# Ib Math Sl Formula Booklet

Mathematics SL formula booklet

For use during the course and in the examinations First examinations 2014

Published March 2012 © International Baccalaureate Organization 2012

Mathematical studies SL: Formula booklet

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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

2 3

3 4 4 5 5 6

Mathematics SL formula booklet

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Formulae

Prior learning

Area of a parallelogram Area of a triangle

A= b × h

= A

1 (b × h) 2

1 ( a + b) h 2

Area of a trapezium

= A

Area of a circle Circumference of a circle Volume of a pyramid

A = πr 2

C = 2πr

= V

1 (area of base × vertical height) 3

Volume of a cuboid (rectangular prism) Volume of a cylinder Area of the curved surface of a cylinder Volume of a sphere

V =l × w × h

V = πr 2 h

A= 2πrh

V=

4 3 πr 3

Volume of a cone

V=

d=

1 2 πr h 3

( x1 − x2 ) 2 + ( y1 − y2 ) 2 + ( z1 − z2 ) 2

Distance between two points ( x1 , y1 , z1 ) and ( x2 , y2 , z2 ) Coordinates of the midpoint of a line segment with endpoints ( x1 , y1 , z1 ) and ( x2 , y2 , z2 )

x1 + x2 y1 + y2 z1 + z2 , , 2 2 2

Mathematics SL formula booklet

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Topics

Topic 1—Algebra

1.1 The nth term of an arithmetic sequence The sum of n terms of an arithmetic sequence The nth term of a geometric sequence un = u1 + (n − 1)d

S n=

n n (2u1 + (n − 1)d ) = (u1 + un ) 2 2

un = u1r n −1

The sum of n terms of a u1 (r n − 1) u (1 − r n ) , r ≠1 = = 1 Sn finite geometric sequence r −1 1− r The sum of an infinite geometric sequence 1.2 Exponents and logarithms Laws of logarithms S∞ = u1 , r 0

− cos ∫ sin x dx = x + C = ∫ cos x dx sin x + C

∫e

6.5 Area under a curve between x = a and x = b

x

d= e x + C x

b

A = ∫ y dx

a

b Volume of revolution V = ∫ πy 2 dx a about the x-axis from x = a to...

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