Ollie has been my science tutor for what must be close-ish to a year! He is very good at explaining, and uses the whiteboard very well to visually explain the science. If i do not understand something the first time, he tries to find other ways to explain it. He also goes above and beyond to help me in his free time by creating revision guides to help me revise for my GCSEs. I

Houssein, 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.

When dealing with powers of complex numbers, always start by putting the quantity into exponential form.

** i** has a magnitude of

**i = exp(iπ/2)**

Now the expression is in exponential form, taking the square root is easy, using basic exponential math.

**sqrt(i) = (exp(iπ/2))^(1/2) = exp(iπ/4)**

This quantity has a modulus of** 1** and an argument of

**sqrt(i) = (1 + i)/sqrt(2)**

Answered by Jamie L.

Studies Physics at Exeter

Problems of this style are solved using the chain rule.

To begin, define the quantity inside the brackets as *u*

**u = 6x-1** such that **y = u^7**

It is now useful to write the chain rule. We can see

**dy/dx = du/dx x dy/du**

as the ** du **'cancel'. Now, all we need to do is differentiate two simple expressions:

**du/dx = 6 **and **dy/du = 7u^6**

Substituting these expressions back into the chain rule:

**dy/dx = 42u^6**

Finally, substitute ** u **into this expression to give the final answer,

**dy/dx = 42(6x-1)^6**

Answered by Jamie L.

Studies Physics at Exeter

In order to find the value of x we can first factorise the equation.

To factorise a quadratic we put it in the form:

(x+a)(x+b)=0

When multiplying out this general term we get:

x^2 + bx + ax + ab = 0

This can be simplified to :

x^2 + (a+b)x + ab = 0

Therefore we know that we need to find two integers that add to 8 and multiply to 15

First we find the integers that can multiply to 15:

1x15=15

3x5=15

We can see that out of these two possibilities of integer pairs to be used in the factorisation, 3 and 5 add to give 8.

Therefore : a + b = 8

ab=15

a=3 b=5

(x+3)(x+5)=0

Therefore x+3=0 or x+5=0

This rearranges to give x=-3 or x=-5

Answered by Clare B.

Studies Biochemistry with maths at Exeter

let y=arsinh(x)

x=sinh(y)=(e^{y} - e^{-y})/2

2x=e^{y }- e^{-}^{y}

2x*e^{y}=e^{y}-1 (multiply bye^{y})

0=(e^{y})^{2}-2xe^{y}-1

This is a quadratic in e^{y} with coefficients: a=1,b=-2x,c=-1

Usinng the quadratic formula (and simplifying):

e^y=x +/- sqrt(x^{2}+1)

but e^{y}=x-sqrt(x^{2}+1) isn't possible as e^{y}>0 for all y.

so e^{y}=x+sqrt(x^{2}+1)

y=ln(x+sqrt(x^{2}+1))

arsinh(x)=ln(x+sqrt(x^{2}+1)).

(Note that sqrt(x) is standard notation for 'the square root of x' on computers).

Answered by Joe B.

Studies Mathematics G100 at Bath

Elasticity of demand, or more formally Price Elasticity of Demand (PED) is a measure of the extent to which the amount of a good demanded by consumers varies with response to a change in its price. It can be measured by the percentage change in quantity demanded divided by the percentage change in the price. As increases in price almost always cause a drop in demand (with the rare exception of Giffen goods), PED is usually a negative number (or 0) ranging from 0 (perfectly inelastic demand) to minus infinity (perfectly elastic demand).

Answered by Noah C.

Studies PPE at Oxford, Magdalen College

When proving trigonometric identites, we must show that the left hand side of the equation = the right hand side. Here we will start with the left hand side (LHS) and show that it is equivalent to the right hand side (RHS).

LHS=2sin(2x)-3cos(2x)-3sin(x)+3

Using the double angle rules for sin(2x) and cos(2x);

LHS=2(2sin(x)cos(x))-3(cos^{2}(x)-sin^{2}(x))-3sin(x)+3

Notice that the RHS has sin(x) factorised out, meaning that every term in the LHS has a common factor of sin(x). Currently the LHS has a cos^{2}x term, but we can change this to a sin^{2}x term using the identity: cos^{2}(x)=1-sin^{2}(x)

LHS=2(2cos(x)sin(x))-3(1-sin^{2}(x)-sin^{2}(x))-3sin(x)+3

=4cos(x)sin(x)-3(1-2sin^{2}(x))-3sin(x)+3

=4cos(x)sin(x)-3+6sin^{2}(x)-3sin(x)+3

=4cos(x)sin(x)+6sin^{2}(x)-3sin(x)

=sin(x)(4cos(x)+6sin(x)-3)

=RHS

We have shown that LHS=RHS, therefore the proof is complete.

Answered by Joe B.

Studies Mathematics G100 at Bath

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