ALGEBRA

• Basic Algebraic Operations
  • Addition, Subtraction, Multiplication, and Division of algebraic expressions.
  • Simplification of algebraic expressions using various techniques.
• Polynomials
  • Types of Polynomials: Monomials, binomials, and trinomials.
  • Operations on Polynomials: Addition, subtraction, multiplication, and division.
  • Factorization: Methods like factoring by grouping, using algebraic identities, and special cases such as quadratic polynomials.
  • Roots of Polynomials: Finding roots using methods such as factoring and the Rational Root Theorem.
• Equations and Inequalities
  • Linear Equations: Solving single-variable and multi-variable linear equations.
  • Quadratic Equations: Methods of solving including factoring, completing the square, and using the quadratic formula.
  • Cubic and Higher-Degree Equations: Basic solutions and factoring techniques.
  • Simultaneous Equations: Solving systems of linear equations using substitution, elimination, and matrix methods.
  • Inequalities: Solving linear inequalities and systems of inequalities.
• Algebraic Identities
  • Basic Identities: Such as (a+b)2=a2+2ab+b2(a + b)^2 = a^2 + 2ab + b^2(a+b)2=a2+2ab+b2, (a−b)2=a2−2ab+b2(a – b)^2 = a^2 – 2ab + b^2(a−b)2=a2−2ab+b2, and (a+b)(a−b)=a2−b2(a + b)(a – b) = a^2 – b^2(a+b)(a−b)=a2−b2.
  • Sum and Product of Roots: For quadratic and cubic equations.
• Quadratic Functions
  • Graphing Quadratic Functions: Understanding the parabolic shape and properties such as vertex, axis of symmetry, and direction of opening.
  • Vertex Form: Converting to and from vertex form (y=a(x−h)2+k)(y = a(x – h)^2 + k)(y=a(x−h)2+k).
• Exponential and Logarithmic Functions
  • Properties of Exponents: Laws of exponents and their application.
  • Logarithms: Basic properties and solving logarithmic equations.
• Sequences and Series
  • Arithmetic Progressions (AP): Understanding the common difference, nth term, and sum of the first n terms.
  • Geometric Progressions (GP): Understanding the common ratio, nth term, and sum of the first n terms.
• Applications of Algebra
  • Word Problems: Translating real-world problems into algebraic equations and solving them.
  • Age Problems, Profit and Loss, Time and Work, and Mixtures: Specific types of algebraic word problems.