math formula reference

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bDIPLOMA PROGRAMME

MATHEMATICS SLINFORMATION BOOKLET

For use by teachers and students, during the course and in the examinations

First examinations 2006

International Baccalaureate Organization

Buenos Aires Cardiff Geneva New York Singapore


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Diploma Programme

Mathematics SL

Information Booklet

International Baccalaureate Organization, Geneva, CH-1218, Switzerland

First published in November 2004

by the International Baccalaureate Organization

Peterson House, Malthouse Avenue, Cardiff Gate

Cardiff, Wales GB CF23 8GL

UNITED KINGDOM

Tel: + 44 29 2054 7777Fax: + 44 29 2054 7778

Web site: www.ibo.org

International Baccalaureate Organization 2004

The IBO is grateful for permission to reproduce and/or translate any copyright

material used in this publication. Acknowledgments are included, where

appropriate, and, if notified, the IBO will be pleased to rectify any errors or

omissions at the earliest opportunity.

IBO merchandise and publications in its official and working languages can be

purchased through the online catalogue at www.ibo.org, found by selecting

Publications from the shortcuts box. General ordering queries should bedirected to the sales department in Cardiff.

Tel: +44 29 2054 7746

Fax: +44 29 2054 7779

E-mail: [email protected]

Printed in the United Kingdom by Antony Rowe Ltd, Chippenham, Wiltshire.

565b


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CONTENTS

Formulae 1

Presumed knowledge 1

Topic 1Algebra 2

Topic 2Functions and equations 2

Topic 3Circular functions and trigonometry 3

Topic 4Matrices 3

Topic 5Vectors 4

Topic 6Statistics and probability 5

Topic 7Calculus 6

Area under the standard normal curve (topic 6.11) 7

Inverse normal probabilities (topic 6.11) 8


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International Baccalaureate Organization 2004 1

Formulae

Presumed knowledge

Area of a parallelogram ( )= A b h , where bis the base, his the height

Area of a triangle1

( )2

= A b h , where bis the base, his the height

Area of a trapezium1

( )2

= +A a b h , where aand bare the parallel sides, his the height

Area of a circle2

= A r , where ris the radius

Circumference of a circle 2= C r , where ris the radius

Volume of a pyramid1

(area of base vertical height)3

= V

Volume of a cuboid = V l w h , where lis the length, wis the width, his the height

Volume of a cylinder 2= V r h , where ris the radius, his the height

Area of the curved surface ofa cylinder

2= A rh , where ris the radius, his the height

Volume of a sphere34

3

= V r , where ris the radius

Volume of a cone21

3= V r h , where ris the radius, his the height

Distance between two

points 1 1( , )y and 2 2( , )x y

2 2

1 2 1 2( ) ( )= + d x x y y

Coordinates of the midpoint ofa line segment with endpoints

1 1( , )y and 2 2( , )y

1 2 1 2,2 2

+ +

x x y y


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2 International Baccalaureate Organization 2004

Topic 1Algebra

The nthterm of an

arithmetic sequence1 ( 1)= + nu u n d

The sum of nterms ofan arithmetic sequence

1 1(2 ( 1) ) ( )2 2

= + = +n nn nS u n d u u

The nthterm of a

geometric sequence

1

1

=

n

nu u r

The sum of nterms of afinite geometric sequence

1 1( 1) (1 )

1 1

= =

n n

n

u r u r S

r r, 1r

1.1

The sum of an infinitegeometric sequence

1 , 11

=

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