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March 29, 2024, 11:43:31 pm

Author Topic: Mathematics Question Thread  (Read 1297203 times)  Share 

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RuiAce

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Re: Mathematics Question Thread
« Reply #435 on: October 05, 2016, 08:40:22 am »
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A particle is moving in a straight life, starting from the origin. At time t seconds the particle has a displacement of x metres from the origin and a velocity v m s^-1. the displacement is given by x=2t - 3ln(t+1). Find the distance travelled by the particle in the first 2 seconds. (HSC Paper 2000).
Can someone please help me out






I had a look: The question actually asks for the first THREE seconds. This will mean that my final answer won't match with the actual answer since you said two seconds (presumably a typo). Also, please indicate any previous parts if there happens to be some in the future.

lha

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Re: Mathematics Question Thread
« Reply #436 on: October 05, 2016, 08:52:37 am »
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What has been the main topic that they have assessed from the prelim course in the hsc exam?

fizzy.123

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Re: Mathematics Question Thread
« Reply #437 on: October 05, 2016, 09:56:34 am »
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What has been the main topic that they have assessed from the prelim course in the hsc exam?

From what ive seen, locus & parabola. Also, just basic algebra and quadratics too.

fizzy.123

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Re: Mathematics Question Thread
« Reply #438 on: October 05, 2016, 09:58:01 am »
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I had a look: The question actually asks for the first THREE seconds. This will mean that my final answer won't match with the actual answer since you said two seconds (presumably a typo). Also, please indicate any previous parts if there happens to be some in the future.

Oh yes sorry! It was a typo. Thank you!

lha

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Re: Mathematics Question Thread
« Reply #439 on: October 05, 2016, 10:04:44 am »
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From what ive seen, locus & parabola. Also, just basic algebra and quadratics too.

Alright thank you! Do you know anywhere that I can find a whole bunch of locus questions from past papers (other than going through every past paper)?

jakesilove

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Re: Mathematics Question Thread
« Reply #440 on: October 05, 2016, 11:10:50 am »
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Alright thank you! Do you know anywhere that I can find a whole bunch of locus questions from past papers (other than going through every past paper)?

Purchase a past paper book that goes by the dotpoint. Other than that, you'll have have to scroll through papers! (Which honestly won't take too long)

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fizzy.123

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Re: Mathematics Question Thread
« Reply #441 on: October 05, 2016, 11:33:16 am »
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I had a look: The question actually asks for the first THREE seconds. This will mean that my final answer won't match with the actual answer since you said two seconds (presumably a typo). Also, please indicate any previous parts if there happens to be some in the future.

in regards to this question, for case one, it is t(1/2) - t(0) & you got 3ln(3/2) - 1. how did you get that because im getting 1 - 3ln(3/2).

RuiAce

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Re: Mathematics Question Thread
« Reply #442 on: October 05, 2016, 12:06:24 pm »
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in regards to this question, for case one, it is t(1/2) - t(0) & you got 3ln(3/2) - 1. how did you get that because im getting 1 - 3ln(3/2).
The absolute value brackets are there for a reason.

Distance is positive, not negative

Daliaradosevic

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Re: Mathematics Question Thread
« Reply #443 on: October 05, 2016, 07:59:56 pm »
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Hey guys so i was just curious as to how to study for the finance (money) area of maths because i am terrible at understanding the question and answering them and i find that theres alot of finance based questions in the exams so please any advice would be grateful!! :)
also i do so so so many practice questions and i still struggle in understanding them!

RuiAce

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Re: Mathematics Question Thread
« Reply #444 on: October 05, 2016, 08:17:25 pm »
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Hey guys so i was just curious as to how to study for the finance (money) area of maths because i am terrible at understanding the question and answering them and i find that theres alot of finance based questions in the exams so please any advice would be grateful!! :)
also i do so so so many practice questions and i still struggle in understanding them!
Effectively, every finance question is just the same thing in different words.

1. We always establish our interest rate first.
2. We start writing our recursive relationship.





3. Make this go on for n years. There is ALWAYS a geometric progression that forms in these types of questions.

4. Use the GP formula

Then whatever last is always a matter of understanding the wording. You will need to provide examples here, clearly indicating where you are stuck in the wording.

And of course, they can hide the yearly/monthly/... repayment from you, the number of years from you or the interest rate from you. The process is still the exact same regardless of which is chosen.
« Last Edit: October 05, 2016, 08:20:59 pm by RuiAce »

IkeaandOfficeworks

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Re: Mathematics Question Thread
« Reply #445 on: October 06, 2016, 12:55:24 pm »
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Hey guys! I'm having trouble with this question. Thank you!  :D

Two dice with their faces numbered 1 to 6 are tossed.

i. By listing the possible outcomes find the probability of

a) one die showing a 6 with other showing at least 4
b) one die showing a 6 with the other showing 3 or less

ii) Deduce from the results in part (i) the probability that neither die show
s a 6.

RuiAce

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Re: Mathematics Question Thread
« Reply #446 on: October 06, 2016, 01:05:39 pm »
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Hey guys! I'm having trouble with this question. Thank you!  :D

Two dice with their faces numbered 1 to 6 are tossed.

i. By listing the possible outcomes find the probability of

a) one die showing a 6 with other showing at least 4
b) one die showing a 6 with the other showing 3 or less

ii) Deduce from the results in part (i) the probability that neither die show
s a 6.

The question asks to list the possibilities, hence you should. However I'll structure my answers as though they weren't listed

Let the rows correspond to the first dice, and the second correspond to the second dice.

The total possible outcomes is always 36

a) Suppose the first dice shows a 6. Then the second die shows either 4, 5 or 6. There are 3 possible choices (going down column 6)
Suppose the second dice shows a 6. Then the first die shows either 4, 5 or 6. There are 3 possible choices (going across row 6)
(6,6) is counted twice, so we deduct it once.

Therefore there are 5 favourable outcomes, so the answer is 5/36

b) Suppose again the first dice shows a 6. Then the second shows either 1, 2 or 3 instead. There are 3 possible choices
And similarly for the second dice
However here, nothing gets counted twice.

Therefore there are 6 favourable outcomes, so the answer is 6/36 = 1/6

For part ii), note that the sum of the above probabilities is 11/36.
Notice that in the above parts, we've catered for all the cases where 6 must appear at least once.

Hence the probability 6 doesn't appear at all is just the complement. This has a probability of 25/36

This can also be deduced from reading off the table, as we are basically asking for the probability that something not in row 6 and/or column 6 is chosen.

BPunjabi

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Re: Mathematics Question Thread
« Reply #447 on: October 06, 2016, 01:20:36 pm »
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Guys I have no Idea how to answer this question at all. Its question 15 b) from the 2015 paper.


I would say for:
i) (triangle)ACB = (triangle)DCF
                  AC=DC (Given)
       (angle)ACB=(angle)DCF (Angles bisect/intesect at 90' - Given)
                - SAS somehow??


             I dont know what else...
i
                   
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RuiAce

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Re: Mathematics Question Thread
« Reply #448 on: October 06, 2016, 01:28:15 pm »
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Guys I have no Idea how to answer this question at all. Its question 15 b) from the 2015 paper.
(Image removed from quote.)

I would say for:
i) (triangle)ACB = (triangle)DCF
                  AC=DC (Given)
       (angle)ACB=(angle)DCF (Angles bisect/intesect at 90' - Given)
                - SAS somehow??


             I dont know what else...
i
                   



AC is not equal to DC either. AD is equal to DC.

And a hint for part (ii) - you were given a pair of similar triangles in part (i). You'd be crazy to not use it.
« Last Edit: October 06, 2016, 02:47:37 pm by RuiAce »

BPunjabi

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Re: Mathematics Question Thread
« Reply #449 on: October 06, 2016, 11:22:25 pm »
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AC is not equal to DC either. AD is equal to DC.

And a hint for part (ii) - you were given a pair of similar triangles in part (i). You'd be crazy to not use it.

Thanks So MUCH!!!
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