**Algebra and Pre-Calculus**

**Tutoring For Students at all Levels of Math**

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Our goal is help students feel confident in their comprehension of Algebra, Algebra 2, and Pre-Calculus. With IQ Learning, you will see an improvement in test scores, as we work to ensure each student understands the topics included in each course before moving on to the next level. Read more about our curriculum or call IQ learning today to learn more about our private tutors.

**Relations and Linear Functions**

- Relations and Functions
- Functions: Definition of Single-value Functions
- Distinguish between Relations and Functions: Algebraic and Graphical
- Discrete and Continuous Functions
- Set and Interval Notations
- Domain and Range for Discrete and Continuous Functions
- Word Problems on Domain and Range

**Linear Equations**

- Write and Solve Linear Equations in one Variable
- Distributive Property with Variable on one side of the Equation
- Distributive Property with Variable on both sides of the Equation

- Write Linear Equations in 2 variables from
- Tables of Values
- Graphs
- Word Problems

- Graph Linear Functions and Equations
- Slopes
- X- and Y-intercepts, Zeros
- Word Problems on Linear Functions

- Solve Word Problems and tables based on rate of change, slopes, intercepts and zeros

**Systems of Linear Equations in 2 variables**

- Word problems

**Linear Inequalities**

- Graphing Linear inequalities in 2 variables
- Writing Linear inequalities in 2 variables from Word Problems

**Quadratic Polynomial Functions**

- Factoring trinomial functions of the form ax2 + bx + c
- Domain and Range of Quadratic Functions in both set and interval notations
- Graph Quadratic Functions from chart of Values, and identify X- and intercepts, Vertex, Minimum and Maximum values, Equation for the Axis of Symmetry
- Graphs of Quadratic Functions: Parent Quadratic Function, y = x2 and its transformations about the X- and the Y-axes

**Quadratic Equations**

- Solve Quadratic Equations by
- Factoring
- Taking Square Roots
- Completing the Squares
- Quadratic Formula

- Use of Discriminants in Quadratic Equations
- Word Problems to set up and solve Quadratic Equations

**Exponential Functions**

- Laws of Exponents: Integers and Rational Numbers
- Simplifying Numeric and Algebraic Expressions involving exponents

- Graphing Exponential Functions y = abx
- Intercepts and Asymptotes
- Evaluate exponential functions and their coefficients from graphs

- Word Problems on Exponents and Exponential Functions

**ALGEBRA 2 CURRICULUM**

**Basic Review of relevant topics of Algebra -1:**Equations and Inequalities in one dimension including Compound Inequalities and Word Problems

**Absolute Value Inequalities in 1-d**

- Solving and plotting the solutions
- Converse: Writing the absolute value inequality from the solution plots

**Graphing Absolute Value Linear Equations**

- Transformations of Absolute Value Linear Equations and Graphing the Transformed Equations
- Word Problems on Absolute Value Linear Equations and their t transformations

**Systems of Inequalities**

- Linear Inequalities
- Solving the linear systems by Graphing the inequalities
- Setting up and Writing the linear inequalities from Word Problems

- Linear and Quadratic Equations
- Writing Systems of one linear and one quadratic equation
- Solving the Systems of one linear and one quadratic equation

**Matrices**

- Order of Matrices, Identity and Null Matrix
- Addition, Subtraction, and Multiplication of Matrices
- Inverse of 3X3 Matrices: Gauss – Jordan Elimination Technique
- Solving Systems of 3 Equations:
- Substitution Method
- Elimination Method
- Matrix Inversion: Gauss – Jordan Elimination Technique

**Exponents and Radicals**

- Brief review on exponents and radicals using whole numbers: nth roots, simplification of radicals, rational exponents
- Exponents and radicals using variables and numbers:
- Simplifying Radical expressions
- Simplifying rational and irrational exponents
- Composition and Inverse of functions (algebraically and graphically)
- Solving radical equations and inequalities

**Quadratic and Square Root Relations and Functions**

- Plotting Quadratic Functions with Transformations

- Writing Quadratic Functions from their Graphs and Word Problems
- Plotting Square Root Functions with Transformations
- Writing Square Root Functions from their Graphs and Word Problems

**Cubic and Cube Root Relations and Functions**

- Plotting Cubic Functions with Transformations
- Writing Cubic Functions from their Graphs and Word Problems
- Plotting Cube Root Functions with Transformations
- Writing Square Root Functions from their Graphs and Word Problems

**Complex numbers**

- Representation, addition, subtraction, and multiplication of complex numbers
- Conjugates and their properties, division of complex numbers
- Simplifying Complex Expressions

**Quadratic Polynomials and Equations**

- Factoring by Grouping, Completing the Squares, Special cases
- Roots of Quadratic Polynomials from Graphs
- Quadratic equations
- Determining roots by a) factoring b) Completing the squares c) Quadratic Formula
- Writing Sum and Products of roots from the Coefficients of Quadratic Equations
- Determining quadratic roots from their sum and products

- Constructing quadratic equations from the Sum and Products of their roots
- Discriminants in quadratic equations: Real and complex roots
- Constructing quadratic equations from their real and complex roots
- Solving Quadratic-like equations
- Word problems on Quadratic equations

**Cubic Polynomials and Equations**

- Factoring by Grouping
- Roots of Cubic equations from graphs
- Determining roots of Cubic Equations by Factoring
- Writing Sums and Products of roots from the Coefficients of Cubic Equations
- Determining cubic roots from their sums and products
- Constructing cubic equations from the Sums and Products of their roots

**Solving Radical Equations and Inequalities**

- Square root, Cube Root and reducible Fourth root Equations and Inequalities
- Word Problems

**Polynomial Functions and Roots**

- Word Problems in Applications to form Polynomial functions
- Graphs of Monomials
- Graphs of Monomials (Power Functions) and their Transformations

- Polynomials
- End Behavior of Polynomials
- Zeros of Polynomials and X-intercepts of the graphs
- Long and Synthetic Division of Polynomials
- Complex Zeros and the Intermediate Value Theorem for Polynomials
- Graphing Polynomials from their Zeros, End behavior and some t test points
- Shapes of graphs near roots with multiplicity (m) > 1
- Local Maxima and Minima of Polynomials
- Remainder Theorem and the Factor theorem
- The Fundamental Theorem of Algebra
- Rational Zero Theorem
- Factoring higher order Polynomials into Linear and Quadratic factors
- Descartes’ Rule of Signs and Upper and Lower Bounds for Polynomial Roots
- Rational, Irrational and complex roots (PNI charts)

**Rational Functions**

- Vertical and Horizontal Asymptotes
- Sign Charts
- Graphing Rational Functions from their Zeros, X- and Y- Intercepts, Asymptotes and Sign Charts
- Word Problems and Applications of Rational Functions

**Exponential Functions**

- Graphs of Exponential Functions
- Writing Exponential Functions from their Graphs
- Properties of Exponential Functions
- Transformation of Exponential Functions
- Comparing Power Functions and Exponential Functions
- Natural Exponential Function (e)
- Modeling Exponential Growth and Decay Applications
- Compound Interest: Discrete and Continuous
- Radioactive Decay

**Logarithmic Functions**

- Definition of Logarithmic Functions and their inverse relationship with the Exponential Functions
- Properties of Log Functions
- Graphs of Log Functions
- Graphing Transformed Log Functions
- Natural Log, Common Log and Base Change Formula
- Properties of Natural Log Functions
- Expanding and Condensing Log Functions
- Solving Exponential and Log Equations using Algebraic and Graphical techniques
- Modeling with Log Functions
- Compound Interest
- Population Growth
- Radioactive Decay
- Newton’s Law of Cooling
- Log scales (Decibels, pH, Richter)
- Comparative modeling: Exponential, Power and Log Functions

Review of Relevant Concepts of Algebra-2

**Polynomial Functions**

- Definition of a polynomial: Term, Coefficient, Exponent, Constant Term
- Adding, Subtracting and Multiplying Polynomials
- Dividing Polynomials: Long and Synthetic Division
- How to Graph Polynomial Functions
- End behavior and Leading Term
- Zeros of Polynomials, X- and Y-intercepts
- Shape of the graphs near Zeros of multiplicity 'm'
- Local Minima and Maxima of Polynomials
- Number of local extrema
- Remainder and Factor Theorems and their Applications
- Factoring Polynomials
- Finding Polynomials with Specified Zeros including Complex and Irrational
- Rational Zeros Theorem and its Applications
- Descartes' Rule of Signs and Lower and Upper Bounds for Roots
- Solving Higher Order Polynomial Equations
- Finding All Roots Real and Imaginary for Polynomials (PNI Charts
- Writing Polynomial Equations
- Writing, Graphing and Solving Polynomial Inequalities

**Power Functions**

- Definition and Analysis of Power Functions
- Graphing Power Functions

**Piecewise Functions**

**Composition of Functions**

**Combine Polynomial Functions and Composites to solve Word Problems in Modeling**

**Rational Functions**

- Introduction
- Vertical, Horizontal and Slant Asymptotes
- Rational Functions in Piecewise Functions
- Graphing and Solving Rational Inequalities

**Optimization**

**Solving Radical Equations**TRIGONOMETRY

- Radian, Degrees, Arc Length
- Trigonometric Functions
- Relationship between Linear and Angular Speed
- Unit Circle: Relationships with Special Right Triangles
- Graphing Sin and Cosine Functions
- Writing Equations of Sin and Cos Functions from their Graphs
- Graphing Rational Trig Functions: Tan, Cot, Sec, Csc and their Asymptotes
- Writing Equations Graphs of Rational Trig Functions
- Inverse Trigonometric Functions (ITFs)
- Graphing ITFs and finding finding their values (Non-calculator and Calculator)
- Word Problems and Applications of Sin and Cos functions
- Fundamental Trigonometric Identities: Trig Pythagoreans
- Simplifying Expressions using the Trig Fundamental Identities
- Solving Trig Equations using the Trig Fundamental Identities
- Trigonometric Proofs
- Sum and Difference Identities
- Proofs and Solving Equations based on Sum and Difference Identities
- Multiple Angle Formulas
- Proofs and Solving Equations based on Multiple Angle Formulas
- Half Angle Formulas
- Proofs and Solving Equations based on Half Angle Formulas
- Law of Sines and Cosines
- Ambiguous Cases in the Law of Sines
- Applications of the Law of Sines and Cosines

**Vectors in two dimensions**

- Definition, Representations
- Finding g Magnitude and Direction
- Addition, Subtraction of Vectors
- Multiplication of Vectors: Dot Products
- Parametric Equations for curves
- Vectors in Space
- Vector Applications in Navigation

**Exponential and Logarithmic Functions**

- Graphing Exponential Functions
- Algebra of Exponential Functions
- Algebra of Exponential Functions with rational exponents
- Solving Exponential Equations without using logs
- Properties of Logarithms
- Solving Exponential and Log Equations

**Exponential and Log Models**

- Logistics model of Growth
- Applications of Logistics Models

**Conics**

- Equations of Circles, Tangents, Chords and other Properties of Circles
- Equations of Ellipses and their Properties
- Equations of Hyperbolas and their Properties
- Equations of Parabolas and their Properties
- General Conic Sections and their Applications
- Solving systems of Conics
- Rotated Conics
- Parametric Forms for Conics
- Vector Applications of parametric Equations for Conics
- Systems of Conics

**Polar Coordinates and Complex Numbers**

- Polar Graphs
- Trigonometric form of Complex Numbers
- De Moivere's Theorem and Application

**Sequences and Series**

- Basic Permutations and Combinations
- Sequences: General Terms, Limits
- Series: Convergence and Divergence
- Tests for Convergence and Divergence

**Binomial Theorem**

- Methods of Deduction and Deduction
- Binomial Theorem
- nth Term of a Binomial Series

**Partial Fractions**

- Linear and Quadratic Factors
- Repeated Linear and Quadratic Forms

**Limits**

- Definitions of Limits
- Properties of Limits
- Existence of Limits
- Techniques for Evaluating Limits
- Limits of Polynomials
- Limita of Rational Functions
- Limits of Trigonometric Functions
- Important Theorems on Limits including the Squeeze Theorem
- One sided Limits
- Infinite Limits and Asymptotes of Functions

**Continuity of Functions**

- Definition and Properties of Continuity
- Left-hand and Right-hand Continuity of Functions
- Discontinuous Functions
- Intermediate value Theorem for Functions

**Derivatives of Functions**

- Definitions and Properties of Derivatives
- Left hand and right hand derivatives
- Relationship between Limits, Continuity and Derivatives
- Derivatives as slopes of tangents
- Derivatives of Polynomial Functions

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