VCE Methods Question Thread!

[Zealous]

Just a quick question, how much simplifying do we have to do in methods?
...or as long as our answer is correct in some form are we correct? (unless otherwise stated)?

So lets say we get an answer which is:

are we expected to take out the 3? to get:


or if we have to find the derivative of:

using chain rule we get:

I actually saw someones solutions for this in which they took out the x here:

to get:


Is all of this simplifying really necessary? Would we lose marks for having a very messy looking quotient rule working out or something?

[Professor Polonsky]

Generally, as long as your final answer is correct, it doesn't have to be factorised or in any particular form unless the question specifically asks for it. I've heard that you don't even have to rationalise surds, but I'd do so to be safe anyway. Simplifying the two examples which you gave seems to be a fairly useless exercise, although it may be required in a particular question.

In Exam 1, I wouldn't bother simplifying your answer at all - it's almost always not required, and is the surest way to make a mistake on an easy question. I think that was even mentioned in the Assessment Report sometime ago.

[flyhighx]

Hi, can someone show the full working out of this question
Given that the curve y=ax^2+b/x has a gradient of -5 at the point (2,-2), find the values of a and b
thanks

[b^3]

The gradient of a function at a point will be the same as the derivative of the function at that point. So first we differentiate the curve.

"try this first, before looking at spoiler"

Now you have one equation, but since we have two unknowns, we need another equation. What other pieces of information that we're given can we pull another equation from? Well we have the point , which means we can find another relationship between and .

"again, try this first before looking at spoiler"

Now you have two simultaneous linear equations, you should be able to solve for and . If you have trouble, post back here

[shadows]

With intersection graphs between f(x) and inverse f(x)

Do we just let one equal x? (Do all intersections occur along y=x) are there any exceptions I should be noted about?


Umm with intersections between exps/logs involving f(x) and inverse, are suppose to know how to work it about by hand... Or is it cas required?

For example


Thanks

[Daenerys Targaryen]

With intersection graphs between f(x) and inverse f(x)

Do we just let one equal x? (Do all intersections occur along y=x) are there any exceptions I should be noted about?

Yes

Umm with intersections between exps/logs involving f(x) and inverse, are suppose to know how to work it about by hand... Or is it cas required?

For example

CAS

[FlorianK]

With intersection graphs between f(x) and inverse f(x)

Do we just let one equal x? (Do all intersections occur along y=x) are there any exceptions I should be noted about?

Yes there are exepections. Let's say f(x)=-x the inverse would be -x as well however letting f(x)=x would give you only 1 (x=0, y=0)) of the infitely many intersections.

Same with f(x)=x³ and f^-1(x)=x^1/3
letting f(x)=x would give you only 1 of the 3 intersections

[b^3]

Yes there are exepections. Let's say f(x)=-x the inverse would be -x as well however letting f(x)=x would give you only 1 (x=0, y=0)) of the infitely many intersections.

Same with f(x)=x³ and f^-1(x)=x^1/3
letting f(x)=x would give you only 1 of the 3 intersections

Basically anything of the form and where is an odd integer.

EDIT: had negative instead of odd... I need sleep.

It's best to sketch it first, and if you can see that it isn't an special case like the above, then just use of as it will be easier to solve if you were required to solve by hand, if it is the special case then use .

[Alwin]

Same with f(x)=x³ and f^-1(x)=x^1/3
letting f(x)=x would give you only 1 of the 3 intersections

I seek to disagree with your second example
f(x) = x^3, and line y = x gives all three intersections, (-1,-1), (0,0) and (1,1)

b^3 gives a great example of a generalisation of exceptions

[FlorianK]

OH I'm sorry I meant f(x)=-x³

[shadows]

Woah thanks guys!

Funny how at school, they just teach to let fx equal to x to find the intersection...

Good to understand everything! I hate having gaps in my knowledge...

Hope guys don't mind answering my questions.. I tend to ask questions out of curiosity..

[jimmy22]

If sinx=-m and  x is less then or equal to 3pi/2, and greater or equal to pi,

Find cosx

[Conic]

If sinx=-m and  x is less then or equal to 3pi/2, and greater or equal to pi,

Find cosx

Use the Pythagorean identity









Since , we know that x is in the 3rd quadrant. This means cos of x is negative.

[shadows]

Sin a = 0.3.     Cos b =0.6.          Tan c= 0.7



How do you find tan(pi/2 - c)

[e^1]

Using complementary angles and the fact that the complement of tangent is cotangent (and vice-versa).