Unit 2: Algebraic Foundations: Unveiling Patterns & Relationships
The chapter provides a comprehensive overview of algebraic foundations, emphasizing the importance of expressions, equations, and their simplification. Key operations such as collecting like terms, expanding brackets, and factoring are illustrated with clear examples. The chapter also involves solving linear equations and inequalities, identifying patterns in sequences, and graphing linear relationships, providing students with essential tools to analyze and communicate mathematical concepts effectively.
Sections
Navigate through the learning materials and practice exercises.
What we have learnt
- Algebra is a powerful tool for describing and predicting change in various systems.
- Simplifying expressions involves combining like terms and applying the distributive property.
- Factoring reveals the structure of algebraic expressions and is essential for solving equations.
- Linear equations can be solved to find variable values, and inequalities represent ranges of solutions.
- Understanding sequences helps in identifying patterns and predicting future terms.
- Graphing linear relationships allows visualization of how variables are related.
Key Concepts
- -- Term
- A single number, variable, or a product/quotient of numbers and variables.
- -- Coefficient
- The numerical part of a term that multiplies a variable.
- -- Like Terms
- Terms that have the exact same variables raised to the exact same powers.
- -- Expression
- A combination of terms using mathematical operations that does not contain an equals sign.
- -- Greatest Common Factor (GCF)
- The largest factor shared by two or more terms.
- -- Linear Equation
- An equation whose graph is a straight line.
- -- Inequality
- A mathematical statement comparing two expressions that are not necessarily equal.
- -- Arithmetic Sequence
- A sequence where the difference between consecutive terms is constant.
- -- Gradient (Slope)
- A measure of the steepness and direction of a line in a graph.
Additional Learning Materials
Supplementary resources to enhance your learning experience.