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HSC Stuff => HSC Maths Stuff => HSC Subjects + Help => HSC Mathematics Extension 1 => Topic started by: Jefferson on January 27, 2020, 02:15:38 pm

Title: Extension 1 - Particle Concentration Question
Post by: Jefferson on January 27, 2020, 02:15:38 pm

Hey Everyone,

I don't quite understand the wording of this question nor where to start (see attachment).
Any help is appreciated.

Thank you!

Title: Re: Extension 1 - Particle Concentration Question
Post by: RuiAce on January 29, 2020, 11:53:58 pm

I can't be sure of this but at first glance it looks like it's just ratios.

Let \(x\) be the amount of concentration of tea we require. That is, a particle concentration of \(x\) should reduce to a particle concentration of 51.8g after passing through sieve B.

A particle concentration of 100g gets reduced to a concentration of 39.6g after passing through sieve B.
\[\text{So we just end up with}\\ \frac{100}{39.6} = \frac{x}{51.8}. \]
The only issue is that I can't justify why ratios work here. But the first thing I thought of was basically linear relationships.

Title: Re: Extension 1 - Particle Concentration Question
Post by: Jefferson on January 30, 2020, 10:28:15 pm

Quote from: RuiAce on January 29, 2020, 11:53:58 pm

I can't be sure of this but at first glance it looks like it's just ratios.

Let \(x\) be the amount of concentration of tea we require. That is, a particle concentration of \(x\) should reduce to a particle concentration of 51.8g after passing through sieve B.

A particle concentration of 100g gets reduced to a concentration of 39.6g after passing through sieve B.
\[\text{So we just end up with}\\ \frac{100}{39.6} = \frac{x}{51.8}. \]
The only issue is that I can't justify why ratios work here. But the first thing I thought of was basically linear relationships.

Thank you RuiAce! The answer is indeed 30.8 g (extra).
Is there any particular reason why they used the word "average" in the question, but not in the information given? :(
Also, I rarely see questions with this many excess information in mathematics. Is this something introduced in the new syllabus?

Thanks,
Jefferson

Title: Re: Extension 1 - Particle Concentration Question
Post by: RuiAce on January 31, 2020, 03:17:49 am

Quote from: Jefferson  on January 30, 2020, 10:28:15 pm

Thank you RuiAce! The answer is indeed 30.8 g (extra).
Is there any particular reason why they used the word "average" in the question, but not in the information given? :(
Also, I rarely see questions with this many excess information in mathematics. Is this something introduced in the new syllabus?

Thanks,
Jefferson

I didn't notice that first time round actually. I feel like the word "average" should've shown up in the question as well. :(

For an assignment, I suppose it's fair enough. Assignments can be investigative tasks requiring students to determine for themselves what's useful. But if this question came from an exam, I would be raising eyebrows in confusion here.