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March 28, 2024, 11:14:28 pm

Author Topic: 3U Maths Question Thread  (Read 1230228 times)  Share 

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imtrying

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Re: 3U Maths Question Thread
« Reply #600 on: August 19, 2016, 09:01:45 pm »
0
Hey! I need a hand with this binomial theorem question (its 11f from the 2012 Ext1 HSC:
I have done part i) with no issues, the answer is -1760, its just part ii) I'm really stuck on.
Thanks, this website is saving my HSC :)
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jakesilove

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Re: 3U Maths Question Thread
« Reply #601 on: August 19, 2016, 09:23:30 pm »
+2
Hey! I need a hand with this binomial theorem question (its 11f from the 2012 Ext1 HSC:
I have done part i) with no issues, the answer is -1760, its just part ii) I'm really stuck on.
Thanks, this website is saving my HSC :)

Hey! I'm glad you're finding Atar Notes useful! I certainly wish I had it in my HSC.

For a question like this, you sort of just brute force your way through until something nice pops out. See my working below!


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imtrying

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Re: 3U Maths Question Thread
« Reply #602 on: August 19, 2016, 09:28:33 pm »
+1
Thank you!
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conic curve

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Re: 3U Maths Question Thread
« Reply #603 on: August 20, 2016, 09:46:42 pm »
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At this point, you need to read the textbook and make sure you understand what inverse sine is.

I'm sorry to say this, but this is because your answer is wrong for a foundation level question.

(In particular, the domain)


Also, the derivative is also in the textbook

I got it now

Anyways the question was let f(x)=sin^-1 x

Following up on that question, the questions were

c. Is f'(x) undefined at x=1 and x=-1. Deduce the tangents to the curve at these points
d. Show that the line y=x is a tangent to the curve y=f(x) at (0,0)

Could someone here please give me hints

Thanks

RuiAce

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Re: 3U Maths Question Thread
« Reply #604 on: August 20, 2016, 09:50:40 pm »
+1
I got it now

Anyways the question was let f(x)=sin^-1 x

Following up on that question, the questions were

c. Is f'(x) undefined at x=1 and x=-1. Deduce the tangents to the curve at these points
d. Show that the line y=x is a tangent to the curve y=f(x) at (0,0)

Could someone here please give me hints

Thanks
Two ways to analyse c), both of which lead to the answer "no".



d) is just your ordinary 2U find the equation of the tangent to y=... at (point, point) just with sine inverse

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Re: 3U Maths Question Thread
« Reply #605 on: August 21, 2016, 12:23:12 am »
+1

RuiAce

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Re: 3U Maths Question Thread
« Reply #606 on: August 21, 2016, 02:46:36 pm »
+1
Lol'ed ;D
The ∞th commandment:

Thou shall not divide by zero.

anotherworld2b

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Re: 3U Maths Question Thread
« Reply #607 on: August 21, 2016, 11:42:41 pm »
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I was wondering is there a way to always be able to graph an exponential function and finding the exponential equation from the graph?

I am really struggling with exponential graphs in terms of drawing them gievn the equation and being unable to find the equation given the graph. The tranformations that can be possible are also being quite an obstacle for me. Please help  :'(

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Re: 3U Maths Question Thread
« Reply #608 on: August 22, 2016, 09:52:51 am »
+1
I was wondering is there a way to always be able to graph an exponential function and finding the exponential equation from the graph?

I am really struggling with exponential graphs in terms of drawing them gievn the equation and being unable to find the equation given the graph. The tranformations that can be possible are also being quite an obstacle for me. Please help  :'(

Perhaps a set of rough rules will help!!

Consider the general form of an exponential function:



(Note that it doesn't have to be the with an 'e', any number works fine, though if you have a negative number there you'll need to adjust this a little the base won't be - this requires complex analysis)

- Higher values of A stretches the curve in the vertical direction. Really, the noticeable impact is that A is the y-intercept, but only if there is no constant C added to the exponent
- Higher values of B means the exponent will increase at a faster rate, the right hand side of the exponential will increase its slope noticeably
- C causes a horizontal shift to the left (for positive values) or right (for negative values)
- D causes a vertical shift upwards (positive values) or downwards (negative values)

These rules might seem very wish-washy, and that's because they are, they should only be a rough guide. You aim should be to gradually develop an intuition for what the different parts of the exponential do. Have a play with sketching different functions on Desmos or something similar, and try to notice the patterns in what you see, that is the best way to develop that intuition ;D
« Last Edit: August 22, 2016, 10:20:30 am by RuiAce »

anotherworld2b

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Re: 3U Maths Question Thread
« Reply #609 on: August 22, 2016, 09:39:45 pm »
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Thank you
I was also wondering how would you evalulate it as a single power and evaulate. Also does evaluate simply mean solve?

Perhaps a set of rough rules will help!!

Consider the general form of an exponential function:



(Note that it doesn't have to be the with an 'e', any number works fine, though if you have a negative number there you'll need to adjust this a little the base won't be - this requires complex analysis)

- Higher values of A stretches the curve in the vertical direction. Really, the noticeable impact is that A is the y-intercept, but only if there is no constant C added to the exponent
- Higher values of B means the exponent will increase at a faster rate, the right hand side of the exponential will increase its slope noticeably
- C causes a horizontal shift to the left (for positive values) or right (for negative values)
- D causes a vertical shift upwards (positive values) or downwards (negative values)

These rules might seem very wish-washy, and that's because they are, they should only be a rough guide. You aim should be to gradually develop an intuition for what the different parts of the exponential do. Have a play with sketching different functions on Desmos or something similar, and try to notice the patterns in what you see, that is the best way to develop that intuition ;D

RuiAce

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Re: 3U Maths Question Thread
« Reply #610 on: August 22, 2016, 09:45:55 pm »
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Thank you
I was also wondering how would you evalulate it as a single power and evaulate. Also does evaluate simply mean solve?


Note: This question belongs to the 2U section as nothing more is demanded on top of the index laws.
« Last Edit: August 22, 2016, 09:47:37 pm by RuiAce »

anotherworld2b

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Re: 3U Maths Question Thread
« Reply #611 on: August 22, 2016, 10:01:57 pm »
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Thank you rui ace
I also tried these questions but i am not getting the right answers. I got 2+25 for a

jakesilove

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Re: 3U Maths Question Thread
« Reply #612 on: August 22, 2016, 10:08:26 pm »
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Thank you rui ace
I also tried these questions but i am not getting the right answers. I got 2+25 for a

For a) you should get 2 + 125. You've correctly square rooted the 4, but after you square root the 25 (to get 5) you need to put it to the power of 3 (resulting in 125).

For b) you can use indices laws to multiply the indices in brackets, then convert to 9 to 3^2. Then, you can add powers when multiplying with the same base
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anotherworld2b

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Re: 3U Maths Question Thread
« Reply #613 on: August 22, 2016, 10:16:11 pm »
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For the answer for a the sheet says its 2/125? Im still a bit confused for b i got (5^2 -3^4)÷ 3^1
For a) you should get 2 + 125. You've correctly square rooted the 4, but after you square root the 25 (to get 5) you need to put it to the power of 3 (resulting in 125).

For b) you can use indices laws to multiply the indices in brackets, then convert to 9 to 3^2. Then, you can add powers when multiplying with the same base

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Re: 3U Maths Question Thread
« Reply #614 on: August 22, 2016, 10:37:20 pm »
+1
For the answer for a the sheet says its 2/125? Im still a bit confused for b i got (5^2 -3^4)÷ 3^1

The answer is definitely wrong there, unless the question is ;D

For B, you are close! Just that 3^1 should only be dividing the 6^4, the 5^2 is unaffected (remember your order of operations) ;D