IB maths - Logarithmic equations

Logarithmic equations
How can we solve the following logarithmic equation:



The answer is here
http://www.ibmaths4u.com/viewtopic.php?f=3&t=411

IB mathematics HL - Binomial Theorem

IB mathematics HL - Binomial Theorem

How can we find the coefficient of of the expansion of ?

The answer is here

http://www.ibmaths4u.com/viewtopic.php?f=3&t=412

IB mathematics Higher Level - Mathematical Induction

IB mathematics Higher Level - Mathematical Induction

How can we prove by induction that is divisible by for every natural number with ?

The answer is here

http://www.ibmaths4u.com/viewtopic.php?f=3&t=413

IB Maths HL - Mathematical Induction Series

IB Maths HL - Mathematical Induction Series

How can we prove by induction that for every natural number with ?

The answer is here

http://www.ibmaths4u.com/viewtopic.php?f=3&t=414

IB maths HL - Mathematical Induction inequality

IB maths HL - Mathematical Induction inequality

How can we prove by induction that for every natural number with ?

The answer is here

http://www.ibmaths4u.com/viewtopic.php?f=3&t=415

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