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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
5045
1
Contents
Prior learning
2
Topics
3
Topic 1—Algebra
3
Topic 2—Functions and equations
4
Topic 3—Circular functions and trigonometry
4
Topic 4—Vectors
5
Topic 5—Statistics and probability
5
Topic 6—Calculus
6
Mathematics SL formula booklet
1
Formulae
Prior learning
A= b × h
Area of a parallelogram
Area of a triangle
=
A
=
A
Area of a trapezium
1
(b × h)
2
1
( a + b) h
2
Area of a circle
A = πr 2
Circumference of a circle
C = 2πr
Volume of a pyramid
=
V
1
(area of base × vertical height)
3
Volume of a cuboid (rectangular prism)
V =l × w × h
Volume of a cylinder
V = πr 2 h
Area of the curved surface of a cylinder
A= 2πrh
Volume of a sphere
Volume of a cone
V=
4 3
πr
3
V=
1 2
πr h
3
Distance between two points ( x1 , y1 , z1 ) and
( x2 , y2 , z2 )
d=
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
( x1 − x2 ) 2 + ( y1 − y2 ) 2 + ( z1 − z2 ) 2
2
Topics
Topic 1—Algebra
The nth term of an
arithmetic sequence
un = u1 + (n − 1)d
The sum of n terms of an
arithmetic sequence
S n=
The nth term of a
geometric sequence
1
...
2
S∞ =
log c a + log c b =
log c ab
a
log c a − log c b =
log c
b
log c a r = r log c a
Change of base
u1
, r <1
1− r
log b a =
x = log a b
log c a
log c b
Binomial coefficient
n
n!
=
r r ! (n − r )!
Binomial theorem
1
...
4
Axis of symmetry of
graph of a quadratic
function
b
f ( x) = 2 + bx + c ⇒ axis of symmetry x =
ax
−
2a
2
...
7
Solutions of a quadratic
equation
ax 2 + bx + c= 0 ⇒
Discriminant
∆ b 2 − 4ac
=
x=
−b ± b 2 − 4ac
, a≠0
2a
Topic 3—Circular functions and trigonometry
Length of an arc
l =θr
Area of a sector
3
...
2
Trigonometric identity
3
...
6
Cosine rule
c 2 = a 2 + b 2 − 2ab cos C ; cos C =
Sine rule
a
b
c
= =
sin A sin B sin C
Area of a triangle
a 2 + b2 − c2
2ab
1
A = ab sin C
2
Mathematics SL formula booklet
4
Topic 4—Vectors
4
...
2
Scalar product
v12 + v2 2 + v32
v =
v ⋅ w = w cos θ
v
v ⋅ w= v1w1 + v2 w2 + v3 w3
Angle between two
vectors
4
...
2
Mean of a set of data
n
x=
∑fx
i i
i =1
n
∑f
i =1
5
...
7
Combined events
Mutually exclusive events
5
...
9
Binomial distribution
Mean
5
...
1
Derivative of f ( x)
6
...
4
Standard integrals
dy
f ( x + h) − f ( x )
= f ′( x) = lim
h →0
dx
h
y = f ( x) ⇒
f ′( x) =n −1
nx
1
cos 2 x
f ( x) = ⇒
ex
f ′( x) =
ex
f ( x) = x ⇒
ln
1
f ′( x) =
x
f
y = g (u ) , u = ( x) ⇒
dy
dv
du
=u + v
dx
dx
dx
y =uv ⇒
u
y=
v
du
dv
v −u
dy
= dx 2 dx
dx
v
⇒
n
dx
∫x=
dy dy du
= ×
dx du dx
x n +1
+ C , n ≠ −1
n +1
1
ln
∫ x dx = x + C ,
x>0
− cos
∫ sin x dx = x + C
=
∫ cos x dx
∫e
6
...
6
Total distance travelled
from t1 to t 2
Mathematics SL formula booklet
distance =
∫
t2
t1
v(t ) dt
6
Mathematics SL formula booklet
7