Struggling with FP2...

OP

Original post by Ayman!

First notice which topics you're losing marks or taking too much time on - these are the areas which you'll need improvement in. Work on your weak areas using textbook questions and the likes. Once you feel more confident, go back to past papers.

I feel like textbook questions are quite different to the exam questions though? Maybe that's the issue? Because sometimes the exam questions can be quite awkward.

Reply 3

Original post by EmmaLouise759

I feel like textbook questions are quite different to the exam questions though? Maybe that's the issue? Because sometimes the exam questions can be quite awkward.

I know the feeling! Personally, I'm not a massive fan of the FP2 textbook.

There is not much content in FP2. I agree with you, however, that the exam questions are tough. There's lots of ways in which they have styled certain questions in the past, and lots of ways they can ask new things in the future.

What I find best is to distill the topics down to all the possible things they can ask you. When you do this, you'll find that there's not much that they can throw at you.

For example with polar coordinates you are assessed on:

•

Tangents parallel to the initial line: consider $\frac{dy}{d\Theta} = 0$

•

Tangents perpendicular to the initial line: consider $\frac{dx}{d\Theta} = 0$

•

Area under a curve (in formula book).

You will find that, by doing literally every exam question, you will see the different styles of polar coordinate questions you can face. Some are simple areas under a curve, some require taking away areas, some require adding areas (these are the hardest to spot. I recall one exam question which required use of C2 area of sectors).

By doing every exam paper out there, supplementing with questions from this book: https://www.amazon.co.uk/Level-Mathematics-Edexcel-Further-Pure/dp/0199117888/ref=sr_1_1?ie=UTF8&qid=1462816996&sr=8-1&keywords=fp2+oxford, I saw my grades jump from a D to A*s.

The integration and differentiation in FP2 is the same standard as C3 and C4. Your revision of these modules will benefit massively.

Part of the fact as to why FP2 is so bloody difficult is that it has incredibly high grade boundaries. Last year's June 2015 paper was a ludicrously high 67/75 for an A. See the attached table for the grades of all current spec papers (A through to E).

Screen Shot 2016-05-09 at 19.06.07.png

What I should ask is what areas do you find the most confusing? What do you tend to lose marks on?

Reply 4

OP

Original post by oinkk

I know the feeling! Personally, I'm not a massive fan of the FP2 textbook.

What I should ask is what areas do you find the most confusing? What do you tend to lose marks on?

Oh my goodness thank you, that was really helpful! I have debated getting that book for quite a while now, would you still say it's worth it with the exam in 4 weeks? Or is it best just to go past paper crazy?

And I don't know, I'm pretty good with the series questions and inequality questions, but the other questions confuse me sometimes. I'll look at them and not really know what they're expecting me to do. Certainly complex plane transformations is quite a tricky topic in my opinion.

Reply 5

Original post by EmmaLouise759

Oh my goodness thank you, that was really helpful! I have debated getting that book for quite a while now, would you still say it's worth it with the exam in 4 weeks? Or is it best just to go past paper crazy?

And I don't know, I'm pretty good with the series questions and inequality questions, but the other questions confuse me sometimes. I'll look at them and not really know what they're expecting me to do. Certainly complex plane transformations is quite a tricky topic in my opinion.

Series and inequalities tend to get you good marks in the exam.

Definitely get the book! And go past paper crazy :-) Even if its just a couple of weeks before the exam, it still has lots of extension questions which I find are very similar to exam questions. It also has some slightly different methods to the FP2 book if you're struggling with certain topics. I have this book for FP3 if you're studying that too, it's been a life-saver.

My best revision tip so far has been to come up with methods for approaching each question.

As for complex number transformations, they're quite difficult. I can do the ones where you're giving

|z|=n

, n being an integer.

•

Rearrange the transformation to give $z =$ something in terms of w.

•

Take the modulus of both sides. If you have a fraction (which you commonly will), you can take the modulus of the top and the bottom separately to multiply both sides by the denominator. If you have a negative sign in front of the fraction, you can drop that here as we're taking the absolute value.

•

Using $|z|=n$ , you can make your substitution so that you have an equation entirely in w (or the plane you're transforming to).

•

Now, $w=u+iv$ . Make this substitution and group the real and imaginary terms in the moduli. You may find it easy to take a common factor of i if there is one.

•

You can then treat both sides as a complex number and take the modulus of them (Pythagoras). This means: $\surd{real^2 + imaginary^2}$ Most likely, you will end up with a quadratic in terms of u or v if there's been multiple parts to a real or imaginary part.

•

Square both sides, and rearrange until the required form is achieved. I love this step cos loads of terms cancel down :-)

•

Complete the square if it needs to be a circle.

There are more complicated cases such as the attached one from June 2014 (R). This took me so long to figure out (around a half an hour I think!). It's these transformations that I need to spend more time looking at.

Screen Shot 2016-05-09 at 19.53.05.png

One month and one half term is plenty of time to make sure that we're ready for these types of questions :-)

Reply 6

Synn

1

Original post by oinkk

Series and inequalities tend to get you good marks in the exam.

Definitely get the book! And go past paper crazy :-) Even if its just a couple of weeks before the exam, it still has lots of extension questions which I find are very similar to exam questions. It also has some slightly different methods to the FP2 book if you're struggling with certain topics. I have this book for FP3 if you're studying that too, it's been a life-saver.

My best revision tip so far has been to come up with methods for approaching each question.

As for complex number transformations, they're quite difficult. I can do the ones where you're giving

|z|=n

, n being an integer.

•

Rearrange the transformation to give $z =$ something in terms of w.

•

Take the modulus of both sides. If you have a fraction (which you commonly will), you can take the modulus of the top and the bottom separately to multiply both sides by the denominator. If you have a negative sign in front of the fraction, you can drop that here as we're taking the absolute value.

•

Using $|z|=n$ , you can make your substitution so that you have an equation entirely in w (or the plane you're transforming to).

•

Now, $w=u+iv$ . Make this substitution and group the real and imaginary terms in the moduli. You may find it easy to take a common factor of i if there is one.

•

You can then treat both sides as a complex number and take the modulus of them (Pythagoras). This means: $\surd{real^2 + imaginary^2}$ Most likely, you will end up with a quadratic in terms of u or v if there's been multiple parts to a real or imaginary part.

•

Square both sides, and rearrange until the required form is achieved. I love this step cos loads of terms cancel down :-)

•

Complete the square if it needs to be a circle.

There are more complicated cases such as the attached one from June 2014 (R). This took me so long to figure out (around a half an hour I think!). It's these transformations that I need to spend more time looking at.

Screen Shot 2016-05-09 at 19.53.05.png

One month and one half term is plenty of time to make sure that we're ready for these types of questions :-)

I have trouble with complex geometry as well especially questions that ask you to sketch something along the lines of

arg(w)-arg(z)=\pi/3

. Other than this and sketching polar graphs i should get a High grade hopefully an A/A* as my mechanics are not as good as my pure work.

Reply 7

OP

Original post by Synn

I have trouble with complex geometry as well especially questions that ask you to sketch something along the lines of

arg(w)-arg(z)=\pi/3

. Other than this and sketching polar graphs i should get a High grade hopefully an A/A* as my mechanics are not as good as my pure work.

Really? I'm thinking I'll be the other way around. I think it's just because the grade boundaries are so high. :angry:

Reply 8

OP

Original post by oinkk

Series and inequalities tend to get you good marks in the exam.

Definitely get the book! And go past paper crazy :-) Even if its just a couple of weeks before the exam, it still has lots of extension questions which I find are very similar to exam questions. It also has some slightly different methods to the FP2 book if you're struggling with certain topics. I have this book for FP3 if you're studying that too, it's been a life-saver.

My best revision tip so far has been to come up with methods for approaching each question.

As for complex number transformations, they're quite difficult. I can do the ones where you're giving

|z|=n

, n being an integer.

•

Rearrange the transformation to give $z =$ something in terms of w.

•

Take the modulus of both sides. If you have a fraction (which you commonly will), you can take the modulus of the top and the bottom separately to multiply both sides by the denominator. If you have a negative sign in front of the fraction, you can drop that here as we're taking the absolute value.

•

Using $|z|=n$ , you can make your substitution so that you have an equation entirely in w (or the plane you're transforming to).

•

Now, $w=u+iv$ . Make this substitution and group the real and imaginary terms in the moduli. You may find it easy to take a common factor of i if there is one.

•

You can then treat both sides as a complex number and take the modulus of them (Pythagoras). This means: $\surd{real^2 + imaginary^2}$ Most likely, you will end up with a quadratic in terms of u or v if there's been multiple parts to a real or imaginary part.

•

Square both sides, and rearrange until the required form is achieved. I love this step cos loads of terms cancel down :-)

•

Complete the square if it needs to be a circle.

There are more complicated cases such as the attached one from June 2014 (R). This took me so long to figure out (around a half an hour I think!). It's these transformations that I need to spend more time looking at.

Screen Shot 2016-05-09 at 19.53.05.png

One month and one half term is plenty of time to make sure that we're ready for these types of questions :-)

Thank you so much! I'll definitely be following your advice. Good luck to you! :h:

Reply 9

Lychee628

19

Im in a similar position but I'd say just keep practicing & it'll be fine dw! :biggrin:

Reply 10

Original post by Synn

I have trouble with complex geometry as well especially questions that ask you to sketch something along the lines of

arg(w)-arg(z)=\pi/3

. Other than this and sketching polar graphs i should get a High grade hopefully an A/A* as my mechanics are not as good as my pure work.

See my image attached. It's a quick diagram of what is actually going on in these problems. I've created one of the more challenging ones, and if there's any errors in my working then please let me know.

Step-by-step:

•

As you said, you would subtract the two arguments if you had a division inside one argument.

•

Let one of these arguments equal some angle $\alpha$ , and let the other equal some other angle $\beta$ .

•

The difference in these two angles is the main angle from the original problem, $\frac{\pi}{4}$

You should note at this point that:

•

$\alpha - \beta$ gives a positive angle. Therefore the angle $\alpha$ must always be greater than $\beta$ .

•

Since $\alpha - \beta$ is less than 90 degrees ( $\frac{\pi}{2}$ radians), the locus of z as P varies is on the major arc of the circle

•

That is to say that if $\alpha - \beta$ is acute, the locus is on the major arc of the circle. If $\alpha - \beta$ is obtuse, the locus lies on the minor arc of the circle.

Make sure you are entirely happy with the two key facts above. They're key to answering these questions.

•

Now, since $\alpha$ is always greater than $\beta$ , the lines do not intersect where you'd normally expect. You have to 'go back' on yourself to the point where they intersect in the negative axis.

•

You can then draw the locus as shown on the diagram.

(edited 7 years ago)

Reply 11

Original post by EmmaLouise759

Thank you so much! I'll definitely be following your advice. Good luck to you! :h:

Good luck to you too!

Reply 12

Synn

1

Original post by oinkk

See my image attached. It's a quick diagram of what is actually going on in these problems. I've created one of the more challenging ones, and if there's any errors in my working then please let me know.

Step-by-step:

•

As you said, you would subtract the two arguments if you had a division inside one argument.

•

Let one of these arguments equal some angle $\alpha$ , and let the other equal some other angle $\beta$ .

•

The difference in these two angles is the main angle from the original problem, $\frac{\pi}{4}$

You should note at this point that:

•

$\alpha - \beta$ gives a positive angle. Therefore the angle $\alpha$ must always be greater than $\beta$ .

•

Since $\alpha - \beta$ is less than 90 degrees ( $\frac{\pi}{2}$ radians), the locus of z as P varies is on the major arc of the circle

•

That is to say that if $\alpha - \beta$ is acute, the locus is on the major arc of the circle. If $\alpha - \beta$ is obtuse, the locus lies on the minor arc of the circle.

Make sure you are entirely happy with the two key facts above. They're key to answering these questions.

•

Now, since $\alpha$ is always greater than $\beta$ , the lines do not intersect where you'd normally expect. You have to 'go back' on yourself to the point where they intersect in the negative axis.

•

You can then draw the locus as shown on the diagram.

Thank you this is very helpful :smile:

Reply 13