Weekly Sessions: June 16 through August 9, 2025

In-Center : Every Monday and Wednesday from 2:00 PM to 3:00 PM

Online: Every Monday and Wednesday from 1:00 PM to 2:00 PM

Week 1: Functions & Graphs

✅ Function Basics

• Definitions, domain and range

• Function notation

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

✅ Transformations & Composition

• Shifts, reflections, stretches/shrinks

• Composition of functions

• Inverse functions (intro and verification)

Week 2: Polynomial & Rational Functions

✅ Polynomial Functions

• Degree, leading coefficient, and end behavior

• Roots/zeros of polynomials

• Factoring techniques and Rational Root Theorem

• Descartes’ Rule of Signs

✅ Polynomial Division & Graph Analysis

• Long and synthetic division

• Analyzing polynomial graphs

• Applications and real-world connections

Week 3: Rational & Exponential Functions

✅ Rational Functions

• Simplifying rational expressions

• Vertical, horizontal, and oblique asymptotes

• Analyzing and sketching rational graphs

✅ Exponential Functions

• Properties of exponents

• Exponential growth and decay models

• Solving exponential equations

Week 4: Logarithmic Functions & Equations

✅ Logarithmic Concepts

• Definition and properties of logarithms

• Change of base formula

• Logarithmic scales (e.g., pH, Richter)

✅ Equations & Modeling

• Solving exponential/logarithmic equations

• Applications in population, finance

• Midterm Assessment

Week 5: Trigonometric Functions & Graphs

✅ Angle Measures & Unit Circle

• Radian vs. degree measure

• Converting units, coterminal and reference angles

• Unit circle definitions of sine, cosine, tangent

✅ Trig Graphs & Identities

• Graphs of sine, cosine, and tangent

• Amplitude, period, and phase shifts

• Trig identities: Pythagorean, reciprocal, quotient

Week 6: Trig Equations, Laws & Applications

✅ Solving Trig Equations

• Using identities to simplify

• General and specific solutions

✅ Triangle Applications

• Law of Sines and Law of Cosines

• SSA, SAS, and AAS cases

• Area formulas including Heron’s formula

Week 7: Sequences, Series & Complex Numbers

✅ Sequences & Series

• Arithmetic and geometric sequences

• Recursive formulas

• Series and sigma notation

• Convergence/divergence

✅ Complex Numbers

• Real vs. imaginary parts

• Operations with complex numbers

• Polar form and De Moivre’s Theorem

Week 8: Vectors, Matrices & Limits

✅ Vectors & Matrices

• Vector operations, magnitude/direction

• Dot product and applications

• Matrix operations, inverses, determinants

• Cramer’s Rule

✅ Conic Sections & Intro to Limits

• Parabolas, circles, ellipses, hyperbolas

• Focus-directrix definitions

• Limits and continuity: graphical and algebraic

• Final Review & Cumulative Exam

Notes:

• Assessment Focus: Weekly quizzes, midterm in Week 4, and a cumulative final exam in Week 8.

• Integrated Practice: Real-life applications embedded weekly to build relevance and depth.

• Flexibility: Teachers can adapt pacing to allow more time for high-need topics.

• College Readiness: Week 8 bridges into calculus concepts and exam prep.