Syllabus

Variables and constants
Coefficients and terms
Algebraic expressions
Writing expressions from words
Evaluating expressions
Order of operations
Combining like terms
Properties of real numbers
    ＊Commutative property
    ＊Associative property
    ＊Distributive property
    ＊Identity and inverse properties
Numerical and algebraic patterns
Translating verbal expressions into algebraic expressions

Meaning of exponents
Laws of exponents
Product of powers
Quotient of powers
Power of a power
Power of a product
Power of a quotient
Zero exponents
Negative exponents
Rational exponents
Scientific notation
Operations with scientific notation

Introduction to polynomials
Monomials, binomials, trinomials
Degree of a polynomial
Classifying polynomials
Adding polynomials
Subtracting polynomials
Multiplying monomials
Multiplying monomials and polynomials
Multiplying binomials
Special products
   ＊Square of a binomial
   ＊Difference of squares
Polynomial identities
Polynomial multiplication using models/area models

Greatest common factor (GCF)
Factoring out the GCF
Factoring monomials
Factoring trinomials
Factoring quadratic expressions
Factoring by grouping
Difference of squares
Perfect-square trinomials
Choosing an appropriate factoring method
Factoring completely
Solving equations by factoring

Properties of equality
One-step equations
Two-step equations
Multi-step equations
Equations with variables on both sides
Equations involving parentheses
Equations involving fractions
Equations involving decimals
Literal equations
Formulas and rearranging formulas
Writing equations from word problems
Solving real-world problems with linear equations
Checking solutions

Understanding inequality symbols
Graphing inequalities on a number line
One-step inequalities
Two-step inequalities
Multi-step inequalities
Inequalities with variables on both sides
Compound inequalities
   ＊AND inequalities
   ＊OR inequalities
Absolute-value inequalities
Graphing solutions
Writing inequalities from real-world situations
Solving and interpreting inequality word problems

Coordinate plane
Ordered pairs
Quadrants
Plotting points
Reading coordinates
Independent and dependent variables
Tables, graphs and equations
Patterns and relationships
Rate of change
Slope
Positive, negative, zero and undefined slope
Finding slope from a graph
Finding slope from two points
Finding slope from a table
Finding slope from an equation

Introduction to functions
Relations vs. functions
Function notation
Domain and range
Evaluating functions
Representing functions
   Tables
   Graphs
   Equations
   Verbal descriptions
Linear functions
Slope-intercept form
Writing equations from graphs
Writing equations from two points Writing equations from slope and a point
Point-slope form
Standard form
Converting between forms
Intercepts
   x-intercept
   y-intercept
Graphing linear functions
Comparing linear functions

Introduction to systems
Graphing systems
Solving by substitution
Solving by elimination
Solving by linear combination
Systems with no solution
Systems with one solution
Systems with infinitely many solutions
Interpreting intersections
Systems of linear inequalities
Graphing systems of inequalities
Real-world systems problems
Modeling with systems of equations

Introduction to sequences
Arithmetic sequences
Common difference Recursive sequences
Explicit formulas
Finding terms of a sequence
Writing arithmetic sequence equations
Geometric sequences
Common ratio
Recursive geometric sequences
Explicit geometric formulas
Comparing arithmetic and geometric sequences
Sequences as functions

Meaning of absolute value
Absolute value expressions
Graphing absolute value functions
Parent function
Transformations of absolute value graphs
Absolute value equations
Absolute value inequalities
Piecewise representation
Real-world applications of absolute value

Translating real-world situations into equations
Rates and proportions
Distance-rate-time problems
Mixture problems
Percent problems
Cost and revenue models
Break-even problems
Simple interest
Direct variation
Inverse relationships
Linear modeling
Interpreting slope and intercepts in context
Analyzing data with linear models

Introduction to quadratic expressions
Quadratic functions
Standard form
Vertex form
Factored form
Graphing quadratic functions
Parabolas
Vertex Axis of symmetry
x-intercepts and y-intercept
Maximum and minimum values
Transformations of quadratic functions
Completing the square
Comparing linear and quadratic functions
Quadratic modeling

Solving by graphing
Solving by square roots
Solving by factoring
Zero-product property
Completing the square
Quadratic formula
Discriminant Number and type of solutions
Real and complex solutions
Choosing an appropriate solving method
Quadratic word problems

Introduction to square roots
Perfect squares
Estimating square roots
Simplifying radicals
Operations with radicals
Rational exponents
Converting between radicals and rational exponents
Solving radical equations
Extraneous solutions

Rational expressions
Domain restrictions
Simplifying rational expressions
Multiplying rational expressions
Dividing rational expressions
Adding and subtracting rational expressions
Complex fractions
Rational equations
Solving rational equations
Checking for extraneous solutions
Rational-function applications

Introduction to exponential functions
Exponential growth
Exponential decay
Growth and decay factors
Writing exponential equations
Graphing exponential functions
Transformations
Comparing linear and exponential functions Tables and graphs of exponential functions Compound interest
Population growth
Depreciation
Real-world exponential models

Reading and interpreting data
Tables and graphs
Scatter plots
Correlation
Positive and negative association
Line of best fit
Linear regression
Residuals
Interpreting regression models
Making predictions
Identifying outliers
Two-way tables
Categorical data
Quantitative data
Statistical modeling

Parent functions
Translations
Reflections
Vertical stretches
Vertical compressions
Horizontal transformations
Transformations of linear functions
Transformations of quadratic functions
Transformations of absolute-value functions
Transformations of exponential functions
Comparing functions in different representations

Identifying variables
Making assumptions
Constructing mathematical models
Linear models
Quadratic models
Exponential models
Interpreting parameters
Using graphs to make predictions
Solving real-world problems
Checking reasonableness of solutions
Communicating mathematical conclusions

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