Edexcel S1 - Explanatory vs Response Variables

Bob · 2012-05-12 01:35:20

If it were me, I'd plan just one more practice (maybe the day before) on the confident ones and concentrate instead mainly on the ones you know will be harder.

In some subjects you have to learn lots of facts but for maths it's mainly knowing how to tackle question types and once you've got that sorted for a topic I'd be surprised if it fades that quickly. So I'd assume the 'easy stuff' will be fine and work on mastering the tough stuff, letting it become clearer gradually over the longer time.

Also, with the more advanced stuff, you end up re-doing some earlier stuff anyway because the later stuff all builds on what came before.

Also that word 'dreading'. If you start to get M4 sorted now, it'll make you feel better about all the exams because you'll have reduced that anxiety.

Bob

zetafunc. · 2012-05-12 01:48:15

I agree, that's why I like maths. There is not a lot of waffle, it is a subject which "practice makes perfect" probably applies to more easily than any other... for me, anyway. I know what you mean, the easy stuff in D1 is now so repetitive I've started skipping some of those questions in papers now. I did the same in S1 with calculating quartiles and drawing box plots -- they always ask the same thing so I'm confident with that.

The one topic I really hate in M4 though is relative motion. It feels like I'm doing a STEP paper when I do an M4 paper. I've heard that it's going to be really tough this year too. I just still can't wrap my head around it. I can do the simple problems but when it becomes really complicated with 10+ lines drawn on the same picture and lots of angles, it is just nauseating for me. I even prefer M5 over M4. With M5 there is lots of proof, differential equations, etc. it is so much nicer. With M4 they have these stupid conventions, like having a resistive force pointing the wrong way and they don't even justify why it is so, I had to google around only to find it was just a 'convention'. If you resolve it in the direction it's going you get the wrong answer. Why? I don't know. Should I start on M4 today?

Bob · 2012-05-12 05:10:08

If you show a force acting the 'wrong' way, it should just come out negative at the end ... so it shouldn't matter. Post the question if you want.

Should you start today? Yes, I would.

Bob

zetafunc. · 2012-05-12 05:22:37

Okay, I will start today.

I can't remember the question but it was from the new Edexcel M4 book. I'll see if I can find it when I have time.

From what I remember it was a spring hung from a ceiling undergoing simple harmonic motion, but then encountering a dampening force as it hit the water.

zetafunc. · 2012-05-12 07:18:02

Started back doing some M4 today for the first time in months. It feels really good to be getting back into the swing of mechanics again. I forgot how satisfying it was. I'd been utterly bored to death by D1 and S1 in the past two weeks! A nice diversion from crunching routine algorithms all the time. Thanks for telling me to work on M4 again, I believe I've found my motivation again.

zetafunc. · 2012-05-12 07:52:52

Okay, here is something I don't quite get (it's about resolving). Here's a question from the M4 book.

A particle P, of mass m, is projected upwards from horizontal ground with speed U. The motion takes place in a medium in which the resistance is of magnitude mgk²/v², where v is the speed of P and k is a positive constant. Show that P reaches its maximum height above ground after a time T given by T = (k/g)arctan(U/k).

In their method, they say:

R(^): F = ma

-mg - mgk²/v² = mdv/dt

They have justified having the component of weight and the resistance as negative because they're acting in the direction of x increasing (where x is measured from the ground). Fair enough... but what about the acceleration? How do we know that it's in the opposite direction? If the particle does reach a maximum height, is acceleration not downwards too?

zetafunc. · 2012-05-12 07:54:10

zetafunc. wrote:

They have justified having the component of weight and the resistance as negative because they're acting in the direction of x increasing* (where x is measured from the ground). Fair enough... but what about the acceleration? How do we know that it's in the opposite direction? If the particle does reach a maximum height, is acceleration not downwards too?

*decreasing, it should say, my apologies.

zetafunc. · 2012-05-12 08:16:35

Never mind, if you resolve it my way (weight, resistance downwards, and acceleration downwards also, BUT take initial velocity, U, to be negative), then you do get the right answer. I just had to take the small extra step of using the property that arctanx is an odd function i.e. arctan(-x) = -arctanx, and it came out. What a relief!

Bob · 2012-05-12 19:48:43

If you show a force acting the 'wrong' way, it should just come out negative at the end

This question is an example of that. If you 'pretend' you don't know whether the acceleration is up or down and just represent it by 'a', then the sign will come out at the end and tell you. That's simply because, in algebra, an unknown, a , behaves the same in all your equations whatever its value is, so being negative won't matter.

The only time it would matter is if you were dealing with an inequality and you wanted to multiply or divide by an amount where you didn't know the sign.. Then you'd have to consider both possibilities and see where each led.

Glad you are enjoying maths again; it's the challenges that make it interesting.

Bob

Math Is Fun Forum

#26 2012-05-12 01:35:20

Re: Edexcel S1 - Explanatory vs Response Variables

#27 2012-05-12 01:48:15

Re: Edexcel S1 - Explanatory vs Response Variables

#28 2012-05-12 05:10:08

Re: Edexcel S1 - Explanatory vs Response Variables

#29 2012-05-12 05:22:37

Re: Edexcel S1 - Explanatory vs Response Variables

#30 2012-05-12 07:18:02

Re: Edexcel S1 - Explanatory vs Response Variables

#31 2012-05-12 07:52:52

Re: Edexcel S1 - Explanatory vs Response Variables

#32 2012-05-12 07:54:10

Re: Edexcel S1 - Explanatory vs Response Variables

#33 2012-05-12 08:16:35

Re: Edexcel S1 - Explanatory vs Response Variables

#34 2012-05-12 19:48:43

Re: Edexcel S1 - Explanatory vs Response Variables

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