#AQA Further Maths Paper 2
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@wintry meadow
@violet dock
@frigid smelt
@distant cape
i dont remember who does aqa
Do you guys think more complex numbers will come up
probs a little year
yeah
i hope they dont do a big question on complex numbers
like a roots of unity one
actaully i dont mind that but
doyou think it will be like paper 1 where they was just loads of smaller questions
swear there was like 18 questions
Idm that but I'd hate a series one on complex numbers
ye same
i just couldnt remember what they are called
Nah its gonna be less
Cuz they are gonna make it harder
So less questions but more marks I think
Anyway it's gonna have like 15+ regardless, it's usually around this always
Yeah
i dont think it will be harder
maybe a little bit but not loads
It's gonna be like last year
First paper ez
Then the second one harder
It won't be the same difficulty, no way
yeah i still need to do 2023
gonna do it tomorrow
i think if theres any hard question on 2023 they will reask them in a slightly easier way
/similar concepts
Yeah
The tan5pi/12 ine
Is similar to what they asked in 2023
Basically the exact same thing
Me too
there was like 17 marks already on complex numbers so there might not be any on paper 2
but since the number of questions each year seems to increase if there is like 16 questions they could be one more
i think there will be a coupled differential equation even tho there was lots previously
2 days
There's literally nothing to do for pure 😭
ye
i didnt many paper 2s for paper 1 so i still have quite a few past papers to do
What does ACF mean?
Any correct form
2023 paper 2 was quite hard
like time wise
there was a few questions where you could go down different roots
and it would mean they would take ages
like the 3 marker at the start
also q14
not that they were hard but not many marks
Paper 1 or 2?
Can someone explain how I’d find c and d?
@distant cape
@violet dock
@frigid smelt
@wintry meadow
Fundamental theorem of calculus is coming up
thats one way
for a and b i just thought about it
Further maths people
???
What’s the best way to learn proof by contradiction
bro go somewher else
idk its hardest topic
okay theres a few methods
how would you do it
invariant points you simply multiply by some coordinates x y z and set it equal to x y z
as they dont change
for lines id probably just do eigenvectors
or do they want line of invarent points?
i think its the same thing id assume
Cry bro
yeye
there is another method that i know for 2x2 but its long
@wintry meadow this is just line of invarent points right
yh id say so
for these u might just be able to spot it
idk about invariant plane tho
ye
reflections in like x=0 plane x=0 is invariant plane
but like
for c i didnt even know what the tranformation is
for plane im thinking we multiply by x y z and find some conditions for it
that might nto work tho
give me a sec with it and then ill know
id say that the invariant plane for c is just y = 0 x = 0
which page is that in the book?
for d id say invairant line/plane y = x
ig cuz invariant lines in 3d without specifying the z coordinate just become planes
like in 2d y =x is a line but in 3d its a plane
the method i did was simply multiply the matrices by x y z and set equal to x y z
ok ty
thats probably not the full way or 100% correct way
cuz it could possibly miss solutions
but im guessing its right cuz all numbers are 1 so no scale factors
ye
so
would the plane x=y
be a plane of invarent points
of a invariant plane?
ill send sol in a sec but basically u transform some general coordinates into new coordinates and then sub those new coordinate values into the plane euqation and solve for p and q
i actually have never heard of it
im solving it rn
i think i know
Oh
is that edexcel q
i know how to get p, isolveed it
im not entirely sure abt q
i used online calcluator to find the eignevalues cuz i couldnt be bothered and got tihs
i think q = 6 would be answer
do u have the answers @magic torrent
The worked solution ?
ye
from what i understand an eigen plane can occure when you have an a repeated eigenvalue and each eigenvalue has a non parrallel eigen vector
That's what it seems like
But I still don't get it tbf
It's fine
I can ask my teacher tmr
which bit
What's actually going on
Well I understand it , it's just not sure about the eigenvectors
Do you understand this
oh
Yes
well i think they just picked two non parallel vectors that are perpendicular to the normal of the plane so when you cross product them you would get the plane
i think
Hmm I see
wait
nm
thats waffle
so you know how you can have lines on a plane
i think they just picked two non parallel vectors that would lie on the plane
Ahh ok
ye
There's literally that's the only q on eigenplanes in this book
yeye
i doubt it comes up
but if it did it would be really good because i doubt many people will have gone over it
Yep
what does it mean by corresponding vectors?
were there any series qs on paper 1?
when doing centre of complex circles do we include an i?
would we write it as (3,4)
or centre 3+4i
im not sure😂
i dont think so
i always thought it was like (3,4) but i just saw edexcel q where they did it was 3+4i
idk i think if they ask for centre its (3,4)
but not 100% sure
eigenplane isnt on spec 99% sure, i dont think they can ask it
its in the aqa oxford textbook as well
textbooks do just add extra stuff tho
ye
u want a solution?
nah its fine now
@wintry meadow
Try this one
swear its impossible
@frigid smelt
@magic torrent
yh im struggling with that one
idk how to do it
@wintry meadow
thats the ms
but they subtracted aR2
i did not know you could do that
wouldve taken me a bit to figure that out tbf
its just like minusing row 1 a few times
if a matrix is singular does that mean det M =0
im worried for this exam cos there was 12 days i feel like theres so much little stuff iv forgotten
well not forgotten
but its not at the front of my head
i reckon just do it @patent ledge
Everything on the right hand side of the y axis gets reflected
So
Something like this
The reason is
Can you see how
When you evaluate the negative x values i.e if you were to evaluate f(-2), the y coordinate will be = f(2) so will yield the same y coordinate as the positive side of that same number, if that makes sense ? ( So f(-2)'s y coordinate is the same as f(2)'s y coordinate) and same for all other postive and negative values, so it just reflects in y axis)
ahhh ok ty
have they ever asked 2 simple harmonic motion q's
Matrices
?
@patent ledge do u know
but maybe like a 3 marker or something
probably multiple choice if they do
yeye
no way they throw another entire q
havent gotten full marks on a single coupled de question lol
I want a nasty but nice roots of polynomials w
tbf i dont think theres a topic thats bad that could come up
on specimen paper 1 and 2 there is 2 shm qs one on each paper
numerical methods
tellin ya
theres gonna be a nasty one
deriving the mid ordinate rule
bet thats on it
it will be a nice one im pretty sure
numerical method with second order is long icl
ye
No way they ask this lol
You can't really even derive it, it's kinda just look at the graph and make rectangles
will let you know at like 3:30
Harder then the first one
Yh defo
What did u lot get for modulus of z with the smallest argument
that paper was not bad tbh
The DE question my values for everything were horrible
the complex number one was a bit ass tho
Which
the smallest argument thing
Yh
At first I thought it wanted minimum value so I wasted a bunch of time on the complex argand diagram one
U remember any of your values?
I got it but calc wasn't giving exact values
No but they were all fractions lol
Idk if I got that right 1
I got 0.6 for something tho
And 21/9
Can't remember
Yeah me tok
And lambda for the e^5x one was
Ngl I just setup the integral and used my calculator
I'll probably lose a mark or 2 for that
I don't remember but ye
do you not have to rearrange for x or something
i think they expected you too with the space they gave
I couldn't do the method of difference q
H1ow did u do it
i literally tried every number in the calculator for the second part
Dis u do 3 partial fractions or 2
224 I got
3
i got 71
yeah
Yh ik
Math explained in easy language, plus puzzles, games, quizzes, worksheets and a forum. For K-12 kids, teachers and parents.
Try it there
Maybe I put it in wrong
thats probably rounded
cus on my calc it gave it higher
Same I fucking did that this morning
Yh
Attempted all but couldn't do 2 parts of qs
20 was so many lol
Yeah but it was so time pressured
I think cuz I got 10^-5
I’m glad people agree cos like my friends were saying it was easy
But they slipped the complex numbers q
Could u do method of differences
Which took me AGES holy shit
Ye I mena part a tho
oh yeah
Partial fraction it
Nah
Thank god someone else thought this
Into 3 terms?
Yeh
Ye same
Diagonally
U have to combine the 2 halves
And then like
With the whole -
It was +1/2 +1/2 -1
Basically
On the diagonal
A and B were like 1/35 and 6/35
medium
I didn’t get that
idk i put it in the calculator and it worked
Sounds right though ngl
I got 10/63 and 1/175 for A and B and then for the PI I got 3/2, -3/5 1/10 and -8/225
Which my friend also got
For the PI
Either way method was clear
I managed to do the complex numbers one but took me FUCKING AGES
Yh should be only 2 or 3 lost
What was ur method
I did discriminant with y=mx to find coordinate
And used distance formula
Cuz we had distance
Which gave x value, which gave y value
Sin?
I did sin not tan
Urs works
I did sin cuz we had the hypotenuse which was the distance 4 sqrt 3 from prev part
ye I did that as well but didn’t wanna sub back in to find coords
I found tan theta from gradient
Makes sense
Nah it took so long like it took all my checking time
I didn't check anything I think
Ye fucking hell
Yeah it annoyed me cos I felt I could do it a much neater method so I spent a lot of time trying to think about what would be neater
Was the person wrong about the degree 3 right
Yeah
Also
I put could be 3 5 7 9 etc
Yeh
Yhyh
Cos all the other mocks were different question lengths you aren’t used to it
I normally have like 1h of checking to chill
Like I think question 10 I’m almost done
Ye I think we had highest
But this time omds working to the end
So what do we think grade boy ada dies
I lost marks on minimum 3 qs now
Luckily there wasn’t an evil last q tho
Ye
This I'd say was harder than last year
Yeah probs same cos p2 lower p1 higher
My friends found this paper easy and p1 harder 😁😭😭😭
Which was weird
fair
Ye same someone else said that
like 15 qs were easy then 5 difficult
An1yone remember mcqs
I got 45 for 1 I think
Mcqs?
At the start
I don't remember others
I memorised that formula this morning
Yeah wA
Just gotta hope no vertical circular motion on mechanics now
No that’s so nice
I MISSED THE REDUCTION FORMULA QUESTION 💀💀
I didn’t realise it was there until a minute left
So I just scribbled the ibp to try get a mark 💀
Yeye
I have the solutuon
But it's a good question, yes
That mech paper is hard tbf
@frigid smelt did you think todays paper was harder or easier than paper 1
Sorry
Paper 1
Me personally, harder , but I did better on this paper than paper 1
Ye
Yeye
How did you find it
Yeah
Ye I didn’t get the reduction question as well so sad
Part a or b?
I literally practiced it for sin and tan this morning
I got a but not b
Nah couldn’t prove it
Ah
I'm so mad for not getting the reduction its so easy
Ye
Was it because of mistakes or ?
I just did cos^n-2 not -1
Yeye same I think
It's -1 ye
Wait
And it comes out beaituful
Was it I n-2
Beautiful
no
Yea
Was the subscript n-2
In was on the left
Yeye
And on the RHS I n-2 ye
Oh ok
Why Starbucks in background
And this stupid calculator weren't giving me exact values for the argand diagrams one 🤣
I had to blag it and make it equal
Nah eigenvectors is so easy
Was the vectors q like
b × a then u do that is equal to - a x b
And also invariant planes n stuff I didn't even have time to learn so glad it didn't come up
and -c×a = a×c
Yes something like that
But also
Is
E.g.
8a × b = 8(a× b)
I got an 8 I remember
The a × b they give you, then you times it by 8?
I did
Ok good me too
One sex
then the a×a=0
Yeyeye
Anyway it was a good paper
I don't remember any other qs
N the very last one
Idk where I'm supposed to get a pi from
Tf
Io = 1 ?
No
Well yes
And then u integrate that
To get pi/4
and then do the formula 3 times
Ohhhhh u integrate it
Duhhh
Thank you
💀💀
I didn't integrate it
I was thinking how am I supposed to sub jn pi/4 jnto one
🔥🔥
I made an algebra mistake on the flipping maclaurin one
How did you find it nola?
Good very time pressured tho
Didn’t have that much time to check so probably fucked up some algebra:numbers
But the Qs weren’t bad
Ohh yh also
For the Volume of revolution
Can you just put in calc?
Because it was only 3 marks
Yeah ^^^
As which year
last
what was answer
@wintry meadow
ye
What was the 10 mark diff equation
il try remember
My friends are saying two things
i cant remember all
the solutions to the normal were 5 -9
Alright calm
yh thats right then
I was about to say 😭
a x and x^2 term
People were saying e^2(x) was from the function I was so lost where they got the x from at the pi from lambda e^2x cuz the roots weren’t matching
But thanks for confirming
Was it -0.03?
the 5 was defo in both
- 25 x^2
that doesnt sound right
im not sure tho
i think it was 21e
actually i have no clue
Does anyone remember the function
There was a vector property question?
yes
we were given axb and axc
and then we told find value of
i cant remmeber numbers but eg
(3a +5b+2c)(2a)
no
Ohh
and all u had to do was notice the minus rule and like bxa = -axb etc
Yhh
@signal acorn anoter q
using definition of maclaurin for sinx and binomial approximation give terms upto theta ^3
in
1/(1+sin(theta))^4
EASY
I think it was 21 e^5x + 27x^2 -0.3x
Lhopitals rule? After
Might have been some other negatives the other way on the last 2 tho
no lol
Damn
What did u get for this cos I messed up the algebra and realised with 30s left
I think
Ah u sure tho?
not a clue
Bc when I put it in my calc then it wasn’t close
The numbers I’m pretty sure
yes it is 27
But idk about the +- order
i can show what i did and try to refigure my answer
Yeah I think so too
Yeah cos I knew what to do I just messed it up I’ll redo it now
I am just so tired cos I couldn’t sleep last night
I am now
Alr I’ll try the q now
Ohhhh I’m so stupid 😭😭😭
Forgot the flipping x^3 term and said “didn’t need it” cos I read the expansion at first as to x^2
Then gave it to x^3
its wrong anyway
Alr I got lambda as 3
Ugh….
in what
I got -3/5 x^2
sounds right
For e
That’s fine
i think i put positive
I think it should be 3/2
For e^5x
If I’m not mistaken
Then 1/10 and -8/225 or smth like that
Can’t remember exactly but
Yea
i got 9/21 for something i think
Just divide divide properly
I got both to be negative
then just simplify
Likely
Nice easy 10 marks then
Yes
Someone did 1 / (and expanded ^4 )
That's 0 marks surely right?
Yes
probably 1 if they got sinx maclaurin series
Think so
And a + - 0.6
Idk which one
not paper 2
damn aqa was harder than edexcel
Huh rlly
i knew that there was gonna be volume of revolution parametric
they did i t
Further ?
yh
Oh I didn't even know
Grade boundries gonna be v high theb for edezcel it seems
Cuz apparently p1 was super ez too
yh
AQA too ngl
we will see
what do you think grade boundaries for an A will be?
65 per paper?
ye i fucking hope its not that much higher
Was paper 2 difficult @patent ledge
for A not A*
ye a little bit but i just didnt do as well
What topics came up
Did any matrices come up like inverses
Ye
I would say it would’ve
It did
In terms of k?
Yes haha
ye im just sad i didnt get the reduction formula question
It's all good bro
could of got an extra 9 marks
Yeah aqa always thinks of those silly ways to make people not being able to check
thats like a grade😂
IT DIDNT COME UP?
NO WAY
What was it?
cos^nx
BRO SO FREE A😭
i literally did it for sin and tan this morning and couldnt replicate for cos
😂
i literally looked at the question in the textbook and thought
Split into cos^2 and cos^n-2
Then by parts
Oh wait ur right
With u = cos^n-1x
ye and what did you get
And it comes out lovely
With tan u do n-2 mb
Ye
Did u need to work out a definite integral?
Or was it just reduction formula
Wag1 eith thjs keyboard
There was
Limits
For the second part
You had to do
I6 I think
And the limits were
0 and pi/4
For the whole thing ye
That’s such a nice question
Yeah it is
Was there more calculus
Any vectors?
Did u need to find the characteristic eq tho
Nope
Ohh that fair enough
-(N-1)cos^(n-2)(x)sin(x)
Yeah
yup
Do you still want me to do it ?
nah its fine
I m3ssed up the inverse of the matrix I was so careful idk how
like i knew you had to bring an extra cos out but then i had n-3
U can always mess up on them
actually sucks
U can check tho
As long as u have a follow up q
Ye we did
That's how I knew I got it wrong
I got 2/3 parts correct
And the other didn't work out
So I messed up somewhere
I wish I was born in 2006
You'll see the paper tomorrow right ?
Yeah hopefully 🤞🏾
Nah
Bro has connections
my friend he’s got access to something 😭
😭😭
So he can just send me stuff 💀
Nah but for aqa
But it shoukd b fine
It’s a bit unfair for aqa
What is
And OCR n stuff
Nicee
Yeah you wouldn’t really find them elsewhere would you?
You wouldn't
Yep
I'm sure teachers give these out tho no?
Yh they do
Yh
If the RHS of a second order was
25e^5x + ...x^2 + ..x
If you use
Axe^5x + Bx^2 + Cx
Is it fine
Without + d
i think u need d
Nah u need that
Ax^2+bx+c
Thank you
Ye that’s what I did
Nice
The paper wasn’t hard it was just a lot to do in 2h
Agreed
gl tomorrow
Wait
Why do you need a +d
How are you gonna compare a constant on the left side when there is no constants on the RHS
So d is 0 anyway surely.. ?
Oh wait nvm you get more constant terms on LHS too
Easy 100%
How did you guys find it ?
edexcel?
AQA
was good
U gonna do edexcel regular @signal acorn
Yeah as soon as I get the paper ofcourse
What are some formulas of volumes and areas of shapes we might need to remember for mech?
none probably
ive never seen anything thats required me to memorise shapes
u need to know the CoM formulas tho
but ig if u forget u can derive it
ye
thye might ask like a question that requires you to know volumes of a cone or circle
for some reason i always forget volume of circle and cone
😭
anyway they probably wont
i hope i scrapped an A in paper 2
because im not feeling confident about mechanics
so ur fine then
if i didnt make any mistakes i think i could get like 90 - 95 but i wouldve so made like 80s for me hopefully
last q?
i doubt many people got that
and there was a 3 marker eailer
do u do edexcel regualr or aqa
aqa
nvm then
u defo get an A
just aim for a*
i got no time to revise mech or stats
only night of physics which i cant do anything
gonna have to do some in morning
ye my stats is good however its so easy to lose marks
Have they ever asked us to derive the formula for integrating com
Yeah
Never seen it
@frigid smelt i got k=12
is this paper 1?
so long ago i dont remember
yh
fm?
normal
@violet dock
That's correct
bro the equation was hard, i had to put it into my calculator
Did you get simultaneous equations ?
yes
Oh haha
Yeah ik what you done
Woah
had to put it into the calculator
Yh idk what you done
i made k the subject