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: Foundations & Functions

✅ Concept Overview & Function Review

• Review of functions, domain, and range

• Function notation and operations

• Introduction to rational, radical, and piecewise functions

✅ Polynomial Division & Zeros

• Long division and synthetic division of polynomials

• Finding and interpreting zeros

• Fundamental Theorem of Algebra

Week 2: Rational & Radical Expressions

✅ Rational Expressions & Equations

• Simplifying rational expressions

• Solving rational equations and identifying extraneous solutions

• Real-world applications

✅ Radical Functions

• Graphing square root and cube root functions

• Solving radical equations

• Identifying domain, range, and asymptotes

Week 3: Inverses, Logarithms & Exponentials

✅ Inverse Functions

• Definition and identification of inverse functions

• Verifying inverses algebraically and graphically

• One-to-one functions and restrictions

✅ Exponential & Logarithmic Functions

• Properties, graphs, and applications

• Solving exponential and logarithmic equations

• Real-world modeling (e.g., finance, population)

Week 4: Trigonometry Concepts

✅ Trigonometric Ratios & Unit Circle

• Review of sine, cosine, tangent

• Radians and degrees

• Introduction to the unit circle

✅ Graphing & Inverse Trig Functions

• Graphing sine, cosine, and tangent functions

• Amplitude, period, and phase shift

• Inverse trig functions and their domains/ranges

Week 5: Trig Identities & Applications

✅ Trigonometric Identities

• Pythagorean, reciprocal, co-function identities

• Verifying identities and simplifying expressions

✅ Solving Trig Equations & Triangle Applications

• Solving basic and complex trig equations

• Law of Sines and Law of Cosines

• Applications in geometry and real-world problems

Week 6: Geometry & Conic Sections

✅ Advanced Geometry & Constructions

• Geometric constructions with compass and straightedge

• Proofs with circles, triangles, and parabolas

✅ Conic Sections

• Equations and properties of circles, parabolas, ellipses, and hyperbolas

• Applications in physics and architecture

• Focus-directrix definition of a parabola

Week 7: Sequences, Series, & Probability

✅ Sequences & Series

• Arithmetic and geometric sequences

• Writing recursive and explicit formulas

• Real-world applications and modeling

✅ Probability & Statistics

• Permutations, combinations, and probability rules

• Normal distribution, z-scores

• Confidence intervals and hypothesis testing

Week 8: Modeling, Technology & Review

✅ Mathematical Modeling & Optimization

• Solving real-world problems using polynomial, exponential, and logarithmic models

• Introduction to optimization: maxima and minima problems

✅ Technology, Assessment, & Review

• Using graphing calculators and software

• Review of all major topics with practice assessments

• Preparation for Pre-Calculus, SAT/ACT, and final evaluations

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 pre-calculus concepts and exam prep.