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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.

Find two numbers that multiply together to equal the 3rd term and the product of the same two numbers also needs to equal the 2nd term. This is trial and error but in this case it will be, (x - 4) (x - 4)

Answered by ANTHONY J.

Studies Pure mathematics at Cardiff

1. All photons travel at same speed in a vacuum
2. Photons has no charge
3. The energy of a photon depeds only on its frequency
So, working through it in order: the definition of a photon is: "A quantum of Electromagnetic radiation" - and as we known all EM radiation travels at the speed of light in a vacuum - 1 must be true
Photons are not affected by static electrical or magnetic fields, hence they have no charge - so 2 must be true
Finally, since the energy of a photon comes from the equation E=hf (where h is plancks constants and f is the photons frequency), we can confirm that the photons energy is dependent on the frequency
Therefore, we must realise that all 3 of the above statements are true!

Answered by Calum J.

Studies Computer Science at Durham

The most important thing to do before you even start writing your essay is to plan out what you intend to say. Organise the ideas you wish to express into sections with a clear introduction and conclusion either side of your answer.
Read through the poem you have chosen to write about. If possible, read it aloud and consider the sounds of the words and the rhythm of each sentence as you read from start to finish. Afterwards, take stock of your reaction to the poem: do you feel moved by the story or the images the piece conjures up? Write down your thoughts in the space allocated for your essay plan.
The next step is to now ask yourself what you consider the poem to be about. What do you think the poet wanted to tell the reader? Make a note of your interpretation. Now read through the poem once more with this reading in mind and look for patterns in the text. Look for stylistic techniques: for example, does the poet use alliteration (repetition of the same letter sounds)? What feeling do you think this conveys? Essentially you want to note down in your plan what you think the poet is doing with his use of language and theme, and then looking for clues in the composition of the poem to illustrate your observation.
Gather your observations together in your plan. In your introduction you can outline your overall interpretation of the poem (for example: 'What does William Blake think of the city he is describing in his poem 'London' - is it a happy or a sad place?). Then allocate three paragraphs within which to write about three things you notice about the poem. For each point structure your argument using the **Point - Quote - Analysis** system. Here's an example:
**Point - your idea about the poem's meaning **- e.g: William Blake thinks London is making it's inhabitants unhappy.
**Quote - an example taken from the text that gives your idea **- Stanza 2: 'In every cry of every Man / In every Infants cry of fear'
**Analysis - why does your chosen quote give you your idea **- Content: the repetion of the word 'every' emphasises just how many people are sufferring in London. Style: this emphasis is conveyed to the reader through Blake's use of the same amount of syllables in each line (eight syllables).
Gather three examples of the PQA system together in your essay plan. Put your three ideas inbetween an introduction and conclusion in order to structure a clear and effective essay that demonstrates your understanding of the themes and techniques of your chosen poem.

Answered by Calum A.

Studies Comparative Literature at University College London

We begin by discussing what a Production Possibilities Frontier (PPF) curve is. It is a curve that shows the various combinations of two goods (say cycles and dictionaries) that a firm can produce with given resources and state of technology. Due to the limited nature of resources, the firm cannot produce an infinitely large quantity of both goods and therefore, the firm must make a choice. Hence, in order to increase production of cycles, the firm must reduce production of dictionaries. The sacrifice of units of cycles for units of dictionaries (or vice versa) is the Opportunity Cost. Opportunity Cost is defined as 'the next best alternative foregone'. Thus, in an economy producing only cycles and dictionaries, if 5 dictionaries need to be sacrificed in order to produce one more cycle, then the opportunity cost of producing one more cycle is 5 dictionaries.
The rate at which units of one good need to be sacrificed in order to produce an additional unit of the second good is known as Marginal Rate of Transformation or the Marginal Opportunity Cost. Generally, the opportunity cost rises as you move down the PPF as resources are not equally efficient at producing both goods. This gives rise to the concave shape of the PPF curve.

Answered by Suhasini V.

Studies Economics and Politics at Durham

example: solve the simultaneous equations 3x+2y=4 and 2x+y=3
__1:__ 3x+2y=4

__2:__ 2x+y=3
want to either get same number of x's or same number of y's in equation __1__ and equation __2__

easiest way to do this is by making both equations contain**2y** by multiplying equation __2__ by 2
__2__x2: 2(2x+y=3)

4x+2y=6 call this equation__3__
now you have the same number of y's in both equations you can subtract one from the other so that there are no y's in the overall equation

choose the equation with the highest number of x's to subtract from so that you will not have a negative number of x's left over**3**-**1**: (4x+2y)-(3x+2y)=6-4

4x+2y-3x-2y=6-4

4x-3x + 2y-2y = 6-4

x+0=2

therefore x=2 now you have found what x equals you can substitute this value back into one of your original equations (equation__1__ or equation __2__) to find the value of y. I will sub into **2** as there is only one y in the equation so less working out is needed
sub x into** ****2**: 2x+y=3

2(2)+y=3

4+y=3

y=3-4

y=-1

easiest way to do this is by making both equations contain

4x+2y=6 call this equation

choose the equation with the highest number of x's to subtract from so that you will not have a negative number of x's left over

4x+2y-3x-2y=6-4

4x-3x + 2y-2y = 6-4

x+0=2

therefore x=2 now you have found what x equals you can substitute this value back into one of your original equations (equation

2(2)+y=3

4+y=3

y=3-4

y=-1

Answered by Calum J.

Studies Computer Science at Durham

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