VCE Methods Question Thread!

[nadiaaa]

MightyBeh and JellyBeanz!! You both are geniuses, thank you i finally get it

[YellowTongue]

For the attached question, would the derivative exist when x=1. The solutions say that the derivative doesn't exist at this point, as the original function is undefined. However, as the limit exists at this point (I think), wouldn't the derivative technically still exist?

Have I misunderstood the concept, or have iTute made a mistake?

[solution]

For the attached picture, is answer (1.) in the correct from or is answer (2.) correct?

Also, say a question asks for an coordinates to two decimal places. I solve f(x) = 0 to be x = 92.19890352042034 (because the exact value is too long to write down). Then I solve y = f(92.19890352042034). My question is, for the "method mark" do I have to write y = f(92.19890352042034) or can I write something similar to y = (92.198...) because writing all those numbers can waste time/make careless errors.

[MB_]

A certain curve has its gradient given by \(4e^\frac{-x}{2}\). If the curve crosses the y-axis at y=4, where does it cross the x axis?

Using \(y=ax^2+bx+c\), I've found that c=4 but I'm unsure of where to go from there.

[exit]

Anyone know if its ok to use the matrices+ determinant method to solve for infinite, no, or 1 solution? So much quicker with less chance of error compared to the 'normal' ways. I learnt it in 1/2 but outta course

[MightyBeh]

For the attached picture, is answer (1.) in the correct from or is answer (2.) correct?

Also, say a question asks for an coordinates to two decimal places. I solve f(x) = 0 to be x = 92.19890352042034 (because the exact value is too long to write down). Then I solve y = f(92.19890352042034). My question is, for the "method mark" do I have to write y = f(92.19890352042034) or can I write something similar to y = (92.198...) because writing all those numbers can waste time/make careless errors.

For the image, go for 1. While 2. is technically correct, you're meant to simplify things that can be easily simplied in methods. Wouldn't risk the mark when the answer is right there.

For the decimal places, it's pretty safe to write a 'less exact' number than what you're actually working with on your calculator. Generally if you're rounding to 2dp, your working should be reasonably accurate at 4dp. Just make sure on the calculator you use the full value.

A certain curve has its gradient given by \(4e^\frac{-x}{2}\). If the curve crosses the y-axis at y=4, where does it cross the x axis?

Using \(y=ax^2+bx+c\), I've found that c=4 but I'm unsure of where to go from there.

I think you're meant to integrate the gradient equation and solve for an exponential function to find the x-value. If the answer is \(x=2\ln
\left(\frac{2}{3}\right)\), I can share my working out.

Anyone know if its ok to use the matrices+ determinant method to solve for infinite, no, or 1 solution? So much quicker with less chance of error compared to the 'normal' ways. I learnt it in 1/2 but outta course

I'm also interested in knowing this.

[nadiaaa]

Anyone know if its ok to use the matrices+ determinant method to solve for infinite, no, or 1 solution? So much quicker with less chance of error compared to the 'normal' ways. I learnt it in 1/2 but outta course

Yep you are, my teacher is an examiner and he always tells us to use the matrices way, so i think we are allowed!

[solution]

When solving simulataneous equations for a and b, and the calculator outputs
{a = 2, b = 3}, {a = 3, b = 2}, do we have to list out both situations? This is assuming there are no restrictions for the values of a or b.

[nadiaaa]

Has anyone done vcaa 2015 recently and can help me with part C of this question?
I could find the d value, but i can't find the set of values of D that they want, thanks in advance..

[MB_]

I think you're meant to integrate the gradient equation and solve for an exponential function to find the x-value. If the answer is \(x=2\ln
\left(\frac{2}{3}\right)\), I can share my working out.

Yes that's right, could you share your working?

[solution]

Is it just me or is the answer to 2013 Exam 2 4diii (very last question) incorrect? When I solve for the turning point, I do not get k = 16/3, but I get k = 5.5937807, with a min area of 1.9183868??

[MB_]

For the question attached I've differentiated the function and found the discriminant. Is this the correct working and would the answer be D?

[aliannalevsschool]

If I have two equations - a cubic and a linear equation and the question is asking me to find the x co-ordinate where the distance between the two lines is the greatest? How do I do this?

[MB_]

If I have two equations - a cubic and a linear equation and the question is asking me to find the x co-ordinate where the distance between the two lines is the greatest? How do I do this?

I think you need to find the derivative of the difference between the two functions, make it equal to 0 and solve but someone can correct me if I'm wrong

[NerdyPi]

If I have two equations - a cubic and a linear equation and the question is asking me to find the x co-ordinate where the distance between the two lines is the greatest? How do I do this?

Is there a defined region for the 2 graphs? If so, you can define a new function, which is t the larger function - smaller function (over region specified ). Then derive this new function and find dy/dx = 0
 This is done really easily with CAS. I could post an example if you have the specific question...


 Edit: As MB_ just said