I am currently studying Natural Sciences at Durham University specialising in **maths and physics**. I have been tutoring with MyTutor for over 6 months and have thoroughly enjoyed helping each individual tutee over this online platform. Outside of MyTutor, I also tutored in person during my second year of sixth form and this prompted me to consider online tutoring while at university.

Through my previous experience of tutoring and my general interest in the subject I believe I have developed skills in recognising where a** tutee’s understanding is struggling** and providing relevant assistance to **facilitate their own learning**. Thank you very much for considering me and I look forward to hearing from you.

I am currently studying Natural Sciences at Durham University specialising in **maths and physics**. I have been tutoring with MyTutor for over 6 months and have thoroughly enjoyed helping each individual tutee over this online platform. Outside of MyTutor, I also tutored in person during my second year of sixth form and this prompted me to consider online tutoring while at university.

Through my previous experience of tutoring and my general interest in the subject I believe I have developed skills in recognising where a** tutee’s understanding is struggling** and providing relevant assistance to **facilitate their own learning**. Thank you very much for considering me and I look forward to hearing from you.

In preparation for a tutorial I aim to **set out goals** to complete during the tutorial. Whether this is reviewing a completed piece of work; in depth study into a specific topic area; or doing a general overview of the course through use of past papers, having a key goal allows the tutorial to stay **focussed and productive** and allows me to prepare the relevant material.

Each tutorial is then different depending on the task at hand but in general I will begin by **testing the tutee’s understanding** and probing with tailored questions to find where the tutee is strong and where they need more help. We will then **review the material** they struggled with explaining any difficulties and clarifying any misunderstandings. Finally, the process is concluded by **testing the tutee’s new understanding** of the topic we just covered. If the tutee signs up for multiple sessions then each session can begin by a short review of the last tutorial to ensure the topic is firm in the tutee’s mind.

In preparation for a tutorial I aim to **set out goals** to complete during the tutorial. Whether this is reviewing a completed piece of work; in depth study into a specific topic area; or doing a general overview of the course through use of past papers, having a key goal allows the tutorial to stay **focussed and productive** and allows me to prepare the relevant material.

Each tutorial is then different depending on the task at hand but in general I will begin by **testing the tutee’s understanding** and probing with tailored questions to find where the tutee is strong and where they need more help. We will then **review the material** they struggled with explaining any difficulties and clarifying any misunderstandings. Finally, the process is concluded by **testing the tutee’s new understanding** of the topic we just covered. If the tutee signs up for multiple sessions then each session can begin by a short review of the last tutorial to ensure the topic is firm in the tutee’s mind.

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To begin with, chemical energy in the fuel is released through combustion and becomes thermal energy. This thermal energy is used to heat water which evaporates and become steam. The rising steam turns turbines and the system now contains the kinetic energy of the turning turbines. The turbines are finally linked to a generator which converts the kinetic energy into electricity.

To begin with, chemical energy in the fuel is released through combustion and becomes thermal energy. This thermal energy is used to heat water which evaporates and become steam. The rising steam turns turbines and the system now contains the kinetic energy of the turning turbines. The turbines are finally linked to a generator which converts the kinetic energy into electricity.

In an atom, the mass is concentrated in the nucleus which is at the centre of the atom. The nucleus is composed of neutrons and protons, each with a relative mass of 1. By comparison, the third component of an atom is the electrons which orbit the nucleus and have a relatively neglible mass.

The charge of the atom is defined by the total charge of its components. Electrons have a charge of -1, protons of +1 and neutrons have no charge.

In an atom, the mass is concentrated in the nucleus which is at the centre of the atom. The nucleus is composed of neutrons and protons, each with a relative mass of 1. By comparison, the third component of an atom is the electrons which orbit the nucleus and have a relatively neglible mass.

The charge of the atom is defined by the total charge of its components. Electrons have a charge of -1, protons of +1 and neutrons have no charge.

In order to find the angle that satisfies a trigonometric function, the easiest way is to use the inverse function on a calculator.

E.g. cos(x)=2/3 then one solution is x=cos^-1(2/3).

In order to do this, we can set the subject of the function to u. In other words, we make the inside of the brackets equal to u and then find the new range.

u=17-2x. When x=-180, u=17-2(-180)=377

When x=180, u=17-2(180)=-343.

Therefore, -343 to 377 is our new range for u.

Since sec(u)=-2 and sec(u)=1/cos(u), we can invert both sides to get cos(u)=-1/2.

Using the cos^-1(-1/2) on a calculator we get one solution where u=120. Due to the symmetry around 180 of cos, we can find another solution using the formula 180+(180-120)=240.

To get the two remaining solutions within the range, we can use cos(a)=cos(-a) so the other solutions are -120 and -240.

We have the four solutions: u=-240, -120, 120, 240. And must now convert them back to x.

Since u=17-2x, x=(17-u)/2.

Therefore the solutions are x=128.5, 68.5, -51.5, -111.5 (all in degrees).

In order to find the angle that satisfies a trigonometric function, the easiest way is to use the inverse function on a calculator.

E.g. cos(x)=2/3 then one solution is x=cos^-1(2/3).

In order to do this, we can set the subject of the function to u. In other words, we make the inside of the brackets equal to u and then find the new range.

u=17-2x. When x=-180, u=17-2(-180)=377

When x=180, u=17-2(180)=-343.

Therefore, -343 to 377 is our new range for u.

Since sec(u)=-2 and sec(u)=1/cos(u), we can invert both sides to get cos(u)=-1/2.

Using the cos^-1(-1/2) on a calculator we get one solution where u=120. Due to the symmetry around 180 of cos, we can find another solution using the formula 180+(180-120)=240.

To get the two remaining solutions within the range, we can use cos(a)=cos(-a) so the other solutions are -120 and -240.

We have the four solutions: u=-240, -120, 120, 240. And must now convert them back to x.

Since u=17-2x, x=(17-u)/2.

Therefore the solutions are x=128.5, 68.5, -51.5, -111.5 (all in degrees).