Unit 1 – Introduction to Functions
Introduction to Functions is designed to provide students with a solid foundation in understanding the fundamental concepts of functions. This unit serves as an introduction to the broader field of mathematics, particularly the study of functions, which is a fundamental concept in algebra.
Throughout this unit, students will explore various aspects of functions, including their definition, representation, and behavior. The course aims to develop students’ skills in analyzing, graphing, and manipulating functions to solve problems in real-world contexts.
Unit 2 – Equivalent Algebraic Expressions
Equivalent algebraic expressions are expressions that have the same value regardless of the values assigned to the variables. In other words, they represent the same mathematical relationship or result, even though they may be written differently. Establishing equivalence between algebraic expressions is a fundamental skill in algebra. It allows for simplifying complex expressions, solving equations, proving identities, and making mathematical manipulations more manageable.
Unit 3 – Quadratic Functions
A quadratic function is a type of function in mathematics that can be defined by a quadratic equation. It is a polynomial function of degree 2, meaning the highest power of the variable in the equation is 2. Quadratic functions find applications in various fields, including physics, engineering, finance, optimization problems, and modeling real-world phenomena. They are used to describe and analyze quadratic relationships, such as projectile motion, parabolic trajectories, profit and cost functions, and optimization of quadratic forms.
Unit 4 – Exponential Functions
An exponential function is a type of mathematical function where the independent variable appears as an exponent. Exponential functions have numerous applications in fields such as finance, population growth, radioactive decay, compound interest, bacterial growth, and modeling natural phenomena. They provide a mathematical framework to describe processes that exhibit rapid growth or decay over time.
