**A. Functions**

- Domain and range
- Identify functions
- Evaluate functions
- Find values using function graphs
- Complete a table for a function graph
- Find the slope of a linear function
- Graph a linear function
- Write the equation of a linear function
- Linear functions over unit intervals
- Add, subtract, multiply, and divide functions
- Composition of functions
- Identify inverse functions
- Find values of inverse functions from tables
- Find values of inverse functions from graphs
- Find inverse functions and relations

**B. Families of functions**

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

**C. Quadratic functions**

- Find the maximum or minimum value of a quadratic function
- Characteristics of quadratic functions
- Graph a quadratic function
- Match quadratic functions and graphs
- Solve a quadratic equation using square roots
- Solve a quadratic equation by factoring
- 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

**D. Polynomials**

- Divide polynomials using long division
- Divide polynomials using synthetic division
- Evaluate polynomials using synthetic division
- 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
- Fundamental Theorem of Algebra
- Match polynomials and graphs
- Domain and range of polynomials
- Factor sums and differences of cubes
- Solve equations with sums and differences of cubes
- Factor using a quadratic pattern
- Solve equations using a quadratic pattern
- Pascal’s triangle
- Pascal’s triangle and the Binomial Theorem
- Binomial Theorem I
- Binomial Theorem II

**E. Rational functions**

- Rational functions: asymptotes and excluded values
- Solve rational equations
- Check whether two rational functions are inverses

**F. Exponential and logarithmic functions**

- Domain and range of exponential and logarithmic functions
- Convert between exponential and logarithmic form
- Solve exponential equations by rewriting the base
- Evaluate logarithms
- Change of base formula
- Product property of logarithms
- Quotient property of logarithms
- Power property of logarithms
- Evaluate logarithms using properties

• New! Graph logarithmic functions - Solve exponential equations using logarithms
- Solve logarithmic equations with one logarithm
- Solve logarithmic equations with multiple logarithms
- 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

**G. Radical functions**

- Domain and range of radical functions
- Solve radical equations

**H. Roots and rational exponents**

- Roots of integers
- Roots of rational numbers
- Find roots using a calculator
- Evaluate rational exponents
- Operations with rational exponents
- Simplify radical expressions with variables
- Nth roots
- Simplify expressions involving rational exponents

**I. Systems of equations**

- Solve a system of equations by graphing
- Solve a system of equations by graphing: word problems
- 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 augmented matrices
- Solve a system of equations using augmented matrices: 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

**J. Systems 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

**K. Nonlinear inequalities**

- Graph solutions to quadratic inequalities
- Solve quadratic inequalities
- Graph solutions to higher-degree inequalities
- Solve higher-degree inequalities

**L. 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 2 x 2 matrix
- Inverse of a 3 x 3 matrix
- Identify inverse matrices
- Solve matrix equations using inverses
- Identify transformation matrices
- Transformation matrices: write the vertex matrix
- Transformation matrices: graph the image

**M. Trigonometry**

- Convert between radians and degrees
- Radians and arc length
- Quadrants
- Coterminal and reference angles
- Find trigonometric ratios using right triangles
- Find trigonometric ratios using the unit circle
- Find trigonometric ratios of special angles
- Find trigonometric ratios using reference angles
- Inverses of trigonometric functions
- Inverses of trigonometric functions using a calculator
- Solve trigonometric equations
- 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: Heron’s formula

**N. 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
- Graph sine and cosine functions
- Graph translations of sine and cosine functions

**O. Trigonometric identities**

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

**P. Conic sections**

- Find properties of parabolas
- Write equations of parabolas in vertex form
- Graph parabolas
- Find properties of circles
- Write equations of circles in standard form
- Graph circles
- Find properties of ellipses
- Find the eccentricity of an ellipse
- Write equations of ellipses in standard form
- Find properties of hyperbolas
- Find the eccentricity of a hyperbola
- Write equations of hyperbolas in standard form
- Convert equations of conic sections from general to standard form

**Q. Real numbers**

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

**R. Complex numbers**

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

**S. Complex plane**

- Introduction to the complex plane
- Graph complex numbers
- Addition in the complex plane
- Subtraction in the complex plane
- Graph complex conjugates
- Absolute value in the complex plane
- Midpoints in the complex plane
- Distance in the complex plane

**T. Polar form**

- Find the modulus and argument of a complex number
- Convert complex numbers from rectangular to polar form
- Convert complex numbers from polar to rectangular form
- Convert complex numbers between rectangular and polar form
- Match polar equations and graphs

**U. Two-dimensional vectors**

- Find the magnitude of a vector
- Find the component form of a vector
- Find the direction angle of a vector
- Find the component form of a vector from its magnitude and direction angle
- Graph a resultant vector using the triangle method
- Graph a resultant vector using the parallelogram method
- Add vectors
- Subtract vectors
- Find the magnitude and direction of a vector sum
- Multiply a vector by a scalar
- Find the magnitude of a vector scalar multiple
- Determine the direction of a vector scalar multiple
- Find a unit vector
- Linear combinations of vectors

**V. Three-dimensional vectors**

- Find the magnitude of a three-dimensional vector
- Find the component form of a three-dimensional vector
- Add and subtract three-dimensional vectors
- Scalar multiples of three-dimensional vectors
- Find a three-dimensional unit vector
- Linear combinations of three-dimensional vectors

**W. Sequences and series**

- Find terms of a sequence
- Find terms of a recursive sequence
- Identify a sequence as explicit or recursive
- Find a recursive formula
- Find recursive and explicit formulas
- Convert a recursive formula to an explicit formula
- Convert an explicit formula to a recursive formula
- Convert between explicit and recursive formulas
- 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

**X. Probability**

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

**Y. 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
- Mean, variance, and standard deviation of binomial distributions
- 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
- The Central Limit Theorem
- Use normal distributions to approximate binomial distributions

**Z. 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
- Match correlation coefficients to scatter plots
- Calculate correlation coefficients
- Find the equation of a regression line
- Interpret regression lines
- Analyze a regression line of a data set
- Analyze a regression line using statistics 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

**AA. Limits**

- Find limits using graphs
- Find one-sided limits using graphs
- Determine if a limit exists
- Find limits at vertical asymptotes using graphs
- Determine end behavior using graphs
- Find limits using addition, subtraction, and multiplication laws
- Find limits using the division law
- Find limits using power and root laws
- Find limits using limit laws
- Find limits of polynomials and rational functions
- Find limits involving factorization and rationalization

**BB. Continuity**

- Identify graphs of continuous functions
- Determine continuity using graphs
- Determine one-sided continuity using graphs
- Find and analyze points of discontinuity using graphs
- Determine continuity on an interval using graphs

**CC. Introduction to derivatives**

- Average rate of change I
- Average rate of change II
- Find instantaneous rates of change
- Velocity as a rate of change
- Find values of derivatives using limits
- Find the slope of a tangent line using limits
- Find equations of tangent lines using limits