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Algebra A - Notes Chapter 2 – Linear Equations 2.1 Writing Equations Formula – An equation that states a rule for the relationship between certain quantities. --------------------------------------------------------------------------------------------------------------------- Explore 2.2 Algebra Lab: Solving Equations Algebra Tiles – Used to model solving equations. Solve an Equation – To find the value of the variable that makes the equation true. --------------------------------------------------------------------------------------------------------------------- 2.2 Solving One-Step Equations Solve an Equation – To solve an equation means to isolate the variable having coefficient of 1 on one side of the equation. Equivalent Equation – Equations that have the same solution. --------------------------------------------------------------------------------------------------------------------- Explore 2.3 Algebra Lab: Solving Multi-Step Equations No new vocabulary terms. --------------------------------------------------------------------------------------------------------------------- 2.3 Solving Multi-Step Equations Multi-Step Equations – Multi-step equations are equations that need more than one operation to solve them. Consecutive Integers – Consecutive integers are integers in counting order. Number Theory – The study of numbers and the relationships between them. --------------------------------------------------------------------------------------------------------------------- 2.4 Solving Equations with the Variable on Each Side Identity – An equation that is true for every value of the variable. --------------------------------------------------------------------------------------------------------------------- 2.5 Solving Equations Involving Absolute Value No new vocabulary terms. --------------------------------------------------------------------------------------------------------------------- 2.6 Ratios and Proportions Ratio – A comparison of two numbers by division. The ratios of x and y can be expressed in the following ways: x to y x:y x y Proportion – An equation stating that two ratios are equal is called a proportion. (Ex. Means – In the ratio 4 8 ) 2 4 a c , b and c are the extremes b d Extremes – In the ratio a c , a and d are the extremes b d Rate – The ratio of two measurements having different units of measure is called a rate. Unit Rate – A ratio of two quantities, the second of which is one unit. For example: 350 M&M’s per 1 bag. Scale – A ratio or rate is called a scale when making a model or drawing of something too large or too small to be conveniently drawn to actual size. Scale Model – A model used to represent an object that is too large or too small to be built at actual size. --------------------------------------------------------------------------------------------------------------------- Extend 2.6 Spreadsheet Lab: Descriptive Modeling Metric – A rule for assigning a number to some characteristic or attribute. For example, teachers use metrics to determine grades. Debt-to-income ratio – A metric used by the banking industry to determine if someone qualifies for a loan. It’s calculated by taking how much a person owes per month divided by how much a person makes per month. --------------------------------------------------------------------------------------------------------------------- 2.7 Percent of Change Percent of Change – When an increase or decrease is expressed as a percent. Percent of Increase – The ratio of an amount of increase to the previous amount, expressed as a difference percent. (Think: ) old Percent of Decrease – The ratio of an amount of decrease to the previous amount, expressed as a difference percent. (Think: ) old --------------------------------------------------------------------------------------------------------------------- Extend 2.7 Algebra Lab: Percentiles Percentile – A measure that is often used to report test data, such as standardized test scores. Decile – Values that divide a set of data into ten equal sized parts. The 1st decile contains data up to, but not including, the 10th percentile; the 2nd decile contains data from the 10th percentile up to, but not including, the 20th percentile, and so on. --------------------------------------------------------------------------------------------------------------------- Lesson 2.8 Literal Equations and Dimensional Analysis Literal Equation – A formula or equation with several variables. Dimensional Analysis – The process of carrying units throughout a computation. Unit Analysis – The process of including units of measurement when computing. --------------------------------------------------------------------------------------------------------------------- 2.9 Weighted Averages Weighted Average – The sum of the product of the number of units and the value per unit divided by the sum of the number of units, represented by M. Mixture Problem – Problems in which two or more parts are combined into a whole. Uniform Motion Problems (Also known as Rate Problems) – Problems in which an object moves at a certain speed, or rate. --------------------------------------------------------------------------------------------------------------------End