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

1. (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.

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Okay, I have been told that with some you need to take out a factor first before you can the stretch or translation...
2. (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...3-QP-JUN14.PDF

Q4 on this paper, what comes first stretch or translation? I put translation by stretch?
3. http://filestore.aqa.org.uk/subjects...3-QP-JUN14.PDF

Q5 for this paper, I solved the modulus function question but it rejects values 1 and -1 why is this?!!
4. (Original post by SunDun111)
http://filestore.aqa.org.uk/subjects...3-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...3-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)
5. (Original post by SunDun111)
http://filestore.aqa.org.uk/subjects...3-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.
6. (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

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7. (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?
8. (Original post by SunDun111)
http://filestore.aqa.org.uk/subjects...3-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
9. (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.

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Rotation is part of FP1 and FP4 they require matrix so they won't ask it ever
10. (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)
11. (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
12. (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?
13. (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.
14. (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
Yeah I got you
15. (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?
16. (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.
17. Just did jan 12 & i'm finished with past papers, no more revision now [ i may review every chapter briefly before i sleep though ]
18. 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.
19. (Original post by Dinasaurus)
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.
sin and cos repeat every 360 degrees (2pi)
tan repeats every 180 degrees (pi)

If you're solving sinx = constant:
sin^-1(constant) = x (call this a)
Then do 180 - a for your second value (call it b)
Then you can add or subtract 360 degrees from a and b for all the values

In a similar way, set a= cos^-1(constant), then b = -a and add/subtract 360 for your values

With tan it is slightly easier because you can set a = tan^-1(constant)
Then add/subtract 180 from it to get all your values
20. Anyone know how to draw the graph for y=f(|x|), in comparison to y= |f(x)|

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