Egypt (EN)

Egyptian National Curriculum - English


Pure Mathematics - Algebra and Geometry G12

  • Overview
  • Chapters

Pure Mathematics - Algebra and Geometry for 3rd year of Secondary School

  • 1: Algebra
    1.1: Permutations, Combinations and Binomial Theorem
    1.1.1: Fundamental Counting Principle
    1.1.2: Counting Outcomes with Restrictions
    1.1.3: Counting Using Permutations
    1.1.4: Properties of Permutations
    1.1.5: Counting Using Combinations
    1.1.6: Properties of Combinations
    1.1.7: The Binomial Theorem
    1.1.8: Pascal’s Triangle and the Binomial Theorem
    1.1.9: General Term in the Binomial Theorem
    1.2: Complex Number
    1.2.1: Polar Coordinates
    1.2.2: Argand Diagram
    1.2.3: Modulus of a Complex Number
    1.2.4: The Argument of a Complex Number
    1.2.5: Polar Form of Complex Numbers
    1.2.6: Operations on Complex Numbers in Polar Form
    1.2.7: Exponential Form of a Complex Number
    1.2.8: De Moivre’s Theorem
    1.2.9: De Moivre’s Theorem for Trigonometric Identities
    1.2.10: Cube Roots of Unity
    1.2.11: The nth Roots of Unity
    1.2.12: Arbitrary Roots of Complex Numbers
    1.3: Determinants and Matrices
    1.3.1: Properties of Determinants
    1.3.2: Inverse of a Matrix: The Adjoint Method
    1.3.3: Properties of Inverse Matrices
    1.3.4: Introduction to The System of Linear Equations
    1.3.5: Solving a System of Three Equations Using a Matrix Inverse
    1.3.6: Elementary Row Operations
    1.3.7: Rank of a Matrix: Determinants
  • 2: Analytic Solid Geometry
    2.1: Geometry and Measurement in Two and Three Dimensions
    2.1.1: Points, Midpoints, and Distances in Space
    2.1.2: Equation of a Sphere
    2.1.3: Vectors in Space
    2.1.4: Magnitude of a Vector in 3D
    2.1.5: Scalar Multiplication and Unit Vectors
    2.1.6: Direction Angles and Direction Cosines
    2.1.7: Vector Operations in 3D
    2.1.8: Dot Product in 2D
    2.1.9: Dot Product in 3D
    2.1.10: Angle between Two Vectors in Space
    2.1.11: Vector Projection
    2.1.12: Cross Product in 2D
    2.1.13: Cross Product in 3D
    2.1.14: Parallel and Perpendicular Vectors in Space
    2.1.15: Scalar Triple Product
    2.2: Straight Lines and Planes in Space
    2.2.1: Equation of a Straight Line in Space: Cartesian and Vector Forms
    2.2.2: Equation of a Straight Line in Space: Parametric Form
    2.2.3: Angle between Two Straight Lines in Space
    2.2.4: Equations of Parallel and Perpendicular Lines in Space
    2.2.5: Equation of a Plane: Vector, Scalar, and General Forms
    2.2.6: Equation of a Plane: Intercept and Parametric Forms
    2.2.7: Angle between Two Planes
    2.2.8: Equations of Parallel and Perpendicular Planes
    2.2.9: Intersection of Planes
    2.2.10: Distances between Points and Straight Lines or Planes

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