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Usually we cover both subject knowledge and exam technique, although that can change depending on each individual student. Then we go through diagrams, and they ask questions, and we go from there.

Lots of students say that the classes are too big in school, or that they don't have time to ask teachers after lessons. In my tutorials, we take time to explore things in a little in a bit more detail.

I always look up the board my students are taking so the lessons are really relevant. Then we go through past papers or set texts, whatever the student finds helpful.

I use the shared whiteboard. We make diagrams together and label them, and often the student prints it off because they know it's right and they completely understand it.

After tutoring one girl went and told all her friends the new explanation I gave her. And she was so excited about what she wrote in the exam she emailed me immediately afterwards.

There was one girl who had her exam on Monday. She wanted tuition on Friday, Saturday and Sunday beforehand. It was very intense, but she said the exam went well.

Rearranging is one of the trickier topics in GCSE maths, however as long as you follow it through step by step you shouldn't have a problem.

The question asks you to make 'c' the subject. This means you need to get 'c' on one side of the equation, and all the other terms on the other side of the equation.

Firstly, you should multiplty everything through by 2 to get rid of the fraction:

3c + b = 2(c + a)

3c + b = 2c + 2a

Then, by adding and subtracting terms, move all of the 'c' terms on to one side of the equation and all of the other terms on to the other side of the equation:

3c - 2c = 2a - b

Therefore, your final solution is:

c = 2a - b

This question can be difficult, because it involve a lot of words. This can make it confusing as to what information we really need to use - just work it through step by step.

Sam uses 140g of flour to make 12 cakes. In order to answer this question we need to find out how much flour is used to make 1 cake.

To do this we divide 140 by 12:

140 / 12 = 11 2/3

Next, we must find out how much flour is needed to make 21 cakes.

To do this, we mutiply the number of flour needed to make 1 cake by 21:

11 2/3 x 21 = 244.9999

Because it would be difficult to measure 244.9999g of flour, we simply round up to the nearest whole number:

= 245g of flour is needed to make 21 cakes.

Intertextuality is the relationship between different texts, specifically literary ones. It is the way that texts refer to and influence other texts. Julia Kristeva first used the term in her 1966 work *Word, Dialogue and Novel. *Intertextuality is an important stage in understanding a piece of literature, as it is necessary to see how other works have influenced the author and how different texts are employed in the piece to convey certain meanings. A good example of this is Evelyn Waugh's *A Handful of Dust* in which the title in itself references T. S. Eliot's *The Wasteland* and therefore an understanding of this poem is helpful in analysing the text. Furthermore a study of Jean Rhys's *Wide Sargasso Sea* is greatly enriched by a reading of Charlotte Bronte's *Jane Eyre*.

Answered by Emily B.

Studies English Literature at Durham

It is a quadratic equation and when factorised will be of the form (x +/- a) (x +/- b) = 0. We need to find 2 numbers, a and b, that add together to make the 3 for the 3x term and which are multiplied together to give -54 for the constant term. Because the constant is negative (-54), one of the numbers multiplied to give -54 must be negative and the other must be positive as a positive x negative = negative. Possible numbers:

1.(+ or -)1 x (+ or -)54 = -54

2.(+ or -)2 x (+ or -)27 = -54

3.(+ or -)3 x (+ or -)18 = -54

4.(+ or -)6 x (+ or -)9 = -54

We can exclude the first 3 possibilities as it wouldn't be possible to add them together to make +3 (for 3x). This leaves us with (+ or -)6 and (+ or -)9. If we had (-9) + (+6) we would get -3. If we had (+9) + (-6) we would get +3 which is correct.

This means that a= +9 and b= -6

(x + 9) (x - 6) = 0

In order for the above to =0, one of the brackets needs to=0 because any number, n x 0 = 0

Either: x + 9 = 0 which is rearranged to give x= -9 or x - 6 = 0 which is rearranged to give x= 6.

Therefore x= 6 or -9

Answered by Kate G.

Studies Biochemistry at Exeter

Proof by induction has three core elements to it. To start with you must prove that the statement is true for the 'basic case'. For the most part this is 1, but some questions state it is higher.

Do this by subbing 1 into the equation and ensuring that it is divisible by 3

1^3 =1

5(1)=5

1+5=6 6/3=2 Therefore divisible by three and true for 1.

Then in order to futher prove it, we are going to assume that this is true for n=k

leaving us with the equation k^3+5k=3a as it is divisible by 3.

The next stage is to prove true for n=k+1.

Do this by subbing k+1 into the original equation:

(k+1)^3 +5(k+1)

multiplying this out gives:

k^3+3k^2+3k+1+5k+5

Now we have already established that k^3+5k=3a so through rearranging, k^3=3a-5k.

Subbing this into the k+1 equation gives us:

3d+3k^2+3k-6. Each element is a multiple of three so by taking three out leaves us:

3(d+k^2+k-2) which is a multiple of three and thus divisible by three.

Then leave a concluding statement along the lines of:

'As n^3+5n is true for n=k, then it is true for n=k+1. As it is true for n=1, then it must be true for n is greater than 1'

Answered by Philip D.

Studies Mathematics at Exeter

When analysing primary sources there are two keys areas to consider - content and provenance. We'll look at each in turn.

Firstly content is all about what the source says or shows. What is it explicitly showing/telling us? Is there anything you can read between the lines? If it is a cartoon, what political point is the cartoonist aiming to raise? If it is a picture what is it showing? Are there any particular lines that stand out as being important? What is the tone of such a source (ie Does it sound aggressive? Threatening? Emotional?) Can you work out the purpose of this source - is it meant to inform, enterain, persaude etc...?

Hence content is all about pulling apart what the source actually says and commenting on that in detail.

Provenance is concerned with authorship. When was it written? Who was it written by? What would be the purpose of such a source? Does it have a particular bias? Who is the intended audience? Is it meant to be public (eg a speech) or private (eg a diary entry)? When and where was it published? How will that affect the source?

When looking at both provenance and context you should apply your own knowledge to challenge the source. For example if it was published in Soviet Russia in the 1950s, we can comment on how it was written under an oppressive regime so the author cannot be critical of the government or face the risk of the gulags.

Answered by Callum N.

Studies History at Exeter

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