 # High School Math and Regents Examinations

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 past exam 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 - Geometry (Common Core)

Regents Exam - Algebra 2/Trigonometry (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
 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 January 2010 Integrated Algebra Regents Exam January 2009 Integrated Algebra Regents Exam 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 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

2. Operations

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)

Exponents (Powers)

 Positive, Zero and Negative Exponents Product Rule for Exponents Quotient Rule for Exponents Power Rule for Exponents Rules for Negative Exponents
Factorials

Pre-Algebra Review

 Rational and Irrational Numbers Order of Operations Signed Numbers

Algebra Strand

3. Variables and Expressions

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 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 4. Equations and Inequalities

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

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

5. Patterns, Functions, and Relations

Working with Sets and Venn Diagrams

Definition of Function
 Function Notation Domain and Range of a Function Relations and Functions
6. Trigonometric 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
Geometry Strand

7.  Coordinate Geometry

Slopes and Equations of Lines

Parallels and Perpendiculars Parabolas
 Graphing Parabolas in Vertex Form Graphing Parabolas in Standard Form Graphing Quadratic Functions(Maxima and Minima)
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
11. Probability

Permutations

 Permutation Formula Permutation with Repetition Probability and Permutations
Sample Spaces and Tree Diagrams
 Sample Spaces Tree Diagrams
Theoretical versus Empirical (Experimental) Probability Mutually Exclusive & Independent Events, Complement
 Complement of an Event Mutually Exclusive Events Probability of Independent Events Probability of Dependent Events

Problems Involving AND & OR

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

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

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

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 Similarity of 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

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 Rotations
Dilations

Vector Basics

6.Coordinate Geometry
Slopes and Equations of Lines Midpoint of a Line Segment

Distance Formula

Direct Analytic Proofs (Coordinate Geometry Proofs)

Circles

Worksheets

 Distance Formula dynamically generated Midpoint Formula dynamically generated
4. Patterns, Functions, and Relations 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
Binomial Theorem
 Pascal's Triangle and the Binomial Theorem Binomial Theorem I Binomial Theorem II
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

Reference Angles and Triangles

Unit Circle and Generating Trigonometric Graphs 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 Pythagorean Identities 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

Calculate Area 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
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)
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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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. 