VCE General & Further Maths Question Thread!

[AngelWings]

Hey, I was just wondering if someone could help me on how I would go about this question (geometry and measurement)!

'Two similar cones of radius 4 cm and r cm (smaller than the first) are shown below.
The volume of the larger cone is three times the volume of the smaller cone.
The value of r is closest to...'
Options are 0.8 (A), 1.9 (B), 2.1 (C), 2.5 (D), and 2.8 (E).

Thankyou in advance!!

Spoiler

Knowing that the cones are similar, the volumes of the cones will be = 4³ : r³.
We also know that the volume of the larger cone will be 3x the volume of the smaller one, so 3b: b, where b is the volume of the smaller cone, which is r³. Thus we actually have:

Spoiler

r³ = b
The question states that the larger cone's volume is 3 times that of the smaller cone's.
If I call the smaller cone's volume 'b', then 3b is the larger cone's volume.
We found that smaller cone's volume (b) is also r³ when scaled from length.
Substitute b = r³ into 3b and you get: 3b = 3r³.
3b = 3r³ = 4³ = 64

This can help you find r, which would be:

Spoiler

3r³ = 64
r³ = 64/3
r = cube root of 64/3 = 2.77 cm approx.
which rounds to 2.8.

This gives Option E.

Hope that helps.

when drawing a regression line, what do vcca look for.?
Is it enough to get 2 points on the graph accurate from the equation present or does the line need to go through specific points?

They will intend for you to use some reference points that are not too close to each other and draw the line over the entire graph provided.
Do not draw by eye and take the least squares regression equation into account.
The line usually must go through two important points and have the same general slope as indicated in the equation.
Please see VCAA 2014 E2 Core Question 2b in the Examination Report as a reference.

[elle6299]

Spoiler

Knowing that the cones are similar, the volumes of the cones will be = 4³ : r³.
We also know that the volume of the larger cone will be 3x the volume of the smaller one, so 3b: b, where b is the volume of the smaller cone, which is r³. Thus we actually have:

Spoiler

r³ = b
3b = 3r³ = 4³ = 64

This can help you find r, which would be:

Spoiler

3r³ = 64
r³ = 64/3
r = cube root of 64/3 = 2.77 cm approx.
which rounds to 2.8.

This gives Option E.

Hope that helps.

Thankyou! May I ask, where did you get the 3b = 3r^3

[AngelWings]

Thankyou! May I ask, where did you get the 3b = 3r^3

Oh, sorry! Should've said that b is just an arbitrary number that I used to make the volume of the smaller cone, so it wasn't going to be the same pronumeral (and less confusing).

The question states that the larger cone's volume is 3 times that of the smaller cone's.
If I call the smaller cone's volume 'b', then 3b is the larger cone's volume.
We found that smaller cone's volume (b) is also r³ when scaled from length.
Substitute b = r³ into 3b and you get: 3b = 3r³.

That should make a bit more sense now.

[elle6299]

Oh, sorry! Should've said that b is just an arbitrary number that I used to make the volume of the smaller cone, so it wasn't going to be the same pronumeral (and less confusing).

The question states that the larger cone's volume is 3 times that of the smaller cone's.
If I call the smaller cone's volume 'b', then 3b is the larger cone's volume.
We found that smaller cone's volume (b) is also r³ when scaled from length.
Substitute b = r³ into 3b and you get: 3b = 3r³.

That should make a bit more sense now.

YES!! Thankyou, I've been trying to work out this question since last night!
Thankyou so much x

[masonjar]

heylo,

I just had a quick question about financial stuff.

If they don't give you much information in the question for amortisation tables, what are various ways to find out the different columns in the table? Like the interest, payment, principal reduction ,etc,etc

Thanks

[isobelj]

How do I find the value of the last payment? I thought you had to take the last balance of the loan before it hit negatives and then take interest on that. But apparently you take the payment and add that on to the final balance, but that doesn’t really make sense.. why would you pay more than what the balance is worth? Picture attached is the specific question I’m having trouble with (d).

[pippinpie]

For part d you have to add the amount that remains on the loan after 12 months to the $950 payment as the loan is to be paid within 12 months. Hence, the final payment is 950 + 149.67 = $109967

[emmaline]

When we are using an objective function and are trying to find the maximum or minimum, is it a given that the maximum or minimum point will always be a corner point of the feasible region?

[BlinkieBill]

Hi
For financial questions - does writing down the financial solver inputs actually count as working out??
I want to put some working down for them multi-steps to at least get 1/2 marks ya know

[pippinpie]

Hi
For financial questions - does writing down the financial solver inputs actually count as working out??
I want to put some working down for them multi-steps to at least get 1/2 marks ya know

Yeah, VCAA confirmed this in Examiners Reports for previous years

[pippinpie]

So, I was wondering for Geometry whether VCAA can use angles in degrees, minutes and seconds and if so how would you convert on the CAS...

Because it was on a TSSM practice exam I did and I had never come across it before

Mod edit: Posts merged. Please edit your existing post rather than double posting.

[janepage]

Has anyone done 2015 exam 2, networks question 3???

[emmaline]

Is 'year' numerical or categorical?

[Aaron]

Is 'year' numerical or categorical?

Depends on the context in which 'year' is used. For example, year of birth imo would be categorical. Years old (e.g. 15, 20) would be numerical.

Year could literally mean anything

[Angelx001]

Can someone please help me with 2009 exam 2 VCAA question 4.c
Reducing balance method by $11 046.83 . answer is $11 046.83 as the 'greater depreciation amount' but i don't get what it means by this & how they worked it out??
Thanks heaps1!! !