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
=