VCE Methods Question Thread!

[Lear]

@snowisawesome
Consider the equation f(x)= sin(θ)
Try graphing it on your CAS and you will see that the minimum y value of this is -1 and maximum one. This is because sin(θ) has an amplitude of one and a mean line at y=0. Therefore it can only go up and down by 1.
Since we found a solution where sin(θ)=-2, we can conclude that this does not exist. As the basic graph of sin(θ) NEVER hits a y value of -2. I.e f(x)=-2 is not possible.

[Yertle the Turtle]

Lear is exactly right. In a normal sine graph with no dilations and translations, the y-values will between -1 and 1, and in this case there is no dilations or translations, so there can be no place in which sin(theta)=-2.

[Lear]

Hey, so suppose you want to find the absolute position of a particle or object. We can visualise some movement along the \( x \) and \( y \)-axis, but it's not completely accurate. The intuition behind this lies behind the fact that the movement along the x and y-axis are completely separate, and thus the rate of change differs. Instead, let's introduce a third variable: \( t \) that connects the two movements together. In this way, we can visualise the independent rate of change along the \( x \) axis and the rate of change along the \( y \) axis, both of which can be interpreted as: \( x(t) \) and \( y(t) \) where both are functions of time.

Consider these two parametric equations:



For specific help, please provide an example and any relevant working. But hopefully, a more intuitive approach to parametric equations will help to develop your foundations to the need for parameters.

If i'm not mistaken I believe the person is referring to parameters in the context of simultaneous linear equations. I may be 100% wrong though.
If the question is referring to what I think, my advice would be to 100% learn it how to do it by hand as if VCAA doesn't ask you, your school likely will.
As opengangs said, do you mind posting an example question so we can understand fully what you are referring to?

[Opengangs]

If i'm not mistaken I believe the person is referring to parameters in the context of simultaneous linear equations. I may be 100% wrong though.
If the question is referring to what I think, my advice would be to 100% learn it how to do it by hand as if VCAA doesn't ask you, your school likely will.
As opengangs said, do you mind posting an example question so we can understand fully what you are referring to?

My bad, still got some HSC in me :-) But yeah, a question will help make things clearer!

[VanillaRice]

Hi, I just had a quick question/inquiry about parameters (in the subject of linear simultaneous equations). We went over them very briefly in class and I understand how to use the calculator to formulate an answer etc but I was wondering if we needed to be able to formulate this answer by hand? Edrolo's explanation only covered calculator use but I wasn't sure if we'd ever have to do it by hand, as I came across a question asking for simultaneous equation solutions which included parameters and naturally started doing it by hand but had some difficulties with working it out clearly.
If anyone knows if working them out by hand is necessary, and if so, any basic tips of what to look for (I understand a lot of it does just involve rearranging) to start off doing so, that would be super helpful! Thanks

Are you referring to questions which ask for the values of the parameter which give no, unique or infinite solutions? If so, there are two techniques which you can use to go about it:

1) Looking at the coefficients of x and y, as well as the constant ('y-intercept'). Depending on whether you want no, unique or infinite solutions, you'll need to look at and compare the gradients/y-intercepts of the two equations.

2) Using the matrix determinant. This method was taught in the previous study design, so it may not be referenced in your textbooks.

It's a bit difficult to explain without an example, so if you can provide a question that you have attempted, and we'll see where we can go from there

These types of questions definitely used to appear in Exam 1 in the previous study design. It is yet to appear in the new study design Exam 1s, however, geometric interpretations of systems of simultaneous linear equations is still referenced in the study design, so it might still come up.

[smamsmo22]

Are you referring to questions which ask for the values of the parameter which give no, unique or infinite solutions? If so, there are two techniques which you can use to go about it:

1) Looking at the coefficients of x and y, as well as the constant ('y-intercept'). Depending on whether you want no, unique or infinite solutions, you'll need to look at and compare the gradients/y-intercepts of the two equations.

2) Using the matrix determinant. This method was taught in the previous study design, so it may not be referenced in your textbooks.

It's a bit difficult to explain without an example, so if you can provide a question that you have attempted, and we'll see where we can go from there

These types of questions definitely used to appear in Exam 1 in the previous study design. It is yet to appear in the new study design Exam 1s, however, geometric interpretations of systems of simultaneous linear equations is still referenced in the study design, so it might still come up.

Thanks for that. i attached a somewhat simple question that I did end up getting right when solving by hand, but it took me a few tries and I just didn't feel very sure about where to start when working it out. If you could offer any assistance about how to go about it that would be appreciated!

[VanillaRice]

Thanks for that. i attached a somewhat simple question that I did end up getting right when solving by hand, but it took me a few tries and I just didn't feel very sure about where to start when working it out. If you could offer any assistance about how to go about it that would be appreciated!

It seems I mistook the type of question you were asking about. You should ignore what I said above, since it relates to a different type of question completely. Since there are 3 variables, but only 2 equations, we cannot come up with unique solutions. I'll explain using question 12b:


Since there were 3 variables and only 2 equations, we are only able to give a solution to two of the variables, both in terms of the 3rd variable (in this case, both y and z are written in terms of x).

For questions such as these, my advice would be to try to work with the easiest equation first, rearranging it so you can substitute it into the other equation (like I've done with z here). Another way would be to add the equations directly - this works especially well for instances such as Q12a, where adding the two equations together will give you a solution for z straight away, which you can substitute back in.

Hope this helps

[Lear]

I do not believe you will be tested (atleast by Vcaa) on 3x3 simultaneous equations. The study mentions ‘solution of simple systems of simultaneous linear equation’
While this could possibly be wrong interpretation, having done 3x3 equations by hand, I do not believe they can be categorised as simple.
It would be great if some past students can comment if they have seen 3x3 simultaneous equations on past exam 1s.
I think they do ask you to choose appropriate matrices for solving 3x3 equations though.

[VanillaRice]

I do not believe you will be tested (atleast by Vcaa) on 3x3 simultaneous equations. The study mentions ‘solution of simple systems of simultaneous linear equation’
While this could possibly be wrong interpretation, having done 3x3 equations by hand, I do not believe they can be categorised as simple.
It would be great if some past students can comment if they have seen 3x3 simultaneous equations on past exam 1s.
I think they do ask you to choose appropriate matrices for solving 3x3 equations though.

I believe it says somewhere in the study design that only the geometric interpretation for two equations with two variables can be assessed. Also, since solving systems of simultaneous linear equations using matrices was removed, those types of questions should no longer appear.

[Lear]

Thanks for the insight VanillaRice

[smamsmo22]

It seems I mistook the type of question you were asking about. You should ignore what I said above, since it relates to a different type of question completely. Since there are 3 variables, but only 2 equations, we cannot come up with unique solutions. I'll explain using question 12b:


Since there were 3 variables and only 2 equations, we are only able to give a solution to two of the variables, both in terms of the 3rd variable (in this case, both y and z are written in terms of x).

For questions such as these, my advice would be to try to work with the easiest equation first, rearranging it so you can substitute it into the other equation (like I've done with z here). Another way would be to add the equations directly - this works especially well for instances such as Q12a, where adding the two equations together will give you a solution for z straight away, which you can substitute back in.

Hope this helps

Thank you!

[skrt skrt]

Just wondering if ordinate function is in the study design??

[exit]

Just wondering if ordinate function is in the study design??

You can check the study design but unless you mean something like 'addition of ordinates', I do not think it is in the study design

[skrt skrt]

Yeah sorry thats what i meant, thanksss

[snowisawesome]

does anyone know how to work out tan(θ) = 3/2 without a calculator?