Topics of Mathematics
Topics and types of problems / exercises of Mathematics
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Polynomials and algebraic fractions

        Monomials: Coefficient and degree
        Monomials: Addition and subtraction
        Monomials: Multiplication
        Monomials: Division
        Monomials: Powers
        Polynomials: Addition and subtraction
<R> Polynomials: Multiplication and power
<R> Binomial theorem
<R> Polynomials: Division I: Long division
<R> Polynomials: Division II: Ruffini's rule
<R> Polynomials: Division III: With parameters
        Factoring polynomials I: Common factor
<R> Factoring polynomials II: (a+b)² , (a-b)² , a²-b²
<R> Factoring polynomials III: Ruffini's rule
<R> Algebraic fractions I: Simplifying algebraic fractions
<R> Algebraic fractions II: Multiplications and divisions
<R> Algebraic fractions III: Additions and subtractions

Natural numbers

        Addition and subtraction of natural numbers
        Multiplication of natural numbers I
        Multiplication of natural numbers II
        Division of natural numbers I
        Division of natural numbers II
        Rounding natural numbers
        Expanding natural numbers in powers of 10
        Repeated multiplications as powers
        Powers as repeated multiplications


Descriptive statistics

        One-variable statistics: Ungrouped data
<R> One-variable statistics: Grouped data
<R> Two-variable statistics: Linear regression analysis


Definite integrals

<R> Definite integrals
<R> Area between a curve and the X axis. Basic - No graphs
<R> Area between a curve and the X axis. Basic - With graphs
<R> Area between a curve and the X axis. Advanced - No graphs
<R> Area between a curve and the X axis. Advanced - With graphs
<R> Area between two curves - No graphs
<R> Area between two curves - With graphs
<R> Parameters calculation using definite integrals
<R> Find function by integration of its first derivative
<R> Find function by integration of its second derivative
<R> Volumes of revolution

Indefinite integrals

        Integration by direct method I. Without trigonometrics
        Integration by direct method II. With trigonometrics
<R> Integration by substitution I. Without trigonometrics
<R> Integration by substitution. II With trigonometrics
<R> Integration by parts I
<R> Integration by parts II
<R> Integration by parts III
<R> Integrals of rational functions I
<R> Integrals of rational functions II
<R> Integrals of rational functions III
Study of functions

        Matching linear functions to their graphs
<R> Matching quadratic functions to their graphs
<R> Matching cubic functions to their graphs
<R> Matching functions to their graphs
        Domain of a function I
        Domain of a function II
        Domain of a function III
<R> Inverse functions
<R> Function composition I
<R> Function composition II
        Tangent line to a curve at a point
<R> Tangent line to a curve and parallel to a given line
        Normal line to a curve at a point
<R> Finding polynomial functions involving derivatives
<R> Asymptotes I: Vertical
<R> Asymptotes II: Horizontal
<R> Asymptotes III: Oblique
<R> Asymptotes IV: Vertical, horizontal and oblique
<R> Maxima and minima of a function
<R> Monotonicity and extrema
<R> Inflection points of a function
<R> Concavity and inflection points
<R> Continuity I: Piecewise functions (without parameters)
<R> Continuity II: Piecewise functions (with 1 parameter)
<R> Continuity III: Piecewise functions (with 2 parameters)
<R> Derivability I: Without parameter
<R> Derivability II: With parameters
<R> Analyze function using the graph of its derivative I
<R> Analyze function using the graph of its derivative II
<R> Analyze function using the graph of its derivative III
<R> Optimization











Derivatives

        Average rate of change of a function
<R> Derivative of functions I:      No Chain rule - No Trigonometry
<R> Derivative of functions II:     No Chain rule - Trigonometry
<R> Derivative of functions III:    No Chain rule - No Trigonometry
<R> Derivative of functions IV:   No Chain rule - Trigonometry
<R> Derivative of functions V:    Chain rule -       No Trigonometry
<R> Derivative of functions VI:   Chain rule -       Trigonometry
<R> Derivative of functions VII:  Chain rule -       No Trigonometry
<R> Derivative of functions VIII: Chain rule -       Trigonometry
<R> Derivative of functions IX:   Generalized power rule
<R> Implicit differentiation





Limits

        Limits involving rational functions
<R> Limits involving roots
<R> Limits involving subtraction of roots
<R> Limits of powers
<R> Limits using L'Hôpital's rule








Analytic geometry of Space

        Vectors
        Plane calculations
<R> Line calculations
<R> Alignment, coplanarity and distance of points
<R> Relative position of planes and lines (without parameter)
<R> Relative position of planes and lines (with parameter)
<R> Relative position of two lines (without parameters)
<R> Relative position of two lines (with parameters)

Plane analytical geometry

        Vectors I
<R> Vectors II
<R> Lines I
<R> Lines II
<R> Conics I: Circle
<R> Conics II: Ellipse centered at the origin
<R> Conics III: Ellipse not centered at the origin
<R> Conics IV: Hyperbola centered at the origin
<R> Conics V: Hyperbola not centered at the origin
<R> Conics VI: Parabola. Vertex at the origin
<R> Conics VII: Parabola. Vertex is not at the origin
<R> Conics VIII: Matching equation of conic sections to their graphs



Basic geometry

         Pythagorean theorem I
<R> Pythagorean theorem II
         Similarity
<R> Plane shapes I: straight line segments
<R> Plane shapes II: straight line segments
<R> Plane shapes III: curved line segments
<R> Plane shapes IV: curved line segments
<R> Solid  shapes I: plane surfaces
<R> Solid  shapes II: plane surfaces
<R> Solid  shapes III: curved surfaces
<R> Solid  shapes IV: curved surfaces
Trigonometry

        Trigonometric values from another one
<R> Trigonometric values from two other known
<R> Trigonometric identities
<R> Trigonometric equations
<R> Solving triangles
<R> Solving plane shapes

Complex numbers

        Adding and subtracting complex numbers
        Multiplying and dividing complex numbers in cartesian form
        Rectangular (cartesian) to polar conversion
        Polar to rectangular (cartesian) conversion
        Multiplying and dividing complex numbers in polar form
<R> Powers of complex numbers
<R> Root extraction of complex numbers
<R> Calculation of a parameter
<R> Complex equations
<R> Complex equations + plotting answers



Matrices, determinants and systems of equations

        Additions and subtractions of matrices
<R> Multiplication of matrices
        Determinants 3×3 (without parameters)
<R> Determinants 4×4 (without parameters)
<R> Determinants (with parameters)
<R> Rank of matrices (without parameters)
<R> Rank of matrices (with parameters)
<R> Inverse matrix (without parameters)
<R> Inverse matrix (with parameters)
        Matricial equations I
        Matricial equations II: type AX+B=C
<R> Systems of 2×2 matricial linear equations
        Discuss and solve systems of 3×3 linear equations (without parameters)
<R> Discuss and solve systems of 3×3 linear equations (with parameters)
<R> Diagonalization of 2x2 matrices: Eigenvalues
<R> Diagonalization of 3x3 matrices: Eigenvalues
<R> Diagonalization of 2x2 matrices: Eigenvalues and eigenvectors
<R> Diagonalization of 3x3 matrices: Eigenvalues and eigenvectors
<R> Cayley-Hamilton Theorem: Powers of a matrix
<R> Cayley-Hamilton Theorem: Inverse and powers of a matrix





Systems of non-linear equations

<R> Systems of 2×2 equations (linear and quadratic)
<R> Systems of 2×2 equations (linear and irrational)
<R> Systems of 2×2 exponential equations
<R> Systems of 2×2 logarithmic equations

Systems of linear equations

       Systems of 2×2 linear equations. Integer solutions
       Systems of 2×2 linear equations. Rational solutions
<R> Solving system of 2×2 linear equations by graphing. Integer solutions
<R> Systems of 3×3 linear equations. Integer solutions
<R> Systems of 3×3 linear equations. Rational solutions
<R> System of equations word problems


Inequalities

        Linear inequalities in 1 variable with integer coefficients
        Linear inequalities in 1 variable with rational coefficients
<R> Absolute value inequalities
<R> Quadratic inequalities
<R> Rational inequalities
<R> Inequalities in 2 variables

Equations

<R> Simplifying linear and quadratic expressions

       Linear equations with integer coefficients. Integer solutions
       Linear equations with integer coefficients. Rational solutions
       Linear equations with rational coefficients. Integer solutions
       Linear equations with rational coefficients. Rational solutions

<R> Linear equations word problems (integer coefficients)
<R> Linear equations word problems (rational coefficients)

      Incomplete quadratic equations. Integer solutions
      Incomplete quadratic equations. Rational solutions
      Incomplete quadratic equations. Real solutions

      Complete quadratic equations. Integer solutions
      Complete quadratic equations. Rational solutions
      Complete quadratic equations. Real solutions

<R> Quadratic equations. Constants in the denominator. Integer solutions
<R> Quadratic equations. Constants in the denominator. Rational solutions
<R> Quadratic equations. Constants in the denominator. Real solutions

<R> Quadratic equations. Unknown in the denominator. Integer solutions
<R> Quadratic equations. Unknown in the denominator. Rational solutions
<R> Quadratic equations. Unknown in the denominator. Real solutions

<R> Biquadratic equations. Integer solutions
<R> Biquadratic equations. Rational solutions
<R> Biquadratic equations. Real solutions

<R> Equations involving roots
<R> Exponential equations
<R> Logarithmic equations
Integer numbers

        Addition and subtraction of integer numbers
        Multiplication and division of integer numbers
Decimal numbers

        Addition and subtraction of decimal numbers
        Multiplication of decimal numbers
        Division of decimal numbers
Rational numbers

<R> Placing fractions on the Number Line
<R> Identifying fractions on the Number Line
        Fraction of shaded shapes I
        Fraction of shaded shapes II
        Simplifying fractions
        Reduce to a common denominator
        Sorting fractions
        Addition-subtraction of fractions with like denominators
        Addition-subtraction of fractions with unlike denominators
        Addition, subtraction, multiplication and division with fractions
        Improper fractions to mixed numbers
        Mixed numbers to improper fractions
        Identifying mixed numbers of shaded shapes
        Converting decimal numbers to fractions

Real numbers

<R> Intervals I
<R> Intervals II
<R> Intervals III
<R> Intervals IV
<R> Placing real numbers on the Number Line
        Rounding real numbers
        Convert from standard notation into scientific notation
        Convert from scientific notation into standard notation
        Addition and subtraction in scientific notation
        Multiplication and division in scientific notation

Unit conversion

        Mass conversion (metric)
        Length conversion (metric)
        Time conversion
        Area conversion I (metric)
<R> Area conversion II: Square meter and hectare
<R> Volume conversion I: (metric)
<R> Volume conversion II (metric)
<R> Volume conversion III (metric)
        Temperature conversion I (Celsius - Fahrenheit)
<R> Temperature conversion II (Celsius - Fahrenheit - Kelvin)
<R> Length conversion (metric - imperial)
<R> Mass conversion (metric - imperial)

Sexagesimal system

        Time and clock (I)
        Time and clock (II)
        Addition  (angles and time)
        Subtraction  (angles and time)
        Multiplication by a whole number  (angles and time)
        Division by a whole number   (angles and time)
        Complementary and supplementary angle calculation
        Angle calculation in triangles and other shapes

Powers and roots

        Simplifying powers of natural numbers I
        Simplifying powers of natural numbers II
        Simplifying powers of rational numbers I
        Simplifying powers of rational numbers II
        Calculation of square roots in your head
        Finding square roots using the algorithm
        Root rationalization I: (monomial)
        Root rationalization II: (binomial)
        Root rationalization III: (n-th roots)
        Addition and subtraction of square roots
        Simplifying n-th roots

Percentages

        Percentages: Direct calculations

Sequences and progressions

<R> Arithmetic progressions I
<R> Arithmetic progressions II
<R> Geometric progressions I
<R> Geometric progressions II
<R> Geometric progressions III

Probability

        Probability I: Coins
<R> Probability II: Dice
<R> Probability III: Marbles
<R> Probability IV: Cards
<R> Normal distribution



Divisibility

        Finding set of divisors of a number
        Prime factorization of a number
        Lcm and gcm of natural numbers


Graphing functions

        Formula of a linear function given its graph
<R> Properties of a piecewise function given its graph I
<R> Properties of a piecewise function given its graph II
<R> Formula of a piecewise function given its graph
        Basic I: Linear
        Basic II: Quadratic
<R> Basic III: Piecewise functions. Linear and constant
<R> Basic IV: Piecewise functions. Linear and quadratic
<R> Basic III: Exponential (non base e)
<R> Basic IV: Exponential (base e)
<R> Basic V: Logarithmic
<R> Basic VI: Simple rational
<R> Basic VII: Square root
<R> Advanced I: Cubic polynomial
<R> Advanced II: Rational
<R> Advanced III: Exponential
<R> Advanced IV: Logarithmic



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Topics and subtopics of Mathematics - Worksheet Generators
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Topics and subtopics of Mathematics for the folllowing Worksheet Generators


Mathematics
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Chemistry
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Mathematics
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Physics
Worksheet generator
Physics  +  Chemistry
Worksheet generator
Polynomials and algebraic fractions
Natural numbers
Descriptive statistics
Definite integrals
Indefinite integrals
Graphing functions


Study of functions






Derivatives
Limits







Analytic geometry of Space
Plane analytical geometry

Basic geometry
Trigonometry
Complex numbers
Matrices, determinants and systems of equations
Systems of non-linear equations
Systems of linear equations
Inequalities
Equations
Integer numbers
Decimal numbers
Rational numbers
Real numbers
Unit conversion
Powers and roots
Percentages
Sequences and progressions
Probability



Divisibility
Exponentials and logarithms
Systems of inequalities
Vector space
Exponentials and logarithms

        Exponential expression to logarithmic expression
        Logarithmic expression to exponential expression
<R> Simplifying logarithms
<R> Evaluate logarithms from another one
<R> Exponential equations
<R> Logarithmic equations
<R> Systems of 2×2 exponential equations
<R> Systems of 2×2 logarithmic equations


Systems of inequalities

<R> Systems of 2 linear inequalities in 1 variable
<R> Systems of 2 Linear Inequalities in 2 variables

Vector space

<R> Coordinates of a 2D_vector relative to a given basis
<R> Coordinates of a 3D_vector relative to a given basis
<R> Change of basis matrix for R² vectors
<R> Change of basis matrix for R³ vectors





Sexagesimal system
Differential equations
Differential equations

<R> Separable
<R> Linear equations
<R> Homogeneous equations
<R> Exact equations
<R> Second order homogeneous linear equations with constant coefficients




Note:
<R>  Only available in the registered version.
Blue text: New in this version.