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Statistics and probability formula sheet, Study notes of Statistics

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.

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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
pf3
pf4
pf5

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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 œ 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

  Ÿ 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 

  Ÿ 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

Ÿ c

6.

Derivative of

n

x

1

n n

f x x f x nx



Ÿ c

Derivative of sin x f ( )x sin x Ÿ f c( )x cosx

Derivative of cos x

f ( )x cos x f ( )x sinx

c Ÿ 

Derivative of tan x

2

( ) tan ( )

cos

f x x f x

x

c Ÿ

Derivative of e

x

( ) e ( ) e

x x

f x f x

c Ÿ

Derivative of ln x

f ( )x ln x f ( )x

x

c Ÿ

Chain rule y g u( ) ,

d d d

d d d

y y u

u f x

x u x

Ÿ 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