I am currently reading **Mathematics at Imperial College London**. I’m warm, patient, reliable but most of all, enthusiastic. My tutoring aim is to make you, the tutee, enjoy Maths and deliver exam success.

Throughout sixth form, I helped peers studying Maths comprehend and excel at the subject. I enjoyed seeing them take an interest and progressing their mathematical understanding. I wish to do the same for you. I’ve finished the **Maths and Further Maths** A-level course, achieving** A*s** in both, so consequently I know the A-level course very well and by choosing me as your tutor I can give you an up-to-date knowledge of the course. I took Edexcel Maths at GCSE and A-level and so this I’m most confident teaching this exam board. However, I am more than capable of teaching other exam boards too.

My younger brother is now in his last year of his GCSEs and I’ve been helping him through the course so far. This means that I am familiar with GCSE Maths and what the course entails.

In my tutorials, I will make them** specific to you**. You decide what you want to me to cover, it’s as simple as that. Whether you’re aiming for a C at GCSE or an A* in Further Maths at A-level, I can cater for all you mathematical needs.

Feel free to contact me with any questions or book a ‘Meet the Tutor’ session with me. All the best and hopefully I’ll meet you soon.

I am currently reading **Mathematics at Imperial College London**. I’m warm, patient, reliable but most of all, enthusiastic. My tutoring aim is to make you, the tutee, enjoy Maths and deliver exam success.

Throughout sixth form, I helped peers studying Maths comprehend and excel at the subject. I enjoyed seeing them take an interest and progressing their mathematical understanding. I wish to do the same for you. I’ve finished the **Maths and Further Maths** A-level course, achieving** A*s** in both, so consequently I know the A-level course very well and by choosing me as your tutor I can give you an up-to-date knowledge of the course. I took Edexcel Maths at GCSE and A-level and so this I’m most confident teaching this exam board. However, I am more than capable of teaching other exam boards too.

My younger brother is now in his last year of his GCSEs and I’ve been helping him through the course so far. This means that I am familiar with GCSE Maths and what the course entails.

In my tutorials, I will make them** specific to you**. You decide what you want to me to cover, it’s as simple as that. Whether you’re aiming for a C at GCSE or an A* in Further Maths at A-level, I can cater for all you mathematical needs.

Feel free to contact me with any questions or book a ‘Meet the Tutor’ session with me. All the best and hopefully I’ll meet you soon.

No DBS Check

First, find the x coordinates of where the lines intersect by setting the equations of the lines equal to each other. Then solve the quadratic (or polynomial) equation. Next, integrate both lines individually with the limits being the x coodinates of the intersection. Then subtract the area of the lower line from the area of the upper line to find the area between the two.

For example:

Find the area between y=4x and y=x^{2 }- 2x + 5.

To find the x coordinates, set them equal to each other and solve.

So... 4x = x^{2 }- 2x + 5 => 0 = x^{2 }- 6x + 5. Thus using either the quadratic formula or factorising, we find that these lines intesect when x=1 and x=5

Next, we need to integrate the lines between the limits found.

So... y=4x integrates to => [2x^{2}] and when plugging in x=5, we get 50 and x=1 gives us 2. Thus the area of y=4x bound by the x axis, x=1 and x=5 is 50-2 = 48.

Similarly, y=x^{2 }- 2x + 5 integrates to => [x^{3}/3 - x^{2} + 5x]. Again, we put in x=5 and it gives 125/3 and x=1 gives us 13/3. Thus the area of y=x^{2 }- 2x + 5 bound by the x axis, x=1 and x=5 is 125/3 - 13/3 = 112/3.

We know by ploting the graphs that y=4x is above y=x^{2 }- 2x + 5. Hence, to find the area between these two lines is 48 - 112/3 = 32/3.

First, find the x coordinates of where the lines intersect by setting the equations of the lines equal to each other. Then solve the quadratic (or polynomial) equation. Next, integrate both lines individually with the limits being the x coodinates of the intersection. Then subtract the area of the lower line from the area of the upper line to find the area between the two.

For example:

Find the area between y=4x and y=x^{2 }- 2x + 5.

To find the x coordinates, set them equal to each other and solve.

So... 4x = x^{2 }- 2x + 5 => 0 = x^{2 }- 6x + 5. Thus using either the quadratic formula or factorising, we find that these lines intesect when x=1 and x=5

Next, we need to integrate the lines between the limits found.

So... y=4x integrates to => [2x^{2}] and when plugging in x=5, we get 50 and x=1 gives us 2. Thus the area of y=4x bound by the x axis, x=1 and x=5 is 50-2 = 48.

Similarly, y=x^{2 }- 2x + 5 integrates to => [x^{3}/3 - x^{2} + 5x]. Again, we put in x=5 and it gives 125/3 and x=1 gives us 13/3. Thus the area of y=x^{2 }- 2x + 5 bound by the x axis, x=1 and x=5 is 125/3 - 13/3 = 112/3.

We know by ploting the graphs that y=4x is above y=x^{2 }- 2x + 5. Hence, to find the area between these two lines is 48 - 112/3 = 32/3.