Grade 9 Math Notes 2024-2025 PDF

Algebra Concepts - Study Notes Terms: Terms are single mathematical expressions (numbers, variables, or their combinations). Constants are terms without variables (e.g., 5, -3, 12). Coefficients are numerical factors multiplying variables (e.g., 4 in...

Algebra Concepts - Study Notes Terms: Terms are single mathematical expressions (numbers, variables, or their combinations). Constants are terms without variables (e.g., 5, -3, 12). Coefficients are numerical factors multiplying variables (e.g., 4 in 4x). Like and Unlike Terms: Like terms have the same variable raised to the same power (e.g., 3x and 5x; 2x² and -4x²). Unlike terms have different variables or exponents (e.g., 2x and 3y; x and x²). Distributive Law: The distributive law states a(b + c) = ab + ac. Distribute coefficients across sums or differences within parentheses (e.g., 3(x + 2) = 3x + 6; 2(2x - 4) = 4x - 8). Addition and Subtraction of Linear Expressions: Combine like terms for addition (e.g., 3x + 4x + 2 = 7x + 2). Distribute negative signs and combine like terms for subtraction (e.g., 5x - (2x + 3) = 5x - 2x - 3 = 3x - 3). Factorization: Factorization breaks down an expression into simpler factors. Factoring out the Greatest Common Factor (GCF) is often used (e.g., 6x² + 9x = 3x(2x + 3)). Order of Operations (PEMDAS): Follow the order: Parentheses, Exponents, Multiplication and Division (left to right), Addition and Subtraction (left to right). Example: 3 + 4 × (2 - 1)² = 3 + 4 × 1² = 3 + 4 × 1 = 7. My Goals: Regularly practice factoring and combining like terms. Accurately identify like and unlike terms during simplification. Employ the distributive law for simplifying expressions before operations. Use PEMDAS for accurate calculations in complex expressions. 1. **What is an Equation?** - An equation shows a relationship between variables, using an equal sign, it is different from an expression. 2. **Handling Parentheses:** - When you have parentheses in an equation, remove them first before solving. Solving Word Problems with Linear Equations - **Step 1:** Read the question carefully and find out what you don't know (the unknown). - **Step 2:** Use a variable, like X, to represent the unknown. - **Step 3:** Express other known quantities in terms of X. - **Step 4:** Create an equation based on the information given in the problem. - **Step 5:** Solve the equation. - **Step 6:** Write a clear answer statement that responds to the question. What is a Linear Equation in One Variable? A linear equation in one variable looks like this: - **Example:** aX + B = 0 - Here, 'a' and 'B' are constants, and 'a' cannot be zero. Methods to Solve Linear Equations in One Variable: Here are the common methods: - **A:** Add a term to both sides. - **B:** Subtract a term from both sides. - **C:** Multiply both sides by a constant. - **D:** Divide both sides by a constant.