VCE General & Further Maths Question Thread!

[Yacoubb]

They look good to me.

The only thing that i might've added is for the Coefficient of determination you could also say in the next sentence, "12.46% of the variation in arm span can be explained by other factors such as ......."

Not sure if it's necessary though.

Nah. Checked assessment reports and none have an extra statement regarding causality. I think it would be fair to mention the remaining %age attributed to causality if a question required you to do so.

[Zealous]

Y-intercept:
On average, Jane's final weight at the start of the weight-loss program, is 96kg.

^ Are these templates for such questions okay? Thanks!

Wow, never seen a question asking to describe the y-intercept of a graph like that, but nonetheless could be useful to set out how you want to answer a question.

[Stick]

Would the following explanations be appropriate (they're for linear regression): i've just used example figures.

Coefficient of determination
87.56% of the variation in arm span can be explained by variation in height.

Describing a relationship:
From the scatterplot, it can be seen that there is a strong, negative linear relationship between number of errors on a test and the period of time spent studying, with no outliers.

Gradient:
On average, the final weight of Jane decreases by 1.44kg for every additional day spent working out.

Y-intercept:
On average, Jane's final weight at the start of the weight-loss program, is 96kg.

^ Are these templates for such questions okay? Thanks!

If you don't like the term 'on average', you can use 'expected' for the gradient and y-intercept (I preferred and used these):

Gradient: The final weight of Jane is expected to decrease by 1.44kg for every increase in days working out by 1.

y-intercept: When Jane spends no days working out, the final weight is expected to be 96kg.

Wow, never seen a question asking to describe the y-intercept of a graph like that, but nonetheless could be useful to set out how you want to answer a question.

This is actually really important.

[Yacoubb]

If you don't like the term 'on average', you can use 'expected' for the gradient and y-intercept (I preferred and used these):

Gradient: The final weight of Jane is expected to decrease by 1.44kg for every increase in days working out by 1.

y-intercept: When Jane spends no days working out, the final weight is expected to be 96kg.

This is actually really important.

Ah okay thanks Just realised I had these written in my bound reference! Thanks!

[Mandy360]

Just a quick questions relating to the further core, I got this in a practice exam and had no idea how to work it out:
"A set of bivariate data involves the independent variable x. The mean of x is 31.38 and the standard deviation is 5.38.
The other variable is y and the mean of y is 19.46 and the standard deviation is 5.46.
Pearson's correlation coefficient is -0.813.
The least squares regression line for this data would have an equation closest to:"

A) y=45.4-0.8x
B) y=0.8+43.2x
C) y=9.9-0.8x
D) y=0.8+9.6x
E) y=44.6-0.8x

The know the answer couldn't be B or C and apparently it is A but how do I work it out?

[Yacoubb]

Just a quick questions relating to the further core, I got this in a practice exam and had no idea how to work it out:
"A set of bivariate data involves the independent variable x. The mean of x is 31.38 and the standard deviation is 5.38.
The other variable is y and the mean of y is 19.46 and the standard deviation is 5.46.
Pearson's correlation coefficient is -0.813.
The least squares regression line for this data would have an equation closest to:"

A) y=45.4-0.8x
B) y=0.8+43.2x
C) y=9.9-0.8x
D) y=0.8+9.6x
E) y=44.6-0.8x

The know the answer couldn't be B or C and apparently it is A but how do I work it out?

The equation of a least squares regression line is y = a + bx

a is the y-intercept. This can be found by doing:

a = (mean of y) - b x (mean of x).

b is the gradient. This can be found by:

        (correlation coefficient) x (standard deviation of y)
   b=  __________________________________________
               (standard deviation of x).

So substitute the given values:

b = (-0.831 x 5.46) / 5.38 = -0.8

a = 19.46 - (-0.8 x 31.38) = 45.92

Closest answer is A

[Mandy360]

Thank you

[jimmy22]

Hi,
In Matrices, if you are trying to find for example the number of people living in Town A after 3 years (against the number of people living in Town B, where there originally 100 in each town), so you calculate s(3) = T^3 * s(0), and say this comes to a matrix where there is exactly 95.5 living in town A and 105.5 living in Town B, how do you round?

thanks

[Yacoubb]

Hi,
In Matrices, if you are trying to find for example the number of people living in Town A after 3 years (against the number of people living in Town B, where there originally 100 in each town), so you calculate s(3) = T^3 * s(0), and say this comes to a matrix where there is exactly 95.5 living in town A and 105.5 living in Town B, how do you round?

thanks

You usually round up either way, even if the total should equal 200.

[lala1911]

Hi can someone work out this Number Patterns question and provide the working out? Will be grateful.


The sum of the first three terms of a geometric series is 57 while the infinite sum is 81.
The common ratio is
A. 1/3
B. 2/3
C. 1
D. 3/2
E. 12

[Zealous]

Hi can someone work out this Number Patterns question and provide the working out? Will be grateful.


The sum of the first three terms of a geometric series is 57 while the infinite sum is 81.
The common ratio is
A. 1/3
B. 2/3
C. 1
D. 3/2
E. 12

Set up two equations:

1: Sum to Infinity -



2: Sum of 3 terms -



Solve these two equation simultaneously, for further just use your calculator.

and

[lala1911]

Set up two equations:

1: Sum to Infinity -



2: Sum of 3 terms -



Solve these two equation simultaneously, for further just use your calculator.

and

Thanks a lot.

[tcstudent]

I hoped that it didnt come to this, but i just am attempting to do practice exams on the modules i did at the start of the year matrices and networks, im all good with graphs and relations because i just completed it last week at school lol, however if i have forgotten around 50% of the module should i go over it again or just attempt practice exams and try and find the example in the textbook? OMFG its annoying when this happens

[abcdqdxD]

For questions such as "The top of a two metre section of a 5 metre cone is removed. After the top is removed, the percentage of the total volume remaining is:

I know to calculate it you need to do 1- (2/5)^3 which is essentially entire thing minus top, but I was wondering why we can't do (3/5)^3 which would be bottom bit only and gives a different answer?

[b^3]

The volume that you have remaining is not a cone, (since we are dealing with a cone and not an inverted cone). That's why you need to look at the full cone, and the cone that we have removed from the top, leaving what we have left.