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March 28, 2024, 08:39:27 pm

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BPunjabi

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Re: Mathematics Question Thread
« Reply #450 on: October 07, 2016, 12:05:26 am »
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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.

RUI im still lost... can you help out please!
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RuiAce

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Re: Mathematics Question Thread
« Reply #451 on: October 07, 2016, 12:19:07 am »
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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
                   









onepunchboy

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Re: Mathematics Question Thread
« Reply #452 on: October 07, 2016, 11:11:26 pm »
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Can someone help me with 15) ii. Im not sure about it

jakesilove

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Re: Mathematics Question Thread
« Reply #453 on: October 07, 2016, 11:44:16 pm »
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(Image removed from quote.)

Can someone help me with 15) ii. Im not sure about it

Which ii) did you need help with? There are two in the image you've posted
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RuiAce

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Re: Mathematics Question Thread
« Reply #454 on: October 07, 2016, 11:45:31 pm »
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(Image removed from quote.)

Can someone help me with 15) ii. Im not sure about it



Essentially, 2 is the special number here, because \(y=|2x+3|\) has gradient either 2 or -2. (Which depends on if \( x < -\frac32\) or if \( x >\frac32\), but that's not too important.)

(Note: The critical point here is basically the corner of the absolute value function.)

BOSTES solutions has a diagram.
GeoGebra simulation

Edit: A remark for case 3 - the value of \( m = -\frac23\) was computed by essentially plugging the points \( (0,1) \) and \( \left( \frac32, 0\right) \) into the usual gradient formula \( m = \frac{y_2-y_1}{x_2-x_1} \)
Which ii) did you need help with? There are two in the image you've posted
I just noticed that lol
« Last Edit: October 20, 2018, 08:07:05 pm by RuiAce »

onepunchboy

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Re: Mathematics Question Thread
« Reply #455 on: October 08, 2016, 12:11:04 am »
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oh yea sorry about that, it was the graphing question lol. Thanks rui this really helped

nibblez16

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Re: Mathematics Question Thread
« Reply #456 on: October 08, 2016, 02:29:42 pm »
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Hello, I am sort of having trouble with geometry, for similar triangles etc. How many proofs do we need for each?? ???

RuiAce

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Re: Mathematics Question Thread
« Reply #457 on: October 08, 2016, 02:32:39 pm »
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Hello, I am sort of having trouble with geometry, for similar triangles etc. How many proofs do we need for each?? ???
What do you mean by "each"? You only prove two triangles are similar at a time, not three or four at a time.

Instead, there are three tests that you need to know:
- Equiangular: Two angles in both triangles are equal
- All three sides in proprotion
- Two sides in proportion, included angle equal

(Note: There is a similar one for RHS but it is not needed)

The similarity tests can be matched up with a congruence test
Equiangular VS AAS
3 sides in prop VS SSS
2 sides in prop + inc. angle VS SAS

nibblez16

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Re: Mathematics Question Thread
« Reply #458 on: October 08, 2016, 02:36:31 pm »
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What do you mean by "each"? You only prove two triangles are similar at a time, not three or four at a time.

Instead, there are three tests that you need to know:
- Equiangular: Two angles in both triangles are equal
- All three sides in proprotion
- Two sides in proportion, included angle equal

(Note: There is a similar one for RHS but it is not needed)

The similarity tests can be matched up with a congruence test
Equiangular VS AAS
3 sides in prop VS SSS
2 sides in prop + inc. angle VS SAS

Okay Thanks! What I meant by 'how many proofs for each' was similar triangles, congruent triangles, alternate etc :)

RuiAce

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Re: Mathematics Question Thread
« Reply #459 on: October 08, 2016, 02:40:26 pm »
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Okay Thanks! What I meant by 'how many proofs for each' was similar triangles, congruent triangles, alternate etc :)
These can be found in any textbook. They stem down from properties of the geometric figure we're interested in.


Parallel lines have corresponding angles equal, alternate angles equal and cointerior angles corresponding,
Hence, if one of the following are true:
1. If alternate angles equal
2. If corresponding angles equal
3. If cointerior angles add to 180deg

Then they are parallel


Congruent triangles look the exact same, so they must have the exact same sides and angles.
Therefore
1. SSS works because you just showed all 3 sides match up
2. SAS works because imagine you have two lines equal in size. Join them together. The only thing you can change is the angle. If you fix that angle, you're stuck.
3. AAS works because imagine you have two angles. If two angles are equal, the third is equal because a triangle only has three angles. So what can you do? Make the triangle larger or smaller. If you fix a side, you end up fixing all three sides.
4. RHS - a special case, and only works because right angled triangles are nice

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Re: Mathematics Question Thread
« Reply #460 on: October 08, 2016, 07:43:42 pm »
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Hey Mathematicians,

Do any of you have any tips (besides practice as it doesn't seem to work) on doing geometry-related questions such as Question 10, B from the 2006 HSC exam (http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2006exams/pdf_doc/maths_06.pdf)?

I often struggle to see the connections between what has been given and what is being asked.

Much appreciated. :P

RuiAce

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Re: Mathematics Question Thread
« Reply #461 on: October 08, 2016, 08:37:44 pm »
+1
Hey Mathematicians,

Do any of you have any tips (besides practice as it doesn't seem to work) on doing geometry-related questions such as Question 10, B from the 2006 HSC exam (http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2006exams/pdf_doc/maths_06.pdf)?

I often struggle to see the connections between what has been given and what is being asked.

Much appreciated. :P





____________________________________________




____________________________________________



I will leave you to do the rest of the question. Answers may be found here.
« Last Edit: October 08, 2016, 08:41:25 pm by RuiAce »

jamonwindeyer

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Re: Mathematics Question Thread
« Reply #462 on: October 08, 2016, 11:40:46 pm »
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Hey Mathematicians,

Do any of you have any tips (besides practice as it doesn't seem to work) on doing geometry-related questions such as Question 10, B from the 2006 HSC exam (http://www.boardofstudies.nsw.edu.au/hsc_exams/hsc2006exams/pdf_doc/maths_06.pdf)?

I often struggle to see the connections between what has been given and what is being asked.

Much appreciated. :P

To add to Rui's answer, here are a few of my tips for Geometry questions:

- Leave them until last. So this is more of a general thing, but if you struggle with a question type you need to leave it until last. Get the easy marks first!
- Use some scrap paper or a doodling box or something to write everything you know, and everything you can find out about the situation. Don't try and find the solution, try and find everything. See if any of this helps you spot a solution.
- Work backwards! If you need to prove a result, see if you can reverse engineer it to figure out what path you would need to take. If you need similarity, what angles do you need? What do you need to get those angles? Can you get that info?
- When in doubt, assign pro numerals! It can help make the problem more logical/algebraic :) :)

And practice, because I have to say it ;)

Fadwa9

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Re: Mathematics Question Thread
« Reply #463 on: October 09, 2016, 10:21:01 pm »
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Hi,
Can you please explain how the the solution to question 14 (d) is obtained and how exactly the graph is interpreted [2013 HSC] http://boardofstudies.nsw.edu.au/hsc_exams/2013/pdf_doc/2013-hsc-maths.pdf
« Last Edit: October 09, 2016, 10:23:24 pm by Fadwa9 »

RuiAce

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Re: Mathematics Question Thread
« Reply #464 on: October 09, 2016, 10:38:11 pm »
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Hi,
Can you please explain how the the solution to question 14 (d) is obtained and how exactly the graph is interpreted [2013 HSC] http://boardofstudies.nsw.edu.au/hsc_exams/2013/pdf_doc/2013-hsc-maths.pdf



Material added later on



having obtained the \( -(a-3) \) by again using the formula for the area of a rectangle.

« Last Edit: March 29, 2018, 03:42:33 pm by RuiAce »