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Area under the curve (A2) OCR

So in some questions they want you to get the are under the curve. And because we still live in the dark ages, we're supposed to do that by counting squares, and definitely NOT by the trapezium rule we learned in A level maths, because GOD FORBID we integrate (pun unintended) that into the Physics A level, it's waaaayyy too hard for physics examiners to understand. I'm sorry for that mini-rant, a level physics made me hate physics, which used to be my favorite subject.

Now on with the question lol,
Capture d’écran 2016-06-01 à 18.42.03.png
like how would you even count those?? There isn't enough time in the world? Also what the hell is the mark scheme (attached) talking about?
Attachment not found
Capture d’écran 2016-06-01 à 18.42.13.png22.9KB
Original post by gagafacea1
So in some questions they want you to get the are under the curve. And because we still live in the dark ages, we're supposed to do that by counting squares, and definitely NOT by the trapezium rule we learned in A level maths, because GOD FORBID we integrate (pun unintended) that into the Physics A level, it's waaaayyy too hard for physics examiners to understand. I'm sorry for that mini-rant, a level physics made me hate physics, which used to be my favorite subject.

Now on with the question lol,
Capture d’écran 2016-06-01 à 18.42.03.png
like how would you even count those?? There isn't enough time in the world? Also what the hell is the mark scheme (attached) talking about?
Attachment not found


Um, you can't use the trapezium rule without a function that defines the graph. Otherwise you'd just draw some random convenient trapezia and estimate the area that way, which is probably a worse estimate than simply counting the squares.

Even if you did have a function you could (almost certainly) integrate it between the required limits to get the exact area (by definition of area under a curve).
Original post by IrrationalRoot
Um, you can't use the trapezium rule without a function that defines the graph. Otherwise you'd just draw some random convenient trapezia and estimate the area that way, which is probably a worse estimate than simply counting the squares.

Even if you did have a function you could (almost certainly) integrate it between the required limits to get the exact area (by definition of area under a curve).


You don't need to know the function, the trapezium rule requires the y-values, which can effortlessly be gotten from the graph.
Original post by gagafacea1
You don't need to know the function, the trapezium rule requires the y-values, which can effortlessly be gotten from the graph.


Yes, but then you only get estimates from the points. Trapezium rule is redundant anyway when you have the graph with points plotted. You'd just draw convenient trapezia (not necessarily with a fixed step length) and that's normal estimating.
Original post by IrrationalRoot
Yes, but then you only get estimates from the points. Trapezium rule is redundant anyway when you have the graph with points plotted. You'd just draw convenient trapezia (not necessarily with a fixed step length) and that's normal estimating.


The trapezium rule only makes it so that it's faster to do the estimation. It's kind of an algorithm for me to follow. But the thing is my answer is always out of the wanted range for some reason. Apparently the trapezium rule doesn't give a good estimation, but counting squares does. Which I still don't know how the hell would it be done??
Original post by gagafacea1
The trapezium rule only makes it so that it's faster to do the estimation. It's kind of an algorithm for me to follow. But the thing is my answer is always out of the wanted range for some reason. Apparently the trapezium rule doesn't give a good estimation, but counting squares does. Which I still don't know how the hell would it be done??


Well I have to agree it looks pretty tedious but you can make a chunk of the work a lot easier by working out the area of the central rectangle and only then counting the rest of the squares.
But yeah counting squares is a lot more accurate.

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