Graph of the Reciprocal of a Function

Reciprocal of a Function

The following guidelines are useful in order to sketch the reciprocal of a function given the graph of the original function:


Where is positive or negative then is also positive or negative respectively.

Where has zero(s) then the reciprocal function has vertical asymptote(s) and vice versa.

Where has a horizontal asymptote at y=c then the reciprocal function has also horizontal asymptote at .

Where the original function is increasing then the reciprocal function is decreasing.

Where the original function is decreasing then the reciprocal function is increasing.

If the original function has a maximum at then the reciprocal function has a minimum at .

If the original function has a minimum at then the reciprocal function has a maximum at .

If the original function has a point of inflexion at then the reciprocal function has also a point of inflexion at .

http://www.ibmaths4u.com/viewtopic.php?f=3&t=408

IB Maths HL, SL, Studies Past Papers

One way is to search on Google the following phrase:
“M12/5/MATHL/HP1/ENG/TZ1/XX” in order to find for example the past paper 1 of May 2012 in English of Time Zone 1.
If you want additionally the corresponding markscheme of this paper then you will find it by searching on Google the following phrase
“M12/5/MATHL/HP1/ENG/TZ1/XX/M”

Some of the Google results correspond to official IBO website in order to purchase this past paper which is actually the only legal way and is strongly recommended from this community.

Another way is going directly to the official website of IBO http://www.ibo.org or https://store.ibo.org/diploma-programme ... cheme-pack and search there for the specific past paper.



A list of recent past papers for IB mathematics HL

M11/5/MATHL/HP1/ENG/TZ1/XX in order to find for the past paper 1 of May 2011 in English of Time Zone 1
M11/5/MATHL/HP2/ENG/TZ1/XX in order to find for the past paper 2 of May 2011 in English of Time Zone 1
M11/5/MATHL/HP1/ENG/TZ2/XX in order to find for the past paper 1 of May 2011 in English of Time Zone 2
M11/5/MATHL/HP2/ENG/TZ2/XX in order to find for the past paper 2 of May 2011 in English of Time Zone 2
N11/5/MATHL/HP1/ENG/TZ0/XX in order to find for the past paper 1 of November 2011 in English
N11/5/MATHL/HP2/ENG/TZ0/XX in order to find for the past paper 2 of November 2011 in English
M12/5/MATHL/HP1/ENG/TZ1/XX in order to find for the past paper 1 of May 2012 in English of Time Zone 1
M12/5/MATHL/HP2/ENG/TZ1/XX in order to find for the past paper 2 of May 2012 in English of Time Zone 1
M12/5/MATHL/HP1/ENG/TZ2/XX in order to find for the past paper 1 of May 2012 in English of Time Zone 2
M12/5/MATHL/HP2/ENG/TZ2/XX in order to find for the past paper 2 of May 2012 in English of Time Zone 2
N12/5/MATHL/HP1/ENG/TZ0/XX in order to find for the past paper 1 of November 2012 in English
N12/5/MATHL/HP2/ENG/TZ0/XX in order to find for the past paper 2 of November 2012 in English
M13/5/MATHL/HP1/ENG/TZ1/XX in order to find for the past paper 1 of May 2013 in English of Time Zone 1
M13/5/MATHL/HP2/ENG/TZ1/XX in order to find for the past paper 2 of May 2013 in English of Time Zone 1
M13/5/MATHL/HP1/ENG/TZ2/XX in order to find for the past paper 1 of May 2013 in English of Time Zone 2
M13/5/MATHL/HP2/ENG/TZ2/XX in order to find for the past paper 2 of May 2013 in English of Time Zone 2
N13/5/MATHL/HP1/ENG/TZ0/XX in order to find for the past paper 1 of November 2013 in English
N13/5/MATHL/HP2/ENG/TZ0/XX in order to find for the past paper 2 of November 2013 in English

and the corresponding markschemes

M11/5/MATHL/HP1/ENG/TZ1/XX/M in order to find the markscheme of past paper 1 of May 2011 in English of Time Zone 1
M11/5/MATHL/HP2/ENG/TZ1/XX/M in order to find the markscheme of past paper 2 of May 2011 in English of Time Zone 1
M11/5/MATHL/HP1/ENG/TZ2/XX/M in order to find the markscheme of past paper 1 of May 2011 in English of Time Zone 2
M11/5/MATHL/HP2/ENG/TZ2/XX/M in order to find the markscheme of past paper 2 of May 2011 in English of Time Zone 2
N11/5/MATHL/HP1/ENG/TZ0/XX/M in order to find the markscheme of past paper 1 of November 2011 in English
N11/5/MATHL/HP2/ENG/TZ0/XX/M in order to find the markscheme of past paper 2 of November 2011 in English
M12/5/MATHL/HP1/ENG/TZ1/XX/M in order to find the markscheme of past paper 1 of May 2012 in English of Time Zone 1
M12/5/MATHL/HP2/ENG/TZ1/XX/M in order to find the markscheme of past paper 2 of May 2012 in English of Time Zone 1
M12/5/MATHL/HP1/ENG/TZ2/XX/M in order to find the markscheme of past paper 1 of May 2012 in English of Time Zone 2
M12/5/MATHL/HP2/ENG/TZ2/XX/M in order to find the markscheme of past paper 2 of May 2012 in English of Time Zone 2
N12/5/MATHL/HP1/ENG/TZ0/XX/M in order to find the markscheme of past paper 1 of November 2012 in English
N12/5/MATHL/HP2/ENG/TZ0/XX/M in order to find the markscheme of past paper 2 of November 2012 in English
M13/5/MATHL/HP1/ENG/TZ1/XX/M in order to find the markscheme of past paper 1 of May 2013 in English of Time Zone 1
M13/5/MATHL/HP2/ENG/TZ1/XX/M in order to find the markscheme of past paper 2 of May 2013 in English of Time Zone 1
M13/5/MATHL/HP1/ENG/TZ2/XX/M in order to find the markscheme of past paper 1 of May 2013 in English of Time Zone 2
M13/5/MATHL/HP2/ENG/TZ2/XX/M in order to find the markscheme of past paper 2 of May 2013 in English of Time Zone 2
N13/5/MATHL/HP1/ENG/TZ0/XX/M in order to find the markscheme of past paper 1 of November 2013 in English
N13/5/MATHL/HP2/ENG/TZ0/XX/M in order to find the markscheme of past paper 2 of November 2013 in English

A list of recent past papers for IB mathematics SL

M11/5/MATME/SP1/ENG/TZ1/XX in order to find for the past paper 1 of May 2011 in English of Time Zone 1
M11/5/MATME/SP2/ENG/TZ1/XX in order to find for the past paper 2 of May 2011 in English of Time Zone 1
M11/5/MATME/SP1/ENG/TZ2/XX in order to find for the past paper 1 of May 2011 in English of Time Zone 2
M11/5/MATME/SP2/ENG/TZ2/XX in order to find for the past paper 2 of May 2011 in English of Time Zone 2
N11/5/MATME/SP1/ENG/TZ0/XX in order to find for the past paper 1 of November 2011 in English
N11/5/MATME/SP2/ENG/TZ0/XX in order to find for the past paper 2 of November 2011 in English
M12/5/MATME/SP1/ENG/TZ1/XX in order to find for the past paper 1 of May 2012 in English of Time Zone 1
M12/5/MATME/SP2/ENG/TZ1/XX in order to find for the past paper 2 of May 2012 in English of Time Zone 1
M12/5/MATME/SP1/ENG/TZ2/XX in order to find for the past paper 1 of May 2012 in English of Time Zone 2
M12/5/MATME/SP2/ENG/TZ2/XX in order to find for the past paper 2 of May 2012 in English of Time Zone 2
N12/5/MATME/SP1/ENG/TZ0/XX in order to find for the past paper 1 of November 2012 in English
N12/5/MATME/SP2/ENG/TZ0/XX in order to find for the past paper 2 of November 2012 in English
M13/5/MATME/SP1/ENG/TZ1/XX in order to find for the past paper 1 of May 2013 in English of Time Zone 1
M13/5/MATME/SP2/ENG/TZ1/XX in order to find for the past paper 2 of May 2013 in English of Time Zone 1
M13/5/MATME/SP1/ENG/TZ2/XX in order to find for the past paper 1 of May 2013 in English of Time Zone 2
M13/5/MATME/SP2/ENG/TZ2/XX in order to find for the past paper 2 of May 2013 in English of Time Zone 2
N13/5/MATME/SP1/ENG/TZ0/XX in order to find for the past paper 1 of November 2013 in English
N13/5/MATME/SP2/ENG/TZ0/XX in order to find for the past paper 2 of November 2013 in English

and the corresponding markschemes

M11/5/MATME/SP1/ENG/TZ1/XX/M in order to find the markscheme of past paper 1 of May 2011 in English of Time Zone 1
M11/5/MATME/SP2/ENG/TZ1/XX/M in order to find the markscheme of past paper 2 of May 2011 in English of Time Zone 1
M11/5/MATME/SP1/ENG/TZ2/XX/M in order to find the markscheme of past paper 1 of May 2011 in English of Time Zone 2
M11/5/MATME/SP2/ENG/TZ2/XX/M in order to find the markscheme of past paper 2 of May 2011 in English of Time Zone 2
N11/5/MATME/SP1/ENG/TZ0/XX/M in order to find the markscheme of past paper 1 of November 2011 in English
N11/5/MATME/SP2/ENG/TZ0/XX/M in order to find the markscheme of past paper 2 of November 2011 in English
M12/5/MATME/SP1/ENG/TZ1/XX/M in order to find the markscheme of past paper 1 of May 2012 in English of Time Zone 1
M12/5/MATME/SP2/ENG/TZ1/XX/M in order to find the markscheme of past paper 2 of May 2012 in English of Time Zone 1
M12/5/MATME/SP1/ENG/TZ2/XX/M in order to find the markscheme of past paper 1 of May 2012 in English of Time Zone 2
M12/5/MATME/SP2/ENG/TZ2/XX/M in order to find the markscheme of past paper 2 of May 2012 in English of Time Zone 2
N12/5/MATME/SP1/ENG/TZ0/XX/M in order to find the markscheme of past paper 1 of November 2012 in English
N12/5/MATME/SP2/ENG/TZ0/XX/M in order to find the markscheme of past paper 2 of November 2012 in English
M13/5/MATME/SP1/ENG/TZ1/XX/M in order to find the markscheme of past paper 1 of May 2013 in English of Time Zone 1
M13/5/MATME/SP2/ENG/TZ1/XX/M in order to find the markscheme of past paper 2 of May 2013 in English of Time Zone 1
M13/5/MATME/SP1/ENG/TZ2/XX/M in order to find the markscheme of past paper 1 of May 2013 in English of Time Zone 2
M13/5/MATME/SP2/ENG/TZ2/XX/M in order to find the markscheme of past paper 2 of May 2013 in English of Time Zone 2
N13/5/MATME/SP1/ENG/TZ0/XX/M in order to find the markscheme of past paper 1 of November 2013 in English
N13/5/MATME/SP2/ENG/TZ0/XX/M in order to find the markscheme of past paper 2 of November 2013 in English

A list of recent past papers for IB mathematics SL Studies

M11/5/MATSD/SP1/ENG/TZ1/XX in order to find for the past paper 1 of May 2011 in English of Time Zone 1
M11/5/MATSD/SP2/ENG/TZ1/XX in order to find for the past paper 2 of May 2011 in English of Time Zone 1
M11/5/MATSD/SP1/ENG/TZ2/XX in order to find for the past paper 1 of May 2011 in English of Time Zone 2
M11/5/MATSD/SP2/ENG/TZ2/XX in order to find for the past paper 2 of May 2011 in English of Time Zone 2
N11/5/MATSD/SP1/ENG/TZ0/XX in order to find for the past paper 1 of November 2011 in English
N11/5/MATSD/SP2/ENG/TZ0/XX in order to find for the past paper 2 of November 2011 in English
M12/5/MATSD/SP1/ENG/TZ1/XX in order to find for the past paper 1 of May 2012 in English of Time Zone 1
M12/5/MATSD/SP2/ENG/TZ1/XX in order to find for the past paper 2 of May 2012 in English of Time Zone 1
M12/5/MATSD/SP1/ENG/TZ2/XX in order to find for the past paper 1 of May 2012 in English of Time Zone 2
M12/5/MATSD/SP2/ENG/TZ2/XX in order to find for the past paper 2 of May 2012 in English of Time Zone 2
N12/5/MATSD/SP1/ENG/TZ0/XX in order to find for the past paper 1 of November 2012 in English
N12/5/MATSD/SP2/ENG/TZ0/XX in order to find for the past paper 2 of November 2012 in English
M13/5/MATSD/SP1/ENG/TZ1/XX in order to find for the past paper 1 of May 2013 in English of Time Zone 1
M13/5/MATSD/SP2/ENG/TZ1/XX in order to find for the past paper 2 of May 2013 in English of Time Zone 1
M13/5/MATSD/SP1/ENG/TZ2/XX in order to find for the past paper 1 of May 2013 in English of Time Zone 2
M13/5/MATSD/SP2/ENG/TZ2/XX in order to find for the past paper 2 of May 2013 in English of Time Zone 2
N13/5/MATSD/SP1/ENG/TZ0/XX in order to find for the past paper 1 of November 2013 in English
N13/5/MATSD/SP2/ENG/TZ0/XX in order to find for the past paper 2 of November 2013 in English

and the corresponding markschemes

M11/5/MATSD/SP1/ENG/TZ1/XX/M in order to find the markscheme of past paper 1 of May 2011 in English of Time Zone 1
M11/5/MATSD/SP2/ENG/TZ1/XX/M in order to find the markscheme of past paper 2 of May 2011 in English of Time Zone 1
M11/5/MATSD/SP1/ENG/TZ2/XX/M in order to find the markscheme of past paper 1 of May 2011 in English of Time Zone 2
M11/5/MATSD/SP2/ENG/TZ2/XX/M in order to find the markscheme of past paper 2 of May 2011 in English of Time Zone 2
N11/5/MATSD/SP1/ENG/TZ0/XX/M in order to find the markscheme of past paper 1 of November 2011 in English
N11/5/MATSD/SP2/ENG/TZ0/XX/M in order to find the markscheme of past paper 2 of November 2011 in English
M12/5/MATSD/SP1/ENG/TZ1/XX/M in order to find the markscheme of past paper 1 of May 2012 in English of Time Zone 1
M12/5/MATSD/SP2/ENG/TZ1/XX/M in order to find the markscheme of past paper 2 of May 2012 in English of Time Zone 1
M12/5/MATSD/SP1/ENG/TZ2/XX/M in order to find the markscheme of past paper 1 of May 2012 in English of Time Zone 2
M12/5/MATSD/SP2/ENG/TZ2/XX/M in order to find the markscheme of past paper 2 of May 2012 in English of Time Zone 2
N12/5/MATSD/SP1/ENG/TZ0/XX/M in order to find the markscheme of past paper 1 of November 2012 in English
N12/5/MATSD/SP2/ENG/TZ0/XX/M in order to find the markscheme of past paper 2 of November 2012 in English
M13/5/MATSD/SP1/ENG/TZ1/XX/M in order to find the markscheme of past paper 1 of May 2013 in English of Time Zone 1
M13/5/MATSD/SP2/ENG/TZ1/XX/M in order to find the markscheme of past paper 2 of May 2013 in English of Time Zone 1
M13/5/MATSD/SP1/ENG/TZ2/XX/M in order to find the markscheme of past paper 1 of May 2013 in English of Time Zone 2
M13/5/MATSD/SP2/ENG/TZ2/XX/M in order to find the markscheme of past paper 2 of May 2013 in English of Time Zone 2
N13/5/MATSD/SP1/ENG/TZ0/XX/M in order to find the markscheme of past paper 1 of November 2013 in English
N13/5/MATSD/SP2/ENG/TZ0/XX/M in order to find the markscheme of past paper 2 of November 2013 in English


Hope these help!!

Hard problem on logarithms IB maths HL

How can be solved the following simultaneous equations :

(1)

(2)

The solution is here

http://www.ibmaths4u.com/viewtopic.php?f=3&t=392

IB Maths SL Normal Distribution

IB Mathematics SL Normal Distribution
Answers:

1. random variable X normally distributed with mean 25.
The shaded region between 25 and 27 represents 30% of the distribution.
a). Find P(X>27)
Answer:


b). Find the standard deviation of X
Answer:
Let the random variable X , so that



We know that

Since we don’t know the standard deviation of X, we cannot use the inverse normal. Therefore we have to transform the random variable to that of

, using the transformation

we have the following





Using GDC Casio fx-9860G SD
MAIN MENU > STAT>DIST(F5)>NORM(F1)>InvN>

Setting Tail: right
Area: 0.2
:1
:0

We find that the standardized value is 0.8416

Therefore



2. A random variable X is distributed normally with a mean of 20 and variance 9.
a). Find P(X<(or equal to)24.5)
Answer:

By GDC (Casio) menu>STAT>DIST>NORM>Ncd with Lower:-9*10^99, Upper:24.5, , and you get


b). Let P(X<(or equal to)k)=0.85
ii). Find the value of k.
Answer:

Here you have inverse normal

By GDC (Casio) menu>STAT>DIST>NORM>InvN with Tail:Left, Area:0.85, , and you get

Question and Answer can be found here

http://www.ibmaths4u.com/viewtopic.php?f=11&t=372

IB Maths Revision Notes HL, SL Studies

IB Maths Revision Notes - IB Mathematics HL, SL, Studies Revision Notes by www.IBmaths4u.com


Mathematical Induction for IB Mathematics HL
http://www.ibmaths4u.com/viewtopic.php?f=3&t=370


Trigonometry for IB Mathematics HL
http://www.ibmaths4u.com/viewtopic.php?f=3&t=370


Sequences-Series and Binomial Theorem for IB Mathematics HL
http://www.ibmaths4u.com/viewtopic.php?f=3&t=370


Exponential and Logarithmic Functions for IB Mathematics HL
http://www.ibmaths4u.com/viewtopic.php?f=3&t=370

Non-Smooth Geometry

Month: April 2013

Date: April 29--May 3

Name: Non-Smooth Geometry

Location: Institute for Pure and Applied Mathematics (IPAM), UCLA, Los Angeles, California.

Description

Many contemporary investigations in geometry lead to analytic questions on non-smooth and fractal spaces different from the usual Euclidean setting. In this workshop we intend to pursue some of these directions with an emphasis on more geometric aspects (another workshop in this program on "Analysis on Metric Spaces" has a more analytic bias). Topics will include analytic problems that arise in geometric group theory or for expanding dynamical systems, differentiability properties of Lipschitz functions, currents and isoperimetric problems on metric spaces, quasiconformal geometry of fractals, and sub-Riemannian geometry.

Information

http://www.ipam.ucla.edu/programs/iagws3/.

IB Mathematics SL – Calculus, Application of Differentiation, Kinematics

The question is :

IB Mathematics SL – Calculus, Application of Differentiation, Kinematics

Can someone explain me the basic concepts of Kinematics.

and the answer is at www.ibmaths4u.com

http://www.ibmaths4u.com/viewtopic.php?f=11&t=262

IB Maths SL– Calculus, Application of Differentiation, Kinematics

Velocity (v) measures the rate of change of displacement (s)

i.e.


Acceleration (a) measures the rate of change of velocity (v)

i.e.

When the motion of a particle happens onto the x-axis we have the following basic rules:

If the displacement (s) is positive then the particle is to the right of the origin.
If the displacement (s) is negative then the particle is to the left of the origin.
If the displacement (s) equals zero then the particle is located at the origin.


If the velocity (v) is positive then the particle is moving to the right.
If the velocity (v) is negative then the particle is moving to the left.
If the velocity (v) equals zero then the particle is at rest.


If the acceleration (a) is positive then the velocity of the particle is increasing.
If the acceleration (a) is negative then the velocity of the particle is decreasing.
If the acceleration (a) equals zero then the velocity function has a stationary point.

A very important thing about kinematics is that when both velocity and acceleration are positive or negative, then the speed of the particle is increasing.
If both the velocity and acceleration have opposite signs, then the speed of the particle is decreasing.