VCE Methods Question Thread!

[Zealous]

How do you know what x and h values to use for questions like these?

Look for the closest value of 'x' to 3.9 which would allow you to easily calculate f(x) (without a calculator). 3.9 is close enough to 4, and the square root of 4 is two, so you can set 'x=4' and 'h=-0.1'. VCAA will make it quite obvious as to what 'x' and 'h' values they want you to use.

[knightrider]

Look for the closest value of 'x' to 3.9 which would allow you to easily calculate f(x) (without a calculator). 3.9 is close enough to 4, and the square root of 4 is two, so you can set 'x=4' and 'h=-0.1'. VCAA will make it quite obvious as to what 'x' and 'h' values they want you to use.

Thanks Zealous 

[cosine]

May someone please show me, with hopefully the aid of a diagram (bell curve) how to do this question? Many thanks if you can help

[knightrider]

In this image attached how is E(1)=1 ?

[knightrider]

For this question say we have

How would you do this?

What is the range of this composite function?

[keltingmeith]

In this image attached how is E(1)=1 ?

Claim:

Proof:
To evaluate , we put this into the definition:

With the second line holding by the properties of integration (that is, scalars can come outside the integral), and the third line holding because all of the area under a probability density function is 1. You can also repeat this method for discrete RVs and get the same result.

For this question say we have

How would you do this?

What is the range of this composite function?

... I'm honestly confused by the questions. What do you want to do with the first function? And which composition of the second functions are you looking at, gof or fog?

[cosine]

Solve for expressing solutions in terms of

Tech-free question

[Redoxify]

Hi cosine, I'm not too sure if I'm right, but i'll have a go
tan^2(x)+(1-root3)tan(x) = root 3,
let tan(x) = a

a^2+(1-root(3))a-root(3) = 0,
factorise

(a+1)(a-root(3)) = 0,

therefore
tan(x)=-1, or tan(x) = root(3),

solving for x i get
x= pi/3, 3pi/4, 4pi/3, 7pi/4

[cosine]

Hi cosine, I'm not too sure if I'm right, but i'll have a go
tan^2(x)+(1-root3)tan(x) = root 3,
let tan(x) = a

a^2+(1-root(3))a-root(3) = 0,
factorise

(a+1)(a-root(3)) = 0,

therefore
tan(x)=-1, or tan(x) = root(3),

solving for x i get
x= pi/3, 3pi/4, 4pi/3, 7pi/4

I don't understand what you did here?

[Redoxify]

I don't understand what you did here?

when I let tan(x)=a,
it resulted in
a^2 +(1-root(3))a = root(3)
then transpose to let one side = 0

then it's just a quadratic formula

[cosine]

How did you get from point A to point B

point A
a^2+(1-root(3))a-root(3) = 0,
factorise

point B
(a+1)(a-root(3)) = 0


(Omg, 2000 posts!)

[Redoxify]

How did you get from point A to point B

point A
a^2+(1-root(3))a-root(3) = 0,
factorise

point B
(a+1)(a-root(3)) = 0


(Omg, 2000 posts!)

factorisation by sight, only 1 x -root(3) gives the -root(3),
the middle term is (1-root(3)), therefore when you expand point B, you'll get back to point A

[cosine]

factorisation by sight, only 1 x -root(3) gives the -root(3),
the middle term is (1-root(3)), therefore when you expand point B, you'll get back to point A

How were you able to 'sight' such a difficult sighting? Honestly, I have been on this for quite a while and could not recognise that, any tips?

[Redoxify]

How were you able to 'sight' such a difficult sighting? Honestly, I have been on this for quite a while and could not recognise that, any tips?

Yeah It is quite difficult to sight. For this question, it's best to relate the coefficient of a not a^2, and -root(3), try to find any similarities between them, that's what I done for this question, hope that helps

[cosine]

Yeah It is quite difficult to sight. For this question, it's best to relate the coefficient of a not a^2, and -root(3), try to find any similarities between them, that's what I done for this question, hope that helps

Can you tell me why you didn't initially complete the square, or straight away use the quadratic formula? I