ALGEBRA 1

High school mathematics algebra 1 course notes. Course notes contents: Unit 1: Numbers, Variables and Expressions Real Number System Classification of numbers and their positions on the number line are examined. Differences between natural numbers, integers, rational and irrational numbers Positioning and comparison on the number line Concept and applications of absolute value Exponential expressions and scientific notation Algebraic Expressions Representing numerical relationships with symbols. Concept and use of variable Terms, coefficients, constants Combining like terms Simplifying expressions with the distributive property Calculating by substituting the value of the expression Unit 2: Single Variable Equations and Inequalities First Degree Equations Solving and applications of equations with one unknown. The difference between an equation and an expression One-step and multi-step equations Equations with variables on both sides Solving equations in parentheses Fractional and decimal equations Word problems and real-life applications Ratios and Percentages Ratio and proportion relationships and percentage calculations. The concept of ratio and unit rate Expressing proportional relationships with equations Percentage change, percentage error, interest calculation Scale and similarity problems First-degree inequalities Inequality solutions and representation on the number line. Inequality symbols: , , ≤, ≥ Solving one-step and multi-step inequalities Rule of direction change when multiplying/dividing by a negative Representing the solution set on the number line and interval notation Compound inequalities (AND / OR): intersection and union Absolute Value Equations and Inequalities Algebraic structures containing absolute values. Two-case solution of absolute value equations Absolute value inequalities and their representation on the number line Real-life contexts (tolerance, margin of error) Unit 3: Functions and Linear Relationships The Concept of a Function Input-output relationship and function definition. The difference between a relation and a function The rule that each input corresponds to a single output Vertical line test Forms of function representation: table, graph, rule (f(x)), matching diagram Domain and range Linear Functions Relationships with a constant rate of change. Concept of slope: interpreting as rate of change Formula m = (y₂ - y₁)/(x₂ - x₁) Positive, negative, zero, and undefined slopes Slope-intercept form: y = mx + b Standard form: Ax + By = C Point-slope form: y - y₁ = m(x - x₁) x-intercept and y-intercept points Graphing and Interpretation Graphical representation of linear relationships. Drawing lines in the coordinate plane Creating graphs from table values Writing equations from graphs Interpreting the meaning of intersection points Relationship between slopes of parallel and perpendicular lines Linear Modeling Explaining real data with linear models. Finding the line of best fit from the data table The difference between correlation and causality Estimation with interpolation and extrapolation Discussing the validity limits of the model