VCE Methods Question Thread!

[ahat]

Hey, for questions like (EDIT - hahaha, that's why I was confused) x² > 4, how do we get to the solution x < -2 and x > 2? (i.e. how do we know the direction of the inequality)? It'd be appreciated if someone could please explain this, thanks!

[achre]

Hey, for questions like x² < 4, how do we get to the solution x < -2 and x > 2? (i.e. how do we know the direction of the inequality)? It'd be appreciated if someone could please explain this, thanks!

I think those lines should be in the opposite direction (-2 < x < 2).
You solve it as x < +/-2, for the positive solution the direction is the same x<2 for the negative solution you flip the direction as x>-2, and then write it as an interval (-2, 2).

[Alwin]

Hey, for questions like x² < 4, how do we get to the solution x < -2 and x > 2? (i.e. how do we know the direction of the inequality)? It'd be appreciated if someone could please explain this, thanks!

Erm, I think you got the inequalities wrong?

There are a few ways to approach this:
1. Common sense.  x² = 4,  x² = ± 2. But, if x=0 then x² <0. So it follows that -2 < x < 2
2. Graph. x² < 4 --> x² -4 < 0. Where does the parabola < 0? When it's under the x axis, so in-between the two solutions -2 and 2. So we get -2 < x < 2
3. Algebraically. x² < 4 --> x² -4 < 0 --> (x-2)(x+2)<0  This only happens when one is +ve and the other is -ve. So, x-2>0 and x+2<0 --> x>2 and x<-2 Not poppossible. Or, x-2<0 and x+2>0 --> x<2 and x>-2. Good

[shadows]

Hey, for questions like x² < 4, how do we get to the solution x < -2 and x > 2? (i.e. how do we know the direction of the inequality)? It'd be appreciated if someone could please explain this, thanks!

When solving inequalities that are not linear, it's best to take on a graphical/visual approach.

(Do a rough sketch, prevents mistakes and imo much more straight forward)

[papertowns]

Sorry if this is a stupid question but when it's a 2.5005 is it 2.500 or 2.501 when rounded to 3dp? And will i lose a mark if I rounded off wrong?

[Lejn]

Sorry if this is a stupid question but when it's a 2.5005 is it 2.500 or 2.501 when rounded to 3dp? And will i lose a mark if I rounded off wrong?

2.501 (given that 2.5005 was itself not rounded), I believe you would lose a mark.

[achre]

This question has seriously undermined the confidence boost I got from my last practice exam.
I can get as far as Pr(X > 94)=q but from there to the required answer it almost seems like you have to assume that any value is 0.5 away from the mean 
Detailed solution pretty please.

[Phy124]

Pr(X<106) = q
Pr(x>106) = 1-q
Pr(X<94) = 1-q
Pr(X<100) = 0.5

Pr(94<X<100) = 0.5-(1-q) = q - 0.5

[achre]

Pr(94<X<100) = 0.5-(1-q)

You are a beautiful human being thank you

[ahat]

Hey, I have a few questions:
EDIT: IGNORE THIS QUESTION
y = x² - 4x + 4 is translated k units vertically\so that it is tangential to the line y = 2x. Find the value of k.
This is what I did initially:






(my reasoning - one point of intersection will mean they will be 'tangential')
The answer is incorrect, but I'm wondering if you could point out my flaw.

Secondly, for the graphs below:
Blue > y = x² - 4x + 4 (the original parabola)
Red > y = (x + 5/6)² - 4x + 4 (using the value of k I found)

Why has 5/6 caused more than just a vertical (this can now be completely ignored hahaha)translation? Thanks.

EDIT: Translated vertically.......vertically not horizontally! My gosh ahat!

[zvezda]

Hey, I have a few questions:

y = x² - 4x + 4 is translated k units vertically so that it is tangential to the line y = 2x. Find the value of k.
This is what I did initially:






(my reasoning - one point of intersection will mean they will be 'tangential')
The answer is incorrect, but I'm wondering if you could point out my flaw.

Secondly, for the graphs below:
Blue > y = x² - 4x + 4 (the original parabola)
Red > y = (x + 5/6)² - 4x + 4 (using the value of k I found)

Why has 5/6 caused more than just a vertical translation? Thanks.

The graph is being translated k units vertically. Why have you added (x+k)^2 in you expression?

[Jaswinder]

is k=5?

[ahat]

The graph is being translated k units vertically. Why have you added (x+k)^2 in you expression?

I just came to the same realisation

is k=5?

Yes

[jono88]

f(x)=e^2x - e^-2x.
Find the inverse.

[Stevensmay]

First, our equation is going to be in the form of , where k is the additional vertical translation.

We want the gradient of the two curves to be equal, as then a tangent will occur.

Gradient of y=2x will be 2.



Make these equal to find the x value when the gradient is 2.




Anyone mind finishing this?
Had a complete mind blank.