VCE Methods Question Thread!

[Ionic Doc]

oke so just completed this chapter review and I have a couple of questions I need to clarify. . .
The range of the relation   

latex doesn't seem to allow any space but basically when x, y is an element of Real Numbers

[Evolio]

oke so just completed this chapter review and I have a couple of questions I need to clarify. . .
The range of the relation   

latex doesn't seem to allow any space but basically when x, y is an element of Real Numbers

I would start by making x^2+y^2=9 and then sketch the graph. The y and x-intercepts should be -3 and 3.
The range is referring to the y values. Then...I'm not sure after this. I will try and think about it.

Hello guys.
I was wondering if anyone knew how to differentiate this using the product rule?

[aspiringantelope]

oke so just completed this chapter review and I have a couple of questions I need to clarify. . .
The range of the relation   

latex doesn't seem to allow any space but basically when x, y is an element of Real Numbers

If x,y is an element of R, shouldn't the range be R then?
However, I think it may be
\(\left(-∞,-3\right)\ ∪\ \left(3,∞\right)\)

[KiNSKi01]

Hello guys.
I was wondering if anyone knew how to differentiate this using the product rule?

Same process as any other product rule question but does require you to use the chain rule for the second 'term' ([root[2x-4]) which can also be expressed as (2x-4)^1/2 -> this makes it more clear what you need to do

Hope that's enough to help you

[S_R_K]

Is  - [antiderivative symbol] 1 dx = -x +c or -x -c?

Does it make a difference? c is just any constant that is a subset of R so it won't matter if it is + or -, right? Which is more correct? The answers say +c, but i though that since the antiderivative of 1 is x + c , that due to the negative sign out the front, it becomes -x -c. Am I on the right track?

Thanks, sorry I don't know latex. Unsure how else to represent the indefinite integral.

It doesn't make any difference. Differentiating –x + c and –x – c (where c is a real constant) gives you the same result. Hence, each is an acceptable way of writing the general antiderivative of 1. You could even write the general antiderivative of 1, with respect to x, as x + 41c, since every real number can be written as 41c, for some real number c. It's just a weird way to go about it because writing "+ c" for the constant of integration tends to make any follow-up calculations simpler.

There are some subtleties with the constant(s) of integration that arise when antidifferentiating functions that aren't defined for all real numbers but these tend to be ignored in methods.

[Rameen]

Hi
I was wondering how many points need to be labelled on a log/exponential graph when asked to sketch it. Or should only the asymptotes and the x/y intercept be labelled?
I know that for linear graphs, two points need to be labelled because two points define a line.
Also, when sketching, does there need to be an actual labelled axis, eg x-axis that goes from 1 to 10, or just the points that are needed, such as 5 and 7?

[Sine]

Hi
I was wondering how many points need to be labelled on a log/exponential graph when asked to sketch it. Or should only the asymptotes and the x/y intercept be labelled?
I know that for linear graphs, two points need to be labelled because two points define a line.
Also, when sketching, does there need to be an actual labelled axis, eg x-axis that goes from 1 to 10, or just the points that are needed, such as 5 and 7?

I would go with a minimum of two points in any log graph with good shape + the asymptote. Always include x/y intercepts for all graphs. Although I have seen sometimes when there is only one axis intercept just including that and the asymptote.

VCAA will usually give you the axes to sketch on - if they are nice they will give you labelled x and y axes (which they have done in the past few exam 1's). If not - as long as you have got the correct x/y intercepts, intersections, asymptotes etc that is enough.

[randomnobody69420]

What exam score do you usually need for 45+?

[DBA-144]

What exam score do you usually need for 45+?

Depending on the year, I think that 112-115/120 is pretty good. I'm no expert on this, so don't take this as a confirmed answer haha.

[Rameen]

Does pen have to be used for the methods exams?

[aspiringantelope]

Does pen have to be used for the methods exams?

Pencil would be the ideal choice because if you make a mistake drawing a graph with pen, you wouldn't be able to erase it.
Also, you can erase wrong markings in pencil unlike with a pen.

[AlphaZero]

Does pen have to be used for the methods exams?

Pencil is fine since Methods exams are not scanned for marking.

[Rameen]

Hi. I am having trouble with questions 11b and 12b where I am asked to restrict the domain of one of the functions so that the composite function exists. I am normally alright with these types of questions, however, I am unsure how to do it with a domain of all real numbers except, ____. Your help would be appreciated!

[S_R_K]

(Image removed from quote.)
Hi. I am having trouble with questions 11b and 12b where I am asked to restrict the domain of one of the functions so that the composite function exists. I am normally alright with these types of questions, however, I am unsure how to do it with a domain of all real numbers except, ____. Your help would be appreciated!

The maximal domain of f is [0, ∞), so we need to restrict the domain of g1(x) such that its range is a subset of [0, ∞). A useful method is to sketch a graph of y = g1(x) over its maximal domain (in this case, R \ {3}) and then find all values of x where the graph is above or on the x-axis (ie. where its range intersects [0, ∞)).

If you do this, you'll notice that the graph is above or on the x-axis over the interval [3 – sqrt(2)/2, 3 + sqrt(2)/2] \ {3}. We need to exclude x = 3 from the interval because g1 is undefined at x = 3.

Putting this together, g1(x) ≥ 0 when x is in [3 – sqrt(2)/2, 3 + sqrt(2)/2] \ {3}. Hence, f(g1(x)) is defined whenever x is in [3 – sqrt(2)/2, 3 + sqrt(2)/2] \ {3}. There are other ways of writing the answer, for instance [3 – sqrt(2)/2, 3) U (3, 3 + sqrt(2)/2].

A similar method works for 12b.

[Rameen]

A similar method works for 12b.

Thanks!
For 12b, how do I make the range of f, [0,∞), fit into the domain of g, R/{1}, for g(f1(x)) to be defined ?
The range of f can be written as (-∞, 1) U (1,∞). So would I make sqrt 2-x less than 1 and greater than 1?