Welcome to Fresno Academy

Mathematics Curriculum

Mathematics Syllabus [ 16yr - 18yrs ]

Calculus

  • Limits and Continuity
  • Differentiation and Its Applications
  • Rules of Differentiation (Product, Quotient, Chain Rule)
  • Implicit Differentiation
  • Applications of Derivatives (Optimization, Related Rates)
  • Introduction to Integration
  • Definite and Indefinite Integrals
  • Fundamental Theorem of Calculus
  • Applications of Integration (Area under Curves, Volume of Solids)

Advanced Algebra

  • Solving Higher-Degree Polynomial Equations
  • Complex Numbers and Their Operations
  • Solving Polynomial and Rational Inequalities
  • Logarithmic and Exponential Equations
  • Mathematical Induction
  • Exploring Rational Functions and Asymptotes

Trigonometry

  • Graphing Trigonometric Functions
  • Solving Trigonometric Equations
  • Trigonometric Identities and Proofs
  • Law of Sines and Law of Cosines
  • Applications of Trigonometry in Real-World Problems
  • Polar Coordinates and Graphs
  • Introduction to Vectors and Vector Operations

Statistics and Probability

  • Descriptive Statistics (Mean, Median, Mode, Variance, Standard Deviation)
  • Probability Distributions (Binomial, Poisson, and Normal Distributions)
  • Combinatorics (Permutations and Combinations)
  • Hypothesis Testing
  • Confidence Intervals
  • Data Analysis and Interpretation
  • Correlation and Regression

Sequences and Series

  • Arithmetic Sequences and Series
  • Geometric Sequences and Series
  • Convergence and Divergence of Series
  • Infinite Geometric Series
  • Binomial Theorem and Pascal’s Triangle

Vectors and Matrices

  • Introduction to Vectors in 2D and 3D
  • Vector Operations (Addition, Subtraction, Scalar Multiplication)
  • Dot Product and Cross Product
  • Applications of Vectors in Physics and Engineering
  • Introduction to Matrices
  • Matrix Operations and Determinants
  • Solving Systems of Equations Using Matrices (Gaussian Elimination, Inverse Matrices)

Complex Numbers

  • Operations with Complex Numbers (Addition, Subtraction, Multiplication, Division)
  • Polar Form of Complex Numbers
  • De Moivre’s Theorem
  • Roots of Complex Numbers
  • Applications of Complex Numbers in Engineering and Physics

Pre-Calculus Review

  • Review of Functions and Their Properties
  • Graphing and Transformations of Functions
  • Exponential and Logarithmic Functions
  • Quadratic and Polynomial Functions
  • Rational Functions and Their Graphs

Mathematical Modeling

  • Creating and Analyzing Mathematical Models
  • Using Functions to Model Real-World Phenomena
  • Optimization Problems in Real-Life Applications
  • Interpreting and Analyzing Data for Modeling

Financial Mathematics

  • Compound Interest and Loan Calculations
  • Investment Strategies and Risk Assessment
  • Understanding Annuities and Pensions
  • Taxation, Inflation, and Budgeting
  • Retirement Planning and Savings

Problem-Solving and Critical Thinking

  • Advanced Algebraic and Trigonometric Problem Solving
  • Geometric Applications in Problem Solving
  • Interpretation and Solution of Real-World Word Problems
  • Development of Logical Reasoning and Critical Thinking Skills

Project-Based Learning

  • Real-World Applications of Advanced Mathematics
  • Collaborative Projects and Presentations
  • Mathematical Research and Report Writing

Assessment and Review

  • Regular Quizzes and Tests
  • Formative and Summative Assessments
  • Homework and Classwork Feedback
  • End-of-Term Exams and Comprehensive Reviews