Mathematics: applications and interpretation formula booklet

Diploma Programme

Mathematics: applications and interpretation formula booklet

For use during the course and in the examinations First examinations 2021 Version 1.1

? International Baccalaureate Organization 2019

Contents

Prior learning

SL and HL

2

HL only

2

Topic 1: Number and algebra

SL and HL

3

HL only

4

Topic 2: Functions

SL and HL

5

HL only

5

Topic 3: Geometry and trigonometry

SL and HL

6

HL only

7

Topic 4: Statistics and probability

SL and HL

9

HL only

10

Topic 5: Calculus

SL and HL

11

HL only

11

Prior learning ? SL and HL

Area of a parallelogram

A = bh , where b is the base, h is the height

Area of a triangle

A = 1 (bh) , where b is the base, h is the height 2

Area of a trapezoid Area of a circle

=A 1 (a + b) h , where a and b are the parallel sides, h is the height 2

A = r2 , where r is the radius

Circumference of a circle

C= 2r , where r is the radius

Volume of a cuboid

V = lwh , where l is the length, w is the width, h is the height

Volume of a cylinder

V = r2h , where r is the radius, h is the height

Volume of prism

V = Ah , where A is the area of cross-section, h is the height

Area of the curved surface of A= 2rh , where r is the radius, h is the height

a cylinder

Distance between two

points (x1, y1) and (x2 , y2 )

d = (x1 - x2 )2 + ( y1 - y2 )2

Coordinates of the midpoint of a line segment with endpoints

(x1, y1) and (x2 , y2 )

x1

+ 2

x2

, y1

+ 2

y2

Prior learning ? HL only

Solutions of a quadratic equation

The solutions of ax2 += bx + c =0 are x -b ? b2 - 4ac , a 0 2a

Mathematics: applications and interpretation formula booklet

2

Topic 1: Number and algebra ? SL and HL

SL The nth term of an

1.2 arithmetic sequence

un = u1 + (n -1) d

The sum of n terms of an

arithmetic sequence

Sn=

n 2

(

2u1

+ (n -1) d ) ;

Sn=

n 2

(u1

+

un

)

SL The nth term of a

1.3 geometric sequence

un = u1r n-1

fTinhietesguemomoef tnrictesremqsueonf ca= e Sn

u= 1(rn -1) r -1

u1(1 - rn ) , r 1 1- r

SL Compound interest 1.4

FV =

PV

?

1

+

r 100k

k n

,

where

FV

is

the

future

value,

PV is the present value, n is the number of years,

k is the number of compounding periods per year,

r% is the nominal annual rate of interest

SL 1.5

Exponents and logarithms ax = b x = loga b , where a > 0, b > 0, a 1

SL 1.6 Percentage error

=

vA - vE vE

?100% , where vE is the exact value and vA is

the approximate value of v

Mathematics: applications and interpretation formula booklet

3

Topic 1: Number and algebra ? HL only

AHL Laws of logarithms 1.9

log= a xy loga x + loga y lo= ga xy loga x - loga y loga xm = m loga x

for a, x, y > 0

AHL The sum of an infinite 1.11 geometric sequence

AHL 1.12

Complex numbers Discriminant

S

=

u1 1- r

,

r

< 1

z= a + bi

= b2 - 4ac

AHL 1.13

Modulus-argument (polar) and exponential (Euler) form

z =r (cos + isin ) =rei =r cis

AHL 1.14

Determinant of a 2 ? 2 matrix

A = ac

b

d

det A =A

= ad - bc

Inverse of a 2 ? 2 matrix

=A

a

c

b

d

A=-1

1 d

det

A

-c

-b a

,

ad

bc

AHL 1.15

Power formula for a matrix M n = PDn P -1 , where P is the matrix of eigenvectors and D is

the diagonal matrix of eigenvalues

Mathematics: applications and interpretation formula booklet

4

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