VCE Methods Question Thread!

[Tasmania Jones]

Hey guys,
When a question asks for the domain over which a function is STRICTLY decreasing/increasing, does it include stationary points or endpoints?
Cheers
Tasmania Jones

[knightrider]

[/quote]

You could do it through addition of ordinates I guess, or you can just split it up into its hybrid equations and graph those. Yeah it's definitely within the course.

Thanks

[kinslayer]

How would you graph this question and is it possible that this question can be tested in maths methods

The best way is to graph both equations and then just add the y-coordinates together. You could split up the domains but it's quicker just to get to drawing.

[kinslayer]

Hey guys,
When a question asks for the domain over which a function is STRICTLY decreasing/increasing, does it include stationary points or endpoints?
Cheers
Tasmania Jones

It can include stationary points. For example, f(x) = x^3 is strictly increasing for all real x, yet its first and second derivatives are equal to zero at x = 0.

The endpoints of a domain are usually not very interesting when considering monotonicity (increasing/decreasing) since monotonicity is concerned with intervals rather than points. A point isn't an interval so it does not make sense to talk about whether a function is "monotonic" there.

Put it this way: if a continuous function is strictly increasing/decreasing on some open interval I, then it is also strictly increasing/decreasing (respectively) on the closed interval made up of I together with its endpoints.

[knightrider]

How would you complete the square on the following equation?

[psyxwar]

How would you complete the square on the following equation?

Take out a as a common factor then complete the square as usual. If you're interested you can also derive the quadratic formula doing this

[knightrider]

Take out a as a common factor then complete the square as usual. If you're interested you can also derive the quadratic formula doing this

Could you show me how to do this

For maths methods are you expected to know how to graph circles because in the year 12 books they dont cover this?

[Bronzebottom64]

[Tasmania Jones]

It can include stationary points. For example, f(x) = x^3 is strictly increasing for all real x, yet its first and second derivatives are equal to zero at x = 0.

The endpoints of a domain are usually not very interesting when considering monotonicity (increasing/decreasing) since monotonicity is concerned with intervals rather than points. A point isn't an interval so it does not make sense to talk about whether a function is "monotonic" there.

Put it this way: if a continuous function is strictly increasing/decreasing on some open interval I, then it is also strictly increasing/decreasing (respectively) on the closed interval made up of I together with its endpoints.

Thanks kinslayer 

[knightrider]

For maths methods 3/4 are you expected to know how to graph circles because in the year 12 books they dont cover this?

[psyxwar]

For maths methods 3/4 are you expected to know how to graph circles because in the year 12 books they dont cover this?

uhh I guess? not sure, they're not particularly hard to graph though

(x-h)^2+(y-k)^2=r^2, r is radius, (h,k) is centre

[knightrider]

uhh I guess? not sure, they're not particularly hard to graph though

(x-h)^2+(y-k)^2=r^2, r is radius, (h,k) is centre

thanks and also can anyone tell if they have ever got a question about circles in a year 12 sac

[Mieow]

the answer is h= (10-5r)/2
but why isn't it h=5r/2?

[IndefatigableLover]

(Image removed from quote.)

the answer is h= (10-5r)/2
but why isn't it h=5r/2?

Well if you aligned up your way of similar triangles, you'll see that the 'base' of the triangle (that is the 'r' side) isn't 'r' but 2-r. 'r' is the radius of the cylinder but not the radius of the cone (which is what 2cm). If you took this value then your value for 'h' would have to change since your 'similar triangle' would be wrong (it's not aligned up and wouldn't be a triangle in the end).

To make sense of what I'm saying, in your diagram, draw the triangle you see where the bottom right corner of the cylinder makes with the cone and draw that triangle out and label the sides you make to get that triangle. That's what you need to find which reflects the correct answer.

[bobisnotmyname]

hey guys
i'm having a bit of trouble with the general solutions, so any general tips would be great
I tried this question sin(2x)=1

i got the initial solution as pi/2                   2x=pi*n+(-1)^n *pi/2
and finally x=(pi*n)/2 +(-1)^n *pi/4
however the correct solution was x=n*pi + pi/4
it was a multiple choice question in the Essentials math methods book