#### Online Math Tutors

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## Subject Areas

- Addition
- Multiplication
- Subtraction
- Division
- Inequalities
- Intro to word problems with one variable
- Intro to solving equations with one variable
- Number line
- Introduction to fractions
- Figures/shapes
- Grouping shapes
- Introduction to combinations
- Perimeters of squares and rectangles and triangles
- Addition/Subtraction with fractions
- Order of operations
- Least Common Multiple
- Greatest Common Factor

**6/7 – Basics**- Naming decimal places
- Reading and writing whole numbers
- Rounding numbers

**6/7 – Number Theory**- Divisibility and factors
- Factoring numbers
- Factoring monomials
- Greatest common factor
- Least common multiple

**Arithmetic**- Rounding numbers
- Converting between fractions and decimals
- Converting between percents, fractions, and decimals
- Variable and verbal expressions
- Adding and subtracting integers
- Adding and subtracting decimals
- Adding and subtracting fractions and mixed numbers
- Dividing integers
- Multiplying integers
- Multiplying decimals
- Multiplying and dividing fractions and mixed numbrs
- Order of operations
- Evaluating variable expressions

**Algebraic Expressions**- Graphing single-variable inequalities
- One-step inequalities by adding and subtracting
- One-step inequalities by multiplying and dividing
- Two-step inequalities
- Multi-step inequalities

**Proportion and Percentages**- Converting between percents, fractions, and decimals
- Percent problems, straightforward
- Finding percent change
- Markup, discount, and tax
- Proportions
- Proportions word problems
- Similar figures
- Similar figure word problems
- Simple and compound interest

**Equations**- One-step equations
- Two-step equations
- Word problems
- Multi-step equations

**Plane Figures**- Rigid Transformations
- Translations
- Rotations
- Reflections

- Angle relationships
- The Pythagorean Theorem
- The distance formula
- Classifying triangles and quadrilaterals
- Area of triangles
- Area of squares, rectangles, and parallelograms
- Area of trapezoids
- Area and circumference of circles

- Rigid Transformations
**Solid Figures**- Classifying solids
- Volume
- Surface area

**Linear Functions**- Finding slope
- Graphing lines using slope-intercept form
- Graphing lines using standard form
- Writing linear equations
- Graphing linear inequalities

**Systems of Equations**- Solving systems of linear equations by graphing
- Solving systems of equations by substitution
- Systems of equations word problems

**Polynomials**- Factoring polynomials
- Adding and subtracting polynomials
- Multiplying a polynomial and a monomial
- Multiplying binomials

**Exponents and Radicals**- Multiplication property of exponents
- Division property of exponents
- Powers of products and quotients
- Writing scientific notation
- Square roots

**Word Problems**- One-step equation word problems
- Two-step equation word problems
- Proportion word problems
- Similar figure word problems
- Systems of equations word problems

**Statistics**- Visualizing data
- Center and spread of data
- Scatter plots

Using statistical models

**Basics**- Writing variable expressions
- Order of operations
- Evaluating expressions
- Number sets
- Adding rational numbers
- Adding and subtracting rational numbers
- Multiplying and dividing rational numbers
- The distributive property
- Combining like terms
- Percent of change

**Equations**- One-step equations
- Two-step equations
- Multi-step equations
- Absolute value equations
- Radical equations
- Rational equations
- Solving proportions
- Percent problems
- Distance-rate-time word problems
- Mixture word problems
- Work word problems
- Literal equations

**Linear Equations and Inequalities**- Finding slope from a graph
- Finding slope from two points
- Finding slope from an equation
- Graphing lines using slope-intercept form
- Graphing lines using standard form
- Writing linear equations
- Graphing absolute value equations
- Graphing linear inequalities

**Systems of Equations and Inequalities**- Solving systems of equations by graphing
- Solving systems of equations by elimination
- Solving systems of equations by substitution
- Systems of equations word problems
- Graphing systems of inequalities

**Exponents**- Exponential functions and graphs
- Properties of exponents
- Writing numbers in scientific notation
- Operations with scientific notation

**Polynomials**- Naming polynomials
- Adding and subtracting polynomials
- Multiplying polynomials
- Multiplying special case polynomials
- Factoring quadratic polynomials
- Factoring special case polynomials
- Factoring by grouping
- Dividing polynomials

**Quadratic Functions**- Graphing quadratic functions
- Graphing quadratic inequalities
- Completing the square
- Solving quadratic equations
- by taking square roots
- by factoring
- with quadratic formula
- by completing the square

- Division property of exponents

**Radical Expressions**- Simplifying radicals
- Adding and subtracting radical expressions
- Multiplying radicals
- Dividing radicals
- Using the distance formula
- Using the midpoint formula
- Solving radical equations

**Rational Expressions**- Simplifying rational expressions
- Finding excluded values/restricted values
- Multiplying rational expressions
- Dividing rational expressions
- Dividing polynomials
- Adding and subtracting rational expressions
- Solving rational equations

**Word Problems**- Distance-rate-time word problems
- Mixture word problems
- Work word problems
- Systems of equations word problems

**Trigonometry**- Finding trig ratios
- Finding angles of triangles
- Finding side lengths of triangles

**Statistics**- Visualizing data
- Center and spread of data
- Scatter plots
- Using statistical models

**Review of Algebra**- Review of equations
- Simplifying square roots
- Adding and subtracting square roots
- Multiplying square roots
- Dividing square roots

Basics of Geometry

- Line segments and their measures inches
- Line segments and their measures cm
- Segment Addition Postulate
- Angles and their measures
- Classifying angles
- Naming angles
- The Angle Addition Postulate
- Angle pair relationships
- Understanding geometric diagrams and notation

Parallel Lines and the Coordinate Plane

- Parallel lines and transversals
- Proving lines parallel
- Points in the coordinate plane
- The Midpoint Formula
- The Distance Formula
- Parallel lines in the coordinate plane

Congruent Triangles

- Classifying triangles
- Triangle angle sum
- The Exterior Angle Theorem
- Triangles and congruence
- SSS and SAS congruence
- ASA and AAS congruence
- SSS, SAS, ASA, and AAS congruences combined
- Right triangle congruence
- Isosceles and equilateral triangles

Properties of Triangles

- Midsegment of a triangle
- Angle bisectors
- Medians
- Centroid
- The Triangle Inequality Theorem
- Inequalities in one triangle

Similarity

- Solving proportions
- Similar polygons
- Using similar polygons
- Similar triangles
- Similar right triangles
- Proportional parts in triangles and parallel lines

Quadrilaterals and Polygons

- Classifying quadrilaterals
- Angles in quadrilaterals
- Properties of parallelograms
- Properties of trapezoids
- Areas of triangles and quadrilaterals
- Introduction to polygons
- Polygons and angles
- Areas of regular polygons

Right Triangles

- The Pythagorean Theorem and its Converse
- Multi-step Pythagorean Theorem problems
- Special right triangles
- Multi-step special right triangle problems

Trigonometry

- ratios
- Inverse trig. ratios
- Solving right triangles
- Multi-step trig. problems
- Trigonometry and area

Circles

- Arcs and central angles
- Arcs and chords
- Circumference and area
- Inscribed angles
- Tangents to circles
- Secant angles
- Secant-tangent and tangent-tangent angles
- Segment measures
- Equations of circles

Surface Area and Volume

- Identifying solid figures
- Volume of prisms and cylinders
- Surface area of prisms and cylinders
- Volume of pyramids and cones
- Surface area of pyramids and cones
- More on nets of solids
- Spheres
- Similar solids

Transformations

- Translations
- Rotations
- Reflections
- All transformations combined

Constructions

- Line segments
- Perpendicular segments
- Angles
- Triangles
- Medians of triangles
- Altitudes of triangles
- Angle bisectors
- Circles

Statistics & Probability

- Sample spaces and The Counting Principle
- Independent and dependent events
- Mutually exclusive events
- Permutations
- Combinations
- Permutations vs combinations
- Probability using permutations and combinations

**Basics**- Order of operations
- Evaluating expressions
- Simplifying algebraic expressions

**Equations and Inequalities**- Multi-step equations
- Work word problems
- Distance-rate-time word problems
- Mixture word problems
- Absolute value equations
- Multi-step inequalities
- Compound inequalities
- Absolute value inequalities

**Linear Relations and Functions**- Review of linear equations
- Graphing absolute value functions
- Graphing linear inequalities

**Systems of Equations and Inequalities**- Systems of two linear inequalities
- Systems of two equations
- Systems of two equations, word problems
- Points in three dimensions
- Planes
- Systems of three equations, elimination
- Systems of three equations, substitution
- Cramer’s rule:2×2,3×3

**Matrices**- Basic matrix operations
- Matrix multiplication
- All matrix operations combined
- Determinants:2×2,3×3
- Matrix inverses
- Cramer’s rule:2×2,3×3
- Matrix equations
- Geometric transformations with matrices

**Complex Numbers**- Operations with complex numbers
- Properties of complex numbers
- Rationalizing imaginary denominators

**Polynomial Functions**- Naming and simple operations
- Factoring a sum/difference of cubes
- Factoring by grouping
- Factoring quadratic form
- Factoring using all techniques
- Factors and Zeros
- The Remainder Theorem
- Irrational and Imaginary Root Theorems
- Descartes’ Rule of Signs
- More on factors, zeros, and dividing
- The Rational Root Theorem
- Polynomial equations
- Basic shape of graphs of polynomials
- Graphing polynomial functions
- The Binomial Theorem

**Quadratic Functions and Inequalities**- Properties of parabolas
- Vertex form
- Graphing quadratic inequalities
- Factoring quadratic expressions
- Solving quadratic equations w/ square roots
- Solving quadratic equations by factoring
- Completing the square
- Solving equations by completing the square
- Solving equations with the quadratic formula
- The discriminant

**General Functions**- Evaluating functions
- Function operations
- Inverse functions

**Conic Sections**- Graphing & properties of parabolas
- Equations of parabolas
- Graphing & properties of circles
- Equations of circles
- Graphing & properties of ellipses
- Equations of ellipses
- Graphing & properties of hyperbolas
- Equations of hyperbolas
- Classifying conic sections
- Eccentricity
- Systems of quadratic equations

**Radical Functions and Rational Exponents**- Simplifying radicals
- Operations with radical expressions
- Dividing radical expressions
- Radicals and rational exponents
- Simplifying rational exponents
- Square root equations
- Rational exponent equations
- Graphing radicals

**Rational Expressions**- Graphing simple rational functions
- Graphing general rational functions
- Simplifying rational expressions
- Multiplying / dividing rational expressions
- Adding / subtracting rational expressions
- Complex fractions
- Solving rational equations

**Sequences and Series**- General sequences
- Arithmetic sequences
- Geometric sequences
- Comparing Arithmetic/Geometric Sequences
- General series
- Arithmetic series
- Arithmetic/Geometric Means w/ Sequences
- Finite geometric series
- Infinite geometric series

**Exponential and Logarithmic Functions**- The meaning of logarithms
- Properties of logarithms
- The change of base formula
- Writing logs in terms of others
- Logarithmic equations
- Inverse functions and logarithms
- Exponential equations not requiring logarithms
- Exponential equations requiring logarithms
- Graphing logarithms
- Graphing exponential functions

**Trigonometry**- Right triangle trig: Evaluating ratios
- Right triangle trig: Missing sides/angles
- Angles and angle measure
- Co-terminal angles and reference angles
- Arc length and sector area
- Trig ratios of general angles
- Exact trig ratios of important angles
- The Law of Sines
- The Law of Cosines
- Graphing trig functions
- Translating trig functions
- Angle Sum/Difference Identities
- Double-/Half-Angle Identities

**Statistics & Probability**- Sample spaces and The Counting Principle
- Independent and dependent events
- Mutualy exclusive events
- Permutations
- Combinations
- Permutations vs combinations
- Probability using permutations and combinations

- Functions
- Continuity
- Extrema, intervals of increase and decrease
- Power functions
- Average rates of change
- Transformations of graphs
- Piecewise functions
- Operations
- Inverses

- Power, Polynomial, and Rational Functions
- Graphs, real zeros, and end behavior
- Dividing polynomial functions
- The Remainder Theorem and bounds of real zeros
- Writing polynomial functions and conjugate roots
- Complex zeros & Fundamental Theorem of Algebra
- Graphs of rational functions
- Rational equations
- Polynomial inequalities
- Rational inequalities

- Exponential and Logarithmic Expressions
- Graphing exponential functions
- Exponential equations not requiring logarithms
- Exponents and logarithms
- Evaluating logarithms
- Logarithms and exponents as inverses
- Properties of logarithms
- Writing logs in terms of others
- Exponential equations requiring logarithms
- Logarithmic equations, simple
- Logarithmic equations, hard
- Graphing logarithmic functions
- Compound interest

- Trigonometry
- Angles and angle measure
- Right triangle trigonometry
- Trig functions of any angle
- Graphing trig functions
- Simple trig equations
- Inverse trig functions
- Fundamental identities
- Equations with factoring and fundamental identities
- Sum and Difference Identities
- Multiple-Angle Identities
- Product-to-Sum Identities
- Equations and Multiple-Angle Identities
- The Law of Sines
- The Law of Cosines

- Parametric Equations
- Parametric equations
- Projectile motion

- Polar Coordinates
- Polar coordinates
- Graphs of polar equations
- Polar and rectangular forms of equations
- Polar forms of conic section
- Complex numbers and polar form

- Vectors
- Vector basics
- Vector operations
- Dot products

- Three-Dimensional Vectors
- 3D vector basics
- 3D vector operations
- Vector cross products

- Matrices and Systems
- Matrix operations
- Matrix inverses and determinants
- Matrix equations
- Cramer’s Rule
- Multivariable linear systems and row operations
- Partial fraction decomposition

- Conic Sections
- Parabolas
- Circles
- Ellipses
- Hyperbolas
- Rotations of conic sections

- Discrete Mathematics
- Sample spaces & Fundamental Counting Principle
- Permutations
- Combinations
- Permutations vs combinations
- The Binomial Theorem
- Mathematical induction

- Probability
- Independent and dependent events
- Mutually exclusive events
- Probability with combinatorics
- Probability with combinatorics – binomial

- Sequences and Series
- General sequences and series
- Arithmetic sequences and series
- Geometric sequences and series
- Power series

- Introduction to Calculus
- Limits by direct evaluation
- Limits at kinks and jumps
- Limits at removable discontinuities
- Limits at essential discontinuities
- Limits at infinity
- Definition of the derivative
- Instantaneous rates of change
- Power rule for differentiation
- Motion along a line
- Approximating area under a curve
- Area under a curve by limit of sums
- Indefinite integrals

- Limits
- Limits by Direct Evaluation
- Limits at Jump Discontinuities and Kinks
- Limits at Removable Discontinuities
- Limits at Removable Discontinuities with Trig
- Limits at Essential Discontinuities
- Limits at Infinity

- Applications of Differentiation
- Derivative at a Value
- Slope at a Value
- Tangent Lines
- Normal Lines
- Points of Horizontal Tangents
- Rolle’s Theorem
- Mean Value Theorem
- Intervals of Increase and Decrease
- Intervals of Concavity
- Relative Extrema
- Absolute Extrema
- Optimization
- Curve Sketching
- Comparing a Function and its Derivatives
- Motion Along a Line
- Related Rates
- Differentials
- Newton’s Method
- Limits in Form of Definition of Derivative
- L’Hôpital’s Rule

- Definite Integration
- Approximating Area Under a Curve
- Area Under a Curve by Limit of Sums
- Riemann Sum Tables
- First Fundamental Theorem of Calculus
- Substitution for Definite Integrals
- Mean Value Theorem for Integrals
- Second Fundamental Theorem of Calculus

- Differential Equations
- Slope Fields
- Introduction to Differential Equations
- Separable Equations
- Exponential Growth and Decay

- Continuity
- Determining & Classifying

- Differentiation
- Average Rates of Change
- Definition of the Derivative
- Instantaneous Rates of Change
- Power, Constant, and Sum Rules
- Higher Order Derivatives
- Product Rule
- Quotient Rule
- Chain Rule
- Differentiation Rules with Tables
- Chain Rule with Trig
- Chain Rule with Inverse Trig
- Chain Rule with Natural Logarithms and Exponentials
- Chain Rule with Other Base Logs and Exponentials
- Logarithmic Differentiation
- Implicit Differentiation
- Derivatives of Inverse Functions

- Indefinite Integration
- Power Rule
- Logarithmic Rule and Exponentials
- Trigonometric Functions
- Inverse Trigonometric Forms
- Substitution with Power Rule
- Substitution with Logarithms and Exponentials
- Substitution with Trigonometric Functions
- Substitution with Inverse Trigonometric Forms
- Integration by Parts

- Applications of Integration
- Area Under a Curve
- Area Between Curves
- Volume by Slicing – Washers and Disks
- Volume by Cylinder Method
- Volume Using Known Cross Sections
- Motion Along a Line Revisited