Lets Learn about size and measurement

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This Math still cant make you praise Allah SWT ?!

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Math Project Display

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Math Project Display

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Topic for Final Exam IGCSE Year 9, Number and Probability

1.       Expressing number into words, ex: wording of 104256, 1/3, 1/2, ¼ ?
2.       BIDMAS or BODMAS fraction, whole and decimal number?
3.       Converting Unit and estimation
4.       Rounding, ex: 1234 to the nearest 100?
5.       Ordering fraction and percentage
6.       Using calculator for indices
7.       Standard form or scientific form
8.       Converting Currency
9.       Indices rule, (negative, fraction, whole)
10.   Fraction to decimal, fraction to percentage
11.   Speed and time, hour.
12.   Multiple Number
13.   Ratio, proportion
14.   Basic Probability
15.   Percentage loss and fraction loss
16.   Venn diagram & Shading
17.   Sequence and using formula
18.   Probability Tree Diagram

• More Detail about Number, and watch the tutorial video click here
• Download for speciment paper click here 

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Try Embedding ppt, word, pdf, excell file

Exercise Embedding ppt file




another method for embedding ppt file



Embedding word document




Embedding xls file sheet 1



Embedding xls file whole document

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Specimen Paper A level

CIE Pure Maths P1 Nov 2013

(1)

Video worked solution to 1

(2)

Video worked solution to 2

(3)

Video worked solution to 3

(4)

Video worked solution to 4

(5)

Video worked solution to 5

(6)

Video worked solution to 6

(7)

Video worked solution to 7(i) | 7(ii)

(8)

Video worked solution to 8(i) | 8(ii)

(9)

Video worked solution to 9(a) | 9(b)

(10)

Video worked solution to 10(i) | 10(ii)

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Sets and Venn Diagram

Sets and Venn Diagrams

Sets

A set is a collection of things.

For example, the items you wear is a set: these would include shoes, socks, hat, shirt, pants, and so on.

You write sets inside curly brackets like this:

{socks, shoes, pants, watches, shirts, ...}

You can also have sets of numbers:

• Set of whole numbers: {0, 1, 2, 3, ...}
• Set of prime numbers: {2, 3, 5, 7, 11, 13, 17, ...}

Ten Best Friends

You could have a set made up of your ten best friends:

• {alex, blair, casey, drew, erin, francis, glen, hunter, ira, jade}

Each friend is an "element" (or "member") of the set (it is normal to use lowercase letters for them.)

Now let's say that alex, casey, drew and hunter play Soccer:

Soccer = {alex, casey, drew, hunter}

(The Set "Soccer" is made up of the elements alex, casey, drew and hunter).

And casey, drew and jade play Tennis:

Tennis = {casey, drew, jade}

You could put their names in two separate circles:

Union

You can now list your friends that play Soccer OR Tennis.

This is called a "Union" of sets and has the special symbol ∪:

Soccer ∪ Tennis = {alex, casey, drew, hunter, jade}

Not everyone is in that set ... only your friends that play Soccer or Tennis (or both).

We can also put it in a "Venn Diagram":

Venn Diagram: Union of 2 Sets

A Venn Diagram is clever because it shows lots of information:

• Do you see that alex, casey, drew and hunter are in the "Soccer" set?
• And that casey, drew and jade are in the "Tennis" set?
• And here is the clever thing: casey and drew are in BOTH sets!

Intersection

"Intersection" is when you have to be in BOTH sets.

In our case that means they play both Soccer AND Tennis ... which is casey and drew.

The special symbol for Intersection is an upside down "U" like this: ∩

And this is how we write it down:

Soccer ∩ Tennis = {casey, drew}

In a Venn Diagram:

Venn Diagram: Intersection of 2 Sets

 

Which Way Does That "U" Go?

Think of them as "cups": ∪ would hold more water than ∩, right?

So Union ∪ is the one with more elements than Intersection ∩

Difference

You can also "subtract" one set from another.

For example, taking Soccer and subtracting Tennis means people that play Soccer but NOT Tennis ... which is alex and hunter.

And this is how we write it down:

Soccer − Tennis = {alex, hunter}

In a Venn Diagram:

Venn Diagram: Difference of 2 Sets

Summary So Far

∪ is Union: is in either set
∩ is Intersection: must be in both sets
− is Difference: in one set but not the other

Three Sets

You can also use Venn Diagrams for 3 sets.

Let us say the third set is "Volleyball", which drew, glen and jade play:

Volleyball = {drew, glen, jade}

But let's be more "mathematical" and use a Capital Letter for each set:

• S means the set of Soccer players
• T means the set of Tennis players
• V means the set of Volleyball players

The Venn Diagram is now like this:

Union of 3 Sets: S ∪ T ∪ V

You can see (for example) that:

• drew plays Soccer, Tennis and Volleyball
• jade plays Tennis and Volleyball
• alex and hunter play Soccer, but don't play Tennis or Volleyball
• no-one plays only Tennis

We can now have some fun with Unions and Intersections ...

This is just the set S

S = {alex, casey, drew, hunter}

This is the Union of Sets T and V

T ∪ V = {casey, drew, jade, glen}

This is the Intersection of Sets S and V

S ∩ V = {drew}

And how about this ...

• take the previous set S ∩ V
• then subtract T:

This is the Intersection of Sets S and V minus Set T

(S ∩ V) − T = {}

Hey, there is nothing there!

That is OK, it is just the "Empty Set". It is still a set, so we use the curly brackets with nothing inside: {}

The Empty Set has no elements: {}

Universal Set

The Universal Set is the set that contains everything. Well, not exactlyeverything. Everything that we are interested in now.

Sadly, the symbol is the letter "U" ... which is easy to confuse with the ∪ for Union. You just have to be careful, OK?

In our case the Universal Set is our Ten Best Friends.

U = {alex, blair, casey, drew, erin, francis, glen, hunter, ira, jade}

We can show the Universal Set in a Venn Diagram by putting a box around the whole thing:

Now you can see ALL your ten best friends, neatly sorted into what sport they play (or not!).

And then we can do interesting things like take the whole set and subtract the ones who play Soccer:

We write it this way:

U − S = {blair, erin, francis, glen, ira, jade}

Which says "The Universal Set minus the Soccer Set is the Set {blair, erin, francis, glen, ira, jade}"

In other words "everyone who does not play Soccer".

Complement

And there is a special way of saying "everything that is not", and it is called "complement".

We show it by writing a little "C" like this:

S^c

Which means "everything that is NOT in S", like this:

S^c = {blair, erin, francis, glen, ira, jade}
(just like the U − C example from above)

 Resource:mathisfun.com

Summary

∪ is Union: is in either set
∩ is Intersection: must be in both sets
− is Difference: in one set but not the other
A^c is the Complement of A: everything that is not in A
Empty Set: the set with no elements. Shown by {}
Universal Set: all things we are interested in

Worked Exam Question

Solution

Worksheet
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Probability Tree Diagrams

Calculating probabilities can be hard, sometimes we add them, sometimes we multiply them, and often it is hard to figure out what to do ... tree diagrams to the rescue!

Here is a tree diagram for the toss of a coin:

There are two "branches" (Heads and Tails) The probability of each branch is written on the branch The outcome is written at the end of the branch

We can extend the tree diagram to two tosses of a coin:

How do we calculate the overall probabilities?

• We multiply probabilities along the branches
• We add probabilities down columns

Now we can see such things as:

• The probability of "Head, Head" is 0.5×0.5 = 0.25
• All probabilities add to 1.0 (which is always a good check)
• The probability of getting at least one Head from two tosses is 0.25+0.25+0.25 = 0.75
• ... and more

That was a simple example using independent events (each toss of a coin is independent of the previous toss), but tree diagrams are really wonderful for figuring out dependent events (where an event depends on what happens in the previous event) like this example:

Example: Soccer Game

You are off to soccer, and love being the Goalkeeper, but that depends who is the Coach today:

• with Coach Sam the probability of being Goalkeeper is 0.5
• with Coach Alex the probability of being Goalkeeper is 0.3

Sam is Coach more often ... about 6 out of every 10 games (a probability of 0.6).

So, what is the probability you will be a Goalkeeper today?

Let's build the tree diagram. First we show the two possible coaches: Sam or Alex:

The probability of getting Sam is 0.6, so the probability of Alex must be 0.4 (together the probability is 1)

Now, if you get Sam, there is 0.5 probability of being Goalie (and 0.5 of not being Goalie):

If you get Alex, there is 0.3 probability of being Goalie (and 0.7 not):

The tree diagram is complete, now let's calculate the overall probabilities. This is done by multiplying each probability along the "branches" of the tree.

Here is how to do it for the "Sam, Yes" branch:

(When we take the 0.6 chance of Sam being coach and include the 0.5 chance that Sam will let you be Goalkeeper we end up with an 0.3 chance.)

But we are not done yet! We haven't included Alex as Coach:

An 0.4 chance of Alex as Coach, followed by an 0.3 chance gives 0.12.

Now we add the column:

0.3 + 0.12 = 0.42 probability of being a Goalkeeper today

(That is a 42% chance)

Check

One final step: complete the calculations and make sure they add to 1:

0.3 + 0.3 + 0.12 + 0.28 = 1

Yes, it all adds up.

Conclusion

So there you go, when in doubt draw a tree diagram, multiply along the branches and add the columns. Make sure all probabilities add to 1 and you are good to go.

Resource:Mathisfun.com

Worked Exam Questions

Intro Probability 1

Intro Probability 2

Tree Diagram 1

Tree Diagram 2

Exercise
Question 1 
Question 2 
Question 3 
Question 4 
Question 5
Question 6 
Question 7 
Question 8 
Question 9 
Question 10 

Worksheet Tree Diagram

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Quote of The Day

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My Dear Muslims Youth

You don’t have something called free time, you don’t!

You are member of this Ummah, member of this great Ummah, especially young member of this Ummah, You have to constantly working to make this society better, to do something good for people.

You don’t have free time, you don’t have time to play video games for 6 hours, you don’t have time for grand theft auto, you don’t have time for modern warfare, you don’t have time!, you don’t have time for the movie that’s coming out, you don't have time for watching Champions League,

You have time to do more important things, because you are youth of this Great Ummah.

As a muslim Ummah hold yourself to a high standard, Not just because the elders are telling you, the teachers telling you, parents telling you, or somebody else telling you, But your own conscious should tell you, your Laa Ilaaha Illallah  should tell you man!, It should tell you that you have to be active people,

You will see corruption, injustice around you in society, you will see youth that are getting away from Allah, who do you think will invite them? Me? No!

Those kids that don’t come to the masjid, those kids that don’t come for schooling, I have no way of reaching them, you have to reach them, they are your friends, They hang out with you, not with me. You gotta go to them, you have to be their daai and daaiyah, you have to be an inspiration to them, so you have to make sure that you become a person of concern for those around you,

You don’t just complain about your friends, man.. my friends all they do is watching movies, playing, have you ever advised them? Have you ever given them something more positive to do instead.. have you been a good influence for them?

You know this is what you have to do, may Allah make you the leaders of this ummah, and Allah make you role models for others who have gone away from Allah and bring them closer to Allah, may Allah make all of you good examples of Islam, so when the non muslims who come to this country, to this school, they just see you and they say "Man.. I wanna be a muslim, I wanna be like that guy, I wanna be like that lady".

We want you to be like that, that’s the character you live by, your honesty, your integrity, the way you carry yourself, the respects you to show to others, you know they just see that and they say "Man I wanna be a muslim, this muslim have something special", that is what you have to become,don’t think your gonna give dawah by only handing them a pamphlet or giving them a website address, or showing them a video, the powerful da'wah to islam is the character of a muslims, you are the ambassador of islam, without even opening your mouth.

Especially here, when you have guest coming and they observing us and they are not gonna say "Islam is great but the muslims are messed up", they are not going to think like that, when they saw muslims messed up they will think "Islam is messed up".

Whatever they see you doing, they think that’s Islam, whatever you are doing, no matter when your doing it, you are ambassadors of islam, Allah will ask you and me on the day of judgement, this is what you showed to those who are coming to Islam, are you the reason they came close to islam, or you were the reason, they went even further away from Islam, subhanallah, My Dear.. the Responsibility rests on your shoulder.

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