HSC 2016 General Maths Marathon (1 Viewer)

davidgoes4wce · Feb 2, 2016

Just came back from holiday and surprised to see no General Maths forum open , so decided to open one up.

I came across this question from the 2012 HSC exam paper:

Without looking at the answer I think its D, my only reasoning is the median (the 5th value in this case) is on the line of best fit.

InteGrand · Feb 2, 2016

davidgoes4wce said:
Just came back from holiday and surprised to see no General Maths forum open , so decided to open one up.

I came across this question from the 2012 HSC exam paper:

Without looking at the answer I think its D, my only reasoning is the median (the 5th value in this case) is on the line of best fit.

The answer is (B), I believe. For these three-point median regression lines, we have to divide the data into three 'clumps', consider a line connecting the medians of the outer two clumps, and then move this one-third of the way towards the median of the inner clump. See here for more detail: http://maths.gerrydear.id.au/year12/general/Correlation/02 Median Regression Lines.ppt

davidgoes4wce · Feb 2, 2016

I learnt something new. As you can see there is a cross against this question (as I think they don't cover it anymore. I may be incorrect. Its still good to know )

davidgoes4wce · Feb 18, 2016

$$Jordan is a mechanic who receives a normal rate of pay of \${22.35} per hour for a 40-hour week.$

$When he is needed for emergency call-outs he is paid a special allowance of \$150 for that week. Additionally, each time he is called out to an emergency he is paid at double time for a minimum of 4 hours.$

$In the week beginning 1 March 2012 Jordan worked 40 hours normal time and was needed for emergency call-outs. His emergency call-out log book for the week is shown.$

$Employee: Jordan Furner Week 1/3/12 to 7/3/12 .$

$Date 3/3/12 Duration of call-out: 5 hours$
$Date 5/3/12 Duration of call-out: 1.5 hours$

The 4 multiple choices are:

$A. \$1189.28 \ B. \$1296.30 \ C. \$1334.55 \ D. \$1446.30$

$The answer is D$

InteGrand · Feb 18, 2016

davidgoes4wce said:
$$Jordan is a mechanic who receives a normal rate of pay of \${22.35} per hour for a 40-hour week.$

$When he is needed for emergency call-outs he is paid a special allowance of \$150 for that week. Additionally, each time he is called out to an emergency he is paid at double time for a minimum of 4 hours.$

$In the week beginning 1 March 2012 Jordan worked 40 hours normal time and was needed for emergency call-outs. His emergency call-out log book for the week is shown.$

$Employee: Jordan Furner Week 1/3/12 to 7/3/12 .$

$Date 3/3/12 Duration of call-out: 5 hours$
$Date 5/3/12 Duration of call-out: 1.5 hours$

The 4 multiple choices are:

$A. \$1189.28 \ B. \$1296.30 \ C. \$1334.55 \ D. \$1446.30$

$The answer is D$

$\noindent The main trick is that the double-time emergency payments are for at least 4 hours. So if he did emergency work for fewer than 4 hours, it gets treated as though it was for 4 hours. So his emergency work for the second time was worth a payment of $\boxed{4\times 2\times \$ 22.35}$. The first time was $\boxed{5\times 2\times \$22.35}$. He also earned $\boxed{40\times \$22.35}$ for his normal work, and $\boxed{\$150}$ of special allowance for emergency call-outs. So the answer is obtained by summing these four boxed amounts, giving (D).$

davidgoes4wce · Feb 18, 2016

InteGrand · Feb 18, 2016

davidgoes4wce said:
$I don't have a clue how to get that one.$

$$My thinking was to multiply 22.35 x 40 =\$894 for normal pay. Special allowance being called out 1 time in a week, means \$300 for the week. The double overtime comes from multiplying \$22.35 x 2 x 6.5=\$290.55. I get a value of \$1,334.55$

The special allowance is a one-off for having at least one emergency call-out in the week.

davidgoes4wce · Feb 20, 2016

Was doing this question in the early morning:

$$ I've always done questions like these using the formula for arc length of $ l=r \theta$

$$ In this question what I did was convert the $ 230 \degree $ to radians by multiplying it be $ \frac{\pi}{180} $ to give me $\frac{23\pi}{36}. $ I then multiplied this by the radius given and added up the two radiuses to give me my perimeter. I'm just a bit confused of the times when we should use $ l=r \theta $ and $ l=2r \times \frac{\theta}{360}$

InteGrand · Feb 20, 2016

davidgoes4wce said:
Was doing this question in the early morning:

$$ I've always done questions like these using the formula for arc length of $ l=r \theta$

$$ In this question what I did was convert the $ 230 \degree $ to radians by multiplying it be $ \frac{\pi}{180} $ to give me $\frac{23\pi}{36}. $ I then multiplied this by the radius given and added up the two radiuses to give me my perimeter. I'm just a bit confused of the times when we should use $ l=r \theta $ and $ l=2r \times \frac{\theta}{360}$

$\noindent The formula $\ell = r\theta$ is for when $\theta$ is in radians. If the angle is in degrees, say $\phi ^\circ$, the arc length would be $\frac{\phi}{360}\times 2\pi r$.$

BLIT2014 · Feb 20, 2016

davidgoes4wce said:
Was doing this question in the early morning:

$$ I've always done questions like these using the formula for arc length of $ l=r \theta$

$$ In this question what I did was convert the $ 230 \degree $ to radians by multiplying it be $ \frac{\pi}{180} $ to give me $\frac{23\pi}{36}. $ I then multiplied this by the radius given and added up the two radiuses to give me my perimeter. I'm just a bit confused of the times when we should use $ l=r \theta $ and $ l=2r \times \frac{\theta}{360}$

The l=r\theta isn't actually on the formula sheet, so you are just talking about general mathematics, unless that formula was given to you to use, then I'd doubt you'd be required to do it.

http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-general-2-formulae-14.pdf

InteGrand · Feb 20, 2016

BLIT2014 said:
The l=r\theta isn't actually on the formula sheet, so you are just talking about general mathematics, unless that formula was given to you to use, then I'd doubt you'd be required to do it.

http://www.boardofstudies.nsw.edu.au/syllabus_hsc/pdf_doc/maths-general-2-formulae-14.pdf

He might be talking about 2U Maths, since this looks like a typical 2U question (calculating arc lengths of circles).

Edit: oh wait, never mind, there's a formula for when the angle is in degrees in the General Maths formula sheet. So it is probably a General Maths question.

BLIT2014 · Feb 20, 2016

InteGrand said:
He might be talking about 2U Maths, since this looks like a typical 2U question (calculating arc lengths of circles).

(He might have meant to put this in his other maths thread but put it here by mistake).

I've seen it used in General Mathematics papers a lot of times too

InteGrand · Feb 20, 2016

BLIT2014 said:
I've seen it used in General Mathematics papers a lot of times too

Yeah, it probably is a General Maths Q.

davidgoes4wce · Feb 20, 2016

I just remember from doing high school level maths textbooks in the past , there was a question that asked us to convert from degrees to radians and using either method it would still result in the same answer but based on that calculation I was wrong.

davidgoes4wce · Feb 20, 2016

InteGrand said:
He might be talking about 2U Maths, since this looks like a typical 2U question (calculating arc lengths of circles).

Edit: oh wait, never mind, there's a formula for when the angle is in degrees in the General Maths formula sheet. So it is probably a General Maths question.

This was from the 2012 General Maths HSC Exam Paper as well.

davidgoes4wce · Feb 25, 2016

This question is from the New Century Maths Year 12 textbook by : Klaas Bootsma, Sarah Hamper, Margaret Willard and Robert Yen. I am not sure how to answer Q1, so I thought I would bring it to an open forum for discussion.

InteGrand · Feb 25, 2016

davidgoes4wce said:
This question is from the New Century Maths Year 12 textbook by : Klaas Bootsma, Sarah Hamper, Margaret Willard and Robert Yen. I am not sure how to answer Q1, so I thought I would bring it to an open forum for discussion.

This is a maths question?

Nailgun · Feb 25, 2016

davidgoes4wce said:
This question is from the New Century Maths Year 12 textbook by : Klaas Bootsma, Sarah Hamper, Margaret Willard and Robert Yen. I am not sure how to answer Q1, so I thought I would bring it to an open forum for discussion.

wtf ahahahha
this is why general gets a bad rap lol

davidgoes4wce · Feb 25, 2016

OK I have decided to have an attempt at this question:

1. Water reduction - they are aiming to reduce water reduction by installing a water tank to the toilet and garden irrigation system

2. Thermal comfort- refers to keeping the house cool in summer and warm in winter. By having insulation in the ceiling, walls and floors this target can be achieved.

3. Energy- reduction can be reduced by using a 6 star reverse cycle air-conditioning system . This in turn produces a more efficient and is cost-saving for the consumer.

davidgoes4wce · Feb 25, 2016

Learnt a new term in maths today 'great circle- A slice through the centre of a sphere.

HSC 2016 General Maths Marathon (1 Viewer)

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