a scientific notation which is used when using large numbers to find out great
values such as 1.5x1015 is the standard form of 1,500,000,000,000,000. Why standard form?

Standard form is used as it is a much simpler way of writing very large or small number. It

makes these numbers easier to read and less liable to make errors. A standard form is written in
this form: If the number is large, such as: 9,500,000,000,000= 9.5x1012 (move 12 decimal

places to meet the requirements for standard form which the coefficient must be from 1 to 9


with only one decimal place) If the number is very small, such as: 0.00000000005=5.0x1011

(move 11 decimal places in order to have 1 decimal place like the standard form where the

coefficient must be from 1 to 9


Problem Solving: Solve every problem and convert them to standard form.


1. Earth is actually 6,000,000,000,000,000,000,000,000 kg.

Ans: 6.0x1024kg


2. The distance of Saturn from the Sun is 1,429,000,000 km.

Ans: 1.429x109 km

3. 3x5x105=?



Ans: 1.5x106. Change the standard forms back to the original notation.

4. 6.535x10-5 =?

Ans: 0.00006535 5. (5.5x105)x(5.5x105) Ans: 30.25x1010

------------------------------------------------------------------------------------------------

Lesson Time (Fractions and decimals)

- Fractions:

The word fraction means part, so part of a quantity or a unit is called a fraction of it.


The bottom number of a fraction is denominator and it describes the number of equal-sized

parts into which the whole number has been divided. The top number of a fraction is numerator

and states how many of the equal parts are being considered. All fractions can be written as

finite/infinite, recurring/non recurring decimal numbers. Link to lesson on irrational numbers.

------------------------------------------------------------------------------------------------

-Decimals

Decimals includes finite/infinite, recurring/non recurring decimal numbers. Finite or terminating

decimals are

decimals that are exact and can be expressed easily and have not been rounded off as the

decimals can end easily. Such as: 0.125. Recurring decimals are decimals that keep repeating the

last decimal place(s) over and over again and do not end easily. The never-ending last decimal

place is represented by dots and line which are placed over the repeating digits. In addition,


some recurring decimals have a regular pattern in it. Such as 5.353535……(with a pattern of 5

and 3). Non recurring and infinite or terminating decimal numbers have decimal places that

cannot be expressed exactly and easily, their decimal places keep going on and do not repeat or

have no regular pattern in it. Such as: 0.1395934……

------------------------------------------------------------------------------------------------

Lesson Time (Ratio, rate, average speed and uniform speed)

-Ratio

Ratio is a comparison between of 2 quantities that are counted in the

same units. But always remember that it is the quantities that have units but not the ratio. A

ratio can be converted to a fraction as both of them have the same units of the 2 quantities. \

a:a2 = a/a2

Note! The quantities must be a countable number and not 0. *Always remember that the

order of the ratio is very important and the first quantity must always be the first number that

is mentioned in a statement or problem. Ratio includes equivalent ratio which is referring to 2

quantities that have the same factors and can be simplified by a same number. It is the same as

the equivalent fraction as you need to find the common factors.

------------------------------------------------------------------------------------------------


-Rate

A rate is a measurement

or degree of 2 quantities that have different units. We often use rate to show the production in a

limited or specific time(usually per minute or hour).

------------------------------------------------------------------------------------------------

-Speed(average and uniform speed)

Speed is the rate of distance travelled in per specific unit of time. Such as: A train is travelling at the average speed 85km/h to another country. Speed is often used when
motion occurs to see how fast or slow an object moves over a distance.


*Speed= distance travelled/ time taken to travel

= distance(km/m/cm) /Time(hours/ minutes/ seconds

Speed includes uniform and average speed. Uniform speed is a speed that remains unchanged

while travelling. It is also known as constant speed. Average Speed is used when the speed is not

constant and changes throughout the whole distance while travelling. We must get the total

distance travelled and total time as to obtain the average speed.



*Average Speed= total distance traveled/total time used

Must Revise!


------------------------------------------------------------------------------------------------



-Formula Study:

Speed:
*Speed= distance travelled/ time taken to travel

= distance(km/m/cm) /Time(hours/ minutes/ seconds)



*Average Speed= total distance travelled /total time used



Total Distance= average speed /total time used



*Total Time= total distance / average speed


------------------------------------------------------------------------------------------------


-HCF and LCM

- Highest Common Factor(HCF) and Lowest Common Multiple(LCM)


- Highest Common Factor(HCF) is a common factor of the 2 or more different numbers. It is the


highest common factor among all the common factors. It is often used to express numbers in its


simplest form.



- Lowest Common Multiple(LCM) is a common multiple of the 2 or more different numbers. It is

the lowest common multiple among all the common multiples. It is often used to express the

same denominators in fractions.


-Worked Example

1. A:B=3:5, and B:C=3:5, what is A:B:C?

Method: A:B B:C
3 : 5 3 : 5 (lowest common multiple[LCM])

As the quantity of B is the same, we need to find out the common multiple of the number in

order to make the 2 numbers the same.

Multiple of 5: 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100

Multiple of 3: 6, 9, 12, 15, 18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63

A:B
= 3:5

B:C
= 3:5

LCM of 3 and 5=15

Therefore

A:B:C
= 9:15:25

Ans: 9:15:25

2. Printer A can print up to 200 copies of worksheets in 5 minutes. It will take 10 hours to print out an order of worksheets. However, printer B is also used to speed up the production in a faster rate than printer A. After printer A had printed for 3 hours, printer B started to print. As all the worksheets are printed in another 1 hour, find the rate of printer B.

Method:
Rate of printing (printer A)= 200/5
= 40 worksheets per minute


10 hours of printing (printer A)= 40x600
= 24000 worksheets


3 hours of printing (printer A)=40x180
= 7200 worksheets


Printer A and B had to print=24000-7200
=16800 in an hour


1 hour of printing (printer A)= 40x60
= 2400

number of worksheets printed in 1 hour (Printer B)= 16800-2400
=14400


Rate of printing (printer B)= 14400/60
= 240 worksheets per minute

Ans: The rate of printer B is 240 worksheets per minute.


3. Motorists A, B and C are travelling from Town X to Town Y which is 48km apart. When motorist A reached Town Y, motorists B and C are still travelling with 12km and 15km left respectively to travel. How far will motorist C be when motorist B reached Town Y?

Method:
Distance travelled by Motorist B= 48km-12km
= 36km


Distance travelled by Motorist C= 48km-15km
= 33km

Motorist A: Motorist B: Motorist C
Divide by 3 48km : 36km : 33km
16km : 12km : 11km
Every 16km Motorist A travels, Motorist B will travel 12km and Motorist C will travel 11km.
8-7=1
1 unit=48km 12km
=4km

Ans: 4km


Exercise Time:
Express each ratio as its simplest form.

1. (12x14) : (3x7x6)


2. 0.266: 0.824

3. 50km: 0.25km

Ans:

1. (12x14) : (3x7x6)
= 168 : 126 Divide by 8
= 8 : 6 Divide by 2
= 4 : 3

Ans: 4:3


2. 0.266: 0.824
= 266/1000 : 824/1000
= 133/1000 : 412/1000
= 133:412 (Cancel away the 1000)


Ans: 133:12


3. 50km : 0.25km Convert into metres
= 50000m : 250m Divide by 10
= 5000 : 25 Divide by 25
= 200 : 1

Ans: 200 : 1

------------------------------------------------------------------------------------------------


Variables increasing (or decreasing) together need not always be in direct
proportion. For example:


(i) physical changes in human beings occur with time but not necessarily in a predetermined
ratio.


(ii) changes in weight and height among individuals are not in any known proportion and

(iii) there is no direct relationship or ratio between the height of a tree and the number
of leaves growing on its branches. Think of some more similar examples.


------------------------------------------------------------------------------------------------

End of lesson

Unusual Theorems

Unusual Theorems

Theorem 1.

A sheet of writing paper is a lazy dog.

Proof: A sheet of paper is an ink-lined plane. An inclined plane is a slope up. A slow pup is a lazy dog. Therefore, a sheet of writing paper is a lazy dog.

Theorem 2.

A peanut butter sandwich is better than eternal happiness.

Proof: A peanut butter sandwich is better than nothing. But nothing is better than eternal happiness. Therefore, a peanut butter sandwich is better than eternal happiness.

Theorem 3.

A crocodile is longer than it is wide.

Proof: A crocodile is long on the top and the bottom, but it is green only on the top; consequently, a crocodile is longer than it is green. A crocodile is green along both its length and width, but it is wide only along its width; consequently, a crocodile is greener than it is wide. Therefore, a crocodile is longer than it is wide. Q.E.D

Theorem 4.

Every horse has an infinite number of legs.

Proof : Horses have an even number of legs. Behind they have two legs, and in front they have fore legs. This makes six legs, which is certainly an odd number of legs for a horse. But the only number that is both odd and even is infinity. Therefore, horses have an infinite number of legs.

Theorem 5.

Napoleon was a poor general.

Proof: Most men have an even number of arias. Napoleon was warned that Wellington would meet him at Waterloo. To be forewarned is to be forearmed. But four arms is certainly an odd number of arms for a man. The only number that is both even and odd is infinity. Therefore, Napoleon had an infinite number of arms in his battle against Wellington. Since Napoleon still lost the battle, he must have been a very poor general indeed.l2

Theorem 6.

If 1/0 = ¥ , then 1/¥ = .

Proof (by rotation). Given 1/0 = ¥ , rotate both sides 90° counterclockwise and obtain -10 = 8 . Subtract 8 from both sides: - 18 = 0. Finally, rotate both sides 90° in the reverse direction: 1/¥ = 0.

Theorem 7.

Death comes to no man.

Proof. As is well known and celebrated in legend and song, when we approach death, our whole life flashes in front of us. This short review—if it is to be complete—must also include the moment we approached death and the flashback of our life. But this second flash must by the necessity of completeness include another flash of life. And that flashback must include still another and another, etc., etc. Hence, although we may approach death, all eternity is not enough time for us to reach it.
—This is known as "Leinbach's Proof" from Flight into Darkness by Arthur Schnitzler.


Theorem 8.

Christmas = Halloween = Thanksgiving (at least for assembly language programmers).

Proof: By definition, Christmas = Dec. 25; Halloween = Oct. 31; Thanksgiving = Nov. 27, sometimes. Again by definition,
Dec 25 is 25 base 10 or (2 x 10) + (5 x 1) = 25.
Oct 31 is 31 base 8 or (3 x 8) + (1 x 1) = 25.
Nov 27 is 27 base 9 or (2 x 9) + (7 x 1) = 25.13

P.S. Dec, Oct and Nov are base terms.

( Try this on your calculator if it has "base" functions. Mine has that function.)

Courtesy of http://library.thinkquest.org/

Arithmetic 2

Secondary One Mathematics

-Lesson


Basically, there are four types of arithmetic operation. They are addition, substruction, multiplication and division.


Addition


Addition is the basic operation of arithmetic. In its simplest form, addition combines two numbers, the addends or terms, into a single number, the sum of the numbers. Adding more than two numbers can be viewed as repeated addition; this procedure is known as summation and includes ways to add infinitely many numbers in an infinite series; repeated addition of the number one is the most basic form of counting. Addition is commutative and associative so the order in which the terms are added does not matter. The identity element of addition (the additive identity) is 0, that is, adding zero to any number will yield that same number. Also, the inverse element of addition (the additive inverse) is the opposite of any number, that is, adding the opposite of any number to the number itself will yield the additive identity, 0. For example, the opposite of 7 is (-7), so 7 + (-7) = 0. Addition can be given geometrically as follows. If a and b are the lengths of two sticks, then if we place the sticks one after the other, the length of the stick thus formed will be a+b


Subtraction



Subtraction is essentially the opposite of addition. Subtraction finds the difference between two numbers, the minuend minus the subtrahend. If the minuend is larger than the subtrahend, the
difference will be positive; if the minuend is smaller than the subtrahend, the difference will be negative; and if they are equal, the difference will be zero. Subtraction is neither commutative nor associative. For that reason, it is often helpful to look at subtraction as addition of the minuend and the opposite of the subtrahend, that is a − b = a + (−b). When written as a sum, all the properties of addition hold.


Multiplication



Multiplication is the second basic operation of arithmetic. Multiplication also combines two numbers into a single number, the product. The two original numbers are called the multiplier and the multiplicand, sometimes both simply called factors. Multiplication is best viewed as a scaling operation. If the real numbers are imagined as lying in a line, multiplication by a number, say "x", greater than 1 is the same as stretching everything away from zero uniformly, in such a way that the number 1 itself is stretched to where x was. Similarly, multiplying by a number less than 1 can be imagined as squeezing towards zero. (Again, in such a way that 1 goes to the multiplicand.) Multiplication is commutative and associative; further it is distributive over addition and subtraction. The multiplicative identity is 1, that is, multiplying any number by 1 will yield that same number. Also, the multiplicative inverse is the reciprocal of any number, that is, multiplying the reciprocal of any number by the number itself will yield the multiplicative identity.


Division

Division is essentially the opposite of multiplication. Division finds the quotient of two numbers, the dividend divided by the divisor. Any dividend divided by zero is undefined. For positive numbers, if the dividend is larger than the divisor, the quotient will be greater than one, otherwise it will be less than one (a similar rule applies for negative numbers). The quotient multiplied by the divisor always yields the dividend. Division is neither commutative nor associative. As it is helpful to look at subtraction as addition, it is helpful to look at division as multiplication of the dividend times the reciprocal of the divisor, that is a ÷ b = a × 1/b. When written as a product, it will obey all the properties of multiplication.

-Rules/ formulae



BODMAS- Bracket of Division, Multiplication, Addition and Subtraction



Basically it means that when facing an equation, you should simplify everything in the brackets first, followed by division, multiplication, addition and last but not least, subtraction.



Here's and example: (2+4)x14/7-12=?



Well, if you followed the BODMAS rule, you should get a staggering 0. Wow. Amazing.


-National Education

When was Singapore grouped together with Penang and Malacca to form the Straits Settlements?

Clue: (500x6)/(1+2-1x2/2)+500-174

Answer: Please highlight the blank--> In the year 1826

Well, that's the end for today's lesson. Come back tomorrow for the next lesson. P.S. I wonder why no one has entered the "daily" contest? Hmm.. I wonder why?

-END-

Sources: Wikipedia, Google and images.google

A game.

This is a powerpoint game which you can CHEAT in, but it will not do you good. I recommend you to not see the slides and press F5 as soon as your computer opens this file: PowerPoint game which contains Arithmetic.pps.ppt

I recommend you to use Powerpoint 2000 or below.

Enjoy. Really.

Daily Contests

Daily Contest 1

18/3/09

The rules are simple. First one with the correct answer by 9 p.m. the next day( GMT+8 ) gets a prize. Please collect it within 24 hrs after winner has been announced. Everyone is welcome to take part.

Q. We shall give you an easy one.

What is 1/5 of 1/3 of 1/5 of √(5625x1-1+1)?

Deadline: 1 week from now.(That's ample time to walk to the market more than 101 times)

Arithmetic ( Imaginary Numbers)

Secondary One Mathematics

-Lesson

In Mathematics, imaginary numbers are numbers which squares are negative real number(cannot really simplify and express them in number form) and are denoted by symbols such as "a". The imaginary unit, denoted by i or j.

As you all know, any positive number has only one (positive) square root. For your example, the square root of 4 is 2…… but what is the square root of 2?
We know that there is a way to find out. Let us use an equation that asserts this,
(Square root of 2) = Square-rooted 2 x Square-rooted 2
= 2

*As you know, Square roots are encountered geometrically, as lengths of lines. For example, square root of 2 is the length of the diagonal of a square whose sides have length of 1.

-Facts that aren't really facts

Do you know that the square root of 2=1 + ½+½ +½……?

Actually, (Square root of A) x (Square root of A)
= A
Whereas, –(Square root of A) x –(Square root of A)
still equals to = A

-Problem Solving!

In order to solve ax2 + bx + c = 0 and find the value of x,
We need to use the quadratic formula like this:
x = -b + - [Square root of (b2-4ac)]
----------------------------
2a

The next part is very "chim" as it requires strong knowledge of algebra, and alpha, beta. Ok, maybe not the latter. But nevertheless, this comes under secondary 2, I think.

-The quadratic formula

To find out the number whose square is equal to triple minus four

Quadratic Formula

A = -b + [Square root of (b2-4c)]
----------------------------
2

A = -b - [Square root of (b2-4c)]
----------------------------
2

There! All done. You have come to the end of this lesson. Come back next time for more lessons.