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 :)