Capital Region Private Tutoring

Math - Physics - Test Prep

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NEW VIDEO POSTED!

This is the first video in what will be a work in progress project. You can follow along with me taking the no-calculator section of the SAT exam. Click here to download the official PDF version of the practice exam, and to skip to a particular question.

Check back for more! Subscribe to my YouTube channel to be alerted when I post another.

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About ME

Tutoring is not my day job, but it does give me the opportunity to practice what I'm passionate about: Being a part of a student's success.

Tutoring Region

I live in Rotterdam, but I can travel to mostly anywhere in the Capital Region. Generally I like to find a place that is roughly mid-way between us. But I can certainly meet at your home if need be.

Schenectady Troy Latham Albany Cohoes Scotia Rotterdam Duanesburg Balston Spa Saratoga Springs Colonie

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Subjects Offered

Basic Math and Algebra 1

addition subtraction multiplication division fractions adding fractions common denominator integers counting percentages decimals order of operations combining like terms equations solving equations variables The Real Numbers Properties of Real Numbers Operations on Real Number Equations in One Variable Applications of Equations Using Formulas Rewriting Equations and Formulas Inequalities in One Variable Compound Inequalities Absolute Value Absolute Value Equations Absolute Value Inequalities Graphing and Linear Equations The Rectangular Coordinate System Distance, Midpoint, and Circle Equations The Slope of a Line Graphing Linear Equations Writing Linear Equations Applications of Linear Concepts Fit a Line to Data Inequalities in Two Variables Polynomials Polynomial Basics Techniques for Multiplying Polynomials Techniques for Factoring Special Factoring Solving Equations by Factoring Division of Polynomials Rational Expressions The Basics of Rational Expressions Operations with Rational Expressions Equations with Rational Expressions Applications Variation Roots and Radicals Rational Exponents and Radicals Simplifying Radical Expressions Operations with Radical Expressions Equations with Radicals Square Roots and Irrational Numbers Complex Numbers Applications Relations and Functions An Introduction to Functions Functions, Tables, and Graphs Working with Functions Domain and Range Graphing Important Functions Even and Odd Functions and Symmetry Inverse Linear Functions Exponential Functions Understanding Exponents Define and Use Zero and Negative Exponents Exponential Functions Applying Exponential Functions Relate Geometric Sequences to Exponential Functions The Problem with Zero Quadratic Equations and Inequalities The Basics of Quadratics Graphs of Quadratics Solving by Completing the Square Writing Quadratic Equations Solving with the Quadratic Formula Solving Quadratic Equations and Inequalities by Graphing Equations Quadratic in Form Formulas and Applications Systems of Equations Linear Systems in Two Variables Linear Systems in Three Variables Applications of Linear Systems More Applications of Systems of Equations Working with Systems of Inequalities Non-Linear Systems of Equations Regression Data Analysis and Probability Analyze Surveys and Samples Use Measures of Central Tendency and Dispersion Analyze Data Interpret Stem and Leaf Plots and Histograms Interpret Box-and-Whisker Plots Find Probabilities and Odds Find Probabilities Using Permutations and Combinations Find Probabilities of Disjoint and Overlapping Events Find Probabilities of Independent and Dependent Events Making Good Graphs

Geometry and Trigonometry

shapes angles polygons triangles squares circles area perimeter side length width volume pythagorean theorum right angles obtuse acute formula proof logic parallel isosceles Points, Lines, Planes, & Angles A Game and Some Geometry Points, Lines, and Planes Segments, Rays, and Distance Angles Postulates and Theorems Relating Points, Lines and Planes Deductive Reasoning If-Then Statements; Converses Properties from Algebra Proving Theorems Special Pairs of Angles Perpendicular Lines Planning a Proof Flowchart and Paragraph Proofs Parallel Lines and Planes Definitions Properties of Parallel Lines Proving Lines Parallel Angles of a Triangle Angles of a Polygon Inductive Reasoning Congruent Triangles Congruent Figures Some Ways to Prove Triangles are Congruent Using Congruent Triangles Isosceles Triangle Theorems Other Methods of Proving Triangles Congruent Using more than One Pair of Congruent Triangles Medians, Altitudes, and Perpendicular Bisectors Quadrilaterals Properties of Parallelograms Ways to Prove that Quadrilaterals are Parallelograms Theorems Involving Parallel Lines Special Parallelograms Trapezoids Inequalities in Geometry Inequalities Inverses and Contrapositives Indirect Proof Inequalities for One Triangle Inequalities for Two Triangles Similar Polygons Ratio and Proportion Properties of Proportions Similar Polygons A Postulate for Similar Triangles Theorems for Similar Triangles Proportional Lengths Right Triangles Similarity in Right Triangles The Pythagorean Theorem The Converse of the Pythagorean Theorem Special Right Triangles The Tangent Ratio The Sine and Cosine Ratios Applications of Right Triangle Trigonometry Law of Sines and Law of Cosines Circles Basic Terms Tangents Arcs and Central Angles Arcs and Chords Inscribed Angles Other Angles Circles and Lengths of Segments Constructions and Loci What Construction Means Perpendiculars and Parallels Concurrent Lines Circles Special Segments The Meaning of Locus Locus Problems Locus and Construction Areas of Plane Figures Areas of Rectangles Areas of Parallelograms, Triangles, and Rhombuses Areas of Trapezoids Areas of Regular Polygons Circumferences and Areas of Circles Arc Lengths and Areas of Sectors Ratios of Areas Geometric Probability Areas and Volumes of Solids Prisms Pyramids Cylinders and Cones Spheres Areas and Volume of Similar Solids Coordinate Geometry The Distance Formula Slope of a Line Parallel and Perpendicular Lines Vectors The Midpoint Formula Graphing Linear Equations Writing Linear Equations Organizing Coordinate Proofs Coordinate Geometry Proofs Transformations Mappings and Functions Reflections Translations and Glide Reflections Rotations Dilations Composites of Mappings Inverses and the Identity Symmetry in the Plane and in Space

Algebra 2 and Pre-Calculus

Relations and Functions Function Basics Working with Functions Function Domain and Range Equations of a Line Graphing Functions Quadratic Functions: The Vertex Manipulating Graphs: Shifts and Stretches Manipulating Graphs: Symmetry and Reflections Composite Functions Circles Polynomial and Rational Functions Polynomials: Long Division Polynomials: Synthetic Division The Remainder Theorem The Factor Theorem The Rational Zero Theorem Zeros of Polynomials Graphing Simple Polynomial Functions Rational Functions Graphing Rational Functions Inequalities: Rationals and Radicals Exponential and Logarithmic Functions Function Inverses Finding Function Inverses Exponential Functions Applying Exponential Functions Logarithmic Functions Properties and Graphs of Logarithms Evaluating and Applying Logarithms Solving Exponential and Logarithmic Equations Applying Exponents and Logarithms Special Topics Conic Sections: Parabolas Conic Sections: Ellipses Conic Sections: Hyperbolas Identifying Conic Sections Binomial Coefficients and the Binomial Theorem Arithmetic and Geometric Sequences Induction Combinations, Permutations and Probability Systems of Equations and Matrices Solving Linear Systems by Substitution and Elimination Linear Systems of Equations in Three Variables Using Linear Systems: Investments and Partial Fractions Solving Nonlinear Systems Operations with Matrices The Gauss-Jordan Method Evaluating and Applying Determinants Using Inverses of Matrices to Solve Linear Systems Systems of Inequalities Linear Programming The Trigonometric Functions Angles, Radian Measure, and Arc Length Right Angle Trigonometry The Trigonometric Functions Graphing Sine and Cosine Graphing Sine and Cosine Functions with Vertical and Horizontal Shifts Graphing Other Trigonometric Functions Inverse Trigonometric Functions Trigonometric Identities Basic Trigonometric Identities Simplifying Trigonometric Expressions Determining Whether a Trigonometric Function Is Odd, Even, or Neither Proving Trigonometric Identities Solving Trigonometric Equations The Sum and Difference Identities Double-Angle Identities Other Advanced Identities Applications of Trigonometry The Law of Sines The Law of Cosines Heron's Formula Vectors: Operations and Applications Components of Vectors and Unit Vectors Complex Numbers in Trigonometric Form Using DeMoivre's Theorem to find Powers and Roots of Complex Numbers Functions in Polar Coordinates and their Graphs Topics in Analytic Geometry Rotation of Conics Parametric Equations Graphs of Polar Equations Polar Equations of Conics Limits The Concept of a Limit and Finding Limits Graphically The Limit Laws Evaluating Limits Continuity and Discontinuity Algebra I Review Inequalities and Absolute Value Exponents Linear Equations Linear Equations Part 2 Word Problems with Linear Equations Polynomial Expressions Factoring Factoring Patterns Rational Expressions Working with Rationals Complex Numbers Equations and Inequalities Quadratic Equations and the Quadratic Formula Quadratic Equations: Special Topics Word Problems with Quadratics Radical Equations Variation Solving Inequalities Inequalities: Quadratics, Rationals and Radicals Absolute Value Relations and Functions Function Basics Working with Functions Function Domain and Range Linear Functions: Applications Graphing Functions The Greatest Integer Function Composite Functions Quadratic Functions Quadratic Functions Part 2 Manipulating Graphs: Shifts and Stretches Polynomial and Rational Functions Polynomial Division The Remainder Theorem The Factor Theorem The Rational Root Theorem Zeros of Polynomials Graphing Polynomials Rational Functions Graphing Rational Functions Exponential and Logarithmic Functions Function Inverses Graphing the Inverse Exponential Functions Applying Exponential Functions Logarithmic Functions Solving Logarithmic Equations Properties of Logarithms Applying Logarithmic Functions Solving Exponential and Logarithmic Equations Applying Exponents and Logarithms Systems of Equations Linear Systems of Equations Linear Systems in Three Variables Applying Linear Systems Nonlinear Systems of Equations Systems of Inequalities Linear Programming Curves of Best Fit Conic Sections Parabolas Ellipses Hyperbolas Circles Conic Sections Probability, Statistics and Sequences Combinations and Probability The Binomial Theorem Measures of Center and Variation Binomial Distributions Normal Distributions Sampling Methods and Designing a Study Sequences Introduction to Trigonometry Angles, Radian Measure, and Arc Length Right Angle Trigonometry The Trigonometric Functions Graphing Sine and Cosine Functions with Vertical and Horizontal Shifts Graphing Other Trigonometric Functions Basic Trigonometric Identities Equations and inequalities How to graph functions and linear equations How to solve system of linear equations Matrices Polynomials and radical expressions Quadratic functions and inequalities Conic Sections Polynomial functions Rational expressions Exponential and logarithmic functions Sequences and series Discrete mathematics and probability Trigonometry Relations and Functions Function Basics Working with Functions Function Domain and Range Equations of a Line Graphing Functions Quadratic Functions: The Vertex Manipulating Graphs: Shifts and Stretches Manipulating Graphs: Symmetry and Reflections Composite Functions Circles Polynomial and Rational Functions Polynomials: Long Division Polynomials: Synthetic Division The Remainder Theorem The Factor Theorem The Rational Zero Theorem Zeros of Polynomials Graphing Simple Polynomial Functions Rational Functions Graphing Rational Functions Inequalities: Rationals and Radicals Exponential and Logarithmic Functions Function Inverses Finding Function Inverses Exponential Functions Applying Exponential Functions Logarithmic Functions Properties and Graphs of Logarithms Evaluating and Applying Logarithms Solving Exponential and Logarithmic Equations Applying Exponents and Logarithms Special Topics Conic Sections: Parabolas Conic Sections: Ellipses Conic Sections: Hyperbolas Identifying Conic Sections Binomial Coefficients and the Binomial Theorem Arithmetic and Geometric Sequences Induction Combinations, Permutations and Probability Systems of Equations and Matrices Solving Linear Systems by Substitution and Elimination Linear Systems of Equations in Three Variables Using Linear Systems: Investments and Partial Fractions Solving Nonlinear Systems Operations with Matrices The Gauss-Jordan Method Evaluating and Applying Determinants Using Inverses of Matrices to Solve Linear Systems Systems of Inequalities Linear Programming The Trigonometric Functions Angles, Radian Measure, and Arc Length Right Angle Trigonometry The Trigonometric Functions Graphing Sine and Cosine Graphing Sine and Cosine Functions with Vertical and Horizontal Shifts Graphing Other Trigonometric Functions Inverse Trigonometric Functions Trigonometric Identities Basic Trigonometric Identities Simplifying Trigonometric Expressions Determining Whether a Trigonometric Function Is Odd, Even, or Neither Proving Trigonometric Identities Solving Trigonometric Equations The Sum and Difference Identities Double-Angle Identities Other Advanced Identities Applications of Trigonometry The Law of Sines The Law of Cosines Heron's Formula Vectors: Operations and Applications Components of Vectors and Unit Vectors Complex Numbers in Trigonometric Form Using DeMoivre's Theorem to find Powers and Roots of Complex Numbers Functions in Polar Coordinates and their Graphs Topics in Analytic Geometry Rotation of Conics Parametric Equations Graphs of Polar Equations Polar Equations of Conics Limits The Concept of a Limit and Finding Limits Graphically The Limit Laws Evaluating Limits Continuity and Discontinuity

Calculus

1, 2, and 3
Precalculus Review Overview Functions and Graphing Exponential Functions Inverse Functions Inverse Trigonometric Functions Evaluating Logarithmic Functions Limits The Concept of the Limit Calculating Limits The Squeeze Theorem Continuity and Discontinuity Infinite Limits and Indeterminate Forms Derivatives Understanding the Derivative Using the Derivative Some Special Derivatives The Power Rule The Product and Quotient Rules The Chain Rule Derivatives of Trigonometric Functions Derivatives of the Exponential Function and the Natural Logarithm Implicit Differentiation Differentiating Logarithms Logarithmic Differentiation Derivatives of Inverse Functions Applications of the Derivative Position and Velocity Linear Approximation and Newton's Method Optimization Related Rates An Introduction to Curve Sketching Critical Points Concavity and Inflection Points Graphing Using the Derivative Graphing Functions with Asymptotes Indeterminate Quotients and L'Hospital's Rule Other Indeterminate Forms Integration Antiderivatives Integration by Substitution Illustrating Integration by Substitution The Fundamental Theorem of Calculus Numerical Integration and Tables of Integrals Trigonometric Substitution Techniques of Integration Integrals Involving Powers of Sine and Cosine Integrals Involving Powers of Other Trigonometric Functions An Introduction to Integration by Partial Fractions Integration by Partial Fractions with Repeated Factors Integration by Parts An Introduction to Trigonometric Substitution Trigonometric Substitution Strategy Improper Integrals Applications of Integration Motion Finding the Area between Two Curves Integrating with Respect to y The Average Value of a Function Finding Volumes Using Cross-Sections Disks and Washers Shells Work Moments and Centers of Mass Arc Lengths and Functions Differential Equations Separable Differential Equations Direction Fields Growth and Decay Problems Euler's Method Parametric Equations and Polar Coordinates Understanding Parametric Equations Derivatives and Arc Length of Parametric Equations Understanding Polar Coordinates Polar Functions and Slope Polar Functions and Area Sequences and Series Sequences Infinite Series Convergence and Divergence The Integral Test and p-Series The Comparison and Limit Comparison Test The Alternating Series Test, Absolute and Conditional Convergence The Ratio and Root Test Polynomial Approximations of Elementary Functions Taylor and Maclaurin Polynomials Taylor and Maclaurin Series Power Series Power Series Representations of Functions Review of Differential Calculus The Squeeze Theorem Continuity and Discontinuity Infinite Limits and Indeterminate Forms Implicit Differentiation Logarithmic Differentiation Derivatives of Inverse Functions Indeterminate Quotients and L'Hospital's Rule Other Indeterminate Forms Antiderivatives Techniques of Integration Review of Integration The Fundamental Theorem of Calculus Numerical Integration and Tables of Integrals Integrals Involving Powers of Sine and Cosine Integrals Involving Powers of Other Trigonometric Functions An Introduction to Integration by Partial Fractions Integration by Partial Fractions with Repeated Factors Integration by Parts An Introduction to Trigonometric Substitution Trigonometric Substitution Strategy Improper Integrals Applications of Integration Motion Finding Area between Curves The Average Value of a Function Finding Volumes Using Cross-Sections Disks, Washers, and Shells Work Moments and Centers of Mass Arc Lengths and Functions Parametric Equations and Polar Coordinates Understanding Parametric Equations Derivatives and Arc Length of Parametric Equations Understanding Polar Coordinates Polar Functions and Slope Polar Functions and Area Sequences and Series Sequences Infinite Series Convergence and Divergence The Integral Test and p-Series The Comparison and Limit Comparison Test The Alternating Series Test, Absolute and Conditional Convergence The Ratio and Root Test Applications of Series Polynomial Approximations of Elementary Functions Taylor and Maclaurin Polynomials Taylor and Maclaurin Series Power Series Power Series Representations of Functions Differential Equations Separable Differential Equations Direction Fields Growth and Decay Problems Euler's Method

Physics 1 and 2

with and without Calculus
Kinematics Dynamics: Newton’s laws Circular motion and universal law of gravitation Simple harmonic motion: simple pendulum and mass-spring systems Impulse, linear momentum, and conservation of linear momentum: collisions Work, energy, and conservation of energy Rotational motion: torque, rotational kinematics and energy, rotational dynamics, and conservation of angular momentum Electrostatics: electric charge and electric force DC circuits: resistors only Mechanical waves and sound Thermodynamics: laws of thermodynamics, ideal gases, and kinetic theory 12% Fluid statics and dynamics 13% Electrostatics: electric force, electric field and electric potential 15% DC circuits and RC circuits (steady-state only) 11% Magnetism and electromagnetic induction 16% Geometric and physical optics 17% Quantum physics, atomic, and nuclear physics 16%

Test Prep

SAT, ACT, ASVAB
Solving linear equations and linear inequalities (in these expressions, x is a constant or the product of a constant) Interpreting linear functions Linear inequality and equation word problems Graphing linear equations Linear function word problems Systems of linear inequalities word problems Solving systems of linear equations Use multiple steps to simplify an expression or equation or solve for a variable. Solve for a variable within functions or systems of inequalities with two variables (usually x and y). Determine whether a given point is in a solution set or what value would make an expression have no solution. Select a graph that shows an algebraic equation, or, on the flip side, choose the equation that describes a graph. Indicate how a graph would be affected by a given change in its equation Solving quadratic equations Interpreting nonlinear expressions Quadratic and exponential word problems Radicals and rational exponents Operations with rational expressions and polynomials Polynomial factors and graphs Nonlinear equation graphs Linear and quadratic systems Structure in expressions Isolating quantities Functions #1: Pre-Algebra/Elementary Algebra Pre-Algebra (20-25%) Basic operations using whole numbers, decimals, fractions, and integers Place value Square roots and approximations The concept of exponents Scientific notation Factors Ratio, proportion, and percent Linear equations in one variable Absolute value and ordering numbers by value Elementary counting techniques and simple probability Data collection, representation, and interpretation Understanding simple descriptive statistics body_operations.jpgA basic operations problem. body_stats.jpgA probability problem based on a real-world situation. Elementary Algebra (15-20%) Properties of exponents and square roots Evaluation of algebraic expressions through substitution Using variables to express functional relationships Understanding algebraic operations The solution of quadratic equations by factoring body_elemalg.jpg Two elementary algebra problems. The first uses variables to express a real-world relationship. The second tests evaluation of algebraic expressions through substitution. #2: Intermediate Algebra/Coordinate Geometry Intermediate Algebra (15-20%) The quadratic formula Rational and radical expressions Absolute value equations and inequalities Sequences and patterns Systems of equations Quadratic inequalities Functions and modeling Matrices Roots of polynomials Complex numbers body_matrix.jpg body_intermediatealg.jpg Coordinate Geometry (15-20%) Graphing and the relations between equations and graphs, including points, lines, polynomials, circles, and other curves Graphing inequalities Slope Parallel and perpendicular lines Distance Midpoints Conics body_coordinategeo.jpg #3: Plane Geometry/Trigonometry Plane Geometry (20-25%) Properties and relations of plane figures, including angles and relations among perpendicular and parallel lines Properties of circles, triangles, rectangles, parallelograms, and trapezoids Transformations The concept of proof and proof techniques Volume Applications of geometry to three dimensions body_plane.jpg Trigonometry (5-10%) Trigonometric relations in right triangles Values and properties of trigonometric functions Graphing trigonometric functions Modeling using trigonometric functions Use of trigonometric identities Solving trigonometric equations




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