Partial fractions recognition (1 Viewer)

[Hezz96]

Hey guys,
In a lot of the past HSC integration questions I've done/looked at they seem to give you the tip off that you need to use the partial fractions method if it is required. (They might begin with "Find values of A, B and C such that Ax+B/... + C/... = ..."). Have any of you ever seen an integration question in the HSC where the first thing you need to do is recognise that you need to use the partial fractions method, where they do not give you this tip off?
Cheers

 

[obliviousninja]

Hey guys,
In a lot of the past HSC integration questions I've done/looked at they seem to give you the tip off that you need to use the partial fractions method if it is required. (They might begin with "Find values of A, B and C such that Ax+B/... + C/... = ..."). Have any of you ever seen an integration question in the HSC where the first thing you need to do is recognise that you need to use the partial fractions method, where they do not give you this tip off?
Cheers

Yea I've seen it. Also you sometimes need it when doing resisted motion. Its quite noticeable, if the denominator can be factorised.

 

[Makematics]

Yep they can ask for it. Happens quite often in mechanics when you have dv/dt=g-kv^2 and you gotta integrate

 

[Carrotsticks]

Hey guys,
In a lot of the past HSC integration questions I've done/looked at they seem to give you the tip off that you need to use the partial fractions method if it is required. (They might begin with "Find values of A, B and C such that Ax+B/... + C/... = ..."). Have any of you ever seen an integration question in the HSC where the first thing you need to do is recognise that you need to use the partial fractions method, where they do not give you this tip off?
Cheers

2012 HSC Resisted Motion Problem.

Required the integration of (if I recall correctly)

 

[hit patel]

Wait they tell you what to do? Shouldnt they though?, since the students are exposed to using any of the 3 possible methods for partial fractions, and they might want to test them on one. Well if you get what I mean.

 

[Makematics]

Wait they tell you what to do? Shouldnt they though?, since the students are exposed to using any of the 3 possible methods for partial fractions, and they might want to test them on one. Well if you get what I mean.

There are different methods? You mean equating coefficients, substitution, heaviside? Or something else?

 

[hayabusaboston]

I just remember 1/2sqrt(LHS)

eg

1/(36-x^2) becomes 1/12 outside of (1/(6-x)+1/(6+x))

the LHS is the LHS of the denominator's perfect square.

 

[HeroicPandas]

If you have an integral in this form: (the denominator can be factorised using difference of 2 squares)

Instead of using partial fractions, u can memorise:

 

[Makematics]

If you have an integral in this form: (the denominator can be factorised using difference of 2 squares)

Instead of using partial fractions, u can memorise:

But if they ask you to split it using partial fractions then you have to follow their instructions. Also they really dont like when you use formulas that arent 'syllabus-approved'.

 

[RealiseNothing]

If you have an integral in this form: (the denominator can be factorised using difference of 2 squares)

Instead of using partial fractions, u can memorise:

ewww, memorising formulas

too much effort/10

 

[Makematics]

ewww, memorising formulas

too much effort/10

Doesnt memorise angle between two lines formula ---> loses 3 marks

 

[anomalousdecay]

I'm guessing heaviside isn't board approved though?

I learnt it at UNSW open day lol.

 

[anomalousdecay]

Doesnt memorise angle between two lines formula ---> loses 3 marks

tanx = |m1-m2|/|1+m1m2|?

But all the past paper textbooks and stuff just use that instead of deriving the formula.

 

[Makematics]

I'm guessing heaviside isn't board approved though?

I learnt it at UNSW open day lol.

Best not to use it, but its more recognised than heroic's formula

 

[Makematics]

tanx = |m1-m2|/|1+m1m2|?

But all the past paper textbooks and stuff just use that instead of deriving the formula.

What? I was saying to realise he will lose marks if he doesnt memorise that formula haha. Ive memorised it, theres no need to derive it...

 

[anomalousdecay]

What? I was saying to realise he will lose marks if he doesnt memorise that formula haha. Ive memorised it, theres no need to derive it...

My bad lmao. Trying to derive that or integration by parts will lose 5 minutes in the exam lol.

So much English study that I can't read something properly now XD.

 

[RealiseNothing]

Doesnt memorise angle between two lines formula ---> loses 3 marks

Don't even have to fully remember that. Just know that it is in the form:



To find A, we know that as then and so we want the difference between the gradients. This is because the smaller the difference in the gradients, the smaller the angle. Hence

To find B, we know that when the lines are perpendicular we get which is undefined. So when we should have B=0. If they are perpendicular then it means and so B must be for this to be true.

Now we also know that we want the angle, and so we take the absolute value to ensure that our answer is positive, and we get:



This may look long, but these are really easy tests to ensure you have the formula right and they don't take long to mentally check.

 

[anomalousdecay]

Don't even have to fully remember that. Just know that it is in the form:



To find A, we know that as then and so we want the difference between the gradients. This is because the smaller the difference in the gradients, the smaller the angle. Hence

To find B, we know that when the lines are perpendicular we get which is undefined. So when we should have B=0. If they are perpendicular then it means and so B must be for this to be true.

Now we also know that we want the angle, and so we take the absolute value to ensure that our answer is positive, and we get:



This may look long, but these are really easy tests to ensure you have the formula right and they don't take long to mentally check.

That would be very good uni, but I would say its best to just remember that for HSC.