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High School Math and Regents Examinations




 

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

In this lesson, we will look at

  • 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.

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

Regents Exam - Algebra 1 (Common Core)






Regents Exam - Algebra 2 (Common Core)

Regents Exam - Algebra 2/Trigonometry (Common Core)





Regents Exam - Geometry (Common Core)






January 2014 Algebra 2/Trigonometry Regents Exam
Download the January 2014 Algebra 2/ Trigonometry Exam (pdf) Solutions to questions 1 - 39
January 2014 Geometry Regents Exam
Download the questions for the January 2014 Geometry Regents Exam (pdf) Solutions to questions 1 - 25
June 2013 Integrated Algebra Regents Exam
Download the June 2013 Integrated Algebra  Regents Exam (pdf) Solutions to questions 1 - 25
June 2013 Algebra 2/Trigonometry Regents Exam
Download the June 2013 Algebra 2/ Trigonometry Exam (pdf) Solutions to questions 1 - 27
January 2013 Integrated Algebra Regents Exam
Download the January 2013 Integrated Algebra Regents Exam (pdf) Solutions to questions 1 - 20
Solutions to questions 31 - 38
January 2013 Geometry Regents Exam
Download the questions for the January 2013 Geometry Regents Exam (pdf) Solutions to questions 1 - 25
January 2013 Algebra 2/Trigonometry Regents Exam
Download the January 2013 Algebra 2/ Trigonometry Exam (pdf) Solutions to questions 1 - 35


 
June 2012 Geometry Regents Exam
Download the questions for the June 2012 Geometry Regents Exam (pdf) Solutions to questions 1 - 10
Solutions to questions 11 - 20 Solutions to questions 21 - 30
Solutions to questions 31 - 38  
August 2012 Integrated Algebra Regents Exam
Download the August 2012 Integrated Algebra Regents Exam (pdf) Solutions to questions 1 - 20
January 2010 Integrated Algebra Regents Exam
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
January 2009 Integrated Algebra Regents Exam
Download the January 2009 Integrated Algebra Regents Exam (pdf) Solutions for Questions 1 -12
Solutions for Questions 13 - 33 Solutions for Questions 34 - 39
June 2009 Geometry Regents Exam
Download the June 2009 Geometry Regents Exam (pdf) Solutions for Questions 1 - 4
Solutions for Questions 5 - 8 Solutions for Questions 9 - 12
Solutions for Questions 13 - 16 Solutions for Questions 17 - 20
Solutions for Questions 21 - 24 Solutions for Questions 25 - 28
Solutions for Questions 29 - 32 Solutions for Questions 33 - 37
Algebra 2 and Trigonometry June 2010 Regents Exam
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  
Algebra 2 and Trigonometry 2009 Fall Sampler
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 and Operations Strand

1. Number Theory

Properties of Real Numbers Closure Property
2. Operations

Radicals

Simplifying Radicals Simplifying Radicals that involve Fractions
Simplifying Radical Expressions Adding and Subtracting Radicals
Multiplying Radicals Multiplying Radicals Monomials and Binomials
Dividing Radicals  
Scientific Notation
Convert from Scientific Notation to Standard Notation Convert from Standard Notation to Scientific Notation
Operations on Numbers in Scientific Notation Using a Calculator for Scientific Notation

Fractions, Percents, Ratios, Proportions

Ratio and proportion Percents, Decimals and 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)  
Direct Variation  
Exponents (Powers)

Positive, Zero and Negative Exponents Product Rule for Exponents
Quotient Rule for Exponents Power Rule for Exponents
Rules for Negative Exponents  
Factorials
Factorial Notation Multiplying and Dividing Factorials

Absolute value

Pre-Algebra Review

Rational and Irrational Numbers Order of Operations 
Signed Numbers  


Algebra Strand

3. Variables and Expressions

Algebraic Representations

Addition and Subtraction of Polynomials

Types of Polynomials Adding and Subtracting Polynomials
Multiplication of Polynomials
Multiplying Monomials Multiplying Monomials and Polynomials
Multiplying Binomials using the FOIL method Multiplying Binomials using the Box method
Multiplying Binomials using Distributive Property & Vertical Method  
Division of Polynomials
Divide a Polynomial by a Monomial Dividing Polynomials using Long Division
Dividing Polynomials using Synthetic Division  

Algebraic Fractions

Introduction to Algebraic Fractions Multiplying Algebraic Fractions
Dividing Algebraic Fractions Adding Algebraic Fractions
Adding and Subtracting Algebraic Fractions Examples of Simplifying 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 and 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 and Inequalities Algebraic Translations 

Linear Equations

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 and 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 and 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 and Decay
Linear Inequalities (single variable)

Introduction to Linear Inequalities Solving Inequalities by Adding or Subtracting
Solving Inequalities by Multiplying or Dividing Solving Linear Inequalities
Solving Inequalities with Fractions Solving Inequalities with Variables on both sides
Solving and Graphing Linear Inequalities on a number line  
Graphing Linear Inequalities
Systems of Inequalities


5. Patterns, Functions, and Relations Set-builder and Interval Notation

Working with Sets and Venn Diagrams 

Universal Sets, Subsets, Equal Sets, Disjoint Sets Set Operations - Union, Intersection, Complement
Venn Diagrams Venn Diagram Word Problems
Definition of Function
Function Notation Domain and Range of a Function
Relations and Functions  
6. Trigonometric Functions Pythagorean Theorem 

Trigonometric Ratios (using sine, cosine, tangent)

Trigonometric Functions Sine, Cosine, Tangent Finding Length of Side using Trigonometry
Finding Angle Measure using Trigonometry  

Worksheets

Pythagorean Theorem find the missing side Pythagorean Theorem test for right triangle
Pythagorean Theorem dynamically generated  
Trigonometry using calculator Inverse Trigonometry using calculator
Trigonometry Find the unknown side Trigonometry Find the unknown angle
Using Sine dynamically generated Using Cosine dynamically generated
Using Tangent dynamically generated Using Sine, Cosine or Tangent dynamically generated
Trigonometry Applications & Problems  


 
Geometry Strand

7.  Coordinate Geometry

Slopes and Equations of Lines  

Finding the Slope of a Line Graphing Lines by Plotting Points
Graphing Horizontal and Vertical Lines Graphing Lines using the x-intercept and 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 and Perpendiculars
Equations for Parallel Lines Equations for Perpendicular Lines
Parabolas
Graphing Parabolas in Vertex Form Graphing Parabolas in Standard Form
Graphing Quadratic Functions(Maxima and Minima)  

Graphing Functions and Examining Coefficients

8. Shapes
Area and Perimeter of Polygons & Circles

Perimeter of Polygons Area of Polygons
Circumference of a Circle Area of Circles and Sectors
Area and Perimeter on a Coordinate Plane  
Volume and 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 and 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 and Volume of Cube
Surface Area and Volume of Rectangular Prisms or Cuboids Volume and Surface Area of Cylinder
Volume and Surface Area of Sphere Volume and Surface Area of Square Pyramids
Volume and Surface Area of Cones  


Measurement Strand

9. Measurement

Metric/English Conversions and Rates

English Unit Measurements Metric Unit Measurements
Unit Rate Rate Word Problems

Error in Measurement  

Relative and Percent Error Formulas Error in Measurement
Error in Rounding  
Probability and Statistics Strand

10. Working with Data

Categorizing Data and Bias

Qualitative and Quantitative Data Univariate and 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 and Line of Best Fit Scatter Plots and Correlations
Line of Best fit using a calculator  
Percentiles and More Quartiles
11. Probability
Counting Principle

Permutations

Permutation Formula Permutation with Repetition
Probability and Permutations  
Sample Spaces and Tree Diagrams
Sample Spaces Tree Diagrams
Theoretical versus Empirical (Experimental) Probability
Introduction to Probability Theoretical and 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 and Planes

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

Polygons - Interior and 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 and Surface Area of Sphere Polyhedra and 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 Triamgle
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 and Formal Proof
Logic Statements Negation (NOT) Conjunction (AND) Disjunction (OR) Conditional (IF ... THEN)
Biconditional (IF AND ONLY IF) Related Conditionals Converse, Inverse, Contrapositive
Truth Tables Conjunction, Disjunction, Conditionals Truth Tables for Multiple Statements
Truth Value of Open Sentences Truth Value of Compound Sentences
Truth Value of Negation of Compound Sentences  
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 and Similarity Triangle Congruence SSS and SAS
Triangle Congruence AAS and ASA Triangle Congruence HL (Hypotenuse Leg)
Why SSA and 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 and full rotation angles
Complementary Angles Supplementary Angles
Vertical Angles Linear Pair
Complementary and Supplementary Angles Adjacent, Complementary, Supplementary and Vertical Angles
Using complementary, supplementary, adjacent, and vertical angles  
Triangles
Classify Triangles by Sides and 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 and Angles
Corresponding Angles Alternate Interior Angles
Alternate Exterior Angles Co-Interior Angles
Corresponding and Alternate Angles Problems involving Parallel Lines and 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 and Volume
Proving Triangles are Similar Similar Triangles in Circles and Right Triangles
Pythagorean Theorem and Converse
Pythagorean Theorem Converse of the Pythagorean Theorem
Pythagorean Triples Distance Formula using the Pythagorean Theorem
Law of Cosines  
Circles: Chords, Secants and Tangents
Circle Theorem: Arcs and Chords Circle Theorem :Arcs and Chords
Tangents and Circles Common Tangents
Intersecting Chords Theorem Intersecting Secants Theorem
Intersecting Tangent Secant Theorem  
Circles: Angles and Arcs
Central Angles Inscribed Angles
Angles in Semi-Circles and 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 and Segments
Area of Sectors Area of Segments
5. Transformational Geometry

Transformations and Isometries

Symmetry - Line, Plane, Point, Rotational 

Line and 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 and Glide Reflections

Review of Transformation Notations and Formulas

Vector Basics

An Introduction to Vectors Magnitude and Direction of a Vector
6.Coordinate Geometry
Slopes and Equations of Lines
Graphing Horizontal and 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 and y-intercept
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

Worksheets

Distance Formula dynamically generated Midpoint Formula dynamically generated

4. Patterns, Functions, and Relations
Sequences Sigma Notation and Series
Arithmetic Sequences
Arithmetic Sequences I Arithmetic Sequences II
Arithmetic Sequences Finding the nth Term  
Arithmetic Series
Series and 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 and the Binomial Theorem Binomial Theorem I
Binomial Theorem II  
Relations and Functions
Relations and Functions I Relations and Functions II
Composition of Functions
Composite Functions I Composite Functions II
Inverse Functions
Inverse of a Function I Inverse of a Function II
Exponential and Logarithmic Functions
Introduction to Exponential Functions Introduction to Logarithmic Functions
Exponential and Logarithmic Functions  
Transformations with Functions
Horizontal and Vertical Shifting of Functions or Graphs Reflecting Functions or Graphs
Stretching and Compressing Functions or Graphs Examples that use the different Graph Transformations
5. Coordinate Geometry
Equations of Circles
Equation of Circle I Equation of Circle II
6. Trigonometric Functions
Review of Trigonometric Functions Six Trigonometric Functions, Reciprocal Functions
Special Right Triangles
Trig Ratios of Special Angles

Reference Angles and Triangles

Angles in Standard Position Reference Angles
Unit Circle and 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 and Trig Graphs
Co-functions
Co-functions

Graphing Trig Functions  

Sine and Cosine Graphs Tangent Graphs
Graphing Sinusoidal Functions Transform Sine and Cosine Graphs I
Transform Sine and Cosine Graphs II Secant Graphs
Cosecant Graphs Secant and Cosecant Graphs
Cotangent Graphs  
Inverse Trig Functions and Graphs
Inverse Trigonometric Functions Using Inverse Trigonometry
Pythagorean Identities
Tangent Identity and Pythagorean Identities Reciprocal, Quotient and 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 and 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 and Difference, Double Angle, Half-Angle Formulas
Sum and Difference Formulas(sine and cosine) Sum and Difference Formulas(tangent)
Double Angle Formulas Half Angle Formulas
7.  Measurement Arc Length and Radian Measure
8.  Statistics and Probability

Statistical Studies, Central Tendency and 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 and Correlations
Scatter Plots (using a calculator) Linear Regression (using a calculator)
Correlation Coefficient (using a calculator)  
Permutations and Combinations
Fundamental Counting Principle Permutations
Combinations  
Theoretical and 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 and standard deviation)
Z-Scores  


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