Circle Theorems

Circle theorems!

The joys of circle theorems have finally landed on this page!!!
I always find circle theorems one of the most easiest, along with Pythagorean theory the most easiest of the theorems to learn!
Today we are going to go through the basics of them!!

Lets take a look at a basic labelled diagram!

• The radius is the red line. We know it is the radius because the radius is centre to edge!
• The diameter is the blue line. We know this because the diameter is edge to edge!
• Also we know that the full circle around (the black circle) is the circumference.

The only equations we need to know for this are the area and circumference equations.

Area = πR^{2 = Pi x R x 2} 

Circumference= π x D 

• If we know the radius is 4 then we can work out the diameter is 8.
• If we know the diameter is 6 we can work out the radius is 3 

These are CALCULATOR equations, unless you are a wizz and can do this in your head!!! 

1.A circle has a Diameter of 8, what is the area?

π x r x 2 

In a calculator write π x 4 x 2 

You should get the answer of 50.27 rounded to 2dp.

2. A circle has a radius of 16, what is the Circumference?

π x D

In a calculator write π x 32 

You should get the answer of 100.53 rounded to 2dp

This is all for this blog!! Look out for Circle theorems #2 

We will be looking at labelling the different parts of a circle!!!

 

Thank you for learning :)

Probability tree diagrams

Probability tree diagrams are the one thing I find my peers always forget.

With a little but of encouragement they could be a master at them! 

Unfortunately, I am a student myself so I do not have the qualifications desired for teaching. But I do know how to teach! 

Lets get into it! 

What does a probability tree diagram look like?

•  Like this.
• You are able to add more ''twigs'' depending on what the question is asking you. 
• The single lines, are were you can write the outcome. 
• This makes probability much easier. 

Lets get right into the questions, and how to do it!

1. Jenny has a bag full of Purple and Blue counters.The chance of pulling out a Purple counter is 3/5. She pulls out two counters, one after the other. What is the chance of pulling out a two blue counters. 

So the first thing we need to look at is the probability of Blue counters. So we know that Purple is 3/5 so Blue must be 2/5.

Now we need a tree diagram!!

Plot what we know!!!

• We have added the fraction amount onto the grid!
• now we need to look at what is left:) 

We know if we take one out of the bag we are left with 4. If we take a Purple out we are left with 2/4 and if we take a Blue out we are left with 1/4. We are able to plot that on the tree now, watch.

• I have filled in the tree diagram, can you see what I did?
• If not, leave a comment and i'll email you to help!:)
• Now we have all our information we can answer the question:)

To be able to find this out we need to be able to multiply fractions. To do that we can times the numerators together and the denominators together. And we are asked to see what is the probability of pulling out two blues.

We now multiply both of the Blue fractions:)

2/5 x 1/4 = 2/20 

We can simplify this 

1/10

and we can turn this into percent = 10% 

With probability you should always answer in % unless is says otherwise :)

Thank you for learning :) 

Solving 2-step linear equations

Solving 2-step linear equations are the most simplest algebraic equations to solve:)

They are simply finding out what the letter is:)
Unfortunately it is only a GradeD/Level6 ;(

Things to know:

• Remember what ever you are doing on the one side you are doing the opposite on both of the sides. (For Example: if you're adding on the left, you subtract from both, If you are multiplying on the left, you are dividing from both, and vice versa)

So lets get started :)

Examples
3x+1=13
-1        -1
3x=12
/3    /3 (dividing)
x=4

5x-3=27
+3     +3
5x=30
/5    /5
x=6

x/5+2=37
-2        -2
x/5=35
x5     x5
x=175

Here is 3 questions for you to try :)
1) 2x-3=13
2) 2x+4=10
3)4x-7=29
*Answers I will post in the next maths blog:)

Be sure to comment what you want me to do next :)

Solving simultaneous equations

This is for all you GCSE students, that feel they need to expand there knowledge on Simultaneous equations. For me, solving these equations always had me, until, one day my teacher sat down with me and explained them clear as day.

What is a simultaneous equations?
A Simultaneous equation, if a form of 2 equations with the values  x and y  missing.

What do I need to find?
You will need to find the value of x and y. 

Is it easy?
Yeah it is, really when you get the hang of it!


Rules
If the signs are the same ( + + or --) you take away the equations.
If the signs are different ( -+) you add the equations.
Always substitute the x's or the y's back into the equation.
You need to make sure that atleast, in both equations the y's OR the x's are the same.
Label the equations E.G a,b 1,2.

Lets get started

2x+3y=26 (1)
  x+3y=19 (2)
Already we notice the the y's are the same in both equations, meaning they both have the same value, also it has to positive sign's, so we know we have to minus (-) them. I have also labled the equations 1 and 2
Lets start by taking them away
2x-x= x
3y-3y=0
26-19=7
We can eliminate the y's.
X=7

Substitute the x back into any one formule. 
7+3y=19.
19-7=12
3y=12
y=12/3
y=4

x=7, y=4.

Thanks for Learning.
Part 2 will be up, next week.

How to times any number by 11

How to times any number by 11 between 1-99:)


EXAMPLE

 Take 63x11 for example.

You can not do it in your head can you?
If you can then wow! I can but that's because I know how.

Anyway.
6+3=9
Stick the 9 in the middle of the number

693!!!!! DO IT ON A CALCULATOR IF YOU CAN :)

What about 83x11?

Well, 8 plus 3 is 11. BUT the answer wont be 8113!
You add the 10's

8+1=9 So the 8 becomes a 9. Then stick the 1 in the middle and the 3 at the end.

913- Wasn't that hard, was it?

EXERCISE

78X11
61X11
34X11
47X11
79X11
64X11
52X11
18X11
37X11
99X11

LEAVE THEM IN THE COMMENTS BELOW, SHOW WORKING IF YOU CAN/WANT.

Thanks for reading xox

Maths is life.

Hello, everybody.
So I thought that I would right a Blog that symbolises who I am.

I LOVE MATHS.

So I've decided to start a blog on Tips and Tricks in Maths to help you get those grades.

Comment what you want me to go over with you.

Thanks for reading