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Pre-Algebra 1
Algebra 1
Geometry
Algebra 2
Precalculus
Calculus
Regents Review by Individual Section
Summer 2023 Regents Review
New York State Regents Exams
Algebra 1
Topic A: The Real Number System & Algebraic Expressions
Concept 1: Properties of Real Numbers
Concept 2: Order of Operations; Signed Numbers; Evaluating Absolute Value
Topic B: Linear Equations & Word Problems; Percentage; Distance Problems; Dimensional Analysis
Concept 1: Solving Linear Equations
Concept 2: Solving Equations with Multiple Variables
Concept 3: Number, Consecutive Integer and Separation Problems
Concept 4: Coin, Stamp and Age Problems
Concept 5: Perimeter Problems
Concept 6: Rates and Dimensional Analysis
Concept 7: Percent; Percent Change
Concept 8: Percent Error; Relative Error; Rounding Off
Concept 9: Distance, Speed & Time Problems
Topic C: Inequalities (Interval Notation) & Absolute Value
Concept 1: Solving Absolute Value Equations
Concept 2: Inequalities and interval Notation
Concept 3: Inequality Word Problems
Topic D: Arithmetic and Geometric Sequences
Concept 1: Recursive and Explicit Sequences
Concept 2: Arithmetic Sequences
Concept 3: Geometric Sequences
Topic E: Working with Functions: Domain, Range, One-to-One Functions
Concept 1: Domain, Range and Function Notation; Appropriate Domain for a Situation
Concept 2: Evaluating Functions: Using Graphs to Evaluate a Function
Concept 3: Is a Relation a Function?; The Vertical Line Test
Concept 4: One- to- One Functions; The Horizontal Line Test
Concept 5: The Inverse of a Function
Topic F: Linear Functions, Equation of a Line, Zeros, Slope & Average Rate of Change
Concept 1: Slope
Concept 2: Finding x and y intercepts; Zeros of a Function
Concept 3: Finding the Equation of a Line: y = mx + b; Point-Slope form
Concept 4: Determining if a Point is on a Line
Concept 5: Graphing Linear Equations & Inequalities
Concept 6: Parallel and Perpendicular Lines
Concept 7: Direct Variations; Proportions
Concept 8: Applications of Linear Functions; Matching Expression with Situation
Concept 9: Average Rate of Change
Topic G: Solving Linear Systems of Equations & Inequalities
Concept 1: Solving Systems of Linear Equations Algebraically
Concept 2: Solving Systems of Linear Equations Graphically
Concept 3: Graphing a System of Linear Inequalities
Concept 4: Problem Solving with Systems of Linear Equations
Topic H: Parent Functions; Shifts, Reflections & Stretches; Piecewise Functions; Increasing & Decreasing Functions
Concept 1: Parent Functions; Shifting the Graphs of Functions
Concept 2: Increasing, Decreasing, and Constant Functions
Concept 3: Graphing Piecewise Functions
Concept 4: Interpreting Speed, Distance & Time Graphs
Topic I: Exponents; Exponential & Absolute Value Functions
Concept 1: Multiplying & Dividing Monomials; Working with Exponents
Concept 2: Working with Negative and Zero Exponents
Concept 3: Scientific Notation
Concept 4: Working with Rational (Fractional) Exponents
Concept 5: Solving Exponential Equations
Concept 6: Graphing Exponential & Absolute Value Functions
Concept 7: Applications of Exponential Functions; Growth and Decay
Topic J: Operations with Polynomials
Concept 1: Adding and Subtracting Monomials; Like Terms
Concept 2: Adding and Subtracting Polynomials; Degree & Standard Form of a Polynomial
Concept 3: Multiplying Polynomials; The FOIL Method
Concept 4: Dividing Polynomials; Long Division
Topic K: Techniques of Factoring
Concept 1: Greatest Common Factor (GCF)
Concept 2: Factoring a Difference of Two Squares: D.O.T.S.
Concept 3: Factoring Trinomials
Concept 4: Factoring Trinomials of the form ax^2 + bx + c
Concept 5: Factoring Completely
Concept 6: Factoring by Grouping
Topic L: Rational (Fractional) Expressions & Equations
Concept 1: Reducing Algebraic Fractions
Concept 2: Undefined Fractions
Concept 3: Multiplying and Dividing Algebraic Fractions
Concept 4: Adding and Subtracting Algebraic Fractions
Concept 5: Solving Fractional Equations
Topic M: Radicals & Solving Quadratic Equations
Concept 1: Simplifying Radicals; Irrational Numbers
Concept 2: Adding and Subtracting Radicals
Concept 3: Multiplying and Dividing Radicals
Concept 4: The Pythagorean Theorem (Review Topic)
Concept 5: Solving Quadratic Equations by Factoring & Square Roots
Concept 6: Solving Quadratic Equations Using the Quadratic Formula
Concept 7: Solving Quadratic Equations by Completing The Square
Concept 8: Solving a Linear-Quadratic System Algebraically
Topic N: Graphing Quadratics; The Parabola; Vertex Form; Systems of Equations
Concept 1: Graphing a Quadratic Function; The Parabola: axis of symmetry
Concept 2: Vertex Form of the Equation of a Parabola; domain, range, maximums & minimums
Concept 3: Solving Systems Involving Quadratics Graphically
Concept 4: Shifting, Reflecting, & Stretching the Graphs of Functions
Topic O: Applications of Quadratics
Concept 1: Solving Quadratic Word Problems
Concept 2: Applications of Quadratic Functions
Topic P: Statistics
Concept 1: Surveys, Experiments and Bias
Concept 2: Measures of Central Tendencies: Mean, Mode, Median; Interquartile Range, Outliers
Concept 3: Interquartile Range, Outliers, Quartiles, Skewed and Symmetric Distributions
Concept 4: Standard Deviation
Concept 5: Linear Regression: Line of Best Fit; Correlation Coefficient
Concept 6: Correlation and Causation; Bivariate and Univariate Data
Concept 7: Two-Way Tables
Concept 8: Residuals and Residual Plots
Concept 9: Graphs in Statistics: Histograms (Quartiles), Box & Whisker, Stem & Leaf