Precalculus & Algebra Curriculum
Course Overview

This course prepares students for Calculus by building a strong foundation in algebraic techniques, functions, exponents, and logarithms. It emphasizes problem-solving, symbolic reasoning, and mathematical communication.

Unit 1: Foundations of Algebraic Manipulation

Goal: Develop mastery of algebraic simplification and manipulation techniques.

Lesson 1: Order of Operations (PEMDAS) and simplifying expressions

Lesson 2: Properties of Real Numbers (commutative, associative, distributive)

Lesson 3: Simplifying Algebraic Expressions

Lesson 4: Linear Equations – solving single-variable equations

Lesson 5: Linear Inequalities – solving and graphing on a number line

Lesson 6: Absolute Value Equations & Inequalities

Lesson 7: Systems of Linear Equations (substitution, elimination, matrix methods)

Unit 2: Functions and Graphs

Goal: Understand functions as mathematical models and develop graphing skills.

Lesson 8: Definition of a Function (domain, range, function notation)

Lesson 9: Graphs of Functions (basic shapes, symmetry, intercepts)

Lesson 10: Transformations of Functions (translations, reflections, stretching)

Lesson 11: Combining Functions (addition, subtraction, multiplication, division)

Lesson 12: Composition of Functions

Lesson 13: Inverse Functions – definition and verification

Unit 3: Exponents and Polynomials

Goal: Master the laws of exponents and work fluently with polynomials.

Lesson 14: Laws of Exponents – positive, negative, zero exponents

Lesson 15: Scientific Notation & Applications

Lesson 16: Polynomial Functions – degree, leading coefficient, end behavior

Lesson 17: Operations on Polynomials (addition, subtraction, multiplication)

Lesson 18: Factoring Techniques (GCF, trinomials, difference of squares, sum/difference of cubes)

Lesson 19: Polynomial Equations – solving by factoring and substitution

Lesson 20: Rational Expressions – simplifying, multiplying/dividing, adding/subtracting

Lesson 21: Rational Equations & Applications

Unit 4: Exponential and Logarithmic Functions

Goal: Develop deep understanding of exponential growth/decay and logarithmic scales.

Lesson 22: Exponential Functions – definition and properties

Lesson 23: Graphs of Exponential Functions – growth and decay

Lesson 24: Introduction to Logarithms – definition and inverse of exponentials

Lesson 25: Laws of Logarithms (product, quotient, power rules)

Lesson 26: Change of Base Formula

Lesson 27: Solving Exponential Equations

Lesson 28: Solving Logarithmic Equations

Lesson 29: Applications – exponential growth, half-life, pH, Richter scale

Unit 5: Preparation for Calculus (Optional Extension)

Goal: Bridge to calculus concepts by applying algebra to limits and rates.

Lesson 30: Sequences and Series – arithmetic and geometric

Lesson 31: Introduction to Limits (conceptual, not formal proofs)

Lesson 32: Continuity and Function Behavior

Assessment Strategy

Homework: Practice problems at the end of each lesson.

Quizzes: At the midpoint of each unit.

Unit Exams: Cumulative test per unit.

Final Exam: Covers all units.

Projects (optional):

Population growth modeling with exponentials.

Real-world logarithmic scales (sound, earthquakes, finance).