Introduction to
quantitative methods
Accountancy and Control
,Inhoudsopgave
Week 1. Numbers and Algebra .............................................................................................................................. 2
Different numbers .............................................................................................................................................. 2
Commutative law ............................................................................................................................................... 2
Associative law ................................................................................................................................................... 2
Distributive law .................................................................................................................................................. 2
Factorization....................................................................................................................................................... 2
Multiplication rules ............................................................................................................................................ 4
Adding fractions ............................................................................................................................................. 4
Subtracting fractions ..................................................................................................................................... 4
Multiplication and division of fractions ........................................................................................................ 5
Exponentiation............................................................................................................................................... 5
Summary for all a > 0 ..................................................................................................................................... 5
Order of calculations .......................................................................................................................................... 6
Week 2. Equations, lines and functions ................................................................................................................. 7
General rule ........................................................................................................................................................ 7
Solve system of two linear equations with two variables ................................................................................ 7
General rule ........................................................................................................................................................ 8
First degree function .......................................................................................................................................... 8
From graph to function .................................................................................................................................. 8
The intersection point of two graphs ............................................................................................................ 9
Week 3. Equations, functions .............................................................................................................................. 10
Second degree function (= quadratic function) .............................................................................................. 10
The simplest quadratic function.................................................................................................................. 10
Characteristics of 𝒚 = 𝒂𝒙 + 𝒑𝟐 + 𝒒 ........................................................................................................... 11
Characteristics of 𝒚 = 𝒂𝒙𝟐 + 𝒃𝒙 + 𝒄.......................................................................................................... 12
Intersection of graphs ...................................................................................................................................... 13
Second degree inequalities .............................................................................................................................. 14
‘Two fold’ second degree inequalities ............................................................................................................. 14
From data points to equation .......................................................................................................................... 15
Week 4. Exponential, Power, Root and Logarithmic Functions .......................................................................... 16
Definition .......................................................................................................................................................... 16
Exercises with exponential functions .............................................................................................................. 16
Defintition of 𝒂𝐥𝐨𝐠𝒃 ........................................................................................................................................ 17
Rules of calculation for powers ....................................................................................................................... 18
Rules of calculation for logarithms .................................................................................................................. 18
Definition .......................................................................................................................................................... 19
Definition .......................................................................................................................................................... 19
1
, Week 1. Numbers and Algebra
Different numbers
Natural numbers N are positive numbers (1, 2, 3 … )
Integers numbers Z are the numbers N expanded with the ‘negative’ of the natural number (-1, 0, 1 ..)
𝐴
Rational numbers Q are integers expanded with fractions ( 𝐵 , A ∈ Z, B ∈ Z, 𝐵 ≠ 0 )
Real numbers R are all numbers (N, Z, Q, algebraic numbers (√), transcendental number (π)
Note that: N 𝐶 Z 𝐶 Q 𝐶 R (N is a subset of Z, Z is a subset of Q, Q is a subset or R)
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