utah
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This is a question from an additional maths paper which I have been dwelling on for the past 2 hours or so. I have the mark scheme and hence the answer but I do not understand how it is solved. Please explain if you can make out how. For e.g., why isn't (a)(ii)3.5n or 4n - 1 ?

I understand (a)(i) and (b)(i) since they are really obvious but the rest literally makes me want to strangle a new-born baby.

The question:
(a) An artist makes a sequence of patterns.He uses three types of metal pieces called rods, springs and bobs.He welds them together to make patterns.
In Pattern 2 there are 7 rods, 8 springs and 2 bobs.
In Pattern n there are n bobs.

(i) How many springs are there in Pattern n?
(ii) How many rods are there in Pattern n?

(b) The artist now changes his design to make new patterns with greater widths.The pattern below is called Pattern 3 by 2.In Pattern x by y there are xy bobs.

(i) How many springs are there in Pattern x by y?
(ii) How many rods are there in Pattern x by y?

The answer in accordance to the mark scheme:
(a) (i) 4n
(ii) 3n + 1
(b) (i) 4xy
(ii) Strategy,
e.g. simplify then extend or lookat vertical and horizontal Method leading to correct answer,
e.g. notices 1more row to dimension comparison (x+1)y + x(y+1) ISW (2xy+x+y)
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Chittesh14
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(Original post by utah)
I understand (a)(i) and (b)(i) since they are really obvious but the rest literally makes me want to strangle a new-born baby.
In Pattern 2 there are 7 rods, 8 springs and 2 bobs.
In Pattern n there are n bobs.

(i) How many springs are there in Pattern n?
(ii) How many rods are there in Pattern n?

(b) The artist now changes his design to make new patterns with greater widths.The pattern below is called Pattern 3 by 2.In Pattern x by y there are xy bobs.

(i) How many springs are there in Pattern x by y?
(ii) How many rods are there in Pattern x by y?

The answer in accordance to the mark scheme:
(a) (i) 4n
(ii) 3n + 1
(b) (i) 4xy
(ii) Strategy,
e.g. simplify then extend or lookat vertical and horizontal Method leading to correct answer,
e.g. notices 1more row to dimension comparison (x+1)y + x(y+1) ISW (2xy+x+y)
First of all, if it's the 2nd pattern, it's the 2nd term in the sequence. If there are 8 spring rolls, 8/2 = 4... so the nth term will be 4n. If there are 7 rods, it will be 3n+1 as 6+1=7. You could write 4n-1, but it won't work out for the rest of the terms. If you test it:

1st pattern and 2nd pattern using the 3n+1 nth term: ((3 * 1) + 1) = 4 and ((3 * 2) + 1) = 7
1st pattern and 2nd pattern using the 4n-1 nth term: ((4 * 1) - 1) = 3 and ((4 * 2) - 1) = 7
As you can see the numbers were different in the 1st pattern, as the '4n-1' nth term doesn't work.

So, if the current pattern is n. The number of bobs is equal to the pattern number.
So there are n bobs. Using the nth term rule, we can find out the number of springs & rods.
To work out the number of springs; we use: 4n. There is no number, therefore the answer is just 4n. It is the same with the rods, the answer is 3n+1.

You can use the same principle to work out the answer to (b)(i), as the number of bobs is equal to the pattern. If the pattern is x by y, the number of bobs is xy. Therefore, the number of springs will be 4xy, as the nth term is 4n.

I don't really understand (ii) myself, sorry.
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simonli2575
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I would say the question is a bit ambiguous, if they had given another set of numbers for another pattern, it would have helped.
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utah
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(Original post by Chittesh14)
First of all, if it's the 2nd pattern, it's the 2nd term in the sequence. If there are 8 spring rolls, 8/2 = 4... so the nth term will be 4n. If there are 7 rods, it will be 3n+1 as 6+1=7. You could write 4n-1, but it won't work out for the rest of the terms. If you test it:

1st pattern and 2nd pattern using the 3n+1 nth term: ((3 * 1) + 1) = 4 and ((3 * 2) + 1) = 7
1st pattern and 2nd pattern using the 4n-1 nth term: ((4 * 1) - 1) = 3 and ((4 * 2) - 1) = 7
As you can see the numbers were different in the 1st pattern, as the '4n-1' nth term doesn't work.

So, if the current pattern is n. The number of bobs is equal to the pattern number.
So there are n bobs. Using the nth term rule, we can find out the number of springs & rods.
To work out the number of springs; we use: 4n. There is no number, therefore the answer is just 4n. It is the same with the rods, the answer is 3n+1.

You can use the same principle to work out the answer to (b)(i), as the number of bobs is equal to the pattern. If the pattern is x by y, the number of bobs is xy. Therefore, the number of springs will be 4xy, as the nth term is 4n.

I don't really understand (ii) myself, sorry.
Regarding your answer to (a)(ii): The number of rods in the first pattern is not given, so it could be 3 rods or 4 rods. In fact since we are only given one pattern to work with, the rule for n rods could be anything, i.e. '10n - 13'. It still gives 7 rods for the 2nd pattern. Well at least thats what I understand. But thanks for helping.
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utah
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(Original post by simonli2575)
I would say the question is a bit ambiguous, if they had given another set of numbers for another pattern, it would have helped.
Yes indeed, it really would.
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TenOfThem
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(Original post by utah)
Yes indeed, it really would.
Are you sure there was no more information

A diagram perhaps?
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utah
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(Original post by TenOfThem)
Are you sure there was no more information

A diagram perhaps?
Yes but it didn't offer much.
Here is the link(question 11):
http://www.jonesthesum.greenhill.pem...10_paper_1.pdf
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TenOfThem
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(Original post by utah)
Yes but it didn't offer much.
Here is the link(question 11):
http://www.jonesthesum.greenhill.pem...10_paper_1.pdf
The diagrams answer all your questions you have 3 sets of information for (a) and everything you need for (b)
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utah
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(Original post by TenOfThem)
The diagrams answer all your questions you have 3 sets of information for (a) and everything you need for (b)
How do the diagrams give 3 sets of information? I cant see how the diagrams for each pattern give you the number of rods, springs and bobs present in each pattern.
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TenOfThem
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(Original post by utah)
How do the diagrams give 3 sets of information? I cant see how the diagrams for each pattern give you the number of rods, springs and bobs present in each pattern.
Look at the pattern for 2

Can you see where the 7 rods are, where the 8 springs are, and where the 2 bobs are

It should be obvious
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utah
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(Original post by TenOfThem)
Look at the pattern for 2

Can you see where the 7 rods are, where the 8 springs are, and where the 2 bobs are

It should be obvious
After a good 3 mins and 56 seconds of staring at it, I was able to see it.
And of course I suck.
Thanks a lot.
Oh can you explain how (b)(ii) is done? Just a little bit confused.
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TenOfThem
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(Original post by utah)
After a good 3 mins and 56 seconds of staring at it, I was able to see it.
And of course I suck.
Thanks a lot.
Oh can you explain how (b)(ii) is done? Just a little bit confused.
Look for something general by looking at specifics

You have the rules for 1by
Find the rules for 2by and 3by
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