Very pleased with the way Christopher delivered the lesson, my daughter found it very helpful and came away surprised that she could learn so much so quickly! The lesson was challenging and kept my daughter's focus at all times. Christopher's energetic style of teaching and tangible enthusiasm will hopefully show my daughter that Maths is not a boring subject!

Ayan, Parent

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The formula for the area of a circle is π r^{2}. To use this formula we first need to find r, the radius of the circle. The radius is the distance from the centre of the circle to the edge, and is equal to half of the diameter. The radius of this circle is half of 14, or 14/2 = 7. Now we can use the formula for area. π x 7^{2 }= π x 49 = 153.938..... or 159.3 to 1 decimal place. It is important not to forget units with your final answer if they are given in the question, so the area of our circle C = 159.3 cm^{2}.

Answered by Tamsyn H.

Studies Mathematics at Cardiff

As a university student i know all about the right address that pupils need i can really help them understand math

Answered by Jack L.

Studies computer science at Kings, London

In this example, we want to find values for both x and y which are our unknowns.

So we start by rearranging x to be on its own but still in terms of y. We then can plot it into the next equation.

Hence we get the following equations:

. x=20-4y (See, 4y has been taken over to the other side and hence the sign changes)

. 3x+2y=20

Then we substitute this new value of x in the other equation:

3(20-4y)+2y=20

60-12y+2y=20 (we have multiplied out the 3 and its bracket to simplify)

-10y=20-60 (make sure you change the sign when taking the 60 across!)

-10y=-40

-y=-4 (here we divided 40 by 10)

y=4 (the minus signs cancel each other out)

Now that you've found y we must plot it back into the original equation to find x:

x+4y=20

x+4(4)=20

x+16=20

x=20-16

x=4

Therefore, x=4 and y=4.

Answered by Phillipa S.

Studies Engineering at Exeter

Here we see a real world example of how Pythagoras's Theorem can be used in a practical context. I would drop hints to the student about considering triangles and using this theorem, trying to enable them to be as independant as possible. For example, once the student has received the hint to use Pythagoras's Theorem, we'll move on together trying to see the appropiate triangle in the room. We can then slowly, in a step-by-step fashion proceed through the calculation together.

Answered by Stuart B.

Studies Statistics and Computer Science at St. Andrews Unversity

With sequences we should follow the general formula of **An + B**.

The **n **refers to the position in the sequence i.e. for the 3rd number in the sequence (which is 2 in the above sequence) n=3.

The **A** refers to the *difference between* each number in the sequence. In the case of the sequence above, __A= -3__ (each number is 3 lower than the previous one in the sequence).

The **B **refers to the difference between a particular number in the sequence compared with the number in the same position if it were the 'expected sequence'. In other words if it were just **An**. So for the sequence above it would be -3n so plugging in n=1, the first value in the sequence would be -3 x 1 = -3.

However we can see that this isn't the case, the first number is actually 8. 8 is 11 higher than -3 (8 - -3 = 8+3 = 11). So __B=11__.

Therefore the general formula for this sequence is -3n + 11.

All we now have to do is plug in the values for the poisiton in the sequence into n.

So the 4th term in the sequence is when n = 4:

(-3 x 4) = -12 + 11 = **-1**

And the 50th term in the sequence is when n = 50:

(-3 x 50) = -150 + 11 = **-139**

Answered by Aneesh S.

Studies Medicine MBBS BSc at University College London

We can calculate the area of a circle using the following formula:

A = pi x r^{2}

The area we are given is 16pi. Therefore, we can divide both sides by pi. So,

16pi = pi x r^{2}

becomes

16 = r^{2}

We can squareroot both sides to calculate the value of r.

sqrt16 = sqrt r^{2}

Therefore r = 4

We can then use the formula d = 2r to calculate the diameter.

Therefore the diameter of the circle is 2x4 = 8cm.

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