Roots with conditions (1 Viewer)

[Dumblikeafox]

Current question i'm doing;

Find as a relation between p, q anr r, the condition for the quadratic equation in x

(p^2 - q^2 )x^2 +2q (p + r)x + (q^2 - r^2 = 0) to have equal roots. simplify your answer as far as possible.



Post holiday brain malfunction is upon me, and have no idea what to do. any help would be appreciated

 

[cutemouse]

Discriminant = 0

 

[Dumblikeafox]

b^2-4ac = 0?

 

[Dumblikeafox]

2q(p^2+2pr+r^2) - 4(p^2q^2-q^4+r^2q^2-p^2r^2)=0

 

[Dumblikeafox]

IMO, it's getting worse

 

[cutemouse]

 

[Boxes]

i was expecting a totally different thread, tbh.

 

[Dumblikeafox]

ahh. ok, I'm an idiot

I've been trying to solve that ^ in relation to x.:mad1:

 

[Boxes]

ahh. ok, I'm an idiot

I've been trying to solve that ^ in relation to x.:mad1:

god, how dumb are you?

 

[Dumblikeafox]

i was expecting a totally different thread, tbh.

I'm used to posting catchy titles, often on far more fast moving threads.

 

[Dumblikeafox]

god, how dumb are you?

Sometimes i surprise myself.

Might have something to do with completing from my textbook 11;6,7,8,9 and 16.1through10 in the last day. my mind is a little bit mush

 

[buchanan]

Yes. You are right. It was in the 1988 2 Unit Q10b (but with plusses, not minuses, and real roots):

 

[buchanan]

By the way, you can get the older papers (1967-1994) at

http://www.angelfire.com/ab7/fourunit/2u1967-1994.zip

and newer ones (1995-2009) at

http://www.boardofstudies.nsw.edu.au/hsc_exams

 

[cutemouse]

What were the main differences between the old maths courses (ie. the pre 1981 courses) and the current one?

I know 4U changed alot, like they introduced Volumes, Conic Sections, Additional Complex numbers (eg. DeMoivre's theorem) and Circular motion in mechanics... but I'm not sure how the 2U/3U courses changed.

 

[buchanan]

The 2 and 3 unit courses (previously named Level 2S and Level 2F - S for short, F for full) didn't change as much.

There used to be 3D coordinate geometry and Hooke's law which are no longer in the current courses.

The 4 unit course changed more because originally it was a 2 year course (originally named Level 1). Obviously if you change a 2 year course to a 1 year course, the changes will be more significant.

There was also another lower level course called Level 3 (a bit like General maths).

 

[cutemouse]

There used to be 3D coordinate geometry and Hooke's law which are no longer in the current courses.

Hooke's law... shouldn't that had been in Physics? :S haha But it does explain why Coroneos had a bit on it in his revised book.

What about transformation of axes?

ie. (if I recall correctly) X=xcosθ-ysinθ and Y=xcosθ+ysinθ

I read this is one of Coroneos' books I think.

 

[buchanan]

Yes there were some other changes.

Another example is that division of an interval in ratios was originally in 2 unit. But is now 3 unit.

Others like this are angle of intersection of lines, composite angles in trigonometry, fundamental limit.

Other things were completely removed, like mid-ordinate rule, sums to products and products to sums.

I reckon though that sums to products and products to sums should still be taught in 3 unit. (It was originally in 2 unit!)

 

[cutemouse]

I reckon though that sums to products and products to sums should still be taught in 3 unit. (It was originally in 2 unit!)

Hmm, but would it be of much use?

I know in 4U it could be of use for integration... but I don't think I've come across anything in 3U that would require it.

What's the fundemental limit like? Is it much different to the informal treatment of limits we do now?

BTW, I noticed n the 1967 2U paper, 10 marks were given for sketching a simple trig graph and finding the area underneath it between certain limits... Isn't that a bit too easy? lol

 

[buchanan]

would it be of much use?

Yes indeed. Products to sums and sums to products is VERY useful and greatly simplifies many things. And this is why it should still be taught.

The fundamental limit is

(provided is in radians)

 

[cutemouse]

Which do you think is the hardest 2U paper?