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This Q is making me go insane...

Can someone please explain how I go about answering this Q please? Taken from CIE IGCSE Maths Nov13. I feel like I'm missing the trick....

If you can't make out the picture its the following:
When a+b=6 and ab=7 find a^2+b^2

Bearing in mind its a 1 Mark Question

Thanks!


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Reply 1
Avatar for TeeEm
TeeEm
19
Original post by Gilo98
Can someone please explain how I go about answering this Q please? Taken from CIE IGCSE Maths Nov13. I feel like I'm missing the trick....

If you can't make out the picture its the following:
When a+b=6 and ab=7 find a^2+b^2

Bearing in mind its a 1 Mark Question

Thanks!


Posted from TSR Mobile


either solve simultaneous equations by substitution

or

if you are an A level student note that


(a+b)2 =a2+2ab+b2

does this help?
Original post by Gilo98
Can someone please explain how I go about answering this Q please? Taken from CIE IGCSE Maths Nov13. I feel like I'm missing the trick....

If you can't make out the picture its the following:
When a+b=6 and ab=7 find a^2+b^2

Bearing in mind its a 1 Mark Question

Thanks!


Posted from TSR Mobile


Simultaneous equations would be the quickest way.
Reply 3
Avatar for davros
davros
16
Original post by nebelbon
Simultaneous equations would be the quickest way.


There's no need for simultaneous equations here - you're not being asked to find values for a and b, and in fact it's completely unnecessary to do so!

As TeeEm suggests, just note that a2+b2=(a+b)2−2aba^2 + b^2 = (a + b)^2 - 2ab and then the answer drops out immediately!
Original post by davros
There's no need for simultaneous equations here - you're not being asked to find values for a and b, and in fact it's completely unnecessary to do so!

As TeeEm suggests, just note that a2+b2=(a+b)2−2aba^2 + b^2 = (a + b)^2 - 2ab and then the answer drops out immediately!


I didn't think things like that were studied at GCSE level so i suggested the other method.
Reply 5
Avatar for Gilo98
Gilo98
OP
14
Ah it's so simple now that I see the link. Thank you!! :biggrin:
Reply 6
Avatar for davros
davros
16
Original post by nebelbon
I didn't think things like that were studied at GCSE level so i suggested the other method.


According to the OP it's from the CIE IGCSE exam. CIE is an international board which tends to set harder questions, and IGCSE is different from GCSE anyway :smile:
Reply 7
Avatar for Notnek
Notnek
21
The previous part of this question asks you to expand (a+b)^2 which makes part b) a bit easier. But it seems like most students still struggled with it.

Quote from the examiners report: "There were very few candidates who realised that these two parts were linked and so there were many different methods with no common approach."
Reply 8
Avatar for davros
davros
16
Original post by notnek
The previous part of this question asks you to expand (a+b)^2 which makes part b) a bit easier. But it seems like most students still struggled with it.

Quote from the examiners report: "There were very few candidates who realised that these two parts were linked and so there were many different methods with no common approach."


I sometimes think there really is no hope for humanity when I read things like this!

Do they expect a big red arrow pointing to the first part and a comment saying "Do this you donkeys"?
Reply 9
Avatar for Gilo98
Gilo98
OP
14
To be honest, upon reflection, this clearly isn't that hard of a question but I struggle to criticise myself that much for just simply not seeing the link - I think the donkeys comment is possibly a bit extreme :smile:

Original post by davros
I sometimes think there really is no hope for humanity when I read things like this!

Do they expect a big red arrow pointing to the first part and a comment saying "Do this you donkeys"?
Reply 10
Avatar for Gilo98
Gilo98
OP
14
Original post by notnek
The previous part of this question asks you to expand (a+b)^2 which makes part b) a bit easier. But it seems like most students still struggled with it.

Quote from the examiners report: "There were very few candidates who realised that these two parts were linked and so there were many different methods with no common approach."

Interesting on the examiners report - would you be able to link me to a site where I could access the others? Thanks!!
Reply 11
Avatar for Notnek
Notnek
21
Original post by Gilo98
Interesting on the examiners report - would you be able to link me to a site where I could access the others? Thanks!!

Sorry, I have access to it through a teachers website and so I can't give you the link.
Reply 12
Avatar for Gilo98
Gilo98
OP
14
Original post by notnek
Sorry, I have access to it through a teachers website and so I can't give you the link.

Ah OK, no worries. Oh and check your inbox! Feel so bad for not getting back :frown:
You'll be using this a lot in roots and Coefficients in further maths :smile:
a+b=6
ab=7

a=6-b
a=7/b

6-b=7/b
6b-b^2=7
6b-b^2-7=0
b^2-6b+7=0

(b-7)(b-1)
b=7, b=1

substitute into a+b=6
a=-1, b=7
a=5, b=1

substitute into a^2+b^2
50 and 26
Reply 15
Avatar for davros
davros
16
Original post by RocketCiaranJ
a+b=6
ab=7

etc


That's certainly one method, but completely unnecessary - the question can be solved without finding a and b (and in fact there are similar questions where you might not be able to find values easily and still have to find expressions involving the variables).
Reply 16
Avatar for davros
davros
16
Original post by Gilo98
To be honest, upon reflection, this clearly isn't that hard of a question but I struggle to criticise myself that much for just simply not seeing the link - I think the donkeys comment is possibly a bit extreme :smile:


Unlike in real life, where you're frequently confronted with problems where the solution isn't obvious, it's usually a safe bet in maths exams that later parts of exam questions use something proved in an earlier parts. Maths examiners are actually quite helpful in that regard :smile:
Reply 17
Avatar for Gilo98
Gilo98
OP
14
Original post by davros
Unlike in real life, where you're frequently confronted with problems where the solution isn't obvious, it's usually a safe bet in maths exams that later parts of exam questions use something proved in an earlier parts. Maths examiners are actually quite helpful in that regard :smile:

Luckily I have a few more exams to sit before real world :biggrin: Will remember for future though :h:
Original post by davros
According to the OP it's from the CIE IGCSE exam. CIE is an international board which tends to set harder questions, and IGCSE is different from GCSE anyway :smile:


Ah OK.

The first time i used this was in Further A-Level in FP2 i believe.
Reply 19
Avatar for waxwing
waxwing
5
Original post by davros
I sometimes think there really is no hope for humanity when I read things like this!

Do they expect a big red arrow pointing to the first part and a comment saying "Do this you donkeys"?


Whilst I share the exasperation, part of the problem is that the nature of modern Maths GCSEs (and yes I include IGCSE) encourages this blinkered attitude as everything is just turn the handle, do exactly what it says on the tin.. etc attitude.

So I blame the examiners! No hang on, the politicians.. or something. Anyway, it's definitely not the teachers :smile:

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