Ib Math Sl Formula Booklet
Diploma Programme
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
1
5045
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
1
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
2
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
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
1
5045
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
1
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
2
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