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Kurse
Ãœber Sowiso
Kontakt
Freischalten 
English
Precalculus
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Kursinhalt
Numbers
Introduction
THEORIE
T
1.
On the contents
THEORIE
T
2.
Prerequisite knowledge for Numbers
THEORIE
T
3.
Variables
Integers
THEORIE
T
1.
The notion of integer
ÃœBUNG
Ã
2.
The notion of integer
9
THEORIE
T
3.
Calculating with integers
ÃœBUNG
Ã
4.
Calculating with integers
9
THEORIE
T
5.
Divisors of integers
ÃœBUNG
Ã
6.
Divisors of integers
3
THEORIE
T
7.
Division with remainder
ÃœBUNG
Ã
8.
Division with remainder for integers
3
THEORIE
T
9.
Prime numbers
ÃœBUNG
Ã
10.
Prime numbers
6
THEORIE
T
11.
Greatest common divisor and least common multiple
ÃœBUNG
Ã
12.
Greatest common divisor and least common multiple
8
Rational numbers
THEORIE
T
1.
The notion of rational number
ÃœBUNG
Ã
2.
The notion of rational number
7
THEORIE
T
3.
Addition and subtraction of fractions
ÃœBUNG
Ã
4.
Addition and subtraction of fractions
5
THEORIE
T
5.
Multiplication and division of fractions
ÃœBUNG
Ã
6.
Multiplication and division of fractions
6
THEORIE
T
7.
Ordering of rational numbers
ÃœBUNG
Ã
8.
Ordering of rational numbers
6
THEORIE
T
9.
Integer powers of fractions
ÃœBUNG
Ã
10.
Integer powers of fractions
7
THEORIE
T
11.
Decimal numbers
ÃœBUNG
Ã
12.
Decimal numbers
3
Roots
THEORIE
T
1.
Roots of integers
ÃœBUNG
Ã
2.
Roots of integers
7
THEORIE
T
3.
Roots of fractions
ÃœBUNG
Ã
4.
Roots of fractions
5
THEORIE
T
5.
Higher roots
ÃœBUNG
Ã
6.
Higher roots
6
THEORIE
T
7.
Fractional powers
ÃœBUNG
Ã
8.
Fractional exponents
5
THEORIE
T
9.
Absolute value
ÃœBUNG
Ã
10.
Abolute value
4
Real numbers
THEORIE
T
1.
Ordering of real numbers
ÃœBUNG
Ã
2.
Ordering of real numbers
10
THEORIE
T
3.
The notion of real number
ÃœBUNG
Ã
4.
The notion of real number
7
THEORIE
T
5.
Ordering and decimal development
ÃœBUNG
Ã
6.
Ordering and decimal development
5
THEORIE
T
7.
Approximations of real numbers
ÃœBUNG
Ã
8.
Approximations of real numbers
3
THEORIE
T
9.
Calculating with real numbers
ÃœBUNG
Ã
10.
Calculating with real numbers
5
End
ÃœBUNG
Ã
1.
Applications of real numbers
5
THEORIE
T
2.
Conclusion
Algebra
Introduction
THEORIE
T
1.
On the contents
THEORIE
T
2.
Prerequisite knowledge for Algebra
Arithmetic with Variables
THEORIE
T
1.
Order of operations
ÃœBUNG
Ã
2.
Order of operations
6
THEORIE
T
3.
Calculating with powers
ÃœBUNG
Ã
4.
Calculating with powers
9
THEORIE
T
5.
Expanding brackets
ÃœBUNG
Ã
6.
Expanding brackets
6
THEORIE
T
7.
Moving terms outside brackets
ÃœBUNG
Ã
8.
Moving terms outside brackets
3
Notable Products
THEORIE
T
1.
Expanding brackets
ÃœBUNG
Ã
2.
Expanding brackets
6
THEORIE
T
3.
The square of a sum or a difference
ÃœBUNG
Ã
4.
The square of a sum or a difference
5
THEORIE
T
5.
The difference of two squares
ÃœBUNG
Ã
6.
The difference of two squares
5
Rational Expressions
THEORIE
T
1.
Simplifying fractions
ÃœBUNG
Ã
2.
Simplifying fractions
5
THEORIE
T
3.
Finding a common denominator
ÃœBUNG
Ã
4.
Finding a common denominator
5
Binomial Coefficient
THEORIE
T
1.
Third and fourth powers of binomials
ÃœBUNG
Ã
2.
Third and fourth powers of binomials
6
THEORIE
T
3.
Pascal's triangle
ÃœBUNG
Ã
4.
Pascal's triangle
2
THEORIE
T
5.
Historical interlude: binomial coefficients
THEORIE
T
6.
Binomial coefficients and factorials
ÃœBUNG
Ã
7.
Binomial coefficients and factorials
3
THEORIE
T
8.
Binomial theorem and sigma notation
ÃœBUNG
Ã
9.
Binomial theorem and sigma notation
3
THEORIE
T
10.
Applications of combinatorics
ÃœBUNG
Ã
11.
Applications of combinatorics
9
End of Algebra
ÃœBUNG
Ã
1.
Application of Algebra
3
THEORIE
T
2.
End
Linear Equations with a Single Unknown
Introduction to Linear Equations with a Single Unknown
THEORIE
T
1.
About the content
THEORIE
T
2.
Required prerequisite knowledge
Notion
THEORIE
T
1.
The notion of linear equation
ÃœBUNG
Ã
2.
The notion of linear equation
4
THEORIE
T
3.
Solving by reduction
ÃœBUNG
Ã
4.
Solving by reduction
7
THEORIE
T
5.
The general solution
ÃœBUNG
Ã
6.
General solution
4
Variations
THEORIE
T
1.
Fractional linear equations
ÃœBUNG
Ã
2.
Fractional linear equations
5
THEORIE
T
3.
Equations with absolute values
ÃœBUNG
Ã
4.
Equations with absolute values
10
THEORIE
T
5.
Substitution
ÃœBUNG
Ã
6.
Substitution
4
THEORIE
T
7.
Solving by factorization
ÃœBUNG
Ã
8.
Solving by factorization
5
End of Linear Equations with a Single Unknown
ÃœBUNG
Ã
1.
Applications of Linear Equations with a Single Unknown
9
THEORIE
T
2.
End of Linear Equations with a Single Unknown
Systems of Linear Equations
Introduction to Systems of Linear Equations
THEORIE
T
1.
Introduction to systems of linear equations
THEORIE
T
2.
Required prerequisite
Simple Systems of Linear Equations
THEORIE
T
1.
The notion of parameter
ÃœBUNG
Ã
2.
The notion of parameter
6
THEORIE
T
3.
The notion of system of equations
ÃœBUNG
Ã
4.
The notion of system of equations
5
THEORIE
T
5.
The linear equation of a line
ÃœBUNG
Ã
6.
The linear equation of a line
9
Two Linear Equations
THEORIE
T
1.
Solving systems of equations by substitution
ÃœBUNG
Ã
2.
Solving systems of equations by substitution
4
THEORIE
T
3.
Solving systems of equations by elimination
ÃœBUNG
Ã
4.
Solving systems of equations by elimination
5
THEORIE
T
5.
Equations and lines
ÃœBUNG
Ã
6.
Equations and lines
7
THEORIE
T
7.
Solving systems of equations by substitution
End of Systems of Linear Equations
ÃœBUNG
Ã
1.
Applications of systems of linear equations
3
THEORIE
T
2.
End of system of linear equations
Quadratic Equations
Introduction to Quadratic Equations
THEORIE
T
1.
About the content
THEORIE
T
2.
Required Prerequisites
Quadratic Equations with one Unknown
THEORIE
T
1.
The notion of quadratic equation
ÃœBUNG
Ã
2.
The notion of quadratic equation
4
THEORIE
T
3.
The general solution to a quadratic equation
ÃœBUNG
Ã
4.
The general solution to a quadratic equation
5
Variations
THEORIE
T
1.
Substitution
ÃœBUNG
Ã
2.
Substitution
6
THEORIE
T
3.
Fractional equations
ÃœBUNG
Ã
4.
Fractional equations
3
THEORIE
T
5.
Root equations
ÃœBUNG
Ã
6.
Root equations
3
THEORIE
T
7.
Case distinction
ÃœBUNG
Ã
8.
Case distinction
5
End of Quadratic Equations
ÃœBUNG
Ã
1.
Applications of quadratic equations
2
THEORIE
T
2.
End of quadratic equations
2-dimensional Geometry: Points and Lines
Introduction to 2-dimensional Geometry: Lines, Distances, Pe
THEORIE
T
1.
About the contents
THEORIE
T
2.
Voorkennis 2-Dimensionale meetkunde: punten en lijnen *
Coordinates in 2 dimensions
THEORIE
T
1.
Het assenstelsel *
ÃœBUNG
Ã
2.
The axes
3
THEORIE
T
3.
The notion of vector
ÃœBUNG
Ã
4.
The notion of vector
2
THEORIE
T
5.
Operaties op punten *
ÃœBUNG
Ã
6.
Operations for vectors
3
THEORIE
T
7.
Linear combinations in 2 dimensions
ÃœBUNG
Ã
8.
Linear combinations in 2 dimensions
3
THEORIE
T
9.
Gelijkvormigheid van driehoeken *
ÃœBUNG
Ã
10.
Triangles
4
Lines
THEORIE
T
1.
Lines
ÃœBUNG
Ã
2.
Lines
4
THEORIE
T
3.
Parameter representation and equation of a line
ÃœBUNG
Ã
4.
Parameter representation and equation of a line
6
THEORIE
T
5.
The intersection of two lines
ÃœBUNG
Ã
6.
The intersection of two lines
9
THEORIE
T
7.
Line segments in the plane
ÃœBUNG
Ã
8.
Line segments in the plane
6
THEORIE
T
9.
The point of gravity of a triangle
ÃœBUNG
Ã
10.
The point of gravity of a triangle
4
Area
THEORIE
T
1.
Area
ÃœBUNG
Ã
2.
The notion of surface in the flat plane
3
THEORIE
T
3.
Pythagoras *
ÃœBUNG
Ã
4.
Pythagoras
5
THEORIE
T
5.
Gelijkvormigheid van driehoeken *
ÃœBUNG
Ã
6.
Similarities of triangles
3
Distance and length
THEORIE
T
1.
Afstand in het vlak *
ÃœBUNG
Ã
2.
Distance in the flat plane
3
THEORIE
T
3.
Loodrechte vectoren *
ÃœBUNG
Ã
4.
Perpendicular Vectors
5
THEORIE
T
5.
Distance between point and line
ÃœBUNG
Ã
6.
Distance of a point to a line
5
THEORIE
T
7.
2D Mee PL pt me coord1 *
ÃœBUNG
Ã
8.
Perpendiculars
3
THEORIE
T
9.
Centrum van een driehoek *
ÃœBUNG
Ã
10.
Center and height of a triangle
3
Angles and inner product
THEORIE
T
1.
Gelijkbenige en gelijkzijdige driehoeken *
ÃœBUNG
Ã
2.
Isosceles and Equilateral Triangles
7
THEORIE
T
3.
Right triangles and trigonometric functions
ÃœBUNG
Ã
4.
Cosine
3
THEORIE
T
5.
Normaalvector van een lijn *
ÃœBUNG
Ã
6.
Sinus and Tangent
3
THEORIE
T
7.
Normaalvector van een lijn *
ÃœBUNG
Ã
8.
Addition formulas for angles
5
Inner product and Cross product
THEORIE
T
1.
Inner product in two dimensions
ÃœBUNG
Ã
2.
Inner product in 2 dimensions
3
THEORIE
T
3.
Het standaardinprodict *
ÃœBUNG
Ã
4.
Inner product and line in 2 dimensions
8
THEORIE
T
5.
Normaalvector van een lijn *
ÃœBUNG
Ã
6.
Cross product
2
Bissectrices
THEORIE
T
1.
Bissectrices *
ÃœBUNG
Ã
2.
Bissectrices
7
THEORIE
T
3.
Bissectrices *
ÃœBUNG
Ã
4.
Entered center of a triangle
6
Affine transformations of the flat plane
THEORIE
T
1.
Translaties in 2 dimensies *
ÃœBUNG
Ã
2.
Translations in 2 dimensions
2
THEORIE
T
3.
Draaiing in 2 dimensies *
ÃœBUNG
Ã
4.
Spinning in 2 dimensions
2
THEORIE
T
5.
Spiegelingen in 2 dimensies *
ÃœBUNG
Ã
6.
Reflections in 2 dimensions
2
THEORIE
T
7.
scalarvermenigvuldiging in het vlak *
ÃœBUNG
Ã
8.
Scaling in 2 dimensions
2
THEORIE
T
9.
Samenstelling van transformaties *
ÃœBUNG
Ã
10.
Compositions of transformations
3
End of 2-dimensional Geometry: Lines, Distances, Perpendicul
ÃœBUNG
Ã
1.
Applications of 2-dimensional Geometry: Lines, Distances, Pe
5
THEORIE
T
2.
Besluit van 2-Dimensionale meetkunde: punten en lijnen *
2-Dimensional Geometry: Conic Sections
Introduction to 2-Dimensional Geometry: Conic Sections
THEORIE
T
1.
Inleiding op 2-Dimensionale meetkunde: kegelsneden *
THEORIE
T
2.
Vereiste voorkennis *
Circles
THEORIE
T
1.
Cirkels *
ÃœBUNG
Ã
2.
Cirkels *
7
THEORIE
T
3.
Snijpunten van cirkel en lijn *
ÃœBUNG
Ã
4.
Snijpunten van cirkel en lijn *
7
THEORIE
T
5.
Snijpunten van twee cirkels *
ÃœBUNG
Ã
6.
Snijpunten van twee cirkels *
4
THEORIE
T
7.
De raaklijn aan een cirkel *
ÃœBUNG
Ã
8.
De raaklijn aan een cirkel *
3
THEORIE
T
9.
Gelijkvormigheid van cirkels *
ÃœBUNG
Ã
10.
Gelijkvormigheid van cirkels *
2
THEORIE
T
11.
Parametervoorstellingen van een cirkel *
ÃœBUNG
Ã
12.
Parametervoorstellingen van een cirkel *
7
Parabolen en hyperbolen *
THEORIE
T
1.
Parabolen en hyperbolen *
ÃœBUNG
Ã
2.
Het begrip parabool *
1
THEORIE
T
3.
Gelijkvormigheid van cirkels *
ÃœBUNG
Ã
4.
Gelijkvormigheid van parabolen *
1
Hyperbolen *
THEORIE
T
1.
Hyperbolen *
Ellipses
THEORIE
T
1.
Ellipsen en lijnen *
ÃœBUNG
Ã
2.
2DMee Kegel karakter ellips *
0
Ellipsen en lijnen *
THEORIE
T
1.
Doorsnee van lijn met kegelsnede *
End of 2-Dimensional Geometry: Conic Sections
THEORIE
T
1.
MAX Voorbeeld
ÃœBUNG
Ã
2.
Applications of linear equations with two unknowns
0
Linear Inequalities
Introduction
THEORIE
T
1.
About the content
THEORIE
T
2.
Prerequisite knowledge
Linear Inequalities
THEORIE
T
1.
Solve by reduction
ÃœBUNG
Ã
2.
Solving through reduction
6
THEORIE
T
3.
Solving through equations
ÃœBUNG
Ã
4.
Solving through equations
5
THEORIE
T
5.
Multiple linear inequalities with one unknown
ÃœBUNG
Ã
6.
Multiple linear inequalities with one unknown
2
Variations
THEORIE
T
1.
Fractional linear inequalities
ÃœBUNG
Ã
2.
Fractional linear inequalities
3
THEORIE
T
3.
Linear inequalities with absolute values
ÃœBUNG
Ã
4.
Linear inequalities with absolute values
3
Estimations
THEORIE
T
1.
One linear inequality with two unknowns
ÃœBUNG
Ã
2.
One linear inequality with two unknowns
1
THEORIE
T
3.
Multiple linear inequalities with two unknowns
ÃœBUNG
Ã
4.
Multiple linear inequalities with two unknowns
3
End of Linear Inequalities
ÃœBUNG
Ã
1.
Applications of Linear Inequalities_copy
4
THEORIE
T
2.
End of linear inequalities
Quadratic Inequalities
THEORIE
T
1.
Quadratic inequalities
ÃœBUNG
Ã
2.
One quadratic inequality with one unknown
2
3-Dimensional Geometry
Introduction to 3-Dimensional Geometry
THEORIE
T
1.
Inleiding op 3-Dimensionale meetkunde *
Coordinates and Inner prodct
THEORIE
T
1.
Lineaire combinaties in 2 dimensies *
THEORIE
T
2.
Afstand en lengte in 3 dimensies *
THEORIE
T
3.
Doorsnede van een lijn en een ellipsen *
Three planes
THEORIE
T
1.
De doorsnee van drie vlakken *
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