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# Grade 9 Maths Paper GCSE (and other difficult GCSE questions) watch

1. This paper is great! How long did it take you to make?
2. (Original post by NineOfDiamonds)
This paper is great! How long did it take you to make?
Thank you so much I’d say just shy of one week
3. (Original post by Gent2324)
ah ok, is that the hardest bit or is the -x bit harder? im saying this because im assuming theres some catch to make it really hard or something that i cant see yet?
4. (Original post by Y11_Maths)
kind of, i got that 9root5 -5x + 3 = 0 is that correct so far?
5. (Original post by Gent2324)
kind of, i got that 9root5 -5x + 3 = 0 is that correct so far?
No, how have you come to this conclusion?
6. this paper looks so interesting; I can't wait to do it later
7. (Original post by Toastiekid)
this paper looks so interesting; I can't wait to do it later
Thank youuuuu
8. (Original post by Y11_Maths)
No, how have you come to this conclusion?
y^2 = 45-x^2
so y = root45 - x
y = 3root5 - x

since 3y-2x+3 = 0
3y = 9root5 - 3x
thefore its 9root5-3x-2x+3=0
9root5-5x+3 = 0
9. (Original post by Gent2324)
y^2 = 45-x^2
so y = root45 - x
y = 3root5 - x

since 3y-2x+3 = 0
3y = 9root5 - 3x
thefore its 9root5-3x-2x+3=0
9root5-5x+3 = 0
Have you been taught how to solve simultaneous equations with circle equations?
10. (Original post by Y11_Maths)
Have you been taught how to solve simultaneous equations with circle equations?
no i thought this was just a quadratic one?
11. (Original post by Gent2324)
no i thought this was just a quadratic one?
The equation of a circle is x^2 + y^2 = radius^2
To begin to solve this question you must
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rearrange your first simultaneous equation in the form y= then use this to begin to solve the next one
12. (Original post by Y11_Maths)
The equation of a circle is x^2 + y^2 = radius^2
To begin to solve this question you must
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rearrange your first simultaneous equation in the form y= then use this to begin to solve the next one

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so does x^2+(2/3x-1)^2 = 45 ?

13. (Original post by Gent2324)
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so does x^2+(2/3x-1)^2 = 45 ?

Not quite but right idea.
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3y=2x-3 then divide both sides by 3 and leave as 1 fraction don’t try to simplify. Then do what you were going to do before
14. (Original post by Y11_Maths)
Not quite but right idea.
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3y=2x-3 then divide both sides by 3 and leave as 1 fraction don’t try to simplify. Then do what you were going to do before
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ok so i factored that in and got x^2 + (2x-3/3)^2 = 45
i then got x^2 + (4x^2-12x+9/9) = 45
that correct? if so do i do 45x9 and then equate to zero to get a quadratic and solve for x?
15. (Original post by Gent2324)
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ok so i factored that in and got x^2 + (2x-3/3)^2 = 45
i then got x^2 + (4x^2-12x+9/9) = 45
that correct? if so do i do 45x9 and then equate to zero to get a quadratic and solve for x?
Yes this is correct
16. Bloody fantastic effort. It's such a legitimate looking paper. Isn't question 15 a bit harsh for 4 marks though?

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Let be an integer. Then we're looking at . Without loss of generality for let be a positive integer (can't be zero as ). So , and considering the prime factorisation of , we get and which leads to and , or and which lead to and . We can discount cases like and as if the parities of and are different, then that would imply and are not integers. Clearly the only way to split into a product of two integers with the same parity is or , so .
17. (Original post by Y11_Maths)
Yes this is correct
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ok i done that now but i got 5x^2 - 12x - 396 = 0 and i need to find 2 numbers that add to make -12 and times to make -1580?
18. (Original post by I hate maths)
Bloody fantastic effort. It's such a legitimate looking paper. Isn't question 15 a bit harsh for 4 marks though?

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Let be an integer. Then we're looking at . Without loss of generality for let be a positive integer (can't be zero as ). So , and considering the prime factorisation of , we get and which leads to and , or and which lead to and . We can discount cases like and as if the parities of and are different, then that would imply and are not integers. Clearly the only way to split into a product of two integers with the same parity is or , so .
Haha thank you so much. And yes this is correct. I see what you mean and I’m a harsh individual. They have to work hard for each individual mark
19. (Original post by I hate maths)
Bloody fantastic effort. It's such a legitimate looking paper. Isn't question 15 a bit harsh for 4 marks though?

Spoiler:
Show

Let be an integer. Then we're looking at . Without loss of generality for let be a positive integer (can't be zero as ). So , and considering the prime factorisation of , we get and which leads to and , or and which lead to and . We can discount cases like and as if the parities of and are different, then that would imply and are not integers. Clearly the only way to split into a product of two integers with the same parity is or , so .
I glanced at all the questions a few days ago and I felt the same about this one. I thought I might have missed an easier method.

I haven’t tried all of them but I agree that it looks like a brilliant paper and I bet most A Level students couldn’t come up with a GCSE paper this good.
20. (Original post by Gent2324)
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ok i done that now but i got 5x^2 - 12x - 396 = 0 and i need to find 2 numbers that add to make -12 and times to make -1580?
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Your x^2 term is connected by an addition therefore when you multiply both sides by 9 this turns into 9x^2. And yes you are correct with your method

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Updated: October 2, 2018
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