Detailed Syllabus

Our Algebra 2 syllabus is designed to cover school + competitive-level concepts step by step:

1. Functions & Graph

• Understanding functions, domain & range

• Types of functions: linear, quadratic, exponential, logarithmic, and rational

• Function transformations: shifts, stretches, reflections

• Composition of functions & inverse functions

2. Quadratic Functions & Equations

• Standard, vertex, and factored forms

• Solving quadratics using:

  • Factoring

  • Completing the square

  • Quadratic formula

• Discriminant & nature of roots

• Graphing parabolas and applications in real-life problems

3. Polynomials

• Polynomial operations (addition, subtraction, multiplication, division)

• Remainder & Factor Theorem

• Zeros of polynomials and their relationship with coefficients

• Graphing higher-degree polynomials

• Solving cubic and quartic equations

4. Rational Expressions & Equations

• Simplifying rational expressions

• Finding excluded values

• Solving rational equations

• Applications in real-life scenarios

5. Radical & Exponential Functions

• Simplifying radicals and rational exponents

• Solving radical equations

• Exponential functions & growth/decay models

• Logarithms:

  • Properties & simplifications

  • Solving log equations

  • Logarithmic models in real life

6. Systems of Equations & Inequalities

• Solving linear systems (substitution, elimination, graphing)

• Solving systems with three variables

• Solving nonlinear systems

• Inequalities: linear, quadratic, and rational

• Graphical solution of inequalities

7. Sequences & Series

• Arithmetic sequences & sums

• Geometric sequences & sums

• Infinite series

• Binomial theorem & expansions

8. Complex Numbers

• Introduction to imaginary unit iii

• Operations with complex numbers

• Polar form and modulus-argument representation

• Solving quadratic equations with complex solutions

9. Probability & Statistics (Advanced)

• Conditional probability

• Permutations & combinations

• Normal distribution basics

• Mean, median, mode & standard deviation

• Data interpretation and analysis

10. Matrices & Determinants (Optional but Recommended)

• Matrix basics: types, addition, subtraction, multiplication

• Determinants & their properties

• Solving linear systems using matrices (Cramer’s rule)

• Applications in competitive exams