parametric equations

[light pagoda]

Need help pls on both parts

<@&791435371564892232> 🙏

[tardy zenith]

For the greatest y value you gotta think about why y = 2 + sin(theta) is greatest given this info we know sin can be between -1 and 1 we know its max point y will be when it is 1 as y=2+1 = 3

[glass flax]

wouldn't the first part be when sintheta = 1, since max value of y=2+1

and second part u do when x=0

[tardy zenith]

For the Interecections you need to transform x=0
And make turn cos 2 theta using cos additiona formulae

Cos( 2 theta) = 2 cos^2 (theta)-1

The solve for theta and subsitute for corresponding y

[light pagoda]

Ok I get y=3

How do I find the x coordinate

Of that point

Dw I get that now

Thanks

Sorry @tardy zenith for some reason they want 2 coordinates

I managed to work out 1 but I’m unsure why they do this

The sin^2 theta part

Where does that even come from

[tardy zenith]

For the y intercept yh it makes sense as they have a quadratic

[light pagoda]

I don’t understand

ig I would get 5/6

[tardy zenith]

Did you find for what theta x =0 ?

[light pagoda]

No why do I need to find that

[tardy zenith]

Looking at the graph they gave you they have 2 y intercept

[light pagoda]

Ohhhh

yeah

[tardy zenith]

For part ii there are two y intercept these occur when x=0

X=0 as a result will have 2 corresponding theta

[light pagoda]

I jusr went from doing cos^-1 (1/4) = 1.318 and then subbed that into y parametric

So y = 2 + sin 1.318

[tardy zenith]

No that why i said u should equate x=0 and break it down using cos additiona formulae

[light pagoda]

Yeah I did but there isn’t an addition formula

For

y= 2 + sin theta

I just subbed in my theta

From the quadratic

For y

[tardy zenith]

Cos(2 theta) can be broken into 2cos^2(theta)-1 which mean u now have a 'quadratic ' of theta which will have 2 solution of theta

[light pagoda]

Yeah

But

One is -2

Which is undefinable

so you can’t sub that in

cos^1 (-2) = error

[tardy zenith]

Yh

[light pagoda]

Because it’s only from 1 to -1

[tardy zenith]

Then the next one

[light pagoda]

Next one?

The other value is 1/4

So I did cos^-1 1/4

Theta = 1.318

Then subbed that into y = 1 + sin theta

[tardy zenith]

Yh but youre forgetting one thing which is that you can have 2 values of theta for the same output

For example i think Cos30 and Cos330 are the same

[light pagoda]

Ohhh as in I subtract 2pi from 1.318

[tardy zenith]

Yh to find the other value for y

[light pagoda]

Makes sense ig

I don’t know what way they did it

They made it look easier with the plus minus

[tardy zenith]

The method they use in the MS makes use of the trig identity cos^2 + sin^2 = 1

[light pagoda]

And how does that find the other solution

[tardy zenith]

We know what cos = 1/4

[light pagoda]

yeah

[tardy zenith]

So we can find what sin^2 = 15/16

That means sin = +/- root15/4

[light pagoda]

So how does that identity let us find both of the roots

I don’t get how it works

[tardy zenith]

And they subbed that into there y earlier

[light pagoda]

yeah

[tardy zenith]

When you square root theres both positive and negative solution

But normally we only consider positive for the square root function

[light pagoda]

yeah I get that but it would of never come into my mind to use that identity

to get both solutions

After working out cos theta = 1/4 or -2

[tardy zenith]

As long as you have a method that works its fine

Just make sure you do not forget a solution and always use the graph if they give one

[light pagoda]

Ok thanks a lot, praying I get a parametric question in my paper 3 for Thursday😅

[tardy zenith]

This graph is very helpful for the q as it tells us quite alot about the parametric that it intersects axis twice and that only a single point is at its furtherst

[light pagoda]

yeah

[tardy zenith]

Paper 3 ocr mei b?

[light pagoda]

yeah

How did yk

[tardy zenith]

Its my exam board too

[light pagoda]

Are you also ocr Mei b?

No way

Are you y13

[tardy zenith]

Yh

[light pagoda]

Wow

There’s 3 people now

[tardy zenith]

Who else do yk?

[light pagoda]

What do you think will come up

@crisp beacon

Only other person haha

[tardy zenith]

Numerical methods is likely
Maybe parametrics
And maybe a small DE

[light pagoda]

I’ve done a few past papers and I keep getting around 45-60/65 for pure

[tardy zenith]

Small series question havent seen too much on that yet

[tardy zenith]

Ahh yh ive seen them around

[light pagoda]

I really think we will get modulus

Logs

maybe rate of change

They love those ones

[tardy zenith]

Its possible but logs and modulus normally are bigger qs imo so im not as sure if theyll ask them

[tardy zenith]

Yh DE is likely but they have already asked us a q on it

[light pagoda]

I think I messed up paper 1 because I was too tired lmao… thought the exam was in the morning so I woke up at 6

[tardy zenith]

Nope all maths have been afternoon

[light pagoda]

I was at school from 7am-1pm trying to revise 😭

I was dead for mechanics

Stats was good though

[tardy zenith]

Thats good alot of people liked that paper

[light pagoda]

I couldn’t do a 6 or 9 marker

I did the implicit part and made dy/dx the subject

But then the stationary point one

I had no idea

[tardy zenith]

set dy/dx = 0

[light pagoda]

Yeah that wasn’t my problem

[tardy zenith]

And use implicit and rearrange for dy/dx

[light pagoda]

My problem was differentiating

with m

It was like 9mx and all that

And it didn’t say m was a constant

[tardy zenith]

Treat as constant essentially and then i think i completed square to solve

[light pagoda]

yeah I tried doing implicit differentiation with m lmao

[tardy zenith]

Yh but you can kinda treat it as constant for that case

[light pagoda]

I’d never seen a question like it tbh

[tardy zenith]

Ohh well i mean you dont need 100% for an A*

[light pagoda]

I only want a C…

[tardy zenith]

There were a few qs not seen before i will admit

[light pagoda]

I think I got around 40-50 on mechanics and 55-70 on stats

So I need like 20/80 for a C I think

[tardy zenith]

I messed up myself on one of the questions with tiny arithmatic errors

[tardy zenith]

Well best of luck

[light pagoda]

I’ve made silly mistakes too

I told my friend literally 5 mins before the exam how to do binomial expansion

When the first term isn’t 1

And then in the exam I forgot to multiply it by 8^2/3

I was so pissed

[tardy zenith]

Its fine i also made that mistake in past times

[light pagoda]

I just rushed it because I thought I was in my element

Comprehension is the easiest paper tbf

[tardy zenith]

Yh just read and stay calm

[light pagoda]

Anyway I need to head off and get some sleep

gl with revision

[tardy zenith]

This is also ig the paper with the highest mins per mark

[tardy zenith]

Ty ty

[light pagoda]

yeah

Im sure you’ll get a A or A* idk what your aiming for

[tardy zenith]

Well enjoy

[tardy zenith]

A*

Thanks i hope so

[tardy zenith]

Well if yoy have any qs feel free to ping me or dm

[light pagoda]

Also why has Eveyonr on the student room said the boundaries are gunna be super high😭

I don’t think our papers have been that much easier than prior ones

Plus all the smart people go to the student room

[tardy zenith]

Its a biast data set dw about it . Those on academia related pages and forum are more likely to be those who have A* s and are academic focused. Its not an accurate sample

[light pagoda]

they should be fairly similar to 2023 and 2019

Also wtf happened to our exam board in 2018

[tardy zenith]

Theyve been pretty inline difficulty wise i think its maybe slightly easier but its not gonna cause a mass jump in grade boundaries

[light pagoda]

Have you seen the grade boundaries for 2018

[tardy zenith]

Not the way people have been saying online at least

[tardy zenith]

Yh

[light pagoda]

Crazy

[tardy zenith]

It was possibly easy yr

[light pagoda]

Maybe but

Say you got a D then, in 2019 or 2023 you would of almost got a B

[tardy zenith]

I mean that yr paper did inflate even my marks when i did for prsctice

[tardy zenith]

Yh but youre assuming the person got the same mark its more likely that the style of qs that yr were simpler than they expected

[light pagoda]

I think if there was a to be a increase in grade boundaries it would affect grades A* A B more than a C

so I should be ok even if they go up a little

[tardy zenith]

Yh but the effect does trickle down to other grades

[light pagoda]

Also do you think on that question about drawing the sin2x graph you’ll get a mark for doing the y axis😭

[tardy zenith]

Yh i mean just do your best thats it

[light pagoda]

I accidentally ended mine where cos does for some stupid reason

[tardy zenith]

Maybe if you marked y=1 and y=-1

[light pagoda]

yeah

[tardy zenith]

Normally theres a mark for each corecct iirc: the right defined bounds on axis, shape and intersections

[light pagoda]

Anyway gn, thanks for helping me and good luck for Thursday

[tardy zenith]

Nws any other qs im happy to help. Good luck too