High School Math and Regents Examinations

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We have videos and resources for High School Math based on the topics required for the Regents Exam conducted by NYSED.

Worked solutions for some past years Regents Exam.
Concepts that you will need to know for the Regents Math - Algebra, Geometry, Measurement, Probability, Statistics, Trigonometry.

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The following are past exam questions, videos, walkthroughs, examples, and solutions for the Regents Common Core Exam.

Regents High School Exam - Algebra 1 (Common Core)

Regents Exam - Algebra I

June 2024 Questions & Solutions
January 2024 Questions & Solutions

August 2023 Questions & Solutions
June 2023 Questions & Solutions
January 2023 Questions & Solutions

August 2022 Questions & Solutions
June 2022 Questions & Solutions
June 2021 Questions & Solutions
January 2020 Questions & Solutions

August 2019 Questions & Solutions
June 2019 Questions & Solutions
January 2019 Questions & Solutions

August 2018 Questions & Solutions
June 2018 Questions & Solutions
January 2018 Questions & Solutions

August 2017 Questions & Solutions
June 2017 Questions & Solutions
January 2017 Questions & Solutions

August 2016 Questions & Solutions
June 2016 Questions & Solutions
January 2016 Questions & Solutions

August 2015 Questions & Solutions
June 2015 Questions & Solutions
January 2015 Questions & Solutions

Regents High School Exam - Algebra 2 (Common Core)

Regents Exam - Algebra 2

January 2024 Questions & Solutions

August 2023 Questions & Solutions
June 2023 Questions & Solutions
January 2023 Questions & Solutions

August 2022 Questions & Solutions
June 2022 Questions & Solutions
January 2020 Questions & Solutions

August 2019 Questions & Solutions
June 2019 Questions & Solutions
January 2019 Questions & Solutions

August 2018 Questions & Solutions
June 2018 Questions & Solutions
January 2018 Questions & Solutions

August 2017 Questions & Solutions
June 2017 Questions & Solutions
January 2017 Questions & Solutions

August 2016 Questions & Solutions
June 2016 Questions & Solutions

Regents High School Exam - Geometry (Common Core)

Regents Exam - Algebra 2/Trigonometry (Common Core)

Regents Exam - Algebra 2/Trigonometry

January 2017 Questions & Solutions
August 2016 Questions & Solution

June 2016 Questions & Solutions
January 2016 Questions & Solutions

August 2015 Questions & Solutions
June 2015 Questions & Solutions
January 2015 Questions & Solutions

Integrated Algebra High School Regents Exam

Integrated Algebra Regents Exam

Download the June 2013 Integrated Algebra Regents Exam (pdf)
Solutions to questions 1 - 25

Download the January 2013 Integrated Algebra Regents Exam (pdf)
Solutions to questions 1 - 20
Solutions to questions 31 - 38

Download the August 2012 Integrated Algebra Regents Exam (pdf)
Solutions to questions 1 - 20

Download the January 2010 Integrated Algebra Regents Exam (pdf)
Solutions for Questions 1 - 6
Solutions for Questions 7 - 12
Solutions for Questions 13 - 18
Solutions for Questions 19 - 22
Solutions for Questions 23 - 27
Solutions for Questions 28 - 33
Solutions for Questions 34 - 39

Download the January 2009 Integrated Algebra Regents Exam (pdf)
Solutions for Questions 1 -12
Solutions for Questions 13 - 33
Solutions for Questions 34 - 39

Geometry High School Regents Exam

Algebra 2/Trigonometry High School Regents Exam

Algebra 2/Trigonometry Regents Exam

Download the January 2014 Algebra 2/ Trigonometry Exam (pdf)
Solutions to questions 1 - 39

Download the June 2013 Algebra 2/ Trigonometry Exam (pdf)
Solutions to questions 1 - 27

Download the January 2013 Algebra 2/ Trigonometry Exam (pdf)
Solutions to questions 1 - 35

Download the Algebra 2 & Trigonometry June 2010 Regents Exam (pdf)
Solutions for Questions 1 - 10
Solutions for Questions 11 - 20
Solutions for Questions 21 - 30
Solutions for Questions 31 - 39

Download the Algebra & Trigonometry 2009 Fall Sampler Exam (pdf)
Solutions for Questions 1 - 4
Solutions for Questions 5 - 8
Solutions for Questions 9 - 10
Solutions for Questions 11 - 14
Solutions for Questions 15 - 20
Solutions for Questions 21 - 24
Solutions for Questions 25 - 28
Solutions for Questions 29 - 32
Solutions for Questions 33 - 36
Solutions for Questions 37 - 39

Integrated Algebra

Number Sense & Operations Strand

1. Number Theory

Properties of Real Numbers
Closure Property
2. Operations

Radicals
Simplify Radicals
Simplify Radicals that involve Fractions
Simplify Radical Expressions
Add & Subtract Radicals
Multiply Radicals
Multiply Radicals Monomials & Binomials
Dividing Radicals

Scientific Notation
Scientific Notation to Standard Notation
Standard Notation to Scientific Notation
Operations on Numbers in Scientific Notation
Using a Calculator for Scientific Notation

Fractions, Percents, Ratios, Proportions
Ratio & proportion
Percents, Decimals & Fractions
Percent of a Number
Percent Word Problems

Worksheets
Percent of a Number
Percent Word Problems (Part 1)
Percent Word Problems (Part 2)
Percent Word Problems (Part 3)
Percent Word Problems (Part 4)

** Exponents (Powers)**
Positive, Zero & Negative Exponents
Product Rule for Exponents
Quotient Rule for Exponents
Power Rule for Exponents
Rules for Negative Exponents

** Factorials**
Factorial Notation
Multiply & Divide Factorials

Pre-Algebra Review
Direct Variation
Absolute value
Rational & Irrational Numbers
Order of Operations
Signed Numbers

Algebra Strand

3. Variables & Expressions

Algebraic Representations
Algebraic Representations

Addition & Subtraction of Polynomials
Types of Polynomials
Add & Subtract Polynomials

Multiplication of Polynomials
Multiply Monomials
Multiply Monomials & Polynomials
Multiply Binomials using the FOIL method
Multiply Binomials using the Box method
Multiply Binomials using Distributive Property & Vertical Method

Division of Polynomials
Divide a Polynomial by a Monomial
Divide Polynomials using Long Division
Divide Polynomials using Synthetic Division

Algebraic Fractions
Introduction to Algebraic Fractions
Multiply Algebraic Fractions
Divide Algebraic Fractions
Add Algebraic Fractions
Add & Subtract Algebraic Fractions
Examples of Simplify Algebraic Fractions

Fractional Equations
Solving Fractional Equations I
Solving Fractional Equations II

Factoring
Factoring Common Factors
Factor Perfect Square Trinomials
Factor Difference of Squares
Factor Sum & Difference of Two Cubes

Factor Polynomials by Grouping
Factor Simple Trinomials (for a = 1)
Factor Trinomials (for a > 1)
Factor Trinomials by Guessing
Factor Trinomials by Completing the Square
Factor Completely using the different factoring techniques

Worksheets
Factoring Binomials by Difference of Squares
Factoring Perfect Square Trinomials
Factoring Trinomials or Quadratic Equations
Factoring Different Types of Trinomials (I)
Factoring Different Types of Trinomials (II)
4. Equations & Inequalities

Linear Equations
Algebraic Translations

Solving One-Step Equations
Solving Two-Step Equations
Solving Equations by Combining Like Terms
Distributive Property
Solving Multi-Step Equations
Solving Multi-Step Equations with variables on both sides
Solving Equations with Decimals
Solving Equations with Fractions
Solving Equations with Absolute Value

Systems of Linear Equations (Algebraic & Graphic)
Solving Systems of Equations by Substitution
Solving Systems of Equations by Addition or Elimination
Solving Systems of Equations Graphically
Solving Systems of Equations with Fractions or Decimals

Worksheets
Solving System of Equations by Substitution
Solving System of Equations by Addition
Solving System of Equations by Subtraction
Solving System of Equations by Addition or Subtraction
Solving System of Equations by Multiplication & then Addition or Subtraction

Literal Equations
Solving Literal Equations

Quadratic Equations
Solve Quadratic Equations Square Root Method
Solve Quadratic Equations by Factoring
Solve Quadratic Equations Completing the Square
Solving Quadratic Equations by Graphing
Linear-Quadratic Systems

Exponential Growth & Decay

Linear Inequalities (single variable)
Introduction to Linear Inequalities
Solving Inequalities by Add or Subtract
Solving Inequalities by Multiply or Divide
Solving Linear Inequalities
Solving Inequalities with Fractions
Solving Inequalities with Variables on both sides
Solving & Graphing Linear Inequalities on a number line
Graphing Linear Inequalities
Systems of Inequalities
5. Patterns, Functions, & Relations

Working with Sets & Venn Diagrams
Set-builder & Interval Notation
Universal Sets, Subsets, Equal Sets, Disjoint Sets
Set Operations - Union, Intersection, Complement
Venn Diagrams
Venn Diagram Word Problems

Definition of Function
Function Notation
Domain & Range of a Function
Relations & Functions
6. Trigonometric Functions

Pythagorean Theorem
Pythagorean Theorem

Worksheets
Pythagorean Theorem find the missing side
Pythagorean Theorem test for right triangle
Pythagorean Theorem dynamic

Trigonometric Ratios (using sine, cosine, tangent)
Trigonometric Functions Sine, Cosine, Tangent
Finding Length of Side using Trigonometry
Finding Angle Measure using Trigonometry
Trigonometry using calculator
Inverse Trigonometry using calculator
Trigonometry Find the unknown side
Trigonometry Find the unknown angle
Using Sine dynamic
Using Cosine dynamic
Using Tangent dynamic
Using Sine, Cosine or Tangent dynamically generated
Trigonometry Applications & Problems

Geometry Strand

7. Coordinate Geometry

Slopes & Equations of Lines
Finding the Slope of a Line
Graphing Lines by Plotting Points
Graphing Horizontal & Vertical Lines
Graphing Lines using the x-intercept & y-intercept
Convert a linear equation from standard form to slope-intercept form
Graphing Lines by Slope Intercept Method
Find the equation of a line using the Point Slope Form

Parallels & Perpendiculars
Equations for Parallel Lines
Equations for Perpendicular Lines

Parabolas
Graphing Parabolas in Vertex Form
Graphing Parabolas in Standard Form
Graphing Quadratic Functions(Maxima & Minima)
Graphing Functions & Examining Coefficients
8. Shapes

Area & Perimeter of Polygons & Circles
Perimeter of Polygons
Area of Polygons
Circumference of a Circle
Area of Circles & Sectors
Area & Perimeter on a Coordinate Plane

Volume & Surface Area of Solids
Volume of a Rectangular Prism
Volume of a Cylinder
Volume of a Cone
Surface Area of Rectangular Prism
Surface Area of Cylinder
Surface Area of Cone
Volume & Surface Area of Sphere

Worksheets
Circumference of Circle
Area of Circle
Area & Circumference of Circle dynamically generated
Circle Problems Radius, Diameter, Circumference, Area
Geometry Word Problems

Use Algebra to Solve Perimeter & Area of Rectangle
Surface Area & Volume of Cube
Surface Area & Volume of Rectangular Prisms or Cuboids
Volume & Surface Area of Cylinder
Volume & Surface Area of Sphere
Volume & Surface Area of Square Pyramids
Volume & Surface Area of Cones Measurement Strand
9. Measurement

Metric/English Conversions & Rates
English Unit Measurements
Metric Unit Measurements
Unit Rate
Rate Word Problems

Error in Measurement
Relative & Percent Error Formulas
Error in Measurement & Rounding

Probability & Statistics Strand

10. Working with Data

Categorizing Data & Bias
Qualitative & Quantitative Data
Univariate & Bivariate Data
Bias Data
Central Tendency Mean-Mode-Median

Displaying Data
Histogram
Cumulative frequency histogram
Quartiles, Box & whisker plots, Outliers

Scatter Plots, Correlation, Line of Best Fit, Prediction
Scatter Plot & Line of Best Fit
Scatter Plots & Correlations
Line of Best fit using a calculator

Percentiles and More Quartiles
11. Probability

Counting Principle

Permutations
Permutation Formula
Permutation with Repetition
Probability & Permutations

Sample Spaces & Tree Diagrams
Sample Spaces
Tree Diagrams

Theoretical versus Empirical (Experimental) Probability
Introduction to Probability
Theoretical & Experimental Probability

Mutually Exclusive & Independent Events, Complement
Complement of an Event
Mutually Exclusive Events
Probability of Independent Events
Probability of Dependent Events
Conditional Probability

Problems Involving AND & OR
Probability Addition Rule (“Or”)
Probability Multiplication Rule (“And”)

Worksheets
Probability Problems (I)
Complementary Probability
Probability Problems (II)
Probability & Geometry
Mutually Exclusive Probability
Independent Events Probability
Dependent Events Probability

Geometry

1. Geometric Relationships

Lines & Planes
Undefined Terms - Points, Lines & Planes
Line segments, Rays, Parallel & Skew lines, Parallel planes
Intersecting Lines & Planes
Theorems relating Lines & Planes
Euclidean and Non-Euclidean Geometry

Polygons - Interior & Exterior Angles
Types of Polygons
Interior Angles of Polygons
Exterior Angles of Polygons

Prisms, Pyramids, Cylinders, Cones, Spheres, Platonic Solids
Volume of Prisms
Surface Area of Prisms
Volume of a Pyramid
Surface Area of Pyramid

Volume of a Cylinder
Surface Area of Cylinder
Volume of a Cone
Surface Area of Cone
Volume & Surface Area of Sphere
Polyhedra & Platonic Solids
2. Constructions

Copy an Angle
Bisect an Angle (Angle Bisector)
Bisect a Line Segment (Perpendicular Bisector)
Construct Parallel Lines

Construct Perpendicular Lines
Construct Isosceles, Equilateral Triangles
Construct a Median of a Triangle
Construct the Centroid of a Triangle

Construct an Altitude of a Triangle
Construct the Incenter of a Triangle
Construct the Circumcenter of a Triangle
Construct the Orthocenter of a Triangle
Points of Concurrency - Incenter, Orthocenter, Circumcenter, Centroid
Euler Line
3. Locus

The Basic Locus Theorems
Compound Loci
4. Informal & Formal Proof

Logic Statements
Logic Statements Negation (NOT) Conjunction (AND) Disjunction (OR)
Conditional (IF … THEN)
Biconditional (IF AND ONLY IF)
Related Conditionals Converse, Inverse, Contrapositive

Truth Tables
Truth Tables Conjunction, Disjunction, Conditionals
Truth Tables for Multiple Statements

Writing a Proof - Direct Euclidean Proofs
Two Column Proofs
Flow Chart Proofs
Paragraph Proofs
Writing a Proof - Indirect Euclidean Proofs
Proof by Contradiction

Congruence of Triangles
Congruence & Similarity
Triangle Congruence SSS & SAS
Triangle Congruence AAS & ASA
Triangle Congruence HL (Hypotenuse Leg)
Why SSA & AAA are not Congruence Shortcuts?
CPCTC Corresponding parts of congruent triangles are congruent

Angles
Angle Addition Postulate
Types of Angles acute angles, right angles, obtuse angles, straight angles, reflex angles & full rotation angles
Complementary Angles
Supplementary Angles

Vertical Angles
Linear Pair
Complementary & Supplementary Angles
Adjacent, Complementary, Supplementary & Vertical Angles
Using complementary, supplementary, adjacent, & vertical angles

Triangles
Classify Triangles by Sides & by Angles
Area of Triangles
Area of Triangles using Heron’s Formula

Interior Angles of a Triangle
Exterior Angle Theorem
Isosceles Triangle Theorems
Triangle Inequality Theorems

Parallel Lines & Angles
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Co-Interior Angles
Corresponding & Alternate Angles
Problems involving Parallel Lines & Transversal

Quadrilaterals
Properties of Quadrilaterals
Theorems dealing with Parallelograms
Theorems dealing with Rectangles, Rhombuses, Squares
Theorems dealing with Trapezoids
Mid-Segment (Mid-Line) of a Triangle

Similarity of Triangles
Properties of Similar Triangles
Similarity, Area & Volume
Proving Triangles are Similar
Similar Triangles in Circles & Right Triangles

Pythagorean Theorem & Converse
Pythagorean Theorem
Converse of the Pythagorean Theorem
Pythagorean Triples
Distance Formula using the Pythagorean Theorem
Law of Cosines

Circles: Chords, Secants & Tangents
Circle Theorem: Arcs & Chords
Circle Theorem :Arcs & Chords
Tangents & Circles
Common Tangents
Intersecting Chords Theorem
Intersecting Secants Theorem
Intersecting Tangent Secant Theorem

Circles: Angles & Arcs
Central Angles
Inscribed Angles
Angles in Semi-Circles & Cyclic Quadrilaterals
Tangent Chord Angle
Secants which intersect in a circle
Secants which intersect outside a circle
Arc Length
Congruent Arcs

Circles: Area of Sectors & Segments
Area of Sectors
Area of Segments
5. Transformational Geometry

Transformations and Isometries

Symmetry - Line, Plane, Point, Rotational
Line & Plane Symmetry
Rotational Symmetry
Point Symmetry

Reflections - Line, Point
Reflections in the Coordinate Plane
Line Reflection
Point Reflection

Translations
Translations in the Coordinate Plane
Translations using Vectors

Rotations
Rotations
Rotations about the origin

Dilations
Dilations and Similarity
Composition of Transformations & Glide Reflections
Review of Transformation Notations & Formulas

Vector Basics
An Introduction to Vectors
Magnitude & Direction of a Vector
6. Coordinate Geometry

Slopes & Equations of Lines
Graphing Horizontal & Vertical Lines
Finding the Slope of a Line
Convert a linear equation from standard form to slope-intercept form

Graphing Lines by Slope Intercept Method
Find the equation of a line using the Point Slope Form
Graphing Lines using the x-intercept & y-intercept Greatest Possible Error

Midpoint of a Line Segment
Midpoint Formula

Distance Formula
Distance Formula

Direct Analytic Proofs (Coordinate Geometry Proofs)
Coordinate Geometry Proofs

Linear - Quadratic Systems
Linear Quadratic Systems

Circles
Equation of Circle Equation of Circle I
Equation of Circle II

Worksheets
Distance Formula
Midpoint Formula
7. Patterns, Functions, & Relations

Sequences
Sigma Notation & Series

Arithmetic Sequences
Arithmetic Sequences I
Arithmetic Sequences II
Arithmetic Sequences Finding the nth Term

Arithmetic Series
Series & Summation
Arithmetic Series I
Arithmetic Series II

Geometric Sequences
Geometric Sequences I
Geometric Sequences II
Geometric Sequences Finding the nth Term

Geometric Series
Geometric Series I
Geometric Series II

Recursion Sequences

Binomial Theorem
Pascal’s Triangle & the Binomial Theorem
Binomial Theorem I
Binomial Theorem II

** Relations & Functions**
Relations & Functions I
Relations & Functions II

Composition of Functions
Composite Functions I
Composite Functions II

Inverse Functions
Inverse of a Function I
Inverse of a Function II

Exponential & Logarithmic Functions
Introduction to Exponential Functions
Introduction to Logarithmic Functions
Exponential & Logarithmic Functions

Transformations with Functions
Horizontal & Vertical Shifting of Functions or Graphs
Reflecting Functions or Graphs
Stretching & Compressing Functions or Graphs
Examples that use the different Graph Transformations
8. Trigonometric Functions

Review of Trigonometric Functions
Six Trigonometric Functions, Reciprocal Functions

Special Right Triangles
Trig Ratios of Special Angles

Reference Angles & Triangles
Angles in Standard Position
Reference Angles

Unit Circle & Generating Trigonometric Graphs
Unit Circle Definition of Trigonometric Functions I
Unit Circle Definition of Trigonometric Functions II
Unit Circle Definition of Trigonometric Functions III
Unit Circle & Trig Graphs

Co-functions
Co-functions

Graphing Trig Functions
Sine & Cosine Graphs
Tangent Graphs
Graphing Sinusoidal Functions
Transform Sine & Cosine Graphs I
Transform Sine & Cosine Graphs II
Secant Graphs
Cosecant Graphs
Secant & Cosecant Graphs
Cotangent Graphs

Inverse Trig Functions & Graphs
Inverse Trigonometric Functions
Using Inverse Trigonometry

Pythagorean Identities
Tangent Identity & Pythagorean Identities
Reciprocal, Quotient & Pythagorean Identities

Trigonometric Equations
Introduction to solving trigonometric equations
Solving Trigonometric Equations by Factoring
Solving Trigonometric Equations Using the Quadratic Formula
Solving Trigonometric Equations with Coefficients in the Argument
Solving an Equation Involving an Inverse Trigonometric Function
Solving Word Problems Involving Trigonometric Equations

Law of Sines & Cosines
Law of Sines
Law of Sines - Ambiguous Case
Law of Cosines
Proof of the Law of Sines
Proof of the Law of Cosines

Worksheets
Law of Sines or Sine Rule
Law of Cosines or Cosine Rule

Calculate Area using Trigonometry
Area of Triangle Using Trigonometry
Area of Parallelogram Using Trigonometry

Angle Sum & Difference, Double Angle, Half-Angle Formulas
Sum & Difference Formulas(sine & cosine)
Sum & Difference Formulas(tangent)
Double Angle Formulas
Half Angle Formulas
9. Measurement

Arc Length & Radian Measure

Statistics & Probability

10. Statistics & Probability

Statistical Studies, Central Tendency & Dispersion
Types of Statistical Studies
Central Tendency Mean-Mode-Median
Quartiles, Box & whisker plots, Outliers
Measures of Dispersion(Range, Standard Deviation)
Normal Distribution

Regression Analysis
Regression Analysis
Scatter Plots & Correlations
Scatter Plots (using a calculator)
Linear Regression (using a calculator)
Correlation Coefficient (using a calculator)

Permutations & Combinations
Fundamental Counting Principle
Permutations
Combinations

Theoretical & Empirical Probabilities
Theoretical Probability
Experimental or Empirical Probability
Experimental & Theoretical Probability
Complement of an Event
Mutually Exclusive Events
Probability of Independent Events
Probability of Dependent Events
Conditional Probability
Probability Addition Rule (“Or”)
Probability Multiplication Rule (“And”)

Binomial Probability (Bernoulli Trials)
Binomial Probability
Binomial Experiments
Binomial Probability(using a calculator)
Binomial Probability(using a calculator)
Binomial Probability Examples Exactly, At Least, At Most
Binomial Distribution(mean, variance & standard deviation)
Z-Scores

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