21101 questions

What are some effective techniques that can be used to change key in a composition?

Here is a list of some techiniques: 1) Using a secondary dominant to move to the dominant key 2)Augmented 6th 3)Diminished 7th - use one of the notes within the dominant 7th as a 'leading note' to a desired key 4)Cycle of 5ths 5)Semitone movements - usually within a less tonal piece
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Jenifer M.

Answered by Jenifer, Music A Level tutor with MyTutor


What are the examiners looking for in the essay?

At A-Level the examiners are looking for more than a description. They want to see that you truly understand and therefore look for an analysis. This involves identifying a key feature and then explaining the effect that this has within the piece and how it links in with the rest of the piece.
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Jenifer M.

Answered by Jenifer, Music A Level tutor with MyTutor


Prove that the indefinite integral of I = int(exp(x).cos(x))dx is (1/2)exp(x).sin(x) + (1/2)exp(x).cos(x) + C

Starting with the initial integral of int(exp(x).cos(x))dx we can see that this is going to have to be integrated by parts. This states that the integral of (u . dv/dx)dx is equal to u.v - int(v . du/dx)dx Therefore, by applying this equation we can determine that u=exp(x), dv=sin(x), du=exp(x), v=-cox(x), as integrating sin(x) will give us -cos(x) This gives us int(I) = exp(x).sin(x) - int(exp(x).sin(x))dx As can be seen, this changes the form of the equation but it hasnt become any simpler. At this point we integrate once more by parts. By looking at the 'int(exp(x).sin(x))dx' which we obtained, this can be integrated again. int(exp(x).sin(x))dx = -exp(x).cos(x) + int(exp(x).cos(x))dx Substituting this into the first integral we worked out will give us: I = exp(x).sin(x) + exp(x).cos(x) - int(exp(x).cos(x)) It may seem that we have once again achieved nothing, but by inspecting the equation closely, we can see that we have ended up with the initial integral we were presented with on the RHS of the equation. By moving this negative integral to the other side we can see that we are going to have 2I. Dividing the whole equation by 2 will give us I = (exp(x).sin(x) + exp(x).cos(x))/2 + C (dont forget the constant!). Hence we have obtained an answer to this cyclic integral.
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Sammy A.

Answered by Sammy, Maths A Level tutor with MyTutor


A curve has the equation y = x^4 - 8x^2 + 60x + 7. What is the gradient of the curve when x = 6?

To find the gradient of any curve, we take the derivative. So in this case, we need to take dy/dx. We do this by multiplying the term by the power on x, and then lowering the power by one. For example, for the first term, x4, the power is four, so we multiply x4 by four, and the power becomes three, so we have 4x3. We repeat this for all of the terms individually to get dy/dx = 4x-16x +60. That gives us the gradient at any point. To get the gradient at x = 6 we need to substitute the value in to the new equation, so we get dy/dx = 4 * 63 - 16 * 6 + 60 = 828
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Elizabeth H.

Answered by Elizabeth, Maths A Level tutor with MyTutor


What are the key points of Sutherland's (1939) Theory of Differential Association?

Key points include: Criminal behaviour...  1) is learnt. Southerland is behaviourist in this respect. 2) is learnt through social interaction and communication. Bandura (1961) disagrees, as mere observation is sufficent for social influence. 3) is learnt form personal groups, i.e. friends and family. 4) is learnt by adopting the motives, drives, rationalisations, and attitudes from other criminals. 5) is based on learnt conceptions of the law as either “favourable” or “unfavourable”.  Crime is adopted when the ratio of attitudes (“definitions”) towards crime are more pro-criminal than anti-criminal. 6) is influenced by frequency, duration, priority and intensity. 7) is the same as any learning process. Criminal behaviour can be developed and honed.  8) cannot be a result of general needs and values, as those who are needy do not always turn to crime.
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Whitney L.

Answered by Whitney, Psychology A Level tutor with MyTutor


How to learn vocab?

Learning vocab is not easy and different methods work for different people. Here are just a few suggestions of ways to try... Mind maps
I find it very effective to categorise vocab e.g. Technology. Then for each category I make a colourful mind map full of vocab. I then try to memorise the mindmap by picturing the colours. Lucky dip
This method I love! Rip up a piece of paper and write vocab on each little piece. Try writing the word in English on one side and Spanish on the other. Then put the pieces into a small bag and pull them out individually, making yourself tranlaste the word into the language it doesn't appear in. This is great for reading / writing exams!  Flashcards 
Flashcards are great for fitting a lot of information in a small amount of space. I like to choose 20 key words for an individual topic that I can fit onto one card. Flashcards are great as they're easy to carry around so you can revise on the go!
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Ellie S.

Answered by Ellie, Spanish A Level tutor with MyTutor


What is an ablative absolute, and how do I translate one?

An ablative absolute is a noun + participle phrase which doesn't have any grammatical connection to the rest of the sentence, in which the noun and participle are in the ablative and agree in gender and number. For example:castro cincto, milites oppugnaverunt - with the camp having been surrounded, the soldiers attacked.In the sentence 'castrum oppugnabatur ab militibus cingentibus' (the camp was attacked by the soldiers who were surrounding it), there is no ablative absolute, as the noun and participle 'militibus cingentibus' are the agent and are connected to the rest of the sentence by 'ab'. The most obvious way to spot ablative absolutes is to recognise an ablative noun + participle, but make sure to check for this grammatical connection.When learning this construction, the easiest way to translate these is 'with x having y-ed' or 'with x having been y-ed' - in the first example, 'with the camp having been surrounded, the soldiers attacked'. When you get more confident, you can turn your translation into more natural English; for example 'when the camp had been surrounded, the soldiers attacked'. 'When', 'since' and 'after' are all common ways of translating ablative absolutes.
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Gwyneth E.

Answered by Gwyneth, Latin GCSE tutor with MyTutor


Differentiate x^2+6x+1

All we do here is break down into three parts: x2, 6x & 1.x2 becomes 2x as we multiply by the power and then decrease the power by one.6x becomes 6 and 1 becomes 0.So alltogether we have2x+6
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Samuel I.

Answered by Samuel, Maths A Level tutor with MyTutor

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