Partial Fractions (1 Viewer)

[nichorowitz]

Like the picture:
Is this a general rule that you can express partial fractions with a quadratic on the denominator as three fractions (one with the same quadratic and one with the sqrt of the quadratic).
Thanks

 

[artosis]

Yea, its a general 'formula' that u can use

 

[nichorowitz]

Yea, its a general 'formula' that u can use

sweet thanks. makes things a lot easier.

 

[D94]

It will most likely be a "Question 1" question worth 3 marks, so knowing this is essential for the integration section.

 

[hup]

It will most likely be a "Question 1" question worth 3 marks, so knowing this is essential for the integration section.

its not really because they give you the partial fraction expansion

 

[D94]

its not really because they give you the partial fraction expansion

Not always - just look at the 2010 paper. They don't have to give you the expansion; either way, they are always easy to solve.

 

[hup]

ok soz best to know it

 

[nichorowitz]

It will most likely be a "Question 1" question worth 3 marks, so knowing this is essential for the integration section.

i would say its the best way to approach the question but it's still not essential. you can still do it just having 2 fractions instead of the three.
the integration becomes a lot harder though, but still do able.

 

[D94]

i would say its the best way to approach the question but it's still not essential. you can still do it just having 2 fractions instead of the three.
the integration becomes a lot harder though, but still do able.

No, I meant the concept of partial fractions is essential - not the exact example above.

 

[nichorowitz]

No, I meant the concept of partial fractions is essential - not the exact example above.

haha yeah of course.

 

[Trebla]

You're not expected to know the 'formula' for partial fractions containing repeated factors (see the syllabus). If you do get repeated factors you will generally be given the appropriate form to decompose the fraction.

E.g. You will NOT get directly asked this:



But you can be asked to do this:



You will only get directly asked to integrate if the partial fractions are within the syllabus (i.e. standard cases without repeated factors), otherwise you have to be guided.

 

[D94]

You're not expected to know the 'formula' for partial fractions containing repeated factors (see the syllabus). If you do get repeated factors you will generally be given the appropriate form to decompose the fraction.
...

You will only get directly asked to integrate if the partial fractions are within the syllabus (i.e. standard cases without repeated factors), otherwise you have to be guided.

^ Yes.

The syllabus is vague and makes no reference to such a formula, but there is a general "method" for partial fractions which you need to know, as per the syllabus mentioning:

integrate rational functions whose denominators have simple linear or quadratic factors.

and goes on to give the consideration:

Only rational functions, whose denominators can be broken into a product ofdistinct linear factors, or of a distinct quadratic factor and a linear factor, or of two distinct quadratic factors, need to be considered.

Either way, knowing the repeated factors method can help with efficiency, so you're not lost wondering what just happened in the exam.

 

[nichorowitz]

You're not expected to know the 'formula' for partial fractions containing repeated factors (see the syllabus). If you do get repeated factors you will generally be given the appropriate form to decompose the fraction.

E.g. You will NOT get directly asked this:



But you can be asked to do this:



You will only get directly asked to integrate if the partial fractions are within the syllabus (i.e. standard cases without repeated factors), otherwise you have to be guided.

ok thanks. i've never actually read any of the maths syllabus. worth reading?