Dominic D. GCSE Further Mathematics  tutor, A Level Further Mathemati...

Dominic D.

Currently unavailable: for new students

Degree: MSci Theoretical Physics (Masters) - Birmingham University

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About me

Hi, I'm Dom, a third year Theoretical Physics student at the University of Birmingham. I have always been fascinated by the rich subjects that are maths and physics, and this enthusiasm is conveyed in my teaching. I have previous experience as a tutor and employ a friendly, patient approach. I particularly enjoy explaining concepts in different ways in order to ensure that you gain insight into the topic. I appreciate that everyone learns differently, so my teaching style will be tailored to you, allowing you to gain the most from the tutorials.

About my sessions

What the sessions consist of is entirely up to you and depends on what you would find most useful. Let me know what exam board you are on and the general area you wish to cover in the tutorial, and I will ensure that I am completely up to date with your specific course. Then, as well as improving your fundamental understanding of the topic, I can bring some example questions for us to go through. It is well known that in modern day examinations, exam technique is a considerable factor in achieving excellent marks. As such, I am more than happy for sessions to be focused on this, and we can go through past papers so that you are well prepared for whatever the examiners may throw at you!

For more information about the sessions or anything else, please don’t hesitate to send me a message or book a free ‘Meet the Tutor’ session.

Subjects offered

SubjectQualificationPrices
Further Mathematics A Level £20 /hr
Maths A Level £20 /hr
Physics A Level £20 /hr
Further Mathematics GCSE £18 /hr
Maths GCSE £18 /hr
Physics GCSE £18 /hr

Qualifications

SubjectQualificationLevelGrade
Further MathematicsA-levelA2A*
MathematicsA-levelA2A*
PhysicsA-levelA2A*
ChemistryA-levelA2A*
Human Biology (AS)A-levelA2A
Disclosure and Barring Service

CRB/DBS Standard

No

CRB/DBS Enhanced

No

General Availability

Currently unavailable: for new students

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Ratings and reviews

5from 1 customer review

Mohamed (Parent) December 16 2016

Very helpful. He explains the concept very clearly and makes sure you understand the topic to the fullest.
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Questions Dominic has answered

Solve the differential equation: e^(2y) * (dy/dx) + tan(x) = 0, given that y = 0 when x = 0. Give your answer in the form y = f(x).

This is a question taken from a core 4 paper and is a typical example of a differential equation question. The first thing to notice about this equation is that it is "separable", meaning we can rearrange it to get  e^(2y) dy = - tan(x) dx Now we can solve this by integrating both sides. We ...

This is a question taken from a core 4 paper and is a typical example of a differential equation question.

The first thing to notice about this equation is that it is "separable", meaning we can rearrange it to get 

e^(2y) dy = - tan(x) dx

Now we can solve this by integrating both sides. We know how to integrate the left hand side, and we get (1/2)e^(2y), but how can we integrate -tan(x)?

To see how we can do this, we write

-tan(x) = -sin(x) / cos(x)

Then, we realise that the numerator is the derivative of the denominator, and so integrating -tan(x) gives ln(|cos(x)|) + C, where C is the constant of integration. 

So, we now have that

(1/2)e^(2y) = ln(|cos(x)|) + C

Now we apply the condition that y(x=0) = 0, giving

1/2 = C

Subbing this in, we have

(1/2)e^(2y) = ln(|cos(x)|) + 1/2

Therefore 

e^(2y) = 2ln(|cos(x)|) + 1

The question asked for the answer to be written in the form y = f(x), and so we need to get the y out of the exponent, which we can do by taking ln of both sides to give

2y = ln( 1 + 2ln(|cos(x)|)  )

And so the final answer is

y = (1/2) ln( 1 + 2ln(|cos(x)|) )

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10 months ago

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