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March 29, 2024, 04:43:03 am

Author Topic: Specialist 1/2 Question Thread!  (Read 119958 times)  Share 

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S_R_K

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Re: Specialist 1/2 Question Thread!
« Reply #330 on: March 27, 2020, 06:48:22 pm »
+3
Hey

I needed help with another question:

A tunnel 300 m long has a semicircular cross-section. It requires temporary supports, AB and BC, as shown.
Point B is vertically above D. If AB = 15 m and BC = 8 m, find:
(a)   the diameter of the tunnel

(b)   the height of B above the floor of the tunnel

(c)   the distance D is from the wall at C

(d)   the maximum height a 3-metre-wide truck could be and still pass under the supports.

I just needed help with question d


Thanks  :)

For (d), without assuming that the truck drives down the middle, here's a method to find the maximum height:

Let X and Y be points on AB and BC, respectively, such that XY is 3 m. Then BXY is similar to BAC. From this you can deduce the distance from X to AC (or from Y to AC).

SS1314

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Re: Specialist 1/2 Question Thread!
« Reply #331 on: March 27, 2020, 08:14:27 pm »
0
For (d), without assuming that the truck drives down the middle, here's a method to find the maximum height:

Let X and Y be points on AB and BC, respectively, such that XY is 3 m. Then BXY is similar to BAC. From this you can deduce the distance from X to AC (or from Y to AC).

Thank you  :)
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v.l.o.n.e.

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Re: Specialist 1/2 Question Thread!
« Reply #332 on: April 15, 2020, 12:08:03 pm »
0
ummmm hi guys i'm a year 10 and I have a question on the subject. I was wondering whether it is necessary to know the proofs for all the formulae which are in the book. For example, there's this formula which I saw which was like:

HCF(a,b)=HCF(a,r) if b=aq+r where like all the numbers are integers or something

So for a formula like this, would I need to know the proof for it? I am aware that there is a proofs chapter, but that is more general stuff like "proof that x^4 is greater than y^4 is greater than blah blah".

IN PERORATION, do I need to learn the proofs of formulae? Are they tested on exams or sacs? (I go to mhs so I expect the worst)

S_R_K

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Re: Specialist 1/2 Question Thread!
« Reply #333 on: April 15, 2020, 08:03:29 pm »
+2
You're doing Specialist Maths - if you want to learn maths properly, learn the proofs. Whether you will be asked to reproduce them on an assessment is beside the point. The Cambridge book does not include proofs that are beyond the ability of any reasonably capable student.

ShirinKothari

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Re: Specialist 1/2 Question Thread!
« Reply #334 on: May 03, 2020, 12:18:42 pm »
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Hi all,
I was wondering why there isn't a specialist math 1/2 ATARNOTES complete course notes book?
It would be very helpful if there were to be one, as I am taking specialist maths units 1 & 2 next year.

Kind Regards,
Shirin.

Sine

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Re: Specialist 1/2 Question Thread!
« Reply #335 on: May 03, 2020, 12:28:46 pm »
0
Hi all,
I was wondering why there isn't a specialist math 1/2 ATARNOTES complete course notes book?
It would be very helpful if there were to be one, as I am taking specialist maths units 1 & 2 next year.

Kind Regards,
Shirin.
Not an official response from ATAR Notes but it could possibly be because of the content for Specialist Maths 1/2 differs quite a lot between schools in Victoria. Teachers take a lot of control of this subject and sometimes skip heaps of parts of the study design and add new topics. The reason they do this is because the study design of Spec 1/2 is not a great precursor for preparing for specialist maths 3/4.

bluechai

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Re: Specialist 1/2 Question Thread!
« Reply #336 on: May 15, 2020, 05:14:55 pm »
0
1) the first 3 terms in geometric sequence are 1,p,q. If the first 3 terms of an arithmetic sequence are 1,q,p.
Show that 2p^2 - p - 1 = 0

2) given that geometric series 1+p+q+... converges, find
i) p
i) 1+ p+ q +...

Thanks in advance
« Last Edit: May 15, 2020, 05:21:29 pm by bluechai »

Opengangs

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Re: Specialist 1/2 Question Thread!
« Reply #337 on: May 15, 2020, 05:46:05 pm »
+2
1) the first 3 terms in geometric sequence are 1,p,q. If the first 3 terms of an arithmetic sequence are 1,q,p.
Show that 2p^2 - p - 1 = 0

2) given that geometric series 1+p+q+... converges, find
i) p
i) 1+ p+ q +...

Thanks in advance
1) On the one hand, we have \(q - 1 = p - q\). On the other hand, we have \(\displaystyle \frac{p}{1} = \frac{q}{p}\). So \(p^2 = q\). Then substituting that into our first equation, we get
\begin{align*}
p^2 - 1 &= p - p^2 \\
2p^2 - p - 1 &= 0.
\end{align*}

2)
Again, we use the fact that \(1 + p + q + \dots\) is a geometric series to get
\begin{align*}
\frac{p}{1} = \frac{q}{p} \implies p^2 = q \implies p = \pm \sqrt{q}.
\end{align*}
Since the series converges, then it will converge to \(\displaystyle \frac{a}{1 - r}\) where \(a\) is the first term and \(r\) is the common ratio \(p\). Hence, the series converges to \(\displaystyle \frac{1}{1 - p}\). This assumes that \(|p| < 1\).
Lmk if there are any errors or questions! :))

ErnieTheBirdi

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Re: Specialist 1/2 Question Thread!
« Reply #338 on: May 19, 2020, 09:56:47 am »
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I have an upcoming SAC for Unit 1 for Spesh and its my first Spesh SAC. I was just wondering if someone could give me a heads up or pointers to what to look out for or study to do well on it?

Sine

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Re: Specialist 1/2 Question Thread!
« Reply #339 on: May 19, 2020, 02:01:16 pm »
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I have an upcoming SAC for Unit 1 for Spesh and its my first Spesh SAC. I was just wondering if someone could give me a heads up or pointers to what to look out for or study to do well on it?
What topics have you  learnt so far this year and what will be tested on the sac?

ErnieTheBirdi

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Re: Specialist 1/2 Question Thread!
« Reply #340 on: May 20, 2020, 01:19:18 am »
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What topics have you learnt so far this year and what will be tested on the sac?
I'm not too sure what will be tested, mainly because we've been at home and all? We've done Sequences and series, Circle geometry, Further Trig, Complex and now we are doing Trigonometric ratios and applications. I think our teacher said when we return to school we may be doing Stats

jessieleung

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Re: Specialist 1/2 Question Thread!
« Reply #341 on: June 01, 2020, 08:23:08 am »
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I struggle with geometric proofs. Any good websites with videos and questions that would help me with geometric proofs? Thanks

keltingmeith

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Re: Specialist 1/2 Question Thread!
« Reply #342 on: June 05, 2020, 05:44:19 pm »
+1
I'm not too sure what will be tested, mainly because we've been at home and all? We've done Sequences and series, Circle geometry, Further Trig, Complex and now we are doing Trigonometric ratios and applications. I think our teacher said when we return to school we may be doing Stats

Cool - study those, that'll help.

I struggle with geometric proofs. Any good websites with videos and questions that would help me with geometric proofs? Thanks

Here's a good video with tips. Yes, it's an hour long, but it's REALLY REALLY good, I recommend watching it instead of doing maths study one night. Otherwise, exposure is the best. Just do every question you can find. Look up "examples of geomteric proofs", and instead of reading through, stop at the bit where they say what they're going to prove, and try it yourself. The more tricks you pick up, the easier it'll become. But starting with Grant's 10 tips in that video will help a lot - and he'll even show you how to apply them to a geometric proof! You may have seen the proof before, but still watch - it'll give you an idea of how to approach things.

Another thing you can do: in a lot of your classes, you're given different formulae and asked to take them for granted. They only work because you CAN prove them. So, you should try and prove them - because it's honestly very possible to come up with a convincing argument for all of them even if not a full proof. Here's some properties that I find really fun to prove geometrically:

a) Prove that (x+y)^2=x^2+2xy+y^2
b) Prove (x-y)^2 = x^2-2xy-y^2
c) Prove x^2-y^2=(x-y)(x+y)

It'll help if you think of x as a line with length x, which means that x^2 is a square with side-lengths x - that way these random algebraic letters become shapes that you can play around with. Also, don't be scared to cut these shapes up - actually get a pair of scissors and cut things up, then play around with them! Hands-on learning can often work wonders

SmartWorker

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Re: Specialist 1/2 Question Thread!
« Reply #343 on: July 26, 2020, 09:05:47 pm »
0
Hey All!

When doing the quotient & chain rule for example for this function


Then is this the proper working out? Like am I using the proper notation? Sorry I am new to Latex. Please tell me if there is a quicker accepted way. My teacher makes us write it out using composite functions (she marks whether we have included it), So idk if this is the right way?









Thank you!😀
« Last Edit: July 26, 2020, 09:08:13 pm by SmartWorker »
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keltingmeith

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Re: Specialist 1/2 Question Thread!
« Reply #344 on: July 27, 2020, 12:28:52 am »
+1
Hey All!

When doing the quotient & chain rule for example for this function


Then is this the proper working out? Like am I using the proper notation? Sorry I am new to Latex. Please tell me if there is a quicker accepted way. My teacher makes us write it out using composite functions (she marks whether we have included it), So idk if this is the right way?









Thank you!😀


If you're required to show all steps, then yes that's what it should look like. However, it's totally considered as fine to skip the notation for the chain rule and to just do it. Eg, instead of writing:

tan^2(x)=z^2
.: 2z*z'

To just write:

d/dx (tan^2(x))=2tan(x)*(d/dx)(tan(x))=2tan(x)sec^2(x)