You are Here: Home >< Maths

# Further Maths GCSE AQA Paper 1 (Unofficial mark scheme)

Announcements Posted on
Would YOU be put off a uni with a high crime rate? First 50 to have their say get a £5 Amazon voucher! 27-10-2016
1. (Original post by NiamhM1801)
x
Lol, I don't even know what trig identities are. RIP.
2. [QUOTE=Ano123;65980073]
(Original post by Joelo00)

Given that d/dx (sin2x+cos2x)=k.
It is given further that d/dx (sin2x)= 2sinxcosx,
Find the value of k and hence find the derivative of cos2x.
Too hard?
(You do not have to know how to differentiate trig functions to do this).
3. (Original post by mattedwards8972)
I hope there's nothing to do with the cosine rule with algebra because, even though I can pick up marks on doing the basic part of the questions, I can never seem to pick up all the marks on the question. I hope something like indices comes up on the exam because these are easy marks, more differentiation stuff would be nice too, anything with the second derivative I wouldn't mind. Also maybe a trigonometric proof would be nice as well, if it's a nice easy one. What topics do you hope come up?
Hmm...I don't know I don't mind them
Although topics I'd like would be:
Trig identities
Differentiation/nature of stationary points/increasing and decreasing functions
Something on proof, even though there was one last time
Circles on graphs
Matrices (including combinations of transformations)
F(x) graphs where they give you domains and you have to plot the ranges - absolutely love them!

Things I really don't want:
Angle between side and plane/angle between two planes
Those things that give you something like 5sin²x = 125, find all values of X. Do you know the ones I'm on about? (Obviously you wouldn't get that one as it wouldn't work, was for explanation purposes only)
Can't really think of anything else I hate...
4. (Original post by Chittesh14)
Lol, I don't even know what trig identities are. RIP.
You're given the only ones we need to know on the formula page
5. (Original post by NiamhM1801)
You're given the only ones we need to know on the formula page
No, as in I don't even know what they are - so I wouldn't be able to recognise them.
6. (Original post by NiamhM1801)
Hmm...I don't know I don't mind them
Although topics I'd like would be:
Trig identities
Differentiation/nature of stationary points/increasing and decreasing functions
Something on proof, even though there was one last time
Circles on graphs
Matrices (including combinations of transformations)
F(x) graphs where they give you domains and you have to plot the ranges - absolutely love them!

Things I really don't want:
Angle between side and plane/angle between two planes
Those things that give you something like 5sin²x = 125, find all values of X. Do you know the ones I'm on about? (Obviously you wouldn't get that one as it wouldn't work, was for explanation purposes only)
Can't really think of anything else I hate...
Yeah, I know what you mean, I don't like the angles between a side and a plane either because I can never picture what the angle would be. I'd love quadratic nth terms to come up, and circle on a graphs (maybe with a straight line intersecting the circle twice and in other words using simultaneous equations to work out the values of x and y, I dont even know if thats possible but it seems like an interesting and juicy question I'd like)
7. (Original post by Chittesh14)
No, as in I don't even know what they are - so I wouldn't be able to recognise them.
Oh...I think questions on them are normally worth 3 marks.
If you have a look in some past papers they're normally near the back - you'll just see a lot of tan, sin, cos and 1s normally in a fraction but not always and be asked to prove something.
8. Does anyone have a link to the paper in pdf form that I can view and maybe have a look over for myself.
9. (Original post by mattedwards8972)
Yeah, I know what you mean, I don't like the angles between a side and a plane either because I can never picture what the angle would be. I'd love quadratic nth terms to come up, and circle on a graphs (maybe with a straight line intersecting the circle twice and in other words using simultaneous equations to work out the values of x and y, I dont even know if thats possible but it seems like an interesting and juicy question I'd like)
Yeah - that's the hardest part for me too! Normally I actually draw out the little triangle of sides to try and find the angle, usually it's just a bit of basic trig after that.
And yeah I've seen that a few times actually, that'd be pretty good too!
10. (Original post by jay1212)
Does anyone have a link to the paper in pdf form that I can view and maybe have a look over for myself.
Which paper?
11. (Original post by mattedwards8972)
Yeah, I know what you mean, I don't like the angles between a side and a plane either because I can never picture what the angle would be. I'd love quadratic nth terms to come up, and circle on a graphs (maybe with a straight line intersecting the circle twice and in other words using simultaneous equations to work out the values of x and y, I dont even know if thats possible but it seems like an interesting and juicy question I'd like)
Find the points of intersecgtion of the ellipses with equations

and
.

[Give the each of the coordinates as exact answers.]

You said 'juicy' simultaneous equations.
12. (Original post by NiamhM1801)
Oh...I think questions on them are normally worth 3 marks.
If you have a look in some past papers they're normally near the back - you'll just see a lot of tan, sin, cos and 1s normally in a fraction but not always and be asked to prove something.
It's fine, I'll just learn them and that's it lol tbh.
13. (Original post by Ano123)
Find the points of intersecgtion of the ellipses with equations

and
.

[Give the each of the coordinates as exact answers.]

You said 'juicy' simultaneous equations.
x^2 - 4x + 4 + 5y^2 = 4
x^2 - 4x + 5y^2 = 0

2(x^2 - 2x + 1) + y^2 = 1
2x^2 - 4x + 2 + y^2 = 1
2x^2 - 4x + 1 + y^2 = 0

x^2 - 4x + 5y^2 = 2x^2 - 4x + 1 + y^2
0 = x^2 - 4y^2 + 1
y^2 = -2x^2 + 4x - 1
0 = x^2 - 4(-2x^2 + 4x - 1) + 1
0 = x^2 + 8x^2 - 16x + 4 + 1
0 = 9x^2 - 16x + 5

5y^2 = -x^2 + 4x
5y^2 = - -(\frac{\sqrt 11}{3}) - 4(\frac{\sqrt 11}{3})
5y^2 = - -(11/9) - 4 \sqrt 11 + 12
5y^2 = 11/9 + 4 \sqrt 11 + 12
5y^2 = - 0.04
leave it, i give up on that one.

or otherwise

5y^2 = - (\frac{\sqrt 11}{3}) + 4(\frac{\sqrt 11}{3})
5y^2 = -11/9 + 4 \sqrt 11 + 12
5y^2 = 24.04
y^2 = 4.8
y = 2.19
14. (Original post by Ano123)
x

x = 0.40, y = -0.54
x = 0.40, y = 0.54
x = 1.37, y = -0.85
y = 1.37, y = 0.85
15. (Original post by NiamhM1801)
Yeah - that's the hardest part for me too! Normally I actually draw out the little triangle of sides to try and find the angle, usually it's just a bit of basic trig after that.
And yeah I've seen that a few times actually, that'd be pretty good too!
I think this exam will go well though, I really hope there is something to do with simultaneous equations though because I really did revise that
16. (Original post by Chittesh14)
x^2 - 4x + 4 + 5y^2 = 4
x^2 - 4x + 5y^2 = 0

2(x^2 - 2x + 1) + y^2 = 1
2x^2 - 4x + 2 + y^2 = 1
2x^2 - 4x + 1 + y^2 = 0

x^2 - 4x + 5y^2 = 2x^2 - 4x + 1 + y^2
0 = x^2 - 4y^2 + 1
y^2 = -2x^2 + 4x - 1
0 = x^2 - 4(-2x^2 + 4x - 1) + 1
0 = x^2 + 8x^2 - 16x + 4 + 1
0 = 9x^2 - 16x + 5

5y^2 = -x^2 + 4x
5y^2 = - -(\frac{\sqrt 11}{3}) - 4(\frac{\sqrt 11}{3})
5y^2 = - -(11/9) - 4 \sqrt 11 + 12
5y^2 = 11/9 + 4 \sqrt 11 + 12
5y^2 = - 0.04
leave it, i give up on that one.

or otherwise

5y^2 = - (\frac{\sqrt 11}{3}) + 4(\frac{\sqrt 11}{3})
5y^2 = -11/9 + 4 \sqrt 11 + 12
5y^2 = 24.04
y^2 = 4.8
y = 2.19
I doubt this will come up in the exam??
17. (Original post by guy321)
I doubt this will come up in the exam??
Obviously not , I'm probably wrong anyway lool.
18. (Original post by guy321)
I doubt this will come up in the exam??
Something similar may come up though with a quadratic and a linear straight line where it intersects the quadratic at 2 points and it might ask you to work out the co-ordinates of where both points intersect. That is a much more likely question.
19. (Original post by Chittesh14)
x^2 - 4x + 4 + 5y^2 = 4
x^2 - 4x + 5y^2 = 0

2(x^2 - 2x + 1) + y^2 = 1
2x^2 - 4x + 2 + y^2 = 1
2x^2 - 4x + 1 + y^2 = 0

x^2 - 4x + 5y^2 = 2x^2 - 4x + 1 + y^2
0 = x^2 - 4y^2 + 1
y^2 = -2x^2 + 4x - 1
0 = x^2 - 4(-2x^2 + 4x - 1) + 1
0 = x^2 + 8x^2 - 16x + 4 + 1
0 = 9x^2 - 16x + 5

5y^2 = -x^2 + 4x
5y^2 = - -(\frac{\sqrt 11}{3}) - 4(\frac{\sqrt 11}{3})
5y^2 = - -(11/9) - 4 \sqrt 11 + 12
5y^2 = 11/9 + 4 \sqrt 11 + 12
5y^2 = - 0.04
leave it, i give up on that one.

or otherwise

5y^2 = - (\frac{\sqrt 11}{3}) + 4(\frac{\sqrt 11}{3})
5y^2 = -11/9 + 4 \sqrt 11 + 12
5y^2 = 24.04
y^2 = 4.8
y = 2.19
What I would of done is make both equations equal to -y^2 so then you could make them equal to eachother, rearrange to make it equal to 0, factorise (either normally or through the quadratic formula) and then substitute it back into the original equation like you did afterwards. But I could be completely wrong on that, if I am, lets blame it on being a long day ay
20. (Original post by mattedwards8972)
What I would of done is make both equations equal to -y^2 so then you could make them equal to eachother, rearrange to make it equal to 0, factorise (either normally or through the quadratic formula) and then substitute it back into the original equation like you did afterwards. But I could be completely wrong on that, if I am, lets blame it on being a long day ay
I don't even know what I done.
I done it instead of revising for my Physics exam -__

## Register

Thanks for posting! You just need to create an account in order to submit the post
1. this can't be left blank
2. this can't be left blank
3. this can't be left blank

6 characters or longer with both numbers and letters is safer

4. this can't be left empty
1. Oops, you need to agree to our Ts&Cs to register

Updated: June 28, 2016
TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Today on TSR

Poll
Useful resources