# HSC 2016 General Maths Marathon (1 Viewer)

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#### davidgoes4wce

##### Well-Known Member
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

##### Well-Known Member
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

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#### davidgoes4wce

##### Well-Known Member
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

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

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

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

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

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

The 4 multiple choices are:

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

$\bg_white The answer is D$

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#### InteGrand

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

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

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

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

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

The 4 multiple choices are:

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

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

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#### davidgoes4wce

##### Well-Known Member
$\bg_white I don't have a clue how to get that one.$

$\bg_white My thinking was to multiply 22.35 x 40 =\894 for normal pay. Special allowance being called out 1 time in a week, means \150 for the week. (remember it has to be a minimum of 4 hours). The double overtime comes from multiplying \22.35 x 2 x 6.5=\290.55. I get a value of \fbox{{\1,334.55}}$

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#### InteGrand

##### Well-Known Member
$\bg_white I don't have a clue how to get that one.$

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

#### davidgoes4wce

##### Well-Known Member
Was doing this question in the early morning:

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

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

#### InteGrand

##### Well-Known Member
Was doing this question in the early morning:

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

$\bg_white In this question what I did was convert the 230 \degree to radians by multiplying it be \frac{\pi}{180} to give me \frac{23\pi}{36}. I then multiplied this by the radius given and added up the two radiuses to give me my perimeter. I'm just a bit confused of the times when we should use l=r \theta and l=2r \times \frac{\theta}{360}$
$\bg_white \noindent The formula \ell = r\theta is for when \theta is in radians. If the angle is in degrees, say \phi ^\circ, the arc length would be \frac{\phi}{360}\times 2\pi r.$

#### BLIT2014

##### The pessimistic optimist.
Moderator
Was doing this question in the early morning:

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

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

##### Well-Known Member
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.

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#### BLIT2014

##### The pessimistic optimist.
Moderator
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

##### Well-Known Member
I've seen it used in General Mathematics papers a lot of times too
Yeah, it probably is a General Maths Q.

#### davidgoes4wce

##### Well-Known Member
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

##### Well-Known Member
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.

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#### davidgoes4wce

##### Well-Known Member
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

##### Well-Known Member
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

##### Cole World
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

##### Well-Known Member
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

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

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