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# «Math Elementary Math Mid-level Math Algebra Algebra II Geometry Trigonometry Pre-Calculus Calculus Calculus BC Discrete Math Finite Math Statistics ...»

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Basic Concepts List

for All Available Subjects

Math

Elementary Math Mid-level Math Algebra

Algebra II Geometry Trigonometry

Pre-Calculus Calculus Calculus BC

Discrete Math Finite Math Statistics

Intermediate Statistics

Science

Elementary Science Biology Chemistry

Earth Science Anatomy & Physiology Organic Chemistry Physics – Algebra Based Physics – Calculus Based Microbiology Nursing Humanities Social Studies English Essay Writing College Essay Writing Literature Reading ESL Symbolic Logic Social Sciences Introduction to Psychology Research Methods Introduction to Sociology Business Introductory Accounting Introductory Economics Finance Intermediate Accounting Intermediate Economics Business Law Principles of Management Technology MS Excel MS Word MS PowerPoint Principles of Computer Sci. C++ Java Python Visual Basic Foreign Languages French German Italian Spanish Page | 1 © 2011-16 Tutor.com, Inc.

Confidential – Do Not Distribute Elementary (Grades 4-6) (Back to Math) Algebraic Skills Equations Functions Patterns Geometry Composite and Real World Shapes Coordinates Lines and Angles Perimeter, Area, Volume Position and Direction Similar, Congruent, Symmetric Shapes Sorting and Classifying Three Dimensional Shapes Transformations Two Dimensional Shapes Measurement Converting Units and Measurements Estimates Measuring Time Units and Tools Numbers Coins, Bills, and Collections of Money Counting Decimals - Read, Write, Place Value, Compare Equivalent Numbers - Decimals and Fractions Fractions - Compare and Order Fractions - Read, Write, Model Integers Ordinal Numbers Whole Number - Place Value Whole Numbers - Compare and Order Whole Numbers - Read, Write, Characteristics Operations and Number Relationships Decimals - Operations Estimation Fractions - Operations Number Properties Number Theory: Factors, Multiples, Primes, Divisibility Order of Operations Ratios, Rates, Proportions,

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Algebra, Patterns and Relationships Algebraic Expressions Formulas Functions Graphing Relationships Inequalities Linear Relationships Number and Geometric Patterns Solving Equations Systems of Equations Variables and Substitution Represent and Analyze Quantitative Relationships between Dependent and Independent Variables Use Properties of Operations to Generate Equivalent Expressions Work with Radicals and Integer Exponents Understand the Connections between Proportional Relationships, Lines and Linear Equations Analyze and Solve Linear Equations and Pairs of Simultaneous Linear Equations Define, Evaluate and Compare Functions Use Functions to Model Relationships between Quantities Data and Graphs Experiments and Data Collection Infer, Predict, Evaluate, Compare Data Measures of Central Tendency and Variation Represent, Read, Interpret Data Displays Geometry Circles and Pi Classify Two- and Three-Dimensional Figures Coordinate Plane Drawing, Modeling, and Constructing Figures and Describe the Relationships between them Formulas for Perimeter, Area, Surface Area, Volume Logic and Reasoning Points, Lines, and Planes Properties of Two-Dimensional Figures Understand and Apply the Pythagorean Theorem Similarity, Congruence, and Symmetry Transformations Measurement Estimate and Measure Measurement Systems Measurement Tools Rates, Indirect Measurements, Proportion Numbers Compare and Order Numbers Equivalent Forms of Rational Numbers Estimation and Rounding Exponents and Roots Number Properties Number Theory Concepts Operations to Solve Problems Operations with Integers and Absolute Value

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Page | 6 © 2011-16 Tutor.com, Inc.

Confidential – Do Not Distribute Algebra II (Back to Math) Absolute Value Equations and Inequalities Graphing Absolute Value Equations and Inequalities Solving Absolute Value Equations and Inequalities Conic Sections Properties of Conic Sections Solving Problems with Conic Sections Linear Functions, Equations, and Inequalities Slope, Intercepts, Points on a Line Solving Linear Equations Solving Linear Inequalities Solving Problems with Equations and Inequalities Systems of Equations and Inequalities Writing and Graphing Linear Equations Writing and Graphing Linear Inequalities Matrices Matrices Operations and Problems Numbers Complex Numbers Number Properties Operations with Real Numbers Patterns and Functions Composition and Operations on Functions Graphing Functions and Transformations Inverse of Function Patterns Properties of Functions - Domain and Range Properties of Functions - Zeros, End Behavior, Turning Points Relations and Functions Solving Problems with Functions Translate Between Forms Polynomial, Rational Expressions, Equations and Functions Solving and Graphing Polynomial Equations Solving and Graphing Rational Equations Probability Counting Principles and Sample Spaces Theoretical and Experimental Probability Quadratic Equations, Inequalities, and Functions Complex Solutions to Quadratic Equations Factoring Quadratic Equations Graphing and Properties of Quadratic Equations Solving Quadratic Equations and Inequalities Systems of Nonlinear Equations and Inequalities Radical, Exponential and Logarithmic Equations and Functions Graphing Exponential and Logarithmic Functions Properties of Exponents and Logarithms Radical Expressions, Equations and Rational Exponents Solving Exponential and Logarithmic Equations and inequalities Solving Problems with Exponential and Logarithmic Functions Sequences and Series

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Trigonometric Laws and Identities Trigonometric Laws and Identities Law of Sines and Law of Cosines Trigonometric Identities and Equations Area of Triangles Angular and Linear Velocities Trigonometric Laws and Identities Unit Review Modeling Periodic Phenomenon Vectors Graphing and Operations with Vectors Solving problems with Vectors

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In addition, the concepts below are frequently seen by students in pre-Calculus courses and ones that all

Calculus tutors are expected to know and be able to assist students with:

Circle, ellipse, hyperbola, and parabola Perform translations for various conic sections Arithmetic and Geometric sequences Trigonometric Ratios and Identities Trigonometric graphs Law of Cosines and Law of Sines Functions and Graphs (Linear and Polynomial) Exponential and Logarithmic Functions

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Page | 13 © 2011-16 Tutor.com, Inc.

Confidential – Do Not Distribute Pre-Calculus (Back to Math) Functions Know and use a definition of a function Write a function that describes a relationship between two quantities Perform algebraic operations on functions and apply transformations Write an expression for the composition of one given function with another and find the domain, range, and graph of the composite function Determine whether a function has an inverse and express the inverse, if it exist Know and interpret the function notation for inverses Identify and describe the discontinuities of a function and how these relate to the graph Understand the concept of limit of a function as x approaches a number or infinity Analyze a graph as it approaches an asymptote Computer limits of simple functions Explain how rates of change of functions in different families differ Exponents and Logarithms Use the inverse relationship between exponential and logarithmic functions to solve equations and problems Graph logarithmic functions Graph translations and reflections of functions Compare the large-scale behavior of exponential and logarithmic functions with different bases and recognize that different growth rates are visible in the graphs of the functions Solve exponential and logarithmic equations Find an exponential or logarithmic function to model a given set of data or situation Solve problems involving exponential growth and decay Quadratic Functions Solve quadratic type equations by substitution Apply quadratic functions and their graphs in the context of motion under gravity and simple optimization problems Find a quadratic function to model a given set of data or situation Polynomials Given a polynomial function, find the intervals on which the function’s values are positive and those where it is negative Solve polynomial equations and inequalities of degree of three or higher Graph polynomial functions given in factored form using zeros and their multiplicities, testing the sign on intervals and analyzing the function’s large scale behavior The Remainder Theorem The Factor Theorem Fundamental Theorem of Algebra Rational Functions and Difference Quotients Solve equations and inequalities involving rational functions Graph rational functions; identify asymptotes, analyzing their behavior for large x values and testing intervals Given vertical and horizontal asymptotes, find an expression for a rational function Know and apply the definition and geometric interpretation of difference quotient Simplify difference quotients Interpret difference quotients as rates of change and slopes of secants lines Trigonometric Functions Define and graph and use all trigonometric functions of any angle Convert between radian and degree measure Calculate arc lengths in given circles Graph transformations of the sine and cosine functions Explain the relationship between constants in the formula and transformed graph Page | 14 © 2011-16 Tutor.com, Inc.

Confidential – Do Not Distribute Know basic properties of the inverse trigonometric functions, including their domains and ranges. Recognize their graphs Know the basic trigonometric identities for sine, cosine, and tangent Pythagorean identities Sum and difference formulas Co-functions relationships Double-angle and half angle formulas Solve trigonometric equations using basic identities and inverse trigonometric functions Prove and derive trigonometric identities Find a sinusoidal function to model a given set of data or situation Vectors, Matrices and Systems of Equations Perform operations on vectors in the plan Solve applied problems using vectors Know and apply the algebraic and geometric definitions of the dot product of vectors Know the definitions of matrix addition and multiplication Add, subtract and multiply matrices Multiply a vector by a matrix Represent rotations of the plane as matrices and apply to find the equations of rotated conics Define the inverse of a matrix and computer the inverse of two-by-two and three-by-three matrices Computer determinants of two-by-two and three-by-three matrices Write systems of two and three linear equations in matrix form Solve systems using Gaussian elimination or inverse matrices Represent and solve inequalities in two variables Linear programming Sequence, Series and Mathematical Induction Know, explain and use sigma and factorial notation Write an expression for the nth term Write a particular term of a sequence when given the nth term Understand, explain and use the formulas for the sums of finite arithmetic and geometric sequences Compute the sums of infinite geometric series Understand and apply the convergence criterion for geometric series The principle of mathematical induction Pascal’s triangle Binomial theorem Polar Coordinates, Parameterizations, and Conic Sections Convert between polar and rectangular coordinates Graph functions given in polar coordinates Write complex numbers in polar form De Moivre’s theorem Evaluate parametric equations for given values of the parameter Convert between parametric and rectangular forms of equations Graph curves described by parametric equations Use parametric equations in applied contexts to model situations Identify parabolas, ellipses and hyperbolas from equations Write the equation in standard form and graph parabolas, ellipses and hyperbolas Derive the equation for a conic section from given geometric information Identify key characteristics of a conic section from its equation or graph Identify conic sections whose equations are in polar or parametric form Modeling Mathematics Construct a tangent from a point outside a given circle to a circle Cavalieri’s principle

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Page | 17 © 2011-16 Tutor.com, Inc.

Confidential – Do Not Distribute Intermediate Statistics (Back to Math) Describing Data Numerical summary measures The effect of changing units on summary measures Tabular and graphical methods (dotplots, stemplots, boxplots) Comparing distributions (back to back stemplots, parallel boxplots) Comparing center and spread: within group, between group variation Comparing shapes Comparing outliers and other unusual features (clusters, gaps) Probability Interpreting probability, including long run relative frequency interpretation "Law of Large Numbers" concept Addition rule, multiplication rule, conditional probability and independence Discrete random variables and their probability distributions, including binomial and geometric Mean (expected value) and standard deviation of a random variable Linear transformation of a random variable Combining independent random variables Notion of independence versus dependence Mean and standard deviation for sums and differences of independent random variables Simulation of random behavior and probability distributions The Normal Distribution Properties of the normal distribution Using tables of the normal distribution The normal distribution as a model for measurements Sampling and Experimentation: Planning and conducting a study Methods of data collection (census, sample survey, experiment, observational study) Planning and Conducting Surveys Characteristics of a well-designed and well-conducted survey Populations, samples, and random selection Sources of bias in sampling and surveys Sampling methods, including simple random sampling, stratified random sampling and cluster sampling Planning and Conducting Experiments Characteristics of a well-designed experiment Treatments, control groups, experimental units, random assignments and replication Sources of bias and confounding, including placebo effect and blinding Completely randomized design Randomized block design, including matched pairs design Generalizability of results and types of conclusions that can be drawn from observational studies, experiments and surveys Sampling distribution Sampling distribution of a sample proportion Sampling distribution of a sample mean Central Limit Theorem Sampling distribution of a difference between two independent sample proportions Sampling distribution of a difference between two independent sample means Simulation of sampling distributions t distributions Chi-square distributions F distributions

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