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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