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Gcse maths

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Original post by Ano123
I wish you well in your exams. I may have to post some questions just for you.
Haha, Thank you so much!:smile:
Original post by Ano123
I wish you well in your exams. I may have to post some questions just for you.
Any more questions?:tongue:
Reply 42
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Ano123
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Original post by hamza772000
Any more questions?:tongue:

Prove algebraically that if k k is a posiitive integer greater than 1, k3−k k^3 - k is always divisible by 6. (May be more difficult than normal questions of this type as you won't immediately see that there is a factor of 6 to take out).:smile:
Original post by Ano123
Prove algebraically that if k k is a posiitive integer greater than 1, k3−k k^3 - k is always divisible by 6. (May be more difficult than normal questions of this type as you won't immediately see that there is a factor of 6 to take out).:smile:
Unfortunately, I couldn't get this one, after a lot of attempts I some how got to k^2+3k+2, which makes no sense, I know.:frown: Could you please explain it, would be much appreciated.
Reply 44
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Ano123
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Original post by hamza772000
Unfortunately, I couldn't get this one, after a lot of attempts I some how got to k^2+3k+2, which makes no sense, I know.:frown: Could you please explain it, would be much appreciated.


If you factorise it you get (k−1)k(k+1) (k-1)k(k+1) which is the product of 3 consecutive integers. If you think about it, one of the numbers in 3 consecutive integers is a multiple of 3 and one of them (at least) is a multiple of 2. So you have a multiple of 2 multiplied by a multiple of 3, so product of 3 consecutive Integers is divisible by 6.
Original post by Ano123
If you factorise it you get (k−1)k(k+1) (k-1)k(k+1) which is the product of 3 consecutive integers. If you think about it, one of the numbers in 3 consecutive integers is a multiple of 3 and one of them (at least) is a multiple of 2. So you have a multiple of 2 multiplied by a multiple of 3, so product of 3 consecutive Integers is divisible by 6.
WOW, thanks.:smile: I understand it now. I never thought of it that way. It makes sense now!:smile:
Reply 46
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Ano123
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Original post by hamza772000
WOW, thanks.:smile: I understand it now. I never thought of it that way. It makes sense now!:smile:


It's different to other questions where you have to prove some number is a multiple of another. There is no factor of 6 that easily pops out so its a little bit more hidden.
Original post by Ano123
It's different to other questions where you have to prove some number is a multiple of another. There is no factor of 6 that easily pops out so its a little bit more hidden.
I know, its a little unusual, haven't seen anything like it before. Well, on the bright side at least I understand it now.:smile: Thanks a lot for explaining, and please post more questions, if you have them.:smile:
Reply 48
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Ano123
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Original post by hamza772000
I know, its a little unusual, haven't seen anything like it before. Well, on the bright side at least I understand it now.:smile: Thanks a lot for explaining, and please post more questions, if you have them.:smile:


(a) Solve the equation ax2+bx+c=0 ax^2+bx+c =0 giving your answer in terms of a,b,c a, b, c and D D where D=b2−4ac D=b^2-4ac .
(b) Find the value of D D such that only one solution exists to the quadratic equation.
(c) The line L L with equation y=x+k y=x+k intersects the curve C C with equation x2+y2=1 x^2+y^2=1 .
(i) Show , by forming and solving a pair of simultaneous equations by substituting an expression for y, that
2x2+2kx+(k2−1)=0 2x^2 + 2kx + (k^2-1)=0 .
(ii) Find the values of k k such that the line L L is tangent to the curve C C .
[Hint. The tangents to C C intersect the curve at only one point.]
(edited 7 years ago)
Original post by Ano123
(a) Solve the equation ax2+bx+c=0 ax^2+bx+c =0 giving your answer in terms of a,b,c a, b, c and D D where D=b2−4ac D=b^2-4ac .
(b) Find the value of D D such that only one solution exists to the quadratic equation.
(c) The line L L with equation y=x+k y=x+k intersects the curve C C with equation x2+y2=1 x^2+y^2=1 .
(i) Show , by forming and solving a pair of simultaneous equations by substituting an expression for y, that
2x2+2kx+(k2−1)=0 2x^2 + 2kx + (k^2-1)=0 .
(ii) Find the values of k k such that the line L L is tangent to the curve C C .
[Hint. The tangents to C C intersect the curve at only one point.]
Erm, 1 quick question before I attempt these, are these GCSE questions for the current spec? Just curious.:tongue:
Original post by hamza772000
Hi, I found this file yesterday, it has the predicted topics in it, for both foundation and higher.
https://drive.google.com/file/d/0B0NHL46meQP_cHUzQVBUQm9TdXM/view?usp=sharing


Do you have the same for ocr maths foundation spec b??
Original post by bikiniikilll
Do you have the same for ocr maths foundation spec b??
No, sorry:frown: but I have this link for a predicted paper you could try, its online so you work the answer out and just type it in.

http://onmaths.com/mock_exams/ocr-2016-paper-2-foundation-prediction/
Reply 52
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Ano123
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Original post by hamza772000
Erm, 1 quick question before I attempt these, are these GCSE questions for the current spec? Just curious.:tongue:


Extension questions, for bright pupils like you. They make you think very hard and very carefully about certain topics.
Original post by Ano123
Extension questions, for bright pupils like you. They make you think very hard and very carefully about certain topics.
Oh okay, Thanks. I was just curious because I've never seen anything like these before, they do sure make you think.:smile:
Anyone got the markscheme


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