VCE Methods Question Thread!

[ella04]

I am having trouble understanding this question;

"Using the discriminant, show that the graph of y= 2x^2+6px-2 touches or crosses the x-axis for all values of p."

Thanks in advance

[S_R_K]

I am having trouble understanding this question;

"Using the discriminant, show that the graph of y= 2x^2+6px-2 touches or crosses the x-axis for all values of p."

Thanks in advance

The graph touches or crosses the x-axis if it has one or two x-intercepts. The x-intercepts of the graph correspond to the zeroes of the equation. The number of zeroes of a quadratic can be found using the discriminant.

So once you have found the discriminant (which will be an expression in terms of p), what values does that need to take for the quadratic to have one or two zeroes? Then prove that this inequality is true for all values of p. Do this by writing the discriminant in a form which obviously makes the inequality true. (Hint: x^2 is non-negative for all real numbers x).

[LachlanBarr8]

Does anyone know any websites or apps that when you plug in a function it will tell you what transformations have been applied to it in comparison to another function?

Much appreciated

[Helish]

VCE MATHS METHODS Q&A THREAD

To go straight to posts from 2020, click here.

What is this thread for?
If you have general questions about the VCE Maths Methods course or how to improve in certain areas, this is the place to ask!


Who can/will answer questions?
Everyone is welcome to contribute; even if you're unsure of yourself, providing different perspectives is incredibly valuable.

Please don't be dissuaded by the fact that you haven't finished Year 12, or didn't score as highly as others, or your advice contradicts something else you've seen on this thread, or whatever; none of this disqualifies you from helping others. And if you're worried you do have some sort of misconception, put it out there and someone else can clarify and modify your understanding! 

There'll be a whole bunch of other high-scoring students with their own wealths of wisdom to share with you, including TuteSmart tutors! So you may even get multiple answers from different people offering their insights - very cool.


To ask a question or make a post, you will first need an ATAR Notes account. You probably already have one, but if you don't, it takes about four seconds to sign up - and completely free!

OTHER METHODS RESOURCES

CLICK ME!

* How I Got 50 Raw in Maths Methods
* How I Got a 50 in Maths Methods
* How I Got a Raw 44 in Methods - Tips, Tricks and Regrets
* Guide to using TI-Nspire for METHODS
* How to Solve Normal Distribution questions without using calculator syntax
* Maths Methods Advice: Maximising Your Marks!
* How to Prepare for the Methods 3/4 Exams - Three Weeks Out
* Prepping for the Methods Exam in 6 Days
* 2 Days Until Methods - Last Minute Preparations
* Countdown to the Methods Exam - Part 1
* General Solutions to Circular Functions
* Trinon's guide to Sketching Trig Graphs
* Trinon's guide to Antiderivatives through derivatives
* All you need to know about inequalities!
* Guide to Probability Notation
* The foolproof guide to transformations
* Everything you need to know about Related Rates!
* Introduction to Trigonometry
* How to Sketch Circular Functions Easily!
* Introductory Probability
* HOW TO: Statistical Inference (New study design topic)
* HOW TO: Probability Guide (When and how to use each type of probability)

Original post.

So for those of you keen to indulge yourself in the wonders of methods 3/4 throughout the holiday coz u have nothing better to do, post away your questions in this thread. Everyone can discuss and benefit from this, i'll personally try to answer all the questions that's posted too

the more discussion the better, once a question is posted feel free to post all kinds of solutions, talk about other things related to the question and feel free to go on mathematically related tangents, that's how one improves at maths!

Please keep ALL discussion on this thread relevant & specific to Maths Methods. Any general discussion regarding study habits etc should be directed to the appropriate board. Ask yourself whether your post relates to Methods specifically. Posts that do not fit the scope of this thread will be removed without notice.

ok guys I don't really know how to ask a question on this, so I just pressed the quote button. I am stuck in a dilemma and hope someone can really help me. I am currently in year 11 doing methods and spesh and was considering going to a tutor in y 12. I know this guy who gives guarantee of raw 43+ in spesh and 45+ in methods. However he is very expensive and I cannot afford to go to both. Which one should I join. Currently I am ranked 3 in the entire methods cohort but for spesh IDK what im ranked but I  know I got 58% and the average was 62% plus there are only 6 people doing spesh in the entire year. Which tution class should I join

[parieeelol]

Hey guys Wondering if anybody could help me out with this 1/2 question I can't wrap my head around:

The line L1 has the equation 2y + 3x = 9 . This line intersects the x-axis at A and the y-axis at B. What are the coordinates of the points A and B?

Anything would be appreciated, thank you!

[Evolio]

Hey guys Wondering if anybody could help me out with this 1/2 question I can't wrap my head around:

The line L1 has the equation 2y + 3x = 9 . This line intersects the x-axis at A and the y-axis at B. What are the coordinates of the points A and B?

Anything would be appreciated, thank you!

Hey. So, when it says the line intersects the x-axis at A, they are referring to the x-intercept of the line L1. This means that the coordinate of A would be in the form (x,0) where the y value would be 0. So, you would substitute y=0 into the above equation and solve for 3x=9. This x value will give you a value and so the coordinate of A would be: ( x value found, 0).

When it says line intersects y-axis at B, it is referring to the y-intercept of the line L1. That means that the coordinate at B would be in the form (0,y) where the x value would be 0. So you would substitute x=0 into the above equation, leaving you with 2y=9 which you need to solve. This y value would allow you write the coordinate in the form: (0, y coordinate found)

Which specific part were you struggling by the way? Were you having trouble understanding what the question was asking what to do?

[doubleS]

Can someone help help me out with this

[iamflowting]

Hint.
What transformations do you need to apply to the curve y = g(x) to get to the new curve y = 1 + g(x + 2)? Can you relate these transformations to the different points?

If you still don't understand here are some hints thats progressively get closer to the answer.

Spoiler

The second curve is the exact same shape as the first curve however it has been moved 2 units to the left and 1 unit up.

Spoiler

This means that the shape of the old curve at the point (2, 7) is the exact same as the shape of the new curve at (0, 8 ). What does this say about the tangents at each of these points?

Spoiler

This says that both tangents must have the same slope and therefore must be parallel. So how will we find the new tangent?

Spoiler

You will need to find a line that is parallel to y = 3x + 1 and goes through the new point (0, 8 ).

[statistics]

Weather forecasts are generally right, but not always. For a particular winter, the local forecast predicts rain for
35% of days and rain occurs on 38% of the days. For 25% of winter days, rain was forecast and rain does fall.
 Hint: Use a Venn diagram to help answer the following questions about rainy days.
a) For what percentage of days does it rain without rain being forecast?
13%
b) What is the probability that there was no rain forecast nor did it rain?
0.48
c) On what percentage of days was there either rain or rain forecast?
52%
d) If it is raining, what is the probability that rain was forecast?
Pr(forecast|actual) = 0.25/0.38 = 0.66
e) Are rain and forecast for rain mutually exclusive events? Explain.
P(A and B) = 0.25 which is not equal to 0
so rain are forecast are NOT mutally exclusive
 f) Are rain and forecast for rain independent events? Explain.
P(A) * P(B) = 0.35*0.38 = 0.133 which is not equal to probability P(A and B)
so rain and forecast are NOT independent

Are my answers correct?

[doubleS]

Can anyone help me with how to do this?

[whys]

Can anyone help me with how to do this?

Below, I have given you a successive list of hints. Try figure it out yourself first . If you are still stuck, progress to the next hint.

First hint: What is a tangent line and what is its relation to the power function given?

Second hint

The tangent is a line that has the same gradient at a certain point of the other graph. So, differentiate the power function (you can ''eliminate'' d as it is a constant.)

Third hint

Once you've diffed it, sub in the point x = 9 to get the gradient of the tangent at that point.

Fourth hint

Once you have the gradient of the tangent, you should be able to figure out the value of a. Once you have this, sub in the point x = 9 into the tangent line to get the y-value of the coordinate (c).

Fifth hint

You now have the coordinates of the point the tangent meets the power function. Sub in this point into the power function and solve for d.

[bluechai]

how to solve this u1 probability question ?

suppose that the employees in a certain industry, 35% are female, 72% work full time and 18% of employees are female who work full time

what is probability that randomly chosen employee is female and does not work ?

thanks :  )

[colline]

how to solve this u1 probability q ?
thanks

Sorry if I missed it but what's the actual question?

[bluechai]

Sorry, I just realised I forgot to add it.

[amanaazim]

hey how do you solve this problem.

Sketch the graph of y=x^3-3x+2 and y=-4x.
Show the coordinates of the intercepts and the intersection point (Do not show the coordinate of the maximum turning point of the cubic graph.)