AQA A2 Mathematics MPC3 Core 3 - Wednesday 15th June 2016 [Official Thread]

Original post by Language student

Okay, I have been told that with some you need to take out a factor first before you can the stretch or translation...

http://filestore.aqa.org.uk/subjects/AQA-MPC3-QP-JUN14.PDF

Q4 on this paper, what comes first stretch or translation? I put translation by stretch?

Reply 242

http://filestore.aqa.org.uk/subjects/AQA-MPC3-QP-JUN14.PDF

Q5 for this paper, I solved the modulus function question but it rejects values 1 and -1 why is this?!!

Reply 243

Original post by SunDun111

http://filestore.aqa.org.uk/subjects/AQA-MPC3-QP-JUN14.PDF

Q4 on this paper, what comes first stretch or translation? I put translation by stretch?

See my long post on page 12, I went through that exact question

Original post by SunDun111

http://filestore.aqa.org.uk/subjects/AQA-MPC3-QP-JUN14.PDFQ5 for this paper, I solved the modulus function question but it rejects values 1 and -1 why is this?!!

Because 1 and -1 are not in the domain of f(x)

Reply 244

tanyapotter

20

Original post by SunDun111

http://filestore.aqa.org.uk/subjects/AQA-MPC3-QP-JUN14.PDF

Q5 for this paper, I solved the modulus function question but it rejects values 1 and -1 why is this?!!

if you look at the domain of f(x), x must be greater than or equal to 3.

Reply 245

MahuduElec

5

Original post by Language student

Okay, I have been told that with some you need to take out a factor first before you can the stretch or translation...

That is for when both alter X. There are two ways:

Do it via Inverse BIDMAS, no factorisation required.

Do it by taking a factor out, to get x on its on, ie 2x-2=2(x-1), and then use the BIDMAS order.

Both ways are correct, choose one you prefer and are comfortable with

Posted from TSR Mobile

Reply 246

Language student

2

Original post by bartbarrow

You mean with stretches?

The rules are:

Stretch in x axis scale factor a, replace x with x/a
=> Therefore, a stretch (in x) of sf 1/a, x with be replaced with ax

Same again with y except a => y/a etc

If you are combining translation/stretch then just think about it logically:

Example 1
"Describe a sequence of transformations to translate y=lnx to y=4ln(x-e)" from Jan 12

There will be a stretch and translation (hopefully you can spot that). It can be done in any order but depending on what you choose, the numbers will (sometimes) be different

I recommend you do a translation first because I think it is less hassle

If a translation of (a, b) replaces x with x-a and y with y-b, then we want a translation (e, 0)

With just that transformation we have y=ln(x-e)

Now with y=ln(x-e) we just need to transform it to y=4ln(x-e) or, rewritten, y/4=ln(x-e). With the rules above you can see that the stretch would be in the y axis and we need to replace y with y/4 so the scale factor will just be 4.

In that question the order they are done in does not matter

Example 2
Describe a sequence of transformations that map f(x) => f(2x+2)

You could approach it two ways:

Method 1
f(x) => f(x-2) => f(2x+2)
so translation (-2, 0), stretch sf 1/2 x axis

Method 2
f(x) => f(2x) => f(2(x+1)) or f(2x+2)
so stretch sf 1/2 x axis, translation (-1, 0)

Notice how when you are translating it is x that is being replaced, so you would need to remember that it says 2x not x.

Ohhh thank you so much, for the nice explanation. What about for reflections, how do you know which axis it is? And when it gives a graph of y=f(X) and it asks for a sketch for y=-f(X) how do you know which way to draw the new graph?

Reply 247

Language student

2

Original post by SunDun111

http://filestore.aqa.org.uk/subjects/AQA-MPC3-QP-JUN14.PDF

Q4 on this paper, what comes first stretch or translation? I put translation by stretch?

Omg I was just doing that question and got stuck ahhaha

Reply 248

C0balt

16

Original post by MahuduElec

For when it's two transformations, one altering x one altering y, the order does not matter.

When both alter y, the order follows BIDMAS, so stretches before translations.

When both alter x, the order follows Inverse BIDMAS, so translations before stretches.

For reflections, i dont think the order matters, and I've never seen a rotation one come up in any paper.

Posted from TSR Mobile

Rotation is part of FP1 and FP4 they require matrix so they won't ask it ever

Reply 249

Original post by Language student

Ohhh thank you so much, for the nice explanation. What about for reflections, how do you know which axis it is? And when it gives a graph of y=f(X) and it asks for a sketch for y=-f(X) how do you know which way to draw the new graph?

You will need to think logically for them. Transformations really just come down to remembering a few rules and then thinking each step through.

If you have a plot of y=f(x) and it asks you to plot y=-f(x):

For each x value, f(x) will produce some other value (the same in both y=f(x) and y=-f(x)

The only difference is that in y=-f(x) you are negating the same value of f(x). In other words, each y value for every point on the line has a flipped sign

E.G. y=x^2 => y=-x^2, the graph would be reflected in the x axis (or reflected in the line y=0)

so f(x) => -f(x) is a reflection in the x axis

For y=f(x) => y=f(-x), you are plugging in the negative of each x value, so when plotting f(-x), copy the points of f(x) before x=0 to after x=0 and vice versa. In other words, the graph is translated in the y axis (or x=0)

Reply 250

MahuduElec

5

Original post by C0balt

Rotation is part of FP1 and FP4 they require matrix so they won't ask it ever

Oh yh, I remember learning those 9 matrices in FP1 now, didnt do FP4

Edit: btw I was on about any C3 past paper :yes:

(edited 7 years ago)

Reply 251

Original post by bartbarrow

See my long post on page 12, I went through that exact question

Because 1 and -1 are not in the domain of f(x)

Original post by tanyapotter

if you look at the domain of f(x), x must be greater than or equal to 3.

I get that but do you take G(X) into account as well?

Reply 252

Original post by SunDun111

I get that but do you take G(X) into account as well?

Well g(x) has an infinite domain, but if it didn't you would have to look at the range of f being fed into the g

With the question in June 2014:

If you take x=4, then g(x)=2. The 2 is then fed into f which is not allowed because 2 is not in the domain of f. Even though x is, it is irrelevant because it's not x being put into f, it's g(x), which is 2.

Reply 253

C0balt

16

Original post by MahuduElec

Oh yh, I remember learning those 9 matrices in FP1 now, didnt do FP4

Edit: btw I was on about any C3 past paper :yes:

Yeah I got you

Reply 254

Original post by bartbarrow

Well g(x) has an infinite domain, but if it didn't you would have to look at the range of f being fed into the g

With the question in June 2014:

If you take x=4, then g(x)=2. The 2 is then fed into f which is not allowed because 2 is not in the domain of f. Even though x is, it is irrelevant because it's not x being put into f, it's g(x), which is 2.

Ok kinda makes sense so say I had F(X) and G(X)
I do F(g)X = Constant

And I have to solve it and they is two values, since im subbing G into F I ignore the range for G and only look at F?

Reply 255

Original post by SunDun111

Ok kinda makes sense so say I had F(X) and G(X)
I do F(g)X = Constant

And I have to solve it and they is two values, since im subbing G into F I ignore the range for G and only look at F?

If you're solving fg(x) then the x values you find need to be in the domain of g.

Not sure if it will ever come up in a C3 paper but you would also need to check if the g(x) values are in the domain of f(x). I can't recall it coming up before so you might just be ok to only look at the domain of g.

Reply 256

xs4

12

Just did jan 12 & i'm finished with past papers, no more revision now [ i may review every chapter briefly before i sleep though ]

Reply 257

Dinasaurus

22

I know I should know this by now, but can someone just tell me quickly how often:
Sin, Cos and Tan repeats between 0 and 360 and how to find the other values.

Reply 258