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March 29, 2024, 08:50:22 am

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kector

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Re: Mathematics Question Thread
« Reply #4200 on: May 22, 2019, 07:32:16 pm »
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Hi, not sure what I'm doing wrong, i did P=300, I=0.06 , n=20 , A1= 300(1.06) ---> A20 = 300(1.06)^20

Jane’s mother puts $300 into an account
at the beginning of each year to pay for
Jane’s education in 5 years’ time. If 6%
p.a. interest is paid quarterly, how much
money will Jane’s mother have at the
end of the 5 years?

RuiAce

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Re: Mathematics Question Thread
« Reply #4201 on: May 22, 2019, 07:35:06 pm »
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Hi, not sure what I'm doing wrong, i did P=300, I=0.06 , n=20 , A1= 300(1.06) ---> A20 = 300(1.06)^20

Jane’s mother puts $300 into an account
at the beginning of each year to pay for
Jane’s education in 5 years’ time. If 6%
p.a. interest is paid quarterly, how much
money will Jane’s mother have at the
end of the 5 years?
Have you covered annuities in class? This question involves repeated deposits that each earn interest, not just a single sum, and thus has to be computed the usual way.
\begin{align*}A_1 &= 300(1.06)\\ A_2 &= A_1(1.06) + 300(1.06)\\ &= 300(1.06)^2 + 300(1.06)\\ A_3 &= A_2 (1.06) + 300(1.06)\\ &= 300(1.06)^3 + 300(1.06)^2 + 300(1.06)\\ &\vdots\\ A_{20} &= 300(1.06)^{20} + \dots + 300(1.06)^2 + 300(1.06) \end{align*}
Note that the question says "at the beginning of each year".

kector

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Re: Mathematics Question Thread
« Reply #4202 on: May 22, 2019, 07:36:13 pm »
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Hi, not sure what I'm doing wrong, i did P=300, I=0.06 , n=20 , A1= 300(1.06) ---> A20 = 300(1.06)^20

Jane’s mother puts $300 into an account
at the beginning of each year to pay for
Jane’s education in 5 years’ time. If 6%
p.a. interest is paid quarterly, how much
money will Jane’s mother have at the
end of the 5 years?
Sorry I am also struggling with this question - thank you!
27. Scott borrows $200 000 to buy a house.
If the interest is 6% p.a. and the loan is
over 20 years,
(a) how much is each monthly
repayment?
(b) how much does Scott pay altogether?

A farmer borrows $50 000 for farm
machinery at 18% p.a. over 5 years and
makes equal yearly repayments on the
loan at the end of each year.
(a) How much does he owe at the end
of the first year, just before he makes the
first repayment?
(b) How much is each yearly repayment?

kector

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Re: Mathematics Question Thread
« Reply #4203 on: May 22, 2019, 07:38:33 pm »
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Have you covered annuities in class? This question involves repeated deposits that each earn interest, not just a single sum, and thus has to be computed the usual way.
\begin{align*}A_1 &= 300(1.06)\\ A_2 &= A_1(1.06) + 300(1.06)\\ &= 300(1.06)^2 + 300(1.06)\\ A_3 &= A_2 (1.06) + 300(1.06)\\ &= 300(1.06)^3 + 300(1.06)^2 + 300(1.06)\\ &\vdots\\ A_{20} &= 300(1.06)^{20} + \dots + 300(1.06)^2 + 300(1.06) \end{align*}
Note that the question says "at the beginning of each year".
Ah, i see my mistake, thank you, i've covered it in class and finished recently but need revising it again

fun_jirachi

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Re: Mathematics Question Thread
« Reply #4204 on: May 22, 2019, 08:07:55 pm »
+4


Part b) is actually a lot easier, once you have the above value, multiply it by 60 for the number of repayments he makes to find the amount he pays.

Try the second one yourself with the same approach, and if you need further help please ask :)
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therese07

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Re: Mathematics Question Thread
« Reply #4205 on: May 23, 2019, 07:20:50 pm »
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Hi There!

This isn't a question I'm stuck on but for my maths assessment, I had make an exam full of past HSC questions, only allocating 12 marks. My topic I had to do was geometrical applications of differentiation, and I was wondering if you could take a look, and judge whether these questions have a range of bands (2-6). If they don't, please tell me so I can fix it up  :)

Thank you!
2020: Bachelor of Arts/Bachelor of Law @ Macquarie University

RuiAce

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Re: Mathematics Question Thread
« Reply #4206 on: May 23, 2019, 07:55:55 pm »
+2
Hi There!

This isn't a question I'm stuck on but for my maths assessment, I had make an exam full of past HSC questions, only allocating 12 marks. My topic I had to do was geometrical applications of differentiation, and I was wondering if you could take a look, and judge whether these questions have a range of bands (2-6). If they don't, please tell me so I can fix it up  :)

Thank you!
I would say so. Part a) looks like 2-4 and part b) looks like 3-6

kiwii

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Re: Mathematics Question Thread
« Reply #4207 on: May 27, 2019, 04:35:15 pm »
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Hello!
Just a quick question about probability. When do you do with or without replacement? There were two questions that didn't specify anything, yet one was with replacement and one was without replacement. Does it depend on the context of the question?

RuiAce

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Re: Mathematics Question Thread
« Reply #4208 on: May 27, 2019, 04:45:01 pm »
+2
Hello!
Just a quick question about probability. When do you do with or without replacement? There were two questions that didn't specify anything, yet one was with replacement and one was without replacement. Does it depend on the context of the question?

Usually you can infer it. So yes, depends on context. If you’re still unsure please post the actual relevant questions.

kiwii

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Re: Mathematics Question Thread
« Reply #4209 on: May 27, 2019, 09:48:29 pm »
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Usually you can infer it. So yes, depends on context. If you’re still unsure please post the actual relevant questions.
Thank you!

Kombmail

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Re: Mathematics Question Thread
« Reply #4210 on: May 27, 2019, 09:48:50 pm »
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I just did a motion and differentiation question and I came across this: (c) Describe the motion of the body after 1 s.

Does this mean I draw a graph of the previous data collected from (b) ?
(b)= find the values of x, x differentiated and x second dfiferentiated after 1 s.
-KgkG-

fun_jirachi

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Re: Mathematics Question Thread
« Reply #4211 on: May 27, 2019, 10:10:06 pm »
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I just did a motion and differentiation question and I came across this: (c) Describe the motion of the body after 1 s.

Does this mean I draw a graph of the previous data collected from (b) ?
(b)= find the values of x, x differentiated and x second dfiferentiated after 1 s.

Not necessarily. What the information gives you is an indication of where the body is (displacement), what direction it's moving in, and how fast it's moving (velocity) and if it's speeding up or slowing down (acceleration). This should be enough info to describe the motion of the particle.

For example if at t=1, x=1m, v=2m/s, a=4m/s/s, the particle is 1m to the right of the origin, travelling in the positive direction at 2m/s, and is speeding up at 4m/s/s in the positive direction. You shouldn't really need a graph if you have that information readily available.

Hope this helps :)
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Kombmail

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Re: Mathematics Question Thread
« Reply #4212 on: May 27, 2019, 10:25:27 pm »
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Not necessarily. What the information gives you is an indication of where the body is (displacement), what direction it's moving in, and how fast it's moving (velocity) and if it's speeding up or slowing down (acceleration). This should be enough info to describe the motion of the particle.

For example if at t=1, x=1m, v=2m/s, a=4m/s/s, the particle is 1m to the right of the origin, travelling in the positive direction at 2m/s, and is speeding up at 4m/s/s in the positive direction. You shouldn't really need a graph if you have that information readily available.

Hope this helps :)

thanks mate!
-KgkG-

Kombmail

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Re: Mathematics Question Thread
« Reply #4213 on: May 29, 2019, 09:09:59 pm »
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I am currently doing geometric progression in class and came across this after using the quadratic formula: 4+- * root 6 times 6 times 5.

Does anyone now how this equals to four positive negative three root five?
-KgkG-

fun_jirachi

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Re: Mathematics Question Thread
« Reply #4214 on: May 29, 2019, 09:27:12 pm »
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I think you might mean this (which would make a lot more sense, since what you've written has no equality):

I'm not sure where you got these values from, since remembering the quadratic formula is in the form (and the above doesn't really match any quadratic on inspection):

Other than that though, the expansion and simplification of the surd involves the 'identity' that

Technically you should have |a| for the result moving from the second thing to the third, but ignoring that that's basically how the expansion of surds works :)
« Last Edit: May 29, 2019, 09:31:07 pm by fun_jirachi »
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