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Precalculus
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Course content
Numbers
Introduction
THEORY
T
1.
On the contents
THEORY
T
2.
Prerequisite knowledge for Numbers
THEORY
T
3.
Variables
Integers
THEORY
T
1.
The notion of integer
PRACTICE
P
2.
The notion of integer
9
THEORY
T
3.
Calculating with integers
PRACTICE
P
4.
Calculating with integers
9
THEORY
T
5.
Divisors of integers
PRACTICE
P
6.
Divisors of integers
3
THEORY
T
7.
Division with remainder
PRACTICE
P
8.
Division with remainder for integers
3
THEORY
T
9.
Prime numbers
PRACTICE
P
10.
Prime numbers
6
THEORY
T
11.
Greatest common divisor and least common multiple
PRACTICE
P
12.
Greatest common divisor and least common multiple
8
Rational numbers
THEORY
T
1.
The notion of rational number
PRACTICE
P
2.
The notion of rational number
7
THEORY
T
3.
Addition and subtraction of fractions
PRACTICE
P
4.
Addition and subtraction of fractions
5
THEORY
T
5.
Multiplication and division of fractions
PRACTICE
P
6.
Multiplication and division of fractions
6
THEORY
T
7.
Ordering of rational numbers
PRACTICE
P
8.
Ordering of rational numbers
6
THEORY
T
9.
Integer powers of fractions
PRACTICE
P
10.
Integer powers of fractions
7
THEORY
T
11.
Decimal numbers
PRACTICE
P
12.
Decimal numbers
3
Roots
THEORY
T
1.
Roots of integers
PRACTICE
P
2.
Roots of integers
7
THEORY
T
3.
Roots of fractions
PRACTICE
P
4.
Roots of fractions
5
THEORY
T
5.
Higher roots
PRACTICE
P
6.
Higher roots
6
THEORY
T
7.
Fractional powers
PRACTICE
P
8.
Fractional exponents
5
THEORY
T
9.
Absolute value
PRACTICE
P
10.
Abolute value
4
Real numbers
THEORY
T
1.
Ordering of real numbers
PRACTICE
P
2.
Ordering of real numbers
10
THEORY
T
3.
The notion of real number
PRACTICE
P
4.
The notion of real number
7
THEORY
T
5.
Ordering and decimal development
PRACTICE
P
6.
Ordering and decimal development
5
THEORY
T
7.
Approximations of real numbers
PRACTICE
P
8.
Approximations of real numbers
3
THEORY
T
9.
Calculating with real numbers
PRACTICE
P
10.
Calculating with real numbers
5
End
PRACTICE
P
1.
Applications of real numbers
5
THEORY
T
2.
Conclusion
Algebra
Introduction
THEORY
T
1.
On the contents
THEORY
T
2.
Prerequisite knowledge for Algebra
Arithmetic with Variables
THEORY
T
1.
Order of operations
PRACTICE
P
2.
Order of operations
6
THEORY
T
3.
Calculating with powers
PRACTICE
P
4.
Calculating with powers
9
THEORY
T
5.
Expanding brackets
PRACTICE
P
6.
Expanding brackets
6
THEORY
T
7.
Moving terms outside brackets
PRACTICE
P
8.
Moving terms outside brackets
3
Notable Products
THEORY
T
1.
Expanding brackets
PRACTICE
P
2.
Expanding brackets
6
THEORY
T
3.
The square of a sum or a difference
PRACTICE
P
4.
The square of a sum or a difference
5
THEORY
T
5.
The difference of two squares
PRACTICE
P
6.
The difference of two squares
5
Rational Expressions
THEORY
T
1.
Simplifying fractions
PRACTICE
P
2.
Simplifying fractions
5
THEORY
T
3.
Finding a common denominator
PRACTICE
P
4.
Finding a common denominator
5
Binomial Coefficient
THEORY
T
1.
Third and fourth powers of binomials
PRACTICE
P
2.
Third and fourth powers of binomials
6
THEORY
T
3.
Pascal's triangle
PRACTICE
P
4.
Pascal's triangle
2
THEORY
T
5.
Historical interlude: binomial coefficients
THEORY
T
6.
Binomial coefficients and factorials
PRACTICE
P
7.
Binomial coefficients and factorials
3
THEORY
T
8.
Binomial theorem and sigma notation
PRACTICE
P
9.
Binomial theorem and sigma notation
3
THEORY
T
10.
Applications of combinatorics
PRACTICE
P
11.
Applications of combinatorics
9
End of Algebra
PRACTICE
P
1.
Application of Algebra
3
THEORY
T
2.
End
Linear Equations with a Single Unknown
Introduction to Linear Equations with a Single Unknown
THEORY
T
1.
About the content
THEORY
T
2.
Required prerequisite knowledge
Notion
THEORY
T
1.
The notion of linear equation
PRACTICE
P
2.
The notion of linear equation
4
THEORY
T
3.
Solving by reduction
PRACTICE
P
4.
Solving by reduction
7
THEORY
T
5.
The general solution
PRACTICE
P
6.
General solution
4
Variations
THEORY
T
1.
Fractional linear equations
PRACTICE
P
2.
Fractional linear equations
5
THEORY
T
3.
Equations with absolute values
PRACTICE
P
4.
Equations with absolute values
10
THEORY
T
5.
Substitution
PRACTICE
P
6.
Substitution
4
THEORY
T
7.
Solving by factorization
PRACTICE
P
8.
Solving by factorization
5
End of Linear Equations with a Single Unknown
PRACTICE
P
1.
Applications of Linear Equations with a Single Unknown
9
THEORY
T
2.
End of Linear Equations with a Single Unknown
Systems of Linear Equations
Introduction to Systems of Linear Equations
THEORY
T
1.
Introduction to systems of linear equations
THEORY
T
2.
Required prerequisite
Simple Systems of Linear Equations
THEORY
T
1.
The notion of parameter
PRACTICE
P
2.
The notion of parameter
6
THEORY
T
3.
The notion of system of equations
PRACTICE
P
4.
The notion of system of equations
5
THEORY
T
5.
The linear equation of a line
PRACTICE
P
6.
The linear equation of a line
9
Two Linear Equations
THEORY
T
1.
Solving systems of equations by substitution
PRACTICE
P
2.
Solving systems of equations by substitution
4
THEORY
T
3.
Solving systems of equations by elimination
PRACTICE
P
4.
Solving systems of equations by elimination
5
THEORY
T
5.
Equations and lines
PRACTICE
P
6.
Equations and lines
7
THEORY
T
7.
Solving systems of equations by substitution
End of Systems of Linear Equations
PRACTICE
P
1.
Applications of systems of linear equations
3
THEORY
T
2.
End of system of linear equations
Quadratic Equations
Introduction to Quadratic Equations
THEORY
T
1.
About the content
THEORY
T
2.
Required Prerequisites
Quadratic Equations with one Unknown
THEORY
T
1.
The notion of quadratic equation
PRACTICE
P
2.
The notion of quadratic equation
4
THEORY
T
3.
The general solution to a quadratic equation
PRACTICE
P
4.
The general solution to a quadratic equation
5
Variations
THEORY
T
1.
Substitution
PRACTICE
P
2.
Substitution
6
THEORY
T
3.
Fractional equations
PRACTICE
P
4.
Fractional equations
3
THEORY
T
5.
Root equations
PRACTICE
P
6.
Root equations
3
THEORY
T
7.
Case distinction
PRACTICE
P
8.
Case distinction
5
End of Quadratic Equations
PRACTICE
P
1.
Applications of quadratic equations
2
THEORY
T
2.
End of quadratic equations
2-Dimensional Geometry: Conic Sections
Introduction to 2-Dimensional Geometry: Conic Sections
THEORY
T
1.
Inleiding op 2-Dimensionale meetkunde: kegelsneden *
THEORY
T
2.
Vereiste voorkennis *
Circles
THEORY
T
1.
Cirkels *
PRACTICE
P
2.
Cirkels *
7
THEORY
T
3.
Snijpunten van cirkel en lijn *
PRACTICE
P
4.
Snijpunten van cirkel en lijn *
7
THEORY
T
5.
Snijpunten van twee cirkels *
PRACTICE
P
6.
Snijpunten van twee cirkels *
4
THEORY
T
7.
De raaklijn aan een cirkel *
PRACTICE
P
8.
De raaklijn aan een cirkel *
3
THEORY
T
9.
Gelijkvormigheid van cirkels *
PRACTICE
P
10.
Gelijkvormigheid van cirkels *
2
THEORY
T
11.
Parametervoorstellingen van een cirkel *
PRACTICE
P
12.
Parametervoorstellingen van een cirkel *
7
Parabolen en hyperbolen *
THEORY
T
1.
Parabolen en hyperbolen *
PRACTICE
P
2.
Het begrip parabool *
1
THEORY
T
3.
Gelijkvormigheid van cirkels *
PRACTICE
P
4.
Gelijkvormigheid van parabolen *
1
Hyperbolen *
THEORY
T
1.
Hyperbolen *
Ellipses
THEORY
T
1.
Ellipsen en lijnen *
PRACTICE
P
2.
2DMee Kegel karakter ellips *
0
Ellipsen en lijnen *
THEORY
T
1.
Doorsnee van lijn met kegelsnede *
End of 2-Dimensional Geometry: Conic Sections
THEORY
T
1.
MAX Voorbeeld
PRACTICE
P
2.
Applications of linear equations with two unknowns
0
Linear Inequalities
Introduction
THEORY
T
1.
About the content
THEORY
T
2.
Prerequisite knowledge
Linear Inequalities
THEORY
T
1.
Solve by reduction
PRACTICE
P
2.
Solving through reduction
6
THEORY
T
3.
Solving through equations
PRACTICE
P
4.
Solving through equations
5
THEORY
T
5.
Multiple linear inequalities with one unknown
PRACTICE
P
6.
Multiple linear inequalities with one unknown
2
Variations
THEORY
T
1.
Fractional linear inequalities
PRACTICE
P
2.
Fractional linear inequalities
3
THEORY
T
3.
Linear inequalities with absolute values
PRACTICE
P
4.
Linear inequalities with absolute values
3
Estimations
THEORY
T
1.
One linear inequality with two unknowns
PRACTICE
P
2.
One linear inequality with two unknowns
1
THEORY
T
3.
Multiple linear inequalities with two unknowns
PRACTICE
P
4.
Multiple linear inequalities with two unknowns
3
End of Linear Inequalities
PRACTICE
P
1.
Applications of Linear Inequalities_copy
4
THEORY
T
2.
End of linear inequalities
Quadratic Inequalities
THEORY
T
1.
Quadratic inequalities
PRACTICE
P
2.
One quadratic inequality with one unknown
2
3-Dimensional Geometry
Introduction to 3-Dimensional Geometry
THEORY
T
1.
Inleiding op 3-Dimensionale meetkunde *
Coordinates and Inner prodct
THEORY
T
1.
Lineaire combinaties in 2 dimensies *
THEORY
T
2.
Afstand en lengte in 3 dimensies *
THEORY
T
3.
Doorsnede van een lijn en een ellipsen *
Three planes
THEORY
T
1.
De doorsnee van drie vlakken *
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