Mega A Level Maths Thread MK II

Can someone help me on this C2 Binomial Expansion question, part B. How do I go about these questions? Thanks :-)


Posted from TSR Mobile

Can someone help me on this C2 Binomial Expansion question, part B. How do I go about these questions? Thanks :-)


Posted from TSR Mobile

1 + x/4 = 1.025
x/4 = 0.025
x = 0.1

So sub that into your expansion

Saviour
Thanks for the quick reply

So, I want 95+ UMS in C3.

Any tips?

Also, question...

Parametric Functions, how to we find the second differential again?

Is it differentiating dy/dx wrt to t. And dividing by dt/dx?

OK, there are two ways:

- Firstly, you can convert to cartesian form and find the second derivative as you normally would.

- Secondly, you can find $\frac{dy}{dx}$ in terms of t, and differentiate this:

$\dfrac{dy}{dx} = f(t)$

$\dfrac{d^2y}{dx^2} \dfrac{dx}{dt} = f'(t)$

So:

[(dy/dx) d/dt]/(dt/dx)

What you've written is confusing to read but yes, essentially you differentiate the function for dy/dx with respect to t and divide by dx/dt. I'd always chain rule it how I did though; as I think simply knowing how to do that is better than learning an algorithm for it.

Yeah, that's how I do it... And how it was shown in the mark scheme

So I thought it the convention...

Yes, but if you understand where it comes from you'll be in much better stead than someone who simply knows what you have to do, but doesn't understand why. An example I have for this is M1 vectors:

Take one of the reasonably frequent questions which tell you a vector is, for example, parallel to i. A lot of people will learn these questions as "If parallel to i, j components are 0" and vice-versa. This works, but it's not a good way of approaching said questions. If someone simply understands that two vectors are parallel if they are scalar multiples of each other, then they will be much better off, especially for questions which have it parallel to a less standard vector, like 5i - 14j, for example.

(Also, finally decided to take the plunge and get a profile picture.)

So it's continuation of the chain rule?

Anyone know what M2 Vectors with Variable Acceleration is about? I've not covered M1 vectors because WJEC don't have them.

You can have your acceleration as a function of time. For example:

$a = 2t$

a is the rate of change of velocity with respect to time, so we can write:

$\frac{dv}{dt} = 2t$

and integrate to get $v=t^2 + c$

We can extend this idea to vectors:

a = 2ti+3t^2j

a is the derivative of v with respect to t, so we can integrate both sides with respect to t to get:

v = $t^2$i +$t^3$j

Okay... So that's it? Why use vectors at all? (excuse naivety)

For motion in multiple dimensions. if you don't use vectors you essentially have motion along a single line, which is unhelpful for a lot of physical situations. I believe you can get more dimensions by parametrics but vectors are easier/more effective for higher dimensions.

Can anyone help me with 9(e)? I know you use logs but not sure how...


Thank you so much!


Posted from TSR Mobile

Has anyone given any thought to the pi vs tau debate? The fact that 2pi crops up numerously in maths and physics and that it'd make more sense for tau (2pi) to be used.

That debate is so exasperating. But this sums everything up quite well:
[video="youtube;ZPv1UV0rD8U"]http://www.youtube.com/watch?v=ZPv1UV0rD8U[/video]