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 Post subject: Question 28 - HABS Maths paper 2014Posted: Wed Jan 07, 2015 10:40 pm

Joined: Fri Sep 19, 2014 4:32 pm
Posts: 262

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 Post subject: Re: Question 28 - HABS Maths paper 2014Posted: Wed Jan 07, 2015 10:52 pm

Joined: Fri Sep 19, 2014 4:32 pm
Posts: 262
Here's the question -

We write s(2,5) as an abbreviation for 2+3+4+5 so that s(2,5) = 14

Similarly

S(6,39) = 6+7+8+9+....+ 38 + 39 = 765

Work out:

s(1,3) =
s(6,40) =
s(7, 38) =

s(1,2) - s(2,3) + S (3,4) - s(4,5)+ ......... - S (18,19) + S (19,20) =

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 Post subject: Re: Question 28 - HABS Maths paper 2014Posted: Wed Jan 07, 2015 11:00 pm

Joined: Mon Feb 12, 2007 1:21 pm
Posts: 14000
We've had this before - try searching.

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 Post subject: Re: Question 28 - HABS Maths paper 2014Posted: Thu Jan 08, 2015 12:07 am

Joined: Sun Sep 22, 2013 6:25 pm
Posts: 144
Location: Cheltenham
The long way round is this:

Total = (number of items) x (mean value)

For s(a,b):
number of items = b-a+1
mean value = (a+b)/2
This gives total = (b-a+1)(a+b)/2

So
s(1,3) = 1+2+3 = 6
Check the formula works: s(1,3)=(3-1+1)*(4/2)=3*2=6

Then
s(6,40)=(40-6+1)*(46/2)=35*23=805
s(7,38)=(38-7+1)*(45/2)=32*22.5=720
or alternatively s(7,38)=s(6,40)-6-39-40=805-85=720

The short way is to use the example they have given of s(6,39)=765, like this:
s(1,3)=1+2+3=6
s(6,40)=s(6,39)+40=765+40=805
s(7,38)=s(6,39)-6-39=765-45=720

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 Post subject: Re: Question 28 - HABS Maths paper 2014Posted: Thu Jan 08, 2015 6:38 am

Joined: Mon Mar 03, 2014 12:10 pm
Posts: 30
This is one of those "can you spot the short way" type questions. DebsB has wonderfully given the short way to do the second and third questions, using the answer they have already given for s(6,39).

And in the final question, they're looking to see if you spot that most of the terms cancel each other out:

s(1,2) - s(2,3) + s(3,4) - s(4,5)+ ......... - s(18,19) + s(19,20)
= 1 + 2 - 2 - 3 + 3 + 4 - 4 - 5 + ... - 18 - 19 + 19 + 20
= 1 + 20
= 21

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 Post subject: Re: Question 28 - HABS Maths paper 2014Posted: Thu Jan 08, 2015 10:48 am

Joined: Sun Sep 22, 2013 6:25 pm
Posts: 144
Location: Cheltenham
rah_b92 wrote:
This is one of those "can you spot the short way" type questions. DebsB has wonderfully given the short way to do the second and third questions, using the answer they have already given for s(6,39).

And in the final question, they're looking to see if you spot that most of the terms cancel each other out:

s(1,2) - s(2,3) + s(3,4) - s(4,5)+ ......... - s(18,19) + s(19,20)
= 1 + 2 - 2 - 3 + 3 + 4 - 4 - 5 + ... - 18 - 19 + 19 + 20
= 1 + 20
= 21

Nicely done, rah_b92. I hadn't even noticed that the final question was there. Shocking example of failure to read the question properly - let's hope none of our kids have been throwing marks away by missing stuff out in that way!

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 Post subject: Re: Question 28 - HABS Maths paper 2014Posted: Thu Jan 08, 2015 11:53 am

Joined: Fri Sep 19, 2014 4:32 pm
Posts: 262
thank you everyone

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