ameen
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salam,
please can you confirm that the question is actually from C2 - 'Geometric Sequences / Series' , and not C1 ?
That equation is in my C2 book, but not C1.
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salam,
please can you confirm that the question is actually from C2 - 'Geometric Sequences / Series' , and not C1 ?
That equation is in my C2 book, but not C1.
strider
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Yes, it was interesting. We are currently discussing the nature v. nuture argument. Today's lesson concentrated on feral children (children brought up by wild animals and subsequently adopt many of the behavioural patterns attributed to them; there was a documentary on Channel 4 called 'wild child' and you can check out www.feralchildren.com if you are interested):
Sister, how did the lesson go? Was it interesting? What was your fist lesson about? Most of all, what made you want to study sociology?
In answer to your last question: people fascinate me. Why do some people act the way they do, what influences them, how do certain things affect them etc etc. I'm taking psychology and inshaAllah i want to go onto study psychology in depth at Uni, and as sociology is inter-connected i've decided to study it. Oh, and whoever says psychology/sociology are 'common sense' subjects are very wrong as it is based on research and evidence not just opinions. :giggling:
Ameeratul Layl
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salam,
it is definately C1.
sis strider, you enjoy those lessons and keep us updated.
wasalam
it is definately C1.
sis strider, you enjoy those lessons and keep us updated.
wasalam
ameen
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salam,
here is part of the Formulae-sheet for C2, from Edexcel's website..
you can see that the equation you mentioned in your question is part of the C2 specification:
I think what happened is that they used an equation from a C2 topic - as an example - in the C1 topic you mentioned: 'Evaluating formulae, simlpifying expressions and expanding brackets.'
Last edited:
ameen
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this is how I would evaluate the equation using the values given in the question, although somebody else might know a better way :
a = 3
r = 1/3
n = 4
S = ...
a ( 1 - r ^n )
__________
1 - r
substituting in the values given in the question:
3 [ 1 - (1/3)^4 ]
_____________
1 - (1/3)
simplify top and bottom:
3 [ 1 - (1/81) ]
____________
2/3
then expand brackets:
3 - (1/27)
________
2/3
multiply both top and bottom by 3:
9 - (1/9)
_______
2
simplify top:
80/9
____
2
finally, this simplifies to: S = 80/18 , which further simplifies to 40/9 .
please let me know if I can clarify any part of this answer.
wsalam
a = 3
r = 1/3
n = 4
S = ...
a ( 1 - r ^n )
__________
1 - r
substituting in the values given in the question:
3 [ 1 - (1/3)^4 ]
_____________
1 - (1/3)
simplify top and bottom:
3 [ 1 - (1/81) ]
____________
2/3
then expand brackets:
3 - (1/27)
________
2/3
multiply both top and bottom by 3:
9 - (1/9)
_______
2
simplify top:
80/9
____
2
finally, this simplifies to: S = 80/18 , which further simplifies to 40/9 .
please let me know if I can clarify any part of this answer.
wsalam
Last edited:
Ameeratul Layl
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salam,
Can you show the simplifying step by step please. Infact, everything step by step.
i.e: point out when you are going to change one number to the other side and why. Etc.
wasalam
P.s: It takes a while for things to sink in so please don't get offended if I say I don't understand. Its me!
Can you show the simplifying step by step please. Infact, everything step by step.
i.e: point out when you are going to change one number to the other side and why. Etc.
wasalam
P.s: It takes a while for things to sink in so please don't get offended if I say I don't understand. Its me!
ameen
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salam,
Please see my comments after each step of the answer, given in bold.
a = 3
r = 1/3
n = 4
S = ...
a ( 1 - r ^n )
__________
1 - r
This is the equation given in the question, and you will be trying to find out what 'S' is (left-hand side of the equation), using the values of 'a' , 'r' , and 'n' given in the question, by substituting them into the right-hand side of the equation.
substituting in the values given in the question:
3 [ 1 - (1/3)^4 ]
_____________
1 - (1/3)
Here you simply put in the values of 'a' , 'r' and 'n' , as given in the question, into the right-hand side of the equation (you replace the letters with the numbers). This is because you are trying to find out what 'S' is equal to, and 'S' is equal to everything on the right-hand side of the original equation.
simplify top and bottom:
3 [ 1 - (1/81) ]
____________
2/3
To simplify the top of the fraction, 3 [ 1 - (1/3)^4 ] , you need to work out the (1/3)^4 part. To do this without using a calculator, you need to know that according to one of the 'rules of powers', (1/3)^4 is the same as putting both the top and bottom parts of the fraction to the power of 4, like this:
1^4
____
3^4
and since 1^4 is 1, and 3^4 is 81, this part becomes 1/81 .
To simplify the bottom part of the fraction, 1 - (1/3) , you need to know that '1' can be written as 3/3 , so that instead of working out 1 - (1/3) , you can work out (3/3) - (1/3) instead. (3/3) - (1/3) , is 2/3 , because when the bottom parts of two fractions are the same (which is 3 in this case), you can just subtract the top part of one fraction from the top part of the other fraction, whenever you want to subtract the one fraction from the other (it is one of the 'rules of fractions').
then expand brackets:
3 - (1/27)
________
2/3
To expand 3 [ 1 - (1/81) ] , you multiply what is on the 'outside' (3 in this case), with each term on the inside. So after expansion, this becomes 3 x 1 = 3 , and
3 x (1/81) = 3/81. But 3/81 can be written in a more 'simple' / 'smaller' form, because you can divide both the top and the bottom of this fraction by the same number, to get a more simple fraction which is equivalent to the original. Dividing the top '3' and the bottom '81' by 3 gives 1 and 27 respectively. Therefore, you can write 3/81 as 1/27, as both of these fractions are equivalent, but the latter is 'simpler'.
multiply both top and bottom by 3:
9 - (1/9)
_______
2
Here, you are multiplying top and bottom by 3 because you want to get rid of the fraction at the bottom (the 2/3) . Multiplying the bottom by 3 eliminates this fraction, making the 2/3 become just 2. To multiply the top, 3 - (1/27) , by 3, you need to carry out this expansion: 3 [ 3 - (1/27) ] . So again, you multiply the 3 which is 'outside', with each term inside: 3 x 3 = 9 , and 3 x 1/27 is 3/27. However, once again, 3/27 can be written in a simpler form, by dividing both the top and the bottom by the same number (3 in this case), so 3/27 becomes 1/9 instead.
simplify top:
80/9
____
2
To simplify 9 - (1/9) , you need to write the '9' as a fraction which will allow you to carry out the subtraction without using a calculator. To be able to do this, you need to make the bottom parts of each fraction the same. Looking at the (1/9) , you can see that the bottom part of this fraction is 9, so you should try to also write the '9' in a fraction-form with 9 at the bottom.
This is how you can do this -
think of 9 as:
9
_
1
Using the rule: you have to do to the top whatever you do to the bottom (and vice versa), you can multiply both the top and the bottom of this fraction by 9 , in order to convert it into:
81
__
9
now that you have the '9' written in this form (81/9), with 9 at the bottom of the fraction, you can work out the 9 - (1/9) part, by working out (81/9) - (1/9) instead. The bottom parts of these two fractions are the same, so you can just work out 81 - 1 (subtracting the top parts), to arrive at 80/9.
finally, this simplifies to: S = 80/18 , which further simplifies to 40/9 .
Dividing 80/9 by 2 gives 80/18, because when you divide a fraction by any number, you can simply multiply the bottom part of this fraction by that number (it's one of the 'rules of fractions'). 80/18 finally simplifies to 40/9, because you can divide both the top and the bottom parts of this fraction by 2, to arrive at the fraction, 40/9, which is equivalent to 80/18, but is simpler.
Please let me know if you have any questions about any parts of this post.
wsalam
Please see my comments after each step of the answer, given in bold.
a = 3
r = 1/3
n = 4
S = ...
a ( 1 - r ^n )
__________
1 - r
This is the equation given in the question, and you will be trying to find out what 'S' is (left-hand side of the equation), using the values of 'a' , 'r' , and 'n' given in the question, by substituting them into the right-hand side of the equation.
substituting in the values given in the question:
3 [ 1 - (1/3)^4 ]
_____________
1 - (1/3)
Here you simply put in the values of 'a' , 'r' and 'n' , as given in the question, into the right-hand side of the equation (you replace the letters with the numbers). This is because you are trying to find out what 'S' is equal to, and 'S' is equal to everything on the right-hand side of the original equation.
simplify top and bottom:
3 [ 1 - (1/81) ]
____________
2/3
To simplify the top of the fraction, 3 [ 1 - (1/3)^4 ] , you need to work out the (1/3)^4 part. To do this without using a calculator, you need to know that according to one of the 'rules of powers', (1/3)^4 is the same as putting both the top and bottom parts of the fraction to the power of 4, like this:
1^4
____
3^4
and since 1^4 is 1, and 3^4 is 81, this part becomes 1/81 .
To simplify the bottom part of the fraction, 1 - (1/3) , you need to know that '1' can be written as 3/3 , so that instead of working out 1 - (1/3) , you can work out (3/3) - (1/3) instead. (3/3) - (1/3) , is 2/3 , because when the bottom parts of two fractions are the same (which is 3 in this case), you can just subtract the top part of one fraction from the top part of the other fraction, whenever you want to subtract the one fraction from the other (it is one of the 'rules of fractions').
then expand brackets:
3 - (1/27)
________
2/3
To expand 3 [ 1 - (1/81) ] , you multiply what is on the 'outside' (3 in this case), with each term on the inside. So after expansion, this becomes 3 x 1 = 3 , and
3 x (1/81) = 3/81. But 3/81 can be written in a more 'simple' / 'smaller' form, because you can divide both the top and the bottom of this fraction by the same number, to get a more simple fraction which is equivalent to the original. Dividing the top '3' and the bottom '81' by 3 gives 1 and 27 respectively. Therefore, you can write 3/81 as 1/27, as both of these fractions are equivalent, but the latter is 'simpler'.
multiply both top and bottom by 3:
9 - (1/9)
_______
2
Here, you are multiplying top and bottom by 3 because you want to get rid of the fraction at the bottom (the 2/3) . Multiplying the bottom by 3 eliminates this fraction, making the 2/3 become just 2. To multiply the top, 3 - (1/27) , by 3, you need to carry out this expansion: 3 [ 3 - (1/27) ] . So again, you multiply the 3 which is 'outside', with each term inside: 3 x 3 = 9 , and 3 x 1/27 is 3/27. However, once again, 3/27 can be written in a simpler form, by dividing both the top and the bottom by the same number (3 in this case), so 3/27 becomes 1/9 instead.
simplify top:
80/9
____
2
To simplify 9 - (1/9) , you need to write the '9' as a fraction which will allow you to carry out the subtraction without using a calculator. To be able to do this, you need to make the bottom parts of each fraction the same. Looking at the (1/9) , you can see that the bottom part of this fraction is 9, so you should try to also write the '9' in a fraction-form with 9 at the bottom.
This is how you can do this -
think of 9 as:
9
_
1
Using the rule: you have to do to the top whatever you do to the bottom (and vice versa), you can multiply both the top and the bottom of this fraction by 9 , in order to convert it into:
81
__
9
now that you have the '9' written in this form (81/9), with 9 at the bottom of the fraction, you can work out the 9 - (1/9) part, by working out (81/9) - (1/9) instead. The bottom parts of these two fractions are the same, so you can just work out 81 - 1 (subtracting the top parts), to arrive at 80/9.
finally, this simplifies to: S = 80/18 , which further simplifies to 40/9 .
Dividing 80/9 by 2 gives 80/18, because when you divide a fraction by any number, you can simply multiply the bottom part of this fraction by that number (it's one of the 'rules of fractions'). 80/18 finally simplifies to 40/9, because you can divide both the top and the bottom parts of this fraction by 2, to arrive at the fraction, 40/9, which is equivalent to 80/18, but is simpler.
Please let me know if you have any questions about any parts of this post.
wsalam
Last edited:
Ameeratul Layl
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salam,
jazakAllah brother ameen. I understand it now.alhamdullilah.
If anyone needs help with AS:
Human biology,chemistry,physics...Do let me know!
wasalam
jazakAllah brother ameen. I understand it now.alhamdullilah.
If anyone needs help with AS:
Human biology,chemistry,physics...Do let me know!
wasalam
Ameeratul Layl
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salam,
People, please don't be afraid to ask any questions. There is always someone here to help.InshAllah.
wasalam
People, please don't be afraid to ask any questions. There is always someone here to help.InshAllah.
wasalam
Starseeker
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Okay who can answer this question I need Helpppp:
State two ways in which the structure of a capillary is related to its function
It's for Biology and I dont understand it and Google isnt helping either.
State two ways in which the structure of a capillary is related to its function
It's for Biology and I dont understand it and Google isnt helping either.
Ameeratul Layl
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I'm not going to supply you with the answer but.
Think: What does the capillary consist of (tissue or bone)? What is its structure like and how does the structure help with its job?
Ameeratul Layl
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salam,
I was looking through an exam paper yesterday and today and I just could not get my head around the mark scheme answer. So, could someone answer the question please.
Q)The RAM of Iodine in the Periodic Table is 126.9 on the data sheet. Explain what this value represents.
(3 marks)
I read in the mark scheme it had something to do with radioactive deacy. But, I asked my teacher today and he said the answer is basically...emm..to do with Carbon. He only mentioned a few words so I can't see how that was only a 3 mark question. HIS answer had nothing to do with the mark scheme answer.
Wasalam
I was looking through an exam paper yesterday and today and I just could not get my head around the mark scheme answer. So, could someone answer the question please.
Q)The RAM of Iodine in the Periodic Table is 126.9 on the data sheet. Explain what this value represents.
(3 marks)
I read in the mark scheme it had something to do with radioactive deacy. But, I asked my teacher today and he said the answer is basically...emm..to do with Carbon. He only mentioned a few words so I can't see how that was only a 3 mark question. HIS answer had nothing to do with the mark scheme answer.
Wasalam
ameen
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salam,
These are the two answers I would give:
1) Thin diameter of walls - made of only a single layer of epithelial cells - (so this reduces diffusion-distance).
2) Large surface-area - (so this increases rate of diffusion).
I'm sure there are other answers.
wsalam
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Ameeratul Layl
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[MOUSE]salam,
Br Ameen, you were not meant to provide starseeker with the answer. Your menat to explain. Thats how you learn! [/MOUSE]
[BANANA]Annnyhow, he s the answer from the mark scheme:
Weighted/Weighed/taking into account (relative) abundances/
Intensity/percentages
average/mean mass
of (naturally occuring) isotopes/atoms of different masses[/BANANA]
I am so scared I'm going to fail all my exams. The stress is mounting up already!
wasalam
Br Ameen, you were not meant to provide starseeker with the answer. Your menat to explain. Thats how you learn! [/MOUSE]
[BANANA]Annnyhow, he s the answer from the mark scheme:
Weighted/Weighed/taking into account (relative) abundances/
Intensity/percentages
average/mean mass
of (naturally occuring) isotopes/atoms of different masses[/BANANA]
I am so scared I'm going to fail all my exams. The stress is mounting up already!
wasalam
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I am so scared I'm going to fail all my exams. The stress is mounting up already!
wasalam
:wasalamex
Keep revising sister, and do all that you have power over in this world. Then make lot's of dua' and put your trust in Allaah azawajal
..put your trust in Allah, certainly, Allah loves those who put their trust (in Him). (3:159)
This is the way of Allaah's messenger (peace be upon him.)
Sahih Bukhari Volume 4, Book 56, Number 747
Narrated Rabia bin Abi Abdur-Rahman:
I heard Anas bin Malik describing the Prophet saying, "He was of medium height amongst the people, neither tall nor short; he had a rosy color, neither absolutely white nor deep brown; his hair was neither completely curly nor quite lank. Divine Inspiration was revealed to him when he was forty years old. He stayed ten years in Mecca receiving the Divine Inspiration, and stayed in Medina for ten more years. When he expired, he had scarcely twenty white hairs in his head and beard." Rabi'a said, "I saw some of his hairs and it was red. When I asked about that, I was told that it turned red because of scent. "
Compare yourself to what you're going through, and what the Messenger of Allaah (peace be upon him) went through. And at the end of his life, he only had 20white hairs in total. Look at the seerah (life story) of Rasulullah (sal Allaahu alayhi waSalam) and you'll see how much hardships he faced, but he (peace be upon him) put his trust in Allaah, after doing all the worldly actions he had control over.
So follow that example insha'Allaahu ta'aala.
:salamext:
ameen
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salam,
this is how 'Relative Atomic Mass' (RAM) is defined in an A-Level Chemistry book:
"The Relative Atomic Mass of an element is defined as the mass of one atom of that element relative to 1/12th the mass of one atom of carbon-12."
(this is what sr. asma said above, and also probably what your teacher was talking about when you asked him.)
..the book then continues the definition to say:
"The Relative Atomic Mass is the average of the masses of the stable isotopes of the element, weighted to take into account the relative abundance of each isotope."
So this latter definition is what the mark-scheme is looking for, but the mark-scheme split up this definition into three parts, each part being worth a mark each. I have matched each part of the definition above with the corresponding marking point given in the mark-scheme (below), by using associated colours.
Mark-scheme answer:
- Weighted / Weighed / taking into account (relative) abundances / Intensity / percentages
- average / mean mass
- of (naturally occuring) isotopes / atoms of different masses
If you take these three marking points and combine them together (in the given order) to form one sentence, it can become: 'Weighted - average - of (naturally occuring) isotopes' - which says the same thing as the definition given above.
please let us know if you need help understanding any part of the definition, such as what an 'isotope' is, or what 'relative abundance' means.
wsalam
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Sum-Muslim-Gal
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lol sis^^i thought he was a sis 2..sowie lol
maaan all of you'z are well clever here...alll taking sceince or relating to science good on u all...i think am 2 dumb 4this thread i'll shuhhhHH..
maaan all of you'z are well clever here...alll taking sceince or relating to science good on u all...i think am 2 dumb 4this thread i'll shuhhhHH..