Conics (1 Viewer)

[HisNameIsChris]

Having come within two weeks of my trials and realised that I still haven't satisfactorily learned Conics (fell behind during the year so skipped ahead so I could keep up to date with class work), I now realise that if I was in the exam right now I would not be able to derive many of the formulas to do with Conics.

Does anyone know what parts of Conics can be memorised, and what parts of Conics must be derived? Would you say that all of it should be derived, or could I just memorise the basic parts of the topic and only know how to derive the more advanced parts?

 

[joshualee]

Wow. having studied SAT2 Math2c and Korean mathematics, I am surprised that Australia maths level is almost equal to US maths!

Well, to summerize there are mainly four types of formula you should memorize!

1) Circle

x^2 + y^2 = r^2 ( r = radius )


2) Hyperbola

x<SUP>2</SUP> / a<SUP>2</SUP> - y<SUP>2</SUP> / b<SUP>2</SUP> = 1

Hyperbola has asymptotes : y = ± (b/a)x

a = 1/2 length major axis
b = 1/2 length minor axis
c = distance center to focus

eccentricity = c/a

3) Ellipse
x<SUP>2</SUP> / a<SUP>2</SUP> + y<SUP>2</SUP> / b<SUP>2</SUP> = 1

a = major radius (= 1/2 length major axis)
b = minor radius (= 1/2 length minor axis)
c = distance center to focus


4) Parabola

4py = x^2 (vertical) vice versa

eccentricity = c/a

I'm writing this formula based on the assumption that you understand the notion of conics ( for example. like foci, limits etc)

probably the most important thing (diffcult thing) to understand is parabola.
when I took the math2c exam, ( I do not know about the HSC, but I'm assuming that HSC is not harder than SAT2) if you memorize the formula, it is easy to solve the question ( since SAT2 comprises of multiple choice questions)


I hope this information helped you lol

 

[gurmies]

Almost equal? I was under the impression that it far surpassed it, the Australian scheme I mean.

 

[Aquawhite]

Almost equal? I was under the impression that it far surpassed it, the Australian scheme I mean.

From what I've read and heard, the Australian system seems far more extensive in the Extension parts of the course. Of course the Mathematics (2unit) course is basically on par with the US and many other systems, but the Australian MX2 level maths approaches university level.

 

[lychnobity]

Does anyone know what parts of Conics can be memorised, and what parts of Conics must be derived? Would you say that all of it should be derived, or could I just memorise the basic parts of the topic and only know how to derive the more advanced parts?

Know the tangent eqns (and how to derive them, but generally, know the formula)

What joshualee said is the bare minimum of what you should know anyway. Although, don't remember the parabola and circle information (it's 2 unit or something isn't it?)

Noticed the rectangular hyperbola was missing:
x² / a² - y² / a² = 1

e = √2

Eccentricity formula for ellipse: b²= a²(1 - e²)
for hyperbola: b²= a²(e² - 1)