I am just entering my first year to study Physics at University of Birmingham, I've always enjoyed anything maths based hence my A-level choices, I hope I can help you through your work whether it's GCSE or A-level and maybe even inspire you while doing so.
I've tutored several GCSE students through their final year so have had experience with different students at all different levels. I'm very patient and will try to explain a topic in as many different ways as possible if it helps.
What you want to learn in sessions is entirely up to you. I can work through new problems you haven't seen or help redo any questions you don't understand, I will try to explain using whichever method you prefer whether it's analogies, teaching intuitively, or just giving you the facts if that's what you want.
55mins can be enough to master many topics and I hope you'll have some fun while doing so, hopefully my passion will shine through!
I'm applying to Oxford, can you help me with PAT?
Yes! I've been through the Oxford application process, even though I wasn't given a final offer I still had interviews after getting through the PAT so I'm definetely familiar and with some warning I'll make sure I know how to do any question you want to go through.
Feel free to send me a "Webmail" or book a "Meet the Tutor Session" if you think I may be able to help you at all and I'll get back to you as fast as possible. If you tell me your exam board then I can make sure I'm up to date with exactly what you need to know.
I look forward to meeting you!
As you can see I have not yet filled in my availibility, as soon as I get my schedule I will fill it out but for now if you contact me I will be able to tell you when I'm free. Sorry for the inconvenience.
|Further Mathematics||A Level||£20 /hr|
|Maths||A Level||£20 /hr|
|Physics||A Level||£20 /hr|
|Further Mathematics||GCSE||£18 /hr|
|Maths||13 Plus||£18 /hr|
|Maths||11 Plus||£18 /hr|
|.PAT.||Uni Admissions Test||£25 /hr|
|Before 12pm||12pm - 5pm||After 5pm|
Please get in touch for more detailed availability
So for this question you can use either the product rule or the quotient rule and I'll run through them both.
First the quotient rule:
The quotient rule says that if you have h(x)=f(x)/g(x)
Then h'(x) = (f'(x)g(x)-f(x)g'(x))/(g(x))^2
So using f(x)=cos(2x) and g(x)=x^1/2
then f'(x)=-2sin(2x) and g'(x)=1/2x^-1/2
Plugging this into our formula gives us
h(x) = (-2x^1/2sin(2x)-1/2x^-1/2cos(2x))/x
Always remember to simplify afterwards which gives us
Second the product rule:
What the product rule says is that if
h(x) = f(x)g(x)
then h'(x) = f(x)g'(x) + f'(x)g(x)
So if we say that h(x) = cos(2x)/x^1/2
Then we can say that f(x) = cos(2x) and g(x) = x^-1/2
Using the product rule we have:
f(x) = cos(2x) f'(x) = -2sin(2x)
g(x) = x^-1/2 g'(x) = 1/2x^-3/2
So lastly we know that h(x) = f(x)g'(x) + f'(x)g(x)
So using what we've found out we can say that h(x) = (cos(2x))/(2x^3/2)-(2sin(2x))/x^1/2
Once again simplifying gives us