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Algebra

Standardized Tests

SAT/ACT Standardized Test Prep


Solving Equations

Solving Equations by Adding and Subtracting
Solving Equations by Multiplication and Division
Solving Multi-Step Equations
Solving Equations using Reciprocals
Solving Equations by Combining Like Terms
Solving Equations with Distribution
Solving Equations with Fractions (Fraction Busting)
Solving Equations with Decimals (Decimal Busting)
Solving Equations with Variables on Both Sides
Solving Equations Using Square Roots
Writing Equations
Word Problems- Expressions


Solving Inequalities

Inequalities (Adding and Subtracting)
Inequalities (Multiplication and Division)
Solving Inequalities (Multi-step)
Solving Compound Inequalities


Absolute Value Equations & Inequalities

Absolute Value Equations
Absolute Value Inequalities


Linear Equations

Notes: Linear Equations
Intro to Linear Equations
Linear Equations and Slope
Is it Linear?
Graphing Linear Equations
Slope Formula
Linear Equations- Standard Form
Net Change
Slope Intercept Form
Point Slope Form
Linear Equations- General Form
Linear Equations- Direct Variation
Horizontal Lines
Vertical Lines
Parallel and Perpendicular Slope
Distance between a point and a line
Isolating Variables
Fahrenheit and Celsius Conversions
Finding x- and y- intercepts


Solving Systems

Solving Systems (Substitution)
Solving Systems (Elimination)
Graphing Systems of Inequalities
3 Variable Systems
Nonlinear Systems


Polynomials

Irrational Numbers
Exponents
Multiplying Monomials
Dividing Monomials
Scientific Notation
Intro to Polynomials
Is it a Polynomial?
Notes: Polynomials
Adding and Subtracting Polynomials
Multiplying Polynomials (FOIL)
Dividing Polynomials (Long Division)
Dividing Polynomials (Synthetic Substitution)
Synthetic Substitution
End Behavior- Polynomial Functions
Completing the Square
The Quadratic Formula and the Discriminant
Complex Numbers (Imaginary Numbers)
Polynomials Multiplicity of Roots
Rational Zero Theorem
Descartes’ Rule of Signs
Roots and Zeroes
Linear Factored Form
Quadratic Inequalities
Polynomial Inequalities


Factoring

Factoring out a GCF
Factoring Perfect Square Trinomials
Factoring Trinomials a=1
Factoring u-substitution
Factoring Trinomials a≠1
Factoring: Difference of 2 squares
Factoring: Sum/Difference of 2 cubes
Factor by Grouping
Solving Quadratic Equations by factoring


Radical Expressions & Equations

Adding and Subtracting Square Roots
Multiplying Square Roots
Dividing Square Roots
Radical Expressions
Radical Equations
Square Roots
Simplifying Square Roots
Cube Roots
Simplifying Cube Roots
Adding & Subtracting Cube Roots
Multiplying Cube Roots
Dividing Cube Roots
Radical Exponents
Zero Exponents
Negative Exponents


Word Problems

Word Problems- Linear Equations
Word Problems- Averages
Word Problems- Consecutive Integers
Word Problems- Distance, Rate and Time
Breakeven Word Problems
Word Problems- Ratios and Proportions
Word Problems- Ages
Word Problems- Mixtures and Concentration


Rational Expressions & Equations

Ratios and Proportions
Rational Expressions (Multiplying and Dividing)
Rational Equations
Rational Expressions (Adding and Subtracting)
Direct, Inverse and Joint Variation
Complex Fractions
Partial Fraction Decomposition


Data Analysis

Histograms
Circle Graphs (Pie Charts)
Stem and Leaf Plot (Stemplot)
Mean, Median and Mode
Mean Absolute Deviation
5 Number Summary-Quartiles and IQR
Box and Whisker Plot
Parameter vs Statistic
Scatterplots


Probability

Intro to Probability
Intro to Probability (Multiple Events)
Experimental and Theoretical Probability
Factorials
Combinations and Permutations
Complement of an Event
Probability “At Least One”
Mutually Exclusive Events (Disjoint)
Expected Value and Variance of a Random Variable
Independent Events (Probability)
Conditional Probabilities
Marginal Frequencies and Distributions
Two-Way Tables (Probability)
Tree Diagrams
Probability- Marbles
Probability- Coin Tosses
Probability with Dice
Probability- Round Table
Probability- 5 card Poker Hands
Binomial Distribution Notes


Functions

Evaluating Functions
Evaluating Functions using Graphs
Set Builder Notation
Vertical Line Test
Is it a Function?
Operations of Functions
Notes- Functions
Composite Functions
Inverse Functions and Relations
Interval Notation
Domain and Range (Roots and Denominators)
Parent Functions
Graphing Square Root Functions
Graphing Quadratic Functions
Graphing Cube Root Functions
Graphing Absolute Value Functions
Vertical Asymptotes
Horizontal Asymptotes
Slant Asymptotes
Even and Odd Functions
Evaluating Piecewise Functions
Graphing Piecewise Functions
Absolute Value Functions as Piecewise Functions
Transformations- |f(x)| and f|x|


Sequences and Series

Arithmetic Sequences
Geometric Sequences
Arithmetic Series
Geometric Series
Infinite Geometric Series
Arithmetic Means Between 2 Terms
Summation Notation (Sigma Notation)
Product Notation (Pi Notation)
Finite Sums Formulas

In Summary

Algebra is a branch of mathematics that deals with the study of symbols and the rules for manipulating them. It is used to represent and solve equations, which are statements that describe the relationships between different quantities.

In algebra, we use variables to represent unknown quantities. The most common variable is “x,” but any letter can be used. We can perform mathematical operations on variables just like we do with numbers. For example, we can add, subtract, multiply, and divide variables.

One of the fundamental concepts in algebra is the equation. An equation is a statement that shows that two expressions are equal. For example, the equation “2x + 3 = 7” shows that the expression “2x + 3” is equal to the number 7. To solve an equation, we need to find the value of the variable that makes the equation true.

Another important concept in algebra is the function. A function is a set of ordered pairs of numbers, where the first number in each pair is called the input and the second number is called the output. Functions can be represented graphically, as a curve on a coordinate plane. The graph of a function shows how the output of the function changes as the input changes.

Inequalities are another important concept in algebra. An inequality is a statement that shows that one expression is greater than or less than another expression. For example, the inequality “x > 3” means that the value of x is greater than 3. Inequalities can also be represented graphically, using a number line or a coordinate plane.

Systems of equations are sets of two or more equations that are solved simultaneously. To solve a system of equations, we need to find values for the variables that make all of the equations in the system true at the same time. There are several methods for solving systems of equations, including graphing, substitution, and elimination.

Polynomials are another important topic in algebra. A polynomial is an expression that is made up of variables and constants, with the variables being raised to whole number powers. Polynomials can be added, subtracted, and multiplied, just like numbers. The process of factoring a polynomial involves breaking it down into simpler expressions.

Rational expressions are another topic covered in algebra. A rational expression is an expression that can be written as the ratio of two polynomials. Rational expressions can be simplified by cancelling common factors, just like fractions.

Radicals, or roots, are another topic covered in algebra. A radical is an expression that represents the root of a number or an expression. Radicals can be simplified by using the laws of exponents.

Quadratic equations are another important topic in algebra. A quadratic equation is an equation in the form “ax^2 + bx + c = 0,” where “a,” “b,” and “c” are constants and “x” is the variable. Quadratic equations can be solved using a variety of methods, including factoring and the quadratic formula.

Logarithms are another topic covered in algebra. A logarithm is an exponent that shows the power to which a base must be raised to produce a given number. Logarithms can be used to solve equations and perform other mathematical operations.

Sequences and series are another topic covered in algebra. A sequence is a set of numbers that are listed in a specific order. A series is the sum of the terms in a sequence. Both sequences and series can be represented using mathematical notation and can be used to model real-world situations.

Data analysis is another important topic in algebra. Data analysis involves collecting, organizing, and interpreting data to draw conclusions and make decisions. In algebra, students learn how to use graphs, tables, and statistical measures to analyze data and make predictions.

Matrices are another topic covered in algebra. A matrix is a rectangular array of numbers or expressions, arranged in rows and columns. Matrices can be added, subtracted, and multiplied using special rules. Matrices are often used to represent and solve systems of equations.

Combinatorics is another topic covered in algebra. Combinatorics is the study of counting and arranging objects. In algebra, students learn about permutations, which are arrangements of objects in a specific order, and combinations, which are arrangements of objects without regard to order.

Overall, Algebra 1 is a crucial subject for students interested in pursuing careers in science, engineering, or other fields that require advanced mathematical skills. By mastering the concepts of Algebra 1, students will be well-prepared to tackle more advanced math courses and apply their skills to real-world problems.

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