Hi, I'm Kirill, I'm a 3rd year physicist at Oxford. Whether you are looking for exam preparation or for a better understanding of the material that you are covering in your studies of Maths or Physics, I can help you reach your goals.
A level and GCSE standard Physics, Maths and Further Maths
With both physics and maths, an understanding of what you are fundamentally doing is key. I will endeavour to ensure that you understand both concepts and applications of what you are learning (and maybe gain an enthusiasm for the subjects if that is something you haven’t developed already!), doing so in a friendly and patient way. However, at the same time, having gone through the system myself, I know that a large component of being successful in public examinations is “jumping through the hoops”. I can teach you how to ensure that your knowledge of the subject gives you the grade that you deserve by improving exam technique.
Physics Aptitude Test (PAT) and Interview preparation
Even more so than in A levels, an understanding of what you are fundamentally doing is the key to doing well in the PAT and the interview. I can teach you the correct way to approach problems on the PAT and can check your answers to questions, given that there is no mark scheme available. I can also offer advice on the general application process to Oxford and also an insight into what life at Oxford is actually like. Finally, I can conduct mock interviews if that is something that would be helpful.
|Further Mathematics||A Level||£20 /hr|
|Maths||A Level||£20 /hr|
|Physics||A Level||£20 /hr|
|.PAT.||Uni Admissions Test||£25 /hr|
M (Parent) November 1 2016
Akshay (Student) September 26 2016
This is the sum of a geometric series with an infinite number of terms.
First, find the common ratio:
(-2/9)/(2/3) = -1/3 , (2/27)/(-2/9) = -1/3
Therefore, the common ratio is -1/3
-1<(-1/3)<1 therefore the series will converge to a finite number.
The general formula for a sum of an infinite geometric series is a/(1-r) where a is the first number in the sequence and r is the common ratio.
So, substituting in the numbers, the sum of the series = (2/3)/(1-[-1/3]) = 1/2see more
This is a question testing the knowledge of the equations of constant acceleration (Suvat equations)
First convert the question into a standard form. For example by writing out the variables as follows
s (displacement) = unknown
u (initial velocity) = 10m/s
v (final velocity) = 0m/s
a (acceleration) = 2ms^-2
t (time) = unknown
You know v, u and a and you want to calculate t, therefore the equation you need to use is v = u + a*t
Re-arranging t = (v - u) / a
Finally substituting in v, u and a, t = (10 - 0) / 2 = 5s
So the time taken for the car to stop is 5 seconds.see more
The easiest way of approaching this question is to use De Moivre's formula:
e^(inx) = cos(nx) + isin(nx)
from which it is simple to show that cos(nx) = (e^(inx) + e^(-inx)) / 2 and sin(nx) = (e^(inx))- e^(-inx)) /2i
therefore, cos(4x)sin(x) = (e^(4ix) + e^(-4ix)) * ((e^(ix)) - (e^(-ix)) / 4i
= [e^(5ix) - e^(-5ix) - e^(3ix) + e^(-3ix)] / 4i
= sin(5x)/2 - sin(3x)/2
Finally, integrating, this gives cos(3x)/6 - cos(5x)/10 + integration constant
This can also be done by using various trigonometric identities, however this method is simpler and can continue to be applied to more complex questions.see more