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2 Unit Revising Marathon (2 Viewers)
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MrBrightside
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Re: 2 Unit Revising Marathon HSC '10
Solve: |x -5| = 3
Solve: |x -5| = 3
Re: 2 Unit Revising Marathon HSC '10
|x - 5 | =3
Part one
x-5=3
x=8
Part two
x-5=-3
x=2
Therefore x= 2, 8
Easy
|x - 5 | =3
Part one
x-5=3
x=8
Part two
x-5=-3
x=2
Therefore x= 2, 8
MrBrightside
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Re: 2 Unit Revising Marathon HSC '10
I prefer this though:
x-5 = 3
x = 8
Therefore x = 2 or x = 8
Both ways work, but I've been told that doing it the way I did it solves confusion when people do the other way.
correct, you know this question on maths online, is taught the incorrect way. I saw it today and was like woah that's the wrong way, and its up there on maths online. They changed +- on the end number. Like you did.
I prefer this though:
x-5 = 3
OR
-(x-5) = 3
x = 8
OR
-x + 5 = 3
-x = -2
x = 2
-x = -2
x = 2
Therefore x = 2 or x = 8
Both ways work, but I've been told that doing it the way I did it solves confusion when people do the other way.
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MrBrightside
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Re: 2 Unit Revising Marathon HSC '10
Find the integral of sec^2(5x) dx
Find the integral of sec^2(5x) dx
Re: 2 Unit Revising Marathon HSC '10
| x - 5 |
sub -2 in
| -2 - 5 |
= |-7 |
=7
and 7 isn't equal to 3
Looking at your answer again, i believe you just made a typo
When using absolute values x is always greater than zero otherwise you will get
| x - 5 |
sub -2 in
| -2 - 5 |
= |-7 |
=7
and 7 isn't equal to 3
Looking at your answer again, i believe you just made a typo
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MrBrightside
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Re: 2 Unit Revising Marathon HSC '10
= 1/5 tan 5x
using the standard integral sheet:
= 1/5 tan 5x
Re: 2 Unit Revising Marathon HSC '10
Maths isn't easy to type on computers.
New one
A function ƒ(x) is defined by ƒ(x) =2x2(3– x).
(i)
Find the coordinates of the turning points of y =ƒ(x) and determine their nature.
(ii)
Find the coordinates of the point of inflexion.
(iii) Hence sketch the graph of y =ƒ(x), showing the turning points, the point of inflexion and the points where the curve meets the x-axis.
(iv) What is the minimum value of ƒ(x) for –1 ≤x ≤4?
haha it is fine
Maths isn't easy to type on computers.
New one
A function ƒ(x) is defined by ƒ(x) =2x2(3– x).
(i)
Find the coordinates of the turning points of y =ƒ(x) and determine their nature.
(ii)
Find the coordinates of the point of inflexion.
(iii) Hence sketch the graph of y =ƒ(x), showing the turning points, the point of inflexion and the points where the curve meets the x-axis.
(iv) What is the minimum value of ƒ(x) for –1 ≤x ≤4?
MrBrightside
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MrBrightside
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Re: 2 Unit Revising Marathon HSC '10
correct, but you forgot to + C as it is indefinite.
SpiralFlex
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Re: 2 Unit Revising Marathon HSC '10
Calculate the exact volume formed by the curve
bounded by the lines 
and 
.
Calculate the exact volume formed by the curve
MrBrightside
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Re: 2 Unit Revising Marathon HSC '10
Do you multiply that to become 4x? Or do you just treat it as u = 2x , v = 2(3-x)
haha it is fine
Maths isn't easy to type on computers.
New one
A function ƒ(x) is defined by ƒ(x) =2x2(3– x).
(i)
Find the coordinates of the turning points of y =ƒ(x) and determine their nature.
(ii)
Find the coordinates of the point of inflexion.
(iii) Hence sketch the graph of y =ƒ(x), showing the turning points, the point of inflexion and the points where the curve meets the x-axis.
(iv) What is the minimum value of ƒ(x) for –1 ≤x ≤4?
Do you multiply that to become 4x? Or do you just treat it as u = 2x , v = 2(3-x)
Last edited:
SpiralFlex
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Re: 2 Unit Revising Marathon HSC '10
=2x^2(3-x))
i.=12x-6x^2)
For stationary points,=0)
Hence,
=0)
When
When
=12(1-x))
At>0)
Hence)
is a minimum turning point.
At<0)
Hence,)
is a maximum turning point.
ii. For possible points of inflexion,=0)
=0)
When
As^-, f'(x)>0)
As^+, f'(x)<0)
Hence a change of concavity has occurred, so)
is a point of inflexion.
iii. Cannot draw as we are online.
iv. When
When
Minimum value is
.
This one is quite interesting for 2U students,
i.
For stationary points,
Hence,
When
When
At
Hence
At
Hence,
ii. For possible points of inflexion,
When
As
As
Hence a change of concavity has occurred, so
iii. Cannot draw as we are online.
iv. When
When
Minimum value is
This one is quite interesting for 2U students,
Calculate the exact volume formed by the curve
Last edited:
SpiralFlex
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Re: 2 Unit Revising Marathon HSC '10
Other than that I just know most of Trig, intergration, differeniation and probability
My school is only up to functions! (We have done barely anything)
Other than that I just know most of Trig, intergration, differeniation and probability