**A. Variable expressions**

- Evaluate variable expressions involving integers
- Evaluate variable expressions involving rational numbers
- Simplify variable expressions using properties
- Sort factors of single-variable expressions
- Sort factors of multi-variable expressions

**B. Equations**

- Solve linear equations
- Solve one-step and two-step equations: word problems
- Solve equations: complete the solution
- Solve absolute value equations
- Graph solutions to absolute value equations
- Solve multi-variable equations

**C. Inequalities**

- Graph a linear inequality in one variable
- Write inequalities from graphs
- Write a linear inequality: word problems
- Solve linear inequalities
- Graph solutions to linear inequalities
- Solve absolute value inequalities
- Graph solutions to absolute value inequalities
- Graph a two-variable linear inequality
- Graph solutions to two-variable absolute value inequalities
- Graph solutions to quadratic inequalities
- Solve quadratic inequalities

**D. Functions**

- Domain and range
- Identify functions
- Evaluate functions
- Find values using function graphs
- Complete a table for a function graph

• New! Identify graphs: word problems - Find solutions using a table
- Approximate solutions using a table
- Find the slope of a linear function
- Graph a linear function
- Write the equation of a linear function
- Linear functions over unit intervals
- Average rate of change
- Graph an absolute value function
- Domain and range of absolute value functions: graphs
- Domain and range of absolute value functions: equations
- Transformations of absolute value functions
- Graph piecewise-defined functions

**E. Systems of equations**

- Is (x, y) a solution to the system of equations?
- Solve a system of equations by graphing
- Solve a system of equations by graphing: word problems
- Find the number of solutions to a system of equations
- Classify a system of equations
- Solve a system of equations using substitution
- Solve a system of equations using substitution: word problems
- Solve a system of equations using elimination
- Solve a system of equations using elimination: word problems
- Solve a system of equations using any method
- Solve a system of equations using any method: word problems
- Solve a system of equations in three variables using substitution
- Solve a system of equations in three variables using elimination
- Determine the number of solutions to a system of equations in three variables
- Solve a system of linear and quadratic equations by graphing: parabolas
- Solve a system of linear and quadratic equations: parabolas
- Solve a system of linear and quadratic equations: circles
- Solve a nonlinear system of equations

**F. Systems of inequalities**

- Is (x, y) a solution to the system of inequalities?
- Solve systems of linear inequalities by graphing
- Solve systems of linear and absolute value inequalities by graphing
- Find the vertices of a solution set
- Linear programming

**G. Matrices**

- Matrix vocabulary
- Matrix operation rules
- Add and subtract matrices
- Multiply a matrix by a scalar
- Add and subtract scalar multiples of matrices
- Multiply two matrices
- Simplify matrix expressions
- Properties of matrices
- Solve matrix equations
- Determinant of a matrix
- Is a matrix invertible?
- Inverse of a matrix
- Identify inverse matrices
- Solve matrix equations using inverses
- Identify transformation matrices
- Transformation matrices: write the vertex matrix
- Transformation matrices: graph the image
- Solve a system of equations using augmented matrices
- Solve a system of equations using augmented matrices: word problems

**H. Real numbers**

- Sort rational and irrational numbers
- Classify rational and irrational numbers
- Properties of operations on rational and irrational numbers

**I. Complex numbers**

- Introduction to complex numbers
- Add and subtract complex numbers
- Complex conjugates
- Multiply complex numbers
- Divide complex numbers
- Add, subtract, multiply, and divide complex numbers
- Absolute values of complex numbers
- Powers of i

**J. Factoring**

- Factor out a monomial
- Factor quadratics using algebra tiles
- Factor quadratics
- Factor using a quadratic pattern
- Factor by grouping
- Factor sums and differences of cubes
- Factor polynomials

**K. Quadratic functions**

- Characteristics of quadratic functions: graphs
- Characteristics of quadratic functions: equations
- Complete a function table: quadratic functions
- Transformations of quadratic functions
- Graph a quadratic function
- Solve a quadratic equation using square roots
- Solve a quadratic equation using the zero product property
- Solve a quadratic equation by factoring
- Complete the square
- Solve a quadratic equation by completing the square
- Solve a quadratic equation using the quadratic formula

• New! Solve quadratic equations: word problems - Using the discriminant
- Write a quadratic function in vertex form
- Match quadratic functions and graphs

• New! Domain and range of quadratic functions: graphs - Domain and range of quadratic functions: equations
- Write a quadratic function from its zeros
- Write a quadratic function from its vertex and another point

• New! Interpret parts of quadratic expressions: word problems

**L. Polynomials**

- Polynomial vocabulary
- Add and subtract polynomials
- Multiply polynomials
- Divide polynomials using long division
- Divide polynomials using synthetic division
- Add, subtract, multiply, and divide polynomials
- Evaluate polynomials using synthetic division
- Solve polynomial equations
- Find the roots of factored polynomials
- Write a polynomial from its roots
- Rational root theorem
- Complex conjugate theorem
- Conjugate root theorems
- Descartes’ Rule of Signs
- Match polynomials and graphs
- Domain and range of polynomials
- Fundamental Theorem of Algebra
- Pascal’s triangle
- Pascal’s triangle and the Binomial Theorem
- Binomial Theorem I
- Binomial Theorem II

**M. Radical functions and expressions**

- Roots of integers
- Roots of rational numbers
- Find roots using a calculator
- Simplify radical expressions with variables I
- Simplify radical expressions with variables II
- Nth roots
- Multiply radical expressions
- Simplify radical expressions involving fractions
- Add and subtract radical expressions
- Simplify radical expressions using the distributive property
- Simplify radical expressions using conjugates
- Domain and range of radical functions
- Graph square root functions
- Solve radical equations

**N. Rational exponents**

- Evaluate rational exponents
- Multiplication with rational exponents
- Division with rational exponents
- Power rule
- Simplify expressions involving rational exponents I
- Simplify expressions involving rational exponents II

**O. Rational functions and expressions**

- Rational functions: asymptotes and excluded values
- Evaluate rational expressions I
- Evaluate rational expressions II
- Simplify rational expressions
- Multiply and divide rational expressions
- Add and subtract rational expressions
- Solve rational equations

**P. Function operations**

- Add and subtract functions
- Multiply functions
- Divide functions
- Composition of linear functions: find a value
- Composition of linear functions: find an equation
- Composition of linear and quadratic functions: find a value
- Composition of linear and quadratic functions: find an equation
- Identify inverse functions
- Find values of inverse functions from tables
- Find values of inverse functions from graphs
- Find inverse functions and relations

**Q. Families of functions**

- Function transformation rules
- Translations of functions
- Reflections of functions
- Dilations of functions
- Transformations of functions
- Describe function transformations

**R. Variation**

- Write and solve direct variation equations
- Write and solve inverse variation equations
- Classify variation
- Write joint and combined variation equations I
- Find the constant of variation
- Write joint and combined variation equations II
- Solve variation equations

**S. Logarithms**

- Convert between exponential and logarithmic form: rational bases
- Convert between natural exponential and logarithmic form
- Convert between exponential and logarithmic form: all bases
- Evaluate logarithms
- Evaluate natural logarithms
- Change of base formula
- Evaluate logarithms using a calculator
- Identify properties of logarithms
- Product property of logarithms
- Quotient property of logarithms
- Power property of logarithms
- Properties of logarithms: mixed review
- Evaluate logarithms using properties

**T. Exponential and logarithmic functions**

- Domain and range of exponential and logarithmic functions
- Evaluate exponential functions

• New! Write exponential functions: word problems - Graph exponential functions
- Match exponential functions and graphs

• New! Graph logarithmic functions - Solve exponential equations by rewriting the base
- Solve exponential equations using common logarithms
- Solve exponential equations using natural logarithms
- Solve logarithmic equations I
- Solve logarithmic equations II
- Exponential functions over unit intervals
- Identify linear and exponential functions
- Describe linear and exponential growth and decay
- Exponential growth and decay: word problems
- Compound interest: word problems
- Continuously compounded interest: word problems

**U. Parabolas**

- Identify the direction a parabola opens
- Find the vertex of a parabola
- Find the focus or directrix of a parabola
- Find the axis of symmetry of a parabola
- Write equations of parabolas in vertex form from graphs
- Write equations of parabolas in vertex form using properties
- Convert equations of parabolas from general to vertex form
- Find properties of a parabola from equations in general form
- Graph parabolas

**V. Circles**

- Find the center of a circle
- Find the radius or diameter of a circle
- Write equations of circles in standard form from graphs
- Write equations of circles in standard form using properties
- Convert equations of circles from general to standard form
- Find properties of circles from equations in general form
- Graph circles

**W. Ellipses**

- Find the center, vertices, or co-vertices of an ellipse
- Find the length of the major or minor axes of an ellipse
- Find the foci of an ellipse
- Write equations of ellipses in standard form from graphs
- Write equations of ellipses in standard form using properties
- Convert equations of ellipses from general to standard form
- Find properties of ellipses from equations in general form

**X. Hyperbolas**

- Find the center of a hyperbola
- Find the vertices of a hyperbola
- Find the length of the transverse or conjugate axes of a hyperbola
- Find the equations for the asymptotes of a hyperbola
- Find the foci of a hyperbola
- Write equations of hyperbolas in standard form from graphs
- Write equations of hyperbolas in standard form using properties
- Convert equations of hyperbolas from general to standard form
- Find properties of hyperbolas from equations in general form

**Y. Angle measures**

- Convert between radians and degrees
- Radians and arc length
- Graphs of angles
- Quadrants
- Coterminal angles
- Reference angles

**Z. Trigonometry**

- Pythagorean Theorem and its converse
- Special right triangles
- Trigonometric ratios: sin, cos, and tan
- Trigonometric ratios: csc, sec, and cot
- Trigonometric ratios in similar right triangles
- Find trigonometric ratios using the unit circle
- Sin, cos, and tan of special angles
- Csc, sec, and cot of special angles
- Find trigonometric ratios using reference angles
- Find trigonometric functions using a calculator
- Inverses of sin, cos, and tan: degrees
- Inverses of sin, cos, and tan: radians
- Inverses of csc, sec, and cot
- Solve trigonometric equations I
- Solve trigonometric equations II
- Trigonometric ratios: find a side length
- Trigonometric ratios: find an angle measure
- Solve a right triangle
- Law of Sines
- Law of Cosines
- Solve a triangle
- Area of a triangle: sine formula
- Area of a triangle: Law of Sines

**AA. Trigonometric functions**

- Find properties of sine functions
- Write equations of sine functions from graphs
- Write equations of sine functions using properties
- Graph sine functions
- Graph translations of sine functions
- Find properties of cosine functions
- Write equations of cosine functions from graphs
- Write equations of cosine functions using properties
- Graph cosine functions
- Graph translations of cosine functions
- Find properties of sine and cosine functions
- Write equations of sine and cosine functions from graphs
- Write equations of sine and cosine functions using properties
- Graph sine and cosine functions
- Graph translations of sine and cosine functions

**BB. Trigonometric identities**

- Complementary angle identities
- Symmetry and periodicity of trigonometric functions
- Trigonometric identities I
- Trigonometric identities II

**CC. Sequences and series**

- Find terms of an arithmetic sequence
- Find terms of a geometric sequence
- Evaluate explicit formulas for sequences
- Evaluate recursive formulas for sequences
- Classify formulas and sequences
- Write a formula for an arithmetic sequence
- Write a formula for a geometric sequence
- Write a formula for a recursive sequence
- Convert a recursive formula to an explicit formula
- Convert an explicit formula to a recursive formula
- Convert between explicit and recursive formulas
- Sequences: mixed review
- Identify arithmetic and geometric series
- Introduction to sigma notation
- Find the sum of an arithmetic series
- Find the sum of a finite geometric series
- Introduction to partial sums
- Partial sums of arithmetic series
- Partial sums of geometric series
- Partial sums: mixed review
- Convergent and divergent geometric series
- Find the value of an infinite geometric series
- Write a repeating decimal as a fraction

**DD. Probability**

- Introduction to probability
- Calculate probabilities of events
- Counting principle
- Combinations and permutations
- Find probabilities using combinations and permutations
- Find probabilities using two-way frequency tables
- Identify independent events
- Probability of independent and dependent events
- Find conditional probabilities
- Independence and conditional probability
- Find conditional probabilities using two-way frequency tables
- Find probabilities using the addition rule

**EE. Probability distributions**

- Identify discrete and continuous random variables
- Write a discrete probability distribution
- Graph a discrete probability distribution
- Expected values of random variables
- Variance of random variables
- Standard deviation of random variables
- Write the probability distribution for a game of chance
- Expected values for a game of chance
- Choose the better bet
- Find probabilities using the binomial distribution
- Find probabilities using the normal distribution I
- Find probabilities using the normal distribution II
- Find z-values
- Find values of normal variables
- Distributions of sample means

**FF. Statistics**

- Identify biased samples
- Variance and standard deviation
- Identify an outlier
- Identify an outlier and describe the effect of removing it
- Outliers in scatter plots

• New! Match correlation coefficients to scatter plots

• New! Calculate correlation coefficients - Find the equation of a regression line
- Interpret regression lines
- Analyze a regression line of a data set
- Find confidence intervals for population means
- Find confidence intervals for population proportions
- Interpret confidence intervals for population means
- Experiment design
- Analyze the results of an experiment using simulations