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January 27, 2020, 10:16:20 am

Author Topic: Mathematics Question Thread  (Read 639912 times)  Share 

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Coolmate

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Re: Mathematics Question Thread
« Reply #4335 on: September 11, 2019, 10:16:43 pm »
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Thanks Rui! ;D ;D

Your explanation was very clear and I understood it!

Thanks also, fun_jirachi! ;D ;D That is a good point!
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annabeljxde

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Re: Mathematics Question Thread
« Reply #4336 on: September 11, 2019, 11:02:37 pm »
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Need help with working out this question:
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fun_jirachi

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Re: Mathematics Question Thread
« Reply #4337 on: September 11, 2019, 11:10:09 pm »
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You can think about it as the three points (-12, 4), (0, 0) and (12, 4) being on the parabola x2=4ay. Subbing in the first point or the third point will get you 144=16a, which tells you that the focal length a will be 9 metres. Hence, the answer is D.

Hope this helps :)
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RuiAce

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Re: Mathematics Question Thread
« Reply #4338 on: September 11, 2019, 11:35:48 pm »
+1
Need help with working out this question:

Here's a visual aid to go with fun_jirachi's explanation.



The idea is that ultimately, no matter what it's going to be a parabola. So it's easier to just rotate the paper until it's oriented the same way as an \(x^2=4ay\) parabola. (Note that the vertex was chosen to be \((0,0)\) for the sake of convenience - you could try a different vertex and find that you'll get the same answer, but it's a needless trek.)

dani01

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Re: Mathematics Question Thread
« Reply #4339 on: October 01, 2019, 11:13:52 am »
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I know this is the 2u thread but moderator hasn't posted on standard thread for a quite a bit so I'll just ask on here.
The concentration of salt in Liquid A is 20g per 100 mL and the concentration of salt in Liquid B is 40g per 100 mL. What is the concentration of salt when 250mL of Liquid A is mixed with 250mL of liquid B.
Thanks!

RuiAce

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Re: Mathematics Question Thread
« Reply #4340 on: October 01, 2019, 11:26:04 am »
+2
I know this is the 2u thread but moderator hasn't posted on standard thread for a quite a bit so I'll just ask on here.
The concentration of salt in Liquid A is 20g per 100 mL and the concentration of salt in Liquid B is 40g per 100 mL. What is the concentration of salt when 250mL of Liquid A is mixed with 250mL of liquid B.
Thanks!
(Note: Answers from a non-moderator don't mean they are not credible :). I just don't like providing answers when they're about matters I am not confident on.)

New volume: 250mL + 250mL = 500mL

Original masses:
250mL of Liquid A will have (20/100) * 250 = 50g of salt.
250mL of Liquid B will have (40/100) * 250 = 100g of salt.

New mass of salt = 50g + 100g = 150g.

New concentration: 150/500 = 30/100. Hence 30g per 100mL.

Raissa

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Re: Mathematics Question Thread
« Reply #4341 on: October 01, 2019, 10:09:48 pm »
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Hey I'm really stuck on question 15. c) (ii) HSC 2013. I looked at the solutions but still didn't understand how they got the answer.

RuiAce

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Re: Mathematics Question Thread
« Reply #4342 on: October 01, 2019, 10:13:25 pm »
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Hey I'm really stuck on question 15. c) (ii) HSC 2013. I looked at the solutions but still didn't understand how they got the answer.
You can find a solution for this in the compilation.

(You're welcome to ask for more clarification in any further areas you have trouble with.)
« Last Edit: October 01, 2019, 10:15:32 pm by RuiAce »

therese07

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Re: Mathematics Question Thread
« Reply #4343 on: October 02, 2019, 11:00:25 pm »
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Hey,

As hsc maths is coming up, I wanted to ask, besides doing past hsc  papers, would it be worth doing trial questions?? I know trials are harder than hsc, but has there ever been instances where a maths trial question and itís difficulty been on a hsc paper? Especially in question 16?


Thank you!!
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InnererSchweinehund

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Re: Mathematics Question Thread
« Reply #4344 on: October 04, 2019, 07:55:13 pm »
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Hey,

As hsc maths is coming up, I wanted to ask, besides doing past hsc  papers, would it be worth doing trial questions?? I know trials are harder than hsc, but has there ever been instances where a maths trial question and itís difficulty been on a hsc paper? Especially in question 16?


Thank you!!

Hi therese07!

It's definitely worth continuing to do trial papers in the lead up to the HSC.
I sat the Mathematics HSC last year and definitely found that the trial papers were really beneficial for preparing me for the actual HSC, especially the later questions (Q14 onwards).

I honestly believe that if I hadn't done so many trial papers, I wouldn't have done as well as I did.

Good luck!!
 8)

spnmox

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Re: Mathematics Question Thread
« Reply #4345 on: October 07, 2019, 12:48:56 am »
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hey guys, a few questions from 2018 mc:

The line 3x − 4y + 3 = 0 is a tangent to a circle with centre (3, −2).
What is the equation of the circle?

A runner has four different pairs of shoes.
If two shoes are selected at random, what is the probability that they will be a matching pair?

A radio telescope has a parabolic dish. The width of the opening is 24 m and the distance
along the axis from the vertex to the opening is 4 m, as shown in the diagram. (attached)
What is the focal length of the parabola?

fun_jirachi

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Re: Mathematics Question Thread
« Reply #4346 on: October 07, 2019, 12:15:08 pm »
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hey guys, a few questions from 2018 mc:

The line 3x − 4y + 3 = 0 is a tangent to a circle with centre (3, −2).
What is the equation of the circle?

A runner has four different pairs of shoes.
If two shoes are selected at random, what is the probability that they will be a matching pair?

A radio telescope has a parabolic dish. The width of the opening is 24 m and the distance
along the axis from the vertex to the opening is 4 m, as shown in the diagram. (attached)
What is the focal length of the parabola?


Hey there!

If a line is tangent to a circle, we know that the distance from the centre to the point of contact is the radius, which meets the tangent at a right angle. Basically, we substitute (3, -2) into the perpendicular distance formula, then use the equation of a circle (x-h)2+(y-k)2=r2 to find the answer (given the centre (h, k)).

When picking the shoes, note that when we pick the first shoe we don't actually care what shoe it is; we just care that the second shoe we pick matches the first one. Hence, once we pick the first shoe, there's only one shoe that matches out of the remaining seven ie. the answer is going to be 1/7.

The last one was addressed already further up the page! (about 5 messages or so up :) )

Hope this helps :)
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spnmox

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Re: Mathematics Question Thread
« Reply #4347 on: October 07, 2019, 12:51:28 pm »
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Hey there!

If a line is tangent to a circle, we know that the distance from the centre to the point of contact is the radius, which meets the tangent at a right angle. Basically, we substitute (3, -2) into the perpendicular distance formula, then use the equation of a circle (x-h)2+(y-k)2=r2 to find the answer (given the centre (h, k)).

When picking the shoes, note that when we pick the first shoe we don't actually care what shoe it is; we just care that the second shoe we pick matches the first one. Hence, once we pick the first shoe, there's only one shoe that matches out of the remaining seven ie. the answer is going to be 1/7.

The last one was addressed already further up the page! (about 5 messages or so up :) )

Hope this helps :)

oh, i see haha. thanks very much!

spnmox

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Re: Mathematics Question Thread
« Reply #4348 on: October 08, 2019, 02:50:42 am »
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The quadrilateral formed by (1, 2), (3, 3), (1, 7), (-1, 3) is ?

John has 10 marbles in a bag, 3 of which are green and the rest are yellow. He randomly draws 1 out of
the bag, notes its colour and then puts it back before drawing another out of the bag. What is the
probability that both marbles drawn are the same colour?

is the second one 0.58?? haha i'm so unsure with probability questions

InnererSchweinehund

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Re: Mathematics Question Thread
« Reply #4349 on: October 08, 2019, 08:23:14 am »
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The quadrilateral formed by (1, 2), (3, 3), (1, 7), (-1, 3) is ?

John has 10 marbles in a bag, 3 of which are green and the rest are yellow. He randomly draws 1 out of
the bag, notes its colour and then puts it back before drawing another out of the bag. What is the
probability that both marbles drawn are the same colour?

is the second one 0.58?? haha i'm so unsure with probability questions

Hi!

For the quadrilateral question, I would start by drawing a cartesian plane and plotting the points to create the shape. see first image attached
From this I got the impression that the quadrilateral is a kite, but you would look to prove that by showing that the diagonals of the kite meet at a right angle (I'm not 100% sure but I think you can do this by showing that the gradients of the two diagonals, when multiplied together equal -1)

For the probability question, I used a tree diagram to clearly step it out and show everything I needed to include
It's important to remember that this question uses replacement
see the second image attached

Hope this helps!!