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Qualification => Subject Doubts => GCE AS & A2 Level => Math => Topic started by: Dania on September 21, 2010, 08:53:25 pm

Title: CIE Pure Mathematics Paper 1 Doubt
Post by: Dania on September 21, 2010, 08:53:25 pm

I need HELP, please!

How do I show that the mid-points of 2 3D vectors coincide?

Also,

(a) The fifth term of an arithmetic progression is three times the second term, and the third term is 10.
Find (i) the first term, (ii) the common difference, (iii) the 20th term.

(b) The nth term, t(n), of a sequence is given by - t(n) = p + nq, where p and q are constants.

(i) Write down, in terms of p and q, the 6th term of the sequence.
(ii) Find, in terms of p and q, the sum of the first six terms.

Title: Re: CIE Pure Mathematics Paper 1 Doubt
Post by: S.M.A.T on September 22, 2010, 10:39:03 am

a)i)
2nd term=a+d
 5th term=a+4d

a+4d=3×(a+d)
d=2a

a+2d=10
a+(2×(2a))=10
5a=10
a=2

ii)d=2×2=4
iii)20th term=2+(19×4)=78

b)i)t(6)=p+6q
    
   ii)sum=(n/2)×(L+a),where L is last term
           =(6/2)×(p+6q+p+q)
           =3×(2p+7q)
           =6p+21q
  

Title: Re: CIE Pure Mathematics Paper 1 Doubt
Post by: Dania on September 22, 2010, 12:06:59 pm

Thank You :)

Title: Re: CIE Pure Mathematics Paper 1 Doubt
Post by: Dania on September 22, 2010, 05:50:41 pm

By the way, would you happen to know how I would show that that 2 vectors coincide?

Title: Re: CIE Pure Mathematics Paper 1 Doubt
Post by: S.M.A.T on September 23, 2010, 02:48:49 am

Quote from: dania.chughtai on September 22, 2010, 05:50:41 pm

By the way, would you happen to know how I would show that that 2 vectors coincide?

here (https://studentforums.biz/math/factor-theorem/378)
See post number 378&379 :)

If you have problem please tell me :)

Title: Re: CIE Pure Mathematics Paper 1 Doubt
Post by: astarmathsandphysics on September 24, 2010, 02:27:50 pm

I did a page on my website. Will post a link when I get home.

Title: Re: CIE Pure Mathematics Paper 1 Doubt
Post by: astarmathsandphysics on September 25, 2010, 09:16:02 am

How to find the point of intersection of two lines.

http://astarmathsandphysics.com/a_level_maths_notes/C4/a_level_maths_notes_c4_finding_the_point_of_intersection_of_two_lines_in_three_dimensions.html