Mathematics 1 Formula Sheet

Formula sheet Mathematics 1 for IBA

Quadratic functions
√
- ABC-formula:

D  Discriminant:
y(x) does not have a zero point.
y(x) only has one zero point.
y(x) is a dalparabool.
y(x) is a bergparabool.

Properties of power functions
NB p & q are both integer numbers
1.
2.
3.
4.
5.
6.

7. √

Properties of exponential functions
1.
2.
3.
4.
5.
6.

Properties of logarithmic functions
1.
2.
3.
4.
5.
6.
7.
8.
9.

Difference quotient

,Derivative
With :



List of elementary functions derivative
1.

2.

3.

4.


5.



Rules for calculating complex derivatives
- Product rule


-Quotient rule



-Chain rule
Functions with one variable
( ) ( )

Functions with two variables
1. ( ) ( )
2. ( ) ( )

Differential
- Functions with one variable
For close to 0, we can say that


Differential:
Application of property differential:

- Functions with two variables
Only a change in x:

, Only a change in y:


Change in both x and y:

Where:
, is the total differential (

Marginality
“How much does y change if x increases with 1 unit?”
- Functions with one variable
, at
Thus:

- Functions with two variables
A change in x:


A change in y:


Elasticity
“How much does y increases in percentages for each percentage increase of x?”
- Functions with one variable


And:

- Functions with two variables
( )

( )


Marginal rate of substitution
“How much can x increase and y decrease such that z(x,y) does not change?”



Derivative of the inverse function



The slope of the tangent line at the level curve of U(x,y) in (x,y)=(p,q):