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):
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):
