© International Baccalaureate Organization 2012 5045
Mathematics SL formula booklet
For use during the course and in the examinations
First examinations 2014
Edited in 2015 (version 2)
Diploma Programme
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Statistics and probability formula sheet, Study notes of Statistics
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© International Baccalaureate Organization 2012 5045
Mathematics SL formula booklet
For use during the course and in the examinations
First examinations 2014
Edited in 2015 (version 2)
Diploma Programme
Contents
- Prior learning
- Topics
- Topic 1 —Algebra
- Topic 2—Functions and equations
- Topic 3—Circular functions and trigonometry
- Topic 4—Vectors
- Topic 5—Statistics and probability
- Topic 6—Calculus
Topics
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
S
r r
, rz 1
The sum of an infinite
geometric sequence
1
u
S
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
l Tr
Area of a sector
2
A Tr
3. 2
Trigonometric identity
sin
tan
cos
T
T
T
3.
Pythagorean identity
2 2
cos T sin T 1
Double angle formulae
sin 2 T 2sinT cosT
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
C
ab
Sine rule
sin sin sin
a b c
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
t to
2
t
distance
2
1
( ) d
t
t
v t t
³