Trapezium rule Question help...? Watch

Philip-flop
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For this question, how do you find out what the x values should go up in? (five-equally spaced ordinates). I must be wrong in thinking that these values should go up in intervals of 3 - 1 divide by 5 = 0.4

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Philip-flop
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or would it simply just be 3 - 1 divide by 4 = 0.5 intervals

e.g. 1, 1.5, 2, 2.5, 3
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ULTRALIGHT BEAM
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X = 1 3/2 2 5/2 3
Y = f(1) f(3/2) f(5/2) f(3)
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Zacken
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(Original post by Philip-flop)
or would it simply just be 3 - 1 divide by 4 = 0.5 intervals

e.g. 1, 1.5, 2, 2.5, 3
This is correct.

FWIW, a question with such archaic wording wouldn't come up on an exam paper. Instead, you'll be given a table with the values (mostly) already sorted for you or you'll asked to be deal with # of intervals directly, not this ordinates stuff. This is probably from ancient solomon paper or something.
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ULTRALIGHT BEAM
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(Original post by Zacken)
This is correct.

FWIW, a question with such archaic wording wouldn't come up on an exam paper. Instead, you'll be given a table with the values (mostly) already sorted for you or you'll asked to be deal with # of intervals directly, not this ordinates stuff. This is probably from ancient solomon paper or something.
Ordinates is not an archaic word - it is a mathematical terminology. Contrarily SPs are very good preparation for this very reason.
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Philip-flop
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(Original post by Zacken)
This is correct.

FWIW, a question with such archaic wording wouldn't come up on an exam paper. Instead, you'll be given a table with the values (mostly) already sorted for you or you'll asked to be deal with # of intervals directly, not this ordinates stuff. This is probably from ancient solomon paper or something.
Yes I agree that the wording of the question is very misleading which makes people more prone to mistakes!! And yeah, I'm doing Solomon papers :P

(Original post by ULTRALIGHT BEAM)
Ordinates is not an archaic word - it is a mathematical terminology. Contrarily SPs are very good preparation for this very reason.
Zacken, wasn't suggesting that the word 'ordinates' itself was archaic, I'm sure he meant the way the question was overall written.
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ULTRALIGHT BEAM
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For example, Edex may ask 'How can the approximation be ameliorated', in which an acceptable answer is 'increasing the number of (equally spaced) ordinates'.
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Zacken
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(Original post by Philip-flop)
For this question, how do you find out what the x values should go up in? (five-equally spaced ordinates). I must be wrong in thinking that these values should go up in intervals of 3 - 1 divide by 5 = 0.4

Click to enlarge question...

Name:  Trapezium rule Q.png
Views: 471
Size:  15.4 KB
Okay, I have a few minutes to spare so might as well waffle on about this, Whenever you're given a question of this type you should first look at what they're asking. There is a distinction between ordinates (number of lines) and intervals (number of bars). If they're asking about ordinates or number of lines then your first thing is to either draw on the paper or sketch a squiggly graph. Sometimes you aren't given a diagram in which case, sketching a random squiggly graph to imitate the diagram is essential.

In this example, you'd need to see that "okay, they want five lines or 5 ordinates (same thing)" then you draw 5 lines down as so:



Then you count the number of intervals manually and you see 4 intervals. So now you know that you want to do \frac{3-1}{4} = \frac{2}{4} = 0.5 lengths. Then you can then label each line with the "1.5, 2, 2.5, 3" to help you.

On the other hand - if you were given "we want 5 (equal width) intervals" Then you sketch your graph, etc... and this is what you should draw:



and from there you can see what the width of interval should be and you should be able to label each line with the appropriate x coordinate. Then proceed with the rest of the question normally.

Please, please, please make sure you always do this whenever you're doing this kind of question. It will save you from innumerable mistakes. Even if you're not given a diagram, just sketch a rough one, it doesn't need to be accurate at all.
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Philip-flop
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(Original post by Zacken)
Okay, I have a few minutes to spare so might as well waffle on about this, Whenever you're given a question of this type you should first look at what they're asking. There is a distinction between ordinates (number of lines) and intervals (number of bars). If they're asking about ordinates or number of lines then your first thing is to either draw on the paper or sketch a squiggly graph. Sometimes you aren't given a diagram in which case, sketching a random squiggly graph to imitate the diagram is essential.

In this example, you'd need to see that "okay, they want five lines or 5 ordinates (same thing)" then you draw 5 lines down as so:



Then you count the number of intervals manually and you see 4 intervals. So now you know that you want to do \frac{3-1}{4} = \frac{2}{4} = 0.5 lengths. Then you can then label each line with the "1.5, 2, 2.5, 3" to help you.

On the other hand - if you were given "we want 5 (equal width) intervals" Then you sketch your graph, etc... and this is what you should draw:



and from there you can see what the width of interval should be and you should be able to label each line with the appropriate x coordinate. Then proceed with the rest of the question normally.

Please, please, please make sure you always do this whenever you're doing this kind of question. It will save you from innumerable mistakes. Even if you're not given a diagram, just sketch a rough one, it doesn't need to be accurate at all.
Thank you Zacken!!
This has cleared up so much for me!
I am now aware of the distinction between "ordinates" and "intervals" for these types of questions!! I very much appreciate the time you put in to explain this to me! It means a lot to me as I am self-teaching AS-level Maths so sometimes feel very lost! So... Thank you
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Zacken
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(Original post by Philip-flop)
Thank you Zacken!!
This has cleared up so much for me!
I am now aware of the distinction between "ordinates" and "intervals" for these types of questions!! I very much appreciate the time you put in to explain this to me! It means a lot to me as I am self-teaching AS-level Maths so sometimes feel very lost! So... Thank you
Before I leave you alone, can you attempt this question for me and post up your answer either as picture/scan or just a general textual narrative outline of your method and your answer so I can verify it and your method? It'll help test your understanding!

It's this question:
Spoiler:
Show


And the sketch you should draw is (please do not open this until you have tried the question for yourself and attempted a sketch yourself, only use it to verify yours, you will benefit from not opening this):
Spoiler:
Show
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ULTRALIGHT BEAM
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Really good help Zacken is giving
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Zacken
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(Original post by ULTRALIGHT BEAM)
Really good help Zacken is giving
I'm not always an arrogant ****. :lol: Appreciated.
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Philip-flop
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(Original post by Zacken)
Before I leave you alone, can you attempt this question for me and post up your answer either as picture/scan or just a general textual narrative outline of your method and your answer so I can verify it and your method? It'll help test your understanding!

It's this question:
Spoiler:
Show

And the sketch you should draw is (please do not open this until you have tried the question for yourself and attempted a sketch yourself, only use it to verify yours, you will benefit from not opening this):
Spoiler:
Show
Sorry I had trouble with my scanner.
Here's my answer

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Zacken
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(Original post by Philip-flop)
Sorry I had trouble with my scanner.
Here's my answer
Good news: your method is perfect and that's lovely!

Bad news: I think you may have misread the question and worked with the curve y = x^{1/2} instead of y = x^{1/2}\ln 2x as given in the question; but that's just a misread error so your method is all good! Well done!
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Philip-flop
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(Original post by Zacken)
Good news: your method is perfect and that's lovely!

Bad news: I think you may have misread the question and worked with the curve y = x^{1/2} instead of y = x^{1/2}\ln 2x as given in the question; but that's just a misread error so your method is all good! Well done!
Oh god yeah, that's what I get for skim reading the question
At least I know the correct method now though I've just got to cut out silly little mistakes aha! Thanks a lot Zacken!!
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Zacken
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(Original post by Philip-flop)
Oh god yeah, that's what I get for skim reading the question
At least I know the correct method now though I've just got to cut out silly little mistakes aha! Thanks a lot Zacken!!
No problem! The method is all good and that was a C4 question, by the way, so good on you!
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Philip-flop
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(Original post by Zacken)
No problem! The method is all good and that was a C4 question, by the way, so good on you!
A C4 question?? :eek:
How much harder is A2 Level ?
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Zacken
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(Original post by Philip-flop)
A C4 question?? :eek:
How much harder is A2 Level ?
Depends on the person, I didn't really notice a step-up. But yeah, you should be happy.
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(Original post by ULTRALIGHT BEAM)
Really good help Zacken is giving
Agreed.
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ULTRALIGHT BEAM
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(Original post by Zacken)
Depends on the person, I didn't really notice a step-up. But yeah, you should be happy.
Yeah lol what was the difference between C2 & C4 TR Qs?
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