Download Algebra A

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