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Basic Maths

Algebra, precalculus and calculus for college and university students. Contains topics ranging from numbers to differentiation and integration.

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Course content

Chapter 1: Numbers

  • Integers
    1. Calculating with integers
    2. Integers
    3. Division of integers
  • Negative numbers
    1. Absolute value
  • Fractions
    1. Fractions
    2. Equivalent fractions
    3. Simplifying fractions
    4. Addition and subtraction of fractions
    5. Multiplication and division of fractions
    6. Integer powers of fractions
    7. Decimal numbers
  • Powers and roots
    1. Exponents
    2. Calculating with powers
    3. Roots of integers
    4. Roots of fractions
    5. Standard notation of higher roots
    6. Order of operations for powers and roots

Chapter 2: Algebra

  • Variables
    1. Variables
    2. Sum and product of variables
    3. Substitution
    4. Simplification
    5. Simplification with algebraic rules
  • Calculating with exponents and roots
    1. Integer powers
    2. Calculating with integer exponents
    3. Positive integer exponents
    4. Square roots
    5. Calculating with square roots
    6. Higher degree roots
    7. Calculating with fractional exponents
    8. Order of operations
  • Expanding brackets
    1. Expanding brackets
    2. Expanding double brackets
  • Factorization
    1. Factoring out
    2. Factorization
  • Notable products
    1. The square of a sum or a difference
    2. The difference of two squares
  • Adding and subtracting fractions
    1. Fractions
    2. Simplifying fractions
    3. Addition and subtraction of like fractions
    4. Making fractions similar
    5. Addition and subtraction of fractions
    6. Multiplication of fractions
    7. Division of fractions
    8. Fraction decomposition

Chapter 3: Linear formulas and equations

  • Formulas
    1. Formulas
    2. Dependent and independent variables
    3. Graphs
  • Linear functions
    1. Linear formula
    2. Slope and intercept
    3. Composing a linear formula
    4. Parallel and intersecting linear formulas
  • Linear equations and inequalities
    1. Linear equations
    2. The general solution of a linear equation
    3. Intersection points of linear formulas with the axes
    4. Intersection point of two linear formulas
    5. Linear inequalities
    6. General solution of a linear inequality

Chapter 4: Systems of linear equations

  • An equation of a line
    1. A linear equation with two unknowns
    2. Solution of linear equations with two unknowns
    3. The equation of a line
    4. Composing the equation of a line
  • Two equations with two unknowns
    1. Systems of linear equations
    2. Solving systems of linear equations by substitution
    3. Solving systems of equations by elimination
    4. General solution system of linear equations

Chapter 5: Quadratic equations

  • Parabola
    1. Quadratics
    2. Parabola
  • Solving quadratic equations
    1. Quadratic equations
    2. Solving quadratic equations by factorization
    3. Solving quadratic equations by completing the square
    4. The quadratic formula
  • Drawing parabolas
    1. Intersection of parabolas with the axes
    2. Vertex of a parabola
    3. Drawing of parabolas
    4. Transformations of parabolas
  • Intersection points of parabolas
    1. Intersection points of a parabola with a line
    2. Intersection points of parabolas
  • Quadratic inequalities
    1. Quadratic inequalities

Chapter 6: Functions

  • Domain and range
    1. Function and formula
    2. Function rule
    3. Intervals
    4. Domain
    5. Range
  • Power functions
    1. Power functions
    2. Transformations of power functions
    3. Equations with power functions
  • Higher degree polynomials
    1. Polynomials
    2. Equations with polynomials
    3. Solving higher degree polynomials with factorization
    4. Solving higher degree polynomials with the quadratic equation
    5. Higher degree inequalities
  • Power functions and root functions
    1. Root functions
    2. Transformations of root functions
    3. Root equations
    4. Solving root equations with substitution
    5. Inverse functions
  • Fractional functions
    1. Asymptotes and hyperbolas
    2. Power functions with negative exponents
    3. Transformations of power functions with negative exponents
    4. Linear fractional functions
    5. Linear fractional equations
    6. Inverse of linear fractional functions
    7. Quotient functions

Chapter 7: Exponential functions and logarithms

  • Exponential functions
    1. The exponential function
    2. Exponential equations
    3. Transformations of the exponential function
  • Logarithmic functions
    1. The logarithmic function
    2. Logarithmic equations
    3. Exponential equations
    4. Isolating variables
    5. Rules for logarithms
    6. More logarithmic equations
    7. Change of base
    8. Solving equations using substitution
    9. Graph of logarithmic functions
    10. Transformations of the logarithmic function

Chapter 8: Trigonometry

  • Angles with sine, cosine, and tangent
    1. Angles
    2. Triangles
    3. Rules for fight-angled triangles
    4. Angles in radians
    5. Symmetry in the unit circle
    6. Special values of trigonometric functions
    7. Addition formulas for trigonometric functions
    8. Sine & cosine rules
  • Trigonometric functions
    1. Trigonometric functions
    2. Transformations of trigonometric functions
    3. Inverse trigonometric functions
    4. Trigonometric equations

Chapter 9: Differentiation

  • The derivative
    1. The differene quotient
    2. The difference quotient at a point
    3. The tangent line
    4. The notion of derivative
  • The derivative of power functions
    1. The derivative of power functions
  • Sum and product rule
    1. The sum rule
    2. The product rule
  • Chain rule
    1. Composite functions
    2. The chain rule
  • The derivative of standard functions
    1. The derivative of trigonometric functions
    2. The base e and the natural logarithm
    3. The derivative of the natural logarithm
    4. The derivative of exponential functions and logarithms
  • The quotient rule
    1. The quotient rule
  • Applications of derivatives
    1. Increasing and decreasing
    2. Extreme values
    3. The second derivative
    4. Types of increasing and decreasing
    5. Inflection points
    6. Higher order derivatives

Chapter 10: Integration

  • Antiderivatives
    1. The antiderivative of a function
    2. The antiderivative of a power function
    3. Rules of calculation for antiderivatives
    4. Antiderivatives of known functions
    5. Antiderivatives and the chain rule
  • The definite integral
    1. Definite integral
    2. Area
    3. Area of a surface between curves
    4. Area between curves
    5. Solid of revolution
  • Integration techniques
    1. Substitution method
    2. Trigonometric integrals
    3. Integration by parts
    4. Repeated integration by parts
    5. Known antiderivatives of some quotient functions
    6. Long division with polynomials
    7. Finding the antiderivatives of quotient functions

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