Math by Grades

Math by Topics

$Math Word Problems$

$Probability$

$Set Theory$

Math Worksheets $Math Worksheets$

Math in Video Lessons $Basic Algebra$

$Engineering Math$
$Singapore Math$
Math for Specific Tests $SAT Math$
$ACT Math$
$GMAT Math$
$High School, Regents$

Math Fun and Games $Math Trivia$
$Math Games$

Exam Preparation

Science

Others

$What's New$

Subscribe To This Site

High School Math and Regents Examinations

High School Math based on the topics required for the Regents Exam conducted by NYSED.

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 Bnomails using the Box method
Mulriplying 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 Mesurement
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
Polyhera and Platonic Solids

2. Constructions

Copy an Angle
Bisect an Angle (Angle Bisector)
Bisect a Liine 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
FlowChart 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

Algebra 2 and Trigonometry

1. Operations

Radicals
Simplifying Radicals and Square Roots
Simplifying Radicals that involve Fractions
Simplifying Radical Expressions
Adding and Subtracting Radicals
Multiplying Radicals
Multiplying Radicals - Monomials and Binomials
Dividing Radicals

Negative and Fractional Exponents
Positive, Zero and Negative Exponents
Fractional Powers, Fractional Exponents, Rational Exponents
Simplifying Expressions with Exponents
Rationalizing Denominators

Complex Numbers
Introduction to Complex Numbers
Powers of i
Adding and Subtracting Complex Numbers
Multiplying Complex Numbers
Dividing Complex Numbers
Graphing Complex Numbers

Worksheets
Complex Number Addition
Complex Number Subtraction
Complex Number Multiplication
Complex Number Division

2. Variables and Expressions

Factoring Polynomials - Review and More
Factoring Common Factors
Factor Perfect Square Trinomials
Factor Difference of Squares
Factor Sum and Difference of Two Cubes
Factor Polynomials by Grouping
Factor Polynomials using the Box Method
Factor Polynomials using the AC Method

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
Factoring with Higher Powers

Rational Expressions
Introduction to Rational Expressions
Simplifying Rational Expressions
Adding Rational Expressions
Subtracting Rational Expressions
Multiplying Rational Expressions
Dividing Rational Expressions

Complex Fractions
Simplfy Complex Fractions I
Simplify Complex Fractions II

3. Equations and Inequalities

Absolute Value Equations
Solving Absolute Value Equations

Absolute Value Inequalities
Solving and Graphing Absolute Value Inequalities

Complete the Square
Factor Trinomials by Completing the Square

Quadratic Equations, Discriminant, Quadratic Formula
Solve Quadratic Equations - Square Root Method
Solve Quadratic Equations by Factoring
Solve Quadratic Equations - Completing the Square
Solve Quadratic Equations - Quadratic Formula
Using the Discriminant for Quadratic Equations
Quadratic equations with Complex Roots
Sum and Product of Roots of a Quadratic Equation
Linear Quadratic Systems

Worksheets
Solve Trinomials using Quadratic Formula
Finding Discriminants of Quadratic Polynomials

Quadratic Inequalities
Solving Quadratic Inequalities

Direct and Inverse Variation
Direct Variation
Inverse Variation

Logarithmic Expressions and Equations
Introduction to Logarithms
Exponents and Logarithms
Logarithms - Product Rule
Logarithms - Product & Quotient Rules
Logarithms - Power Rule
Logarithms - Change of Base Rule
Expanding Logarithmic Expressions
Simplifying (or Condensing) Logarithmic Expressions
Simplifying and Expanding Logarithmic Expressions
Solving Logarithmic Equations

Exponential Expressions and Equations
The Number e and Natural Logarithm
Solving Equations involving e and ln

Radical Equations
Solving Radical Equations I
Solving Radical Equations II

Rational Equations
Solving Rational Equations I
Solving Rational Equations II

Rational Inequalities
Solving Rational Inequalities I
Solving Rational Inequalities II

Solving and Graphing Polynomial Equations of Higher Degree
Solving Polynomial Equations
Graphing Polynomial Equations

4. Patterns, Functions, and Relations

Sequences
Sigma Notation and Series

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

Arithemtic 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
Transforming Sine and Cosine Graphs I
Transforming 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 Pythgorean 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

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 and Theoretical Probabilty
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

Custom Search

We welcome your feedback, comments and questions about this site - please submit your feedback via our Feedback page.

Custom Search

Amazon.com Widgets

High School Math and Regents Examinations

January 2010 Integrated Algebra Regents Exam

January 2009 Integrated Algebra Regents Exam

June 2009 Geometry Regents Exam

Algebra 2 and Trigonometry 2009 Fall Sampler