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.

**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**

**January 2014 Geometry Regents Exam**

**June 2013 Integrated Algebra Regents Exam**

**June 2013 Algebra 2/Trigonometry Regents Exam**

**January 2013 Integrated Algebra Regents Exam**

**January 2013 Geometry Regents Exam**

**January 2013 Algebra 2/Trigonometry Regents Exam**

**June 2012 Geometry Regents Exam**

**August 2012 Integrated Algebra Regents Exam**

**January 2010 Integrated Algebra Regents Exam**
**January 2009 Integrated Algebra Regents Exam**

**June 2009 Geometry Regents Exam**
**Algebra 2 and Trigonometry June 2010 Regents Exam**

** Algebra 2 and Trigonometry 2009 Fall Sampler**
### Integrated Algebra

**Number Sense and Operations Strand**

2. Operations

Scientific Notation

Worksheets

Direct
Variation

Exponents (Powers)

Factorials

**Algebra Strand**

Multiplication of Polynomials

Division of Polynomials

Factoring
Worksheets
Algebraic
Translations

Worksheets

Literal Equations
Solving
Literal Equations

Graphing
Linear Inequalities

Systems of Inequalities

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

Definition of Function

6. Trigonometric Functions
Pythagorean Theorem

**Geometry Strand**

Parabolas

Area and Perimeter of Polygons & Circles

Volume and Surface Area of Solids

**Measurement Strand**

**Probability and Statistics Strand**

Displaying Data

Scatter Plots, Correlation, Line of Best Fit, Prediction

Percentiles
and More Quartiles

11. Probability

Counting Principle

Sample Spaces and Tree Diagrams

Theoretical versus Empirical (Experimental) Probability

Mutually Exclusive & Independent Events, Complement

## Geometry

4.Informal and Formal Proof

Writing a Proof - Direct Euclidean Proofs

Writing a Proof - Indirect Euclidean Proofs
Proof
by Contradiction

Angles

Triangles

Quadrilaterals

Similarity of Triangles

Pythagorean Theorem and Converse

Circles: Chords, Secants and Tangents

Circles: Angles and Arcs

5. Transformational Geometry

Reflections - Line, Point

Translations

Rotations

Dilations
Dilations
and Similarity

6.Coordinate Geometry

Slopes and Equations of Lines

Midpoint Formula

Distance Formula

Distance Formula

Direct Analytic Proofs (Coordinate Geometry Proofs)

Coordinate Geometry Proofs

4. Patterns, Functions, and Relations

Arithmetic Sequences

Arithmetic Series

Geometric Sequences

Geometric Series

Recursion
Sequences

Binomial Theorem

Relations and Functions

Composition of Functions

Inverse Functions

Exponential and Logarithmic Functions

Transformations with Functions

5. Coordinate Geometry

Equations of Circles

6. Trigonometric Functions

Special Right Triangles

Trig Ratios of Special Angles

Unit Circle and Generating Trigonometric Graphs

Co-functions

Co-functions

Pythagorean Identities

Trigonometric Equations

Calculate Area using Trigonometry

Angle Sum and Difference, Double Angle, Half-Angle Formulas

7. Measurement Arc Length and Radian Measure

8. Statistics and Probability

Normal
Distribution

Permutations and Combinations

Theoretical and Empirical Probabilities

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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.

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

Download the questions for the January 2014 Geometry Regents Exam (pdf) | Solutions to questions 1 - 25 |

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

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

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

Solutions to questions 31 - 38 | |

Download the questions for the January 2013 Geometry Regents Exam (pdf) | Solutions to questions 1 - 25 |

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

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 |

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

Download the January 2009 Integrated Algebra Regents Exam (pdf) | Solutions for Questions 1 -12 |

Solutions for Questions 13 - 33 | Solutions for Questions 34 - 39 |

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 |

1. Number Theory

Properties of Real Numbers | Closure Property |

Radicals

Simplifying Radicals | Simplifying Radicals that involve Fractions |

Simplifying Radical Expressions | Adding and Subtracting Radicals |

Multiplying Radicals | Multiplying Radicals Monomials and Binomials |

Dividing Radicals |

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 |

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 and Negative Exponents | Product Rule for Exponents |

Quotient Rule for Exponents | Power Rule for Exponents |

Rules for Negative Exponents |

Factorial Notation | Multiplying and Dividing Factorials |

Pre-Algebra Review

Rational and Irrational Numbers | Order of Operations |

Signed Numbers |

3. Variables and Expressions

Algebraic
Representations

Addition and Subtraction of Polynomials

Types of Polynomials | Adding and Subtracting 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 |

Divide a Polynomial by a Monomial | Dividing Polynomials using Long Division |

Dividing Polynomials using Synthetic Division |

Algebraic Fractions

Solving Fractional Equations I | Solving Fractional Equations II |

Linear Equations

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 |

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 |

Quadratic Equations

Solve Quadratic Equations Square Root Method | Solve Quadratic Equations by Factoring |

Solve Quadratic Equations Completing the Square | Solving Quadratic Equations by Graphing |

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 |

Systems of Inequalities

Working with Sets and Venn Diagrams

Universal Sets, Subsets, Equal Sets, Disjoint Sets | Set Operations - Union, Intersection, Complement |

Venn Diagrams | Venn Diagram Word Problems |

Function Notation | Domain and Range of a Function |

Relations and Functions |

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 |

7. Coordinate Geometry

Slopes and Equations of Lines

Equations for Parallel Lines | Equations for Perpendicular Lines |

Graphing Parabolas in Vertex Form | Graphing Parabolas in Standard Form |

Graphing Quadratic Functions(Maxima and Minima) |

Graphing Functions and Examining Coefficients

8. ShapesArea 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 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 |

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 |

10. Working with Data

Categorizing Data and Bias

Qualitative and Quantitative Data | Univariate and Bivariate Data |

Bias Data | Central Tendency Mean-Mode-Median |

Histogram | Cumulative frequency histogram |

Quartiles, Box & whisker plots, Outliers |

Scatter Plot and Line of Best Fit | Scatter Plots and Correlations |

Line of Best fit using a calculator |

11. Probability

Counting Principle

Permutations

Permutation Formula | Permutation with Repetition |

Probability and Permutations |

Sample Spaces | Tree Diagrams |

Introduction to Probability | Theoretical and Experimental Probability |

Complement of an Event | Mutually Exclusive Events |

Probability of Independent Events | Probability of Dependent Events |

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 |

1. Geometric Relationships

Lines and Planes

Polygons - Interior and Exterior Angles

Types of Polygons | Interior Angles of Polygons |

Exterior Angles of Polygons |

Prisms, Pyramids, Cylinders, Cones, Spheres, Platonic Solids

2. Constructions

3. Locus

The Basic Locus Theorems | Compound Loci |

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 |

Two Column Proofs | Flow Chart Proofs |

Paragraph Proofs |

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 |

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 |

Corresponding Angles | Alternate Interior Angles |

Alternate Exterior Angles | Co-Interior Angles |

Corresponding and Alternate Angles | Problems involving Parallel Lines and Transversal |

Properties of Quadrilaterals | Theorems dealing with Parallelograms |

Theorems dealing with Rectangles, Rhombuses, Squares | Theorems dealing with Trapezoids |

Mid-Segment (Mid-Line) of a Triangle |

Properties of Similar Triangles | Similarity, Area and Volume |

Proving Triangles are Similar | Similar Triangles in Circles and Right Triangles |

Pythagorean Theorem | Converse of the Pythagorean Theorem |

Pythagorean Triples | Distance Formula using the Pythagorean Theorem |

Law of Cosines |

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 |

Area of Sectors | Area of Segments |

Transformations and Isometries

Symmetry - Line, Plane, Point, Rotational

Line and Plane Symmetry | Rotational Symmetry |

Point Symmetry |

Reflections in the Coordinate Plane | Line Reflection |

Point Reflection |

Translations in the Coordinate Plane | Translations using Vectors |

Rotations | Rotations about the origin |

Composition of Transformations and Glide Reflections

Review
of Transformation Notations and Formulas

Vector Basics

An Introduction to Vectors | Magnitude and Direction of a Vector |

Slopes and Equations of Lines

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 |

Sequences | Sigma Notation and Series |

Arithmetic Sequences I | Arithmetic Sequences II |

Arithmetic Sequences Finding the nth Term |

Series and Summation | Arithmetic Series I |

Arithmetic Series II |

Geometric Sequences I | Geometric Sequences II |

Geometric Sequences Finding the nth Term |

Geometric Series I | Geometric Series II |

Binomial Theorem

Pascal's Triangle and the Binomial Theorem | Binomial Theorem I |

Binomial Theorem II |

Relations and Functions I | Relations and Functions II |

Composite Functions I | Composite Functions II |

Inverse of a Function I | Inverse of a Function II |

Introduction to Exponential Functions | Introduction to Logarithmic Functions |

Exponential and Logarithmic 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 |

Equations of Circles

Equation of Circle I | Equation of Circle II |

Review of Trigonometric Functions | Six Trigonometric Functions, Reciprocal Functions |

Trig Ratios of Special Angles

Reference Angles and Triangles

Angles in Standard Position | Reference Angles |

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

Graphing Trig Functions

Inverse Trigonometric Functions | Using Inverse Trigonometry |

Tangent Identity and Pythagorean Identities | Reciprocal, Quotient and Pythagorean Identities |

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 |

Area of Triangle Using Trigonometry | Area of Parallelogram Using Trigonometry |

Sum and Difference Formulas(sine and cosine) | Sum and Difference Formulas(tangent) |

Double Angle Formulas | Half Angle Formulas |

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) |

Regression Analysis

Regression Analysis | Scatter Plots and Correlations |

Scatter Plots (using a calculator) | Linear Regression (using a calculator) |

Correlation Coefficient (using a calculator) |

Fundamental Counting Principle | Permutations |

Combinations |

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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You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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