



Study with the several resources on Docsity
Earn points by helping other students or get them with a premium plan
Prepare for your exams
Study with the several resources on Docsity
Earn points to download
Earn points by helping other students or get them with a premium plan
Community
Ask the community for help and clear up your study doubts
Discover the best universities in your country according to Docsity users
Free resources
Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors
Topic 5 describe about statistics and probability in given mean the set of data, probability of an event, conditional probability, binomial distribution, mean and variance.
Typology: Study notes
1 / 7
This page cannot be seen from the preview
Don't miss anything!
© International Baccalaureate Organization 2012 5045
For use during the course and in the examinations
First examinations 2014
Edited in 2015 (version 2)
Diploma Programme
Topic 1—Algebra
1. The nth term of an
arithmetic sequence
1
n
u u n d
The sum of n terms of an
arithmetic sequence
1 1
n n
n n
S u n d u u
The nth term of a
geometric sequence
1
1
n
n
u u r
The sum of n terms of a
finite geometric sequence
1 1
n n
n
u r u r
r r
, rz 1
The sum of an infinite
geometric sequence
1
u
r
f
, r 1
1.
Exponents and logarithms log
x
a
a b x b
Laws of logarithms log log log
c c c
a b ab
log log log
c c c
a
a b
b
log log
r
c c
a r a
Change of base
log
log
log
c
b
c
a
a
b
1.
Binomial coefficient
n n
r r n r
Binomial theorem
1
n n n n r r n
n n
a b a a b a b b
r
Topic 2—Functions and equations
2. 4 Axis of symmetry of graph
of a quadratic function
2
axis of symmetry
b
f x ax bx c x
a
2. Relationships between
logarithmic and
exponential functions
ln
e
x x a
a
log
log
a
x x
a
a x a
2.7 Solutions of a quadratic
equation
2
2
b b ac
ax bx c x a
a
r
z
Discriminant
2
' b 4 ac
Topic 3—Circular functions and trigonometry
3.1 Length of an arc
Area of a sector
2
3. 2
Trigonometric identity
sin
tan
cos
3.
Pythagorean identity
2 2
Double angle formulae
2 2 2 2
c so 2 T cos T sin T 2cos T 1 1 2 sinT
3.
Cosine rule
2 2 2
c a b 2 ab cosC;
2 2 2
cos
a b c
ab
Sine rule
sin sin sin
a b c
Area of a triangle
sin
A ab C
Topic 6—Calculus
6.
Derivative of f ( )x
0
d ( ) ( )
( ) ( ) lim
d
h
y f x h f x
y f x f x
x h
o
c
6.
Derivative of
n
x
1
n n
f x x f x nx
c
Derivative of sin x f ( )x sin x f c( )x cosx
Derivative of cos x
f ( )x cos x f ( )x sinx
c
Derivative of tan x
2
( ) tan ( )
cos
f x x f x
x
c
Derivative of e
x
( ) e ( ) e
x x
f x f x
c
Derivative of ln x
f ( )x ln x f ( )x
x
c
Chain rule y g u( ) ,
d d d
d d d
y y u
u f x
x u x
u
Product rule
d d d
d d d
y v u
y uv u v
x x x
Quotient rule
2
d d
d
d d
d
u v
v u
u y
x x
y
v x v
6. 4 Standard integrals
1
d , 1
n
n
x
x x C n
n
z
³
d x ln x C , x 0
x
³
sin x d x cosx C
³
cos x d x sinx C
³
e d e
³
x x
x C
6. 5 Area under a curve
between x = a and x = b d
b
a
A y x
³
Volume of revolution
about the x-axis from x = a
to x = b
2
ʌ G
b
a
V y x
³
6. Total distance travelled
from
1
2
distance
2
1
( ) d
t
t
v t t
³