ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 unit (2 Viewers)

[theind1996]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Probably a rookie concept, though I guess that's why I'm asking it just to confirm.

For inequalities, do you have to square both sides, or is there an alternative way (I think there is, though I don't fulply remember it - I think it is where you just multiply it though you have two cases.

You can find the discontinuity (what values x cannot equal), and the the equality (if the inequality sign is actually equal - what solutions you would get by solving it), and then test points on either side.

Although I know that Realise has a better method - I think it's called the boundary method.

 

[Examine]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Give an example question?

(x^3-10x)/(x^2+8)>1

 

[Examine]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Like, I'd rather not square it because its a 2 mark question but a long division process if I were to.

 

[theind1996]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

(x^3-10x)/(x^2+8)>1

Using my method, you know that the discontinuity will be where the denominator cannot equal zero, so x^2 - 8 =/= 0. Equality will be where the fraction is = to 1, i.e what values of x is the numerator = to the denominator.

Then draw up a number line and test points in on either side.

 

[deswa1]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

(x^3-10x)/(x^2+8)>1

Denominator is always greater than 0:

x^3-10x>x^2+8 (on multiplying through by x^2+8)

I would never square the whole thing- in cases where the denom could be both positive or negative, just multiply through by the square of the denominator

 

[Sindivyn]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

If you're talking about inequalities with the unknown on the bottom, one method is to multiply both sides by the square of the denominator. Squaring both sides in an inequality can lead to issues. Eg
1>-5
(1)^2>(-5)^2
1>25
Which is false

 

[Timske]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Denominator is always greater than 0:

x^3-10x>x^2+8 (on multiplying through by x^2+8)

I would never square the whole thing- in cases where the denom could be both positive or negative, just multiply through by the square of the denominator

this

 

[D94]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

(x^3-10x)/(x^2+8)>1

I really doubt you'd be asked a question like this, unless you could somehow factorise it and produce a sensible result. You would usually be given a question where the denominator could be either positive or negative for certains values, so the general idea is to multiply both sides by the square of the denominator. It generally simplifies to something you can factorise and then you will be asked to say for which values of x satisfy the inequality.

 

[Examine]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

If two points lie on the same side of an interval and the angle subtended at these points by the interval are equal, then the rwo points and the endpoints of the interval are concyclic.

What does this actually mean and how can it be used?

 

[Examine]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Also, what would the range be of these?

 

[iBibah]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Also, what would the range be of these?

First one, 0<=y<=6

Second one, 0<=y<=2

For other graphs just put them in here to check: http://www.wolframalpha.com/

 

[Aysce]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Also, what would the range be of these?

So you know that f(x) is a semi-circle that intersects the x and y axis at 2 right?

Now imagine the graph of it - what do the values of y range from? It ranges from y=0 to y=2.

NOTE: That is the 2nd question

 

[Examine]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

First one, 0<=y<=6

Second one, 0<=y<=2

For other graphs just put them in here to check: http://www.wolframalpha.com/

Is there a way to find them out if they were questions in an exam?

 

[Examine]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

So you know that f(x) is a semi-circle that intersects the x and y axis at 2 right?

Now imagine the graph of it - what do the values of y range from? It ranges from y=0 to y=2.

NOTE: That is the 2nd question

So you need to basically visualise the graph to find the range?

 

[Aysce]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

So you need to basically visualise the graph to find the range?

It's one way to do it - I normally use it

 

[Examine]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

Ok, then that's fine.

Been doing some other papers, I'm always stuck at circle geometry and parametrics 3D Trig is half half now though I'm getting used to it.

 

[Aysce]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

What do you have trouble with in parametrics? I always love doing it!

 

[iBibah]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

If two points lie on the same side of an interval and the angle subtended at these points by the interval are equal, then the rwo points and the endpoints of the interval are concyclic.

What does this actually mean and how can it be used?

See in this picture how points C and D are on the same side of the interval AB.

Now if angle ACB=angle ADB, it means that ABDC is cyclic.
Because if you remember, angles on the circumference subtended by the same are equal.
Conversely, if two angles subtended by the same chord (or arc) are equal, the four points must lie on the circumference of a circle. (i.e Concyclic)

 

[Examine]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

I guess it's just how the questions are formatted, though I'm just hopeless with circle geometry.

 

[iBibah]

Re: ITT we help examine to get 85 in his Maths extension 1 yearlies so he can do 4 un

So you need to basically visualise the graph to find the range?

Yes you can draw the graph by plotting points or otherwise.

Or if you know the domain, find the maximum and minimum by deriving the function.