It was really useful for my revision to go back through stats as when we covered it in school we rushed through it quite quickly! I found it helpful to use my knowledge in exam questions too as that is usually where I struggle. It was overall just really helpful in terms of revision, expanding some of my knowledge and applying it to questions.

Poonam, Student

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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.

In french, three different kinds of verbs can be made: the '1st group' ones finishing by -er, the '2nd group' ones by -ir and the '3rd group' finishing by any other ending (-oir for example). The '1st group' verbs are the easiest to conjugate in the present tense because the endings are always the sames. For the 1st person, 'Je', the ending is: -e.
For the 2nd person, 'Tu', the ending is: -es.
For the 3rd person, 'Il, Elle, On', the ending is: -e (notice that is it the same as the ending of the 1st person).
For the 4th, 'Nous', the ending is: -on.
For the 5th, 'Vous', the ending is: -ez.
Finally, for the 6th, 'Ils, Elles', the ending is: -ent. In order to conjugate the verb, you have to take the 'infinitif' form of the verb, take the ending away (-er), and then simply replace it by the ending according to the person doing the action. We can now try with an example. 'Danser' means (to) dance, and 'danser' is the 'infinitive' form. It is in the '1st group' category because it finishes in -er. To conjugate it, we need to take away -er, and to replace it with the other endings. So, we only keep 'dans' and add the endings. This gives us:
Je danse
Tu danses
Il, Elle, On danse
Nous dansons
Vous dansez
Ils, Elles dansent.

Answered by Marina K.

Studies Politics,Philosophy and Economics at Exeter

The ways to differentiate a function depend on the function itself. If there is only one x value in the function you can differentiate as normal (hard to explain on a computer), yet if the function contains more than one x value is a separate place, you will need to use another approach such as the chain, product or quotient rule

Answered by Barnaby N.

Studies Economics at Bath

Well we need to define what is meant by a pressure group before we attempt to answer this question. Now a pressure group is a group that tries to influence public policy in the interest of a particular cause and we can see that pressure groups can aid in democracy for several reasons.
Firstly they help compensate for tyranny of the majority. This is achieved by pressure groups representing the issues of minorities and can help bring about substantive change that can help these minorities. For example the Disability Discrimination Act of 1995 came about after over 100,000 disabled people engaged in mass protest. Therefore, we can see pressure groups and pressure group activity to have helped a persecuted minority and this is undoubtedly good for democracy.
Secondly, pressure groups plug the gap in the electoral process. Without pressure groups, people may not get the chance to hold government to account apart from once every 5 years when they vote. Similarly they help compensate for election geography and by this I mean that members of a certain constituency may be voting on matters that are not confined to that constituency. So, for example, the London Cycling Campaign allows people who do not live in a London constituency the opportunity to have a say on cycling in London, through the use and membership of that said pressure group.
Finally, pressure groups encourage participation. Pressure groups can be seen to be an alternative to political parties. As political party membership has decreased, the membership of pressure groups has been on the rise. For example, the conservative party has just over 500,000 members. However, the National Trust has close to 4,000,000 members. The reason for this increase in membership of pressure groups is largely down to the significant ease of access, with sites like 38 degrees allowing for people to sign petitions online.

Answered by Joseph F.

Studies Politics and International Relations at Bristol

In order to get from f(x) to f''(x) we need to differentiate the function f(x) with respect to x and then differentiate the resulting function with respect to x again. When differentiating f(x), split the equation f(x) into smaller parts. These parts should be separated by + and - signs. In this case 5x^3 will be one part, -6x^(4/3) will be another then +2x and finally -3.
Next step would be to differentiate each part separately, then in the end add them together. Following the rules of differentiation, 5x^3 will become 15x^2, as the constant - number that is not x (in this case 5) - is multiplied by the power of x (which is 3) and then power is reduced by 1 to give us 15x^2. Next part, which is -6x^(4/3) will differentiate to -8x^(1/3). Following the rules of differentiation: -6*4/3 = -8; 4/3 - 1 = 1/3
Third part, which is +2x, will differentiate into +2. That's because +2x can be written as +2x^1. So by following the rules we get +2x^0. Since any number to the power of 0 equals to 1, +2x^0 can be written as +2*1 which is +2.
Next part would have been -3, but because it is a constant (it does not contain x) when differentiating it will become 0.
to finish the first step, we need to add all differentiated parts together, giving 15x^2 - (9/2)x^(-1/4) + 2. This is now f'(x). To get to the f''(x), the f'(x) function must be differentiated again with respect to x. Just like before break the equation into parts, separated by + or - sign and differente each of them separately. 15x^2 will become 30x
-(8)x^(1/3) will become -(8/3)x^(-2/3). Be careful with the signs when differentiating, as -8 multiplied by 1/3 will give -8/3 and (1/3)-1 will give -2/3.
Next part which is +2 disappears when differentiating as now it is just a constant, so just like -3 in original equation it will become 0.
Finally, add all differentiated parts together to get 30x - 8/3 x^(-2/3).
With questions like that it is very easy to get signs wrong when differentiating. The best way to make sure this does not happen is to practice these types of questions and not rush it.

Answered by Alexey B.

Studies Economics at Durham

In order to understand this question we must define what modulus-argument form is. The modulus of a complex number is its distance from the origin (0,0) on the Argand Diagram. It is written as |z|.
The argument of a complex number is the angle subtended anticlockwise between the x axis and a line drawn from the origin to the complex number. This is written where the angle is between -π and π radians (where the angle is below the x axis, it is written as a negative because the angle is measured clockwise around the origin). It is written as arg(z).
If you are unaware of what the Argand diagram is, don’t worry, here is a brief explanation!
The Argand diagram is a really useful visual aid for the use of complex numbers where they are split into their real and imaginary components. The real part is represented by a value on the x axis and the imaginary part is represented by a value on the y axis. This allows us to visualise the “size” of complex numbers, in other words the modulus.
The number can be easily shown on the Argand diagram, with the x (real part) value of 1, and the y (imaginary part) value of √3.
To find the modulus of this number which we will now refer to as z, we must effectively find the length of the line drawn from the origin to z. By creating a right angled triangle with the modulus as the hypotenuse, we can see that the other two lengths are 1 and √3.
Pythagoras proved that a^2 +b^2=c^2 which we can use to find the length of the hypotenuse: the modulus. So the |z|^2=(1)^2 +(√3)^2
|z|^2=1+3=4
|z|=2
So we have found the modulus to be 2.
We have defined that arg(z) is the angle between the x axis and the line from the origin to z.
Using trigonometric properties of the right angled triangle drawn we can use the tangent function to find the argument.
We know that tan(x)=Opposite/Adjacent.
The opposite in this case is √3 and the adjacent is 1. Therefore tan(x)=√3/1=√3
Using the inverse tangent function we find that arg(z)=arctan(√3)= π/3 radians.
And there is our final answer, that |z|=2 and arg(z)= π/3.
Extension: What is the modulus-argument form of z= -1-2i
Answer |z|=√5
arg(z)=-2π/3

Answered by Tom M.

Studies Maths at Durham

Operant conditioning uses reinforcement and punishment to strengthen or weaken behaviours, whereas classical conditioning uses associations to make connections between a stimulus and behaviour.

Answered by Simrit S.

Studies Psychology and Language sciences at University College London

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