**Functions**

- Domain and range
- Identify functions
- Linear functions
- Linear functions over unit intervals
- Evaluate functions
- 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

**Families of functions**

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

**Quadratic relations**

- Characteristics of quadratic functions
- Find the maximum or minimum value of a quadratic function
- 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
- Using the discriminant

**Polynomials**

- Divide polynomials using long division
- Write a polynomial from its roots
- Find the roots of factored polynomials
- Rational root theorem
- Complex conjugate theorem
- Conjugate root theorems
- Descartes’ Rule of Signs
- Fundamental Theorem of Algebra
- Match polynomials and graphs
- 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

**Rational functions**

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

**Logarithms**

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

**Exponential and logarithmic functions**

- Domain and range of exponential and logarithmic functions
- Evaluate exponential functions
- Match exponential functions and graphs
- Solve exponential equations by factoring
- Solve exponential equations using common logarithms
- Solve logarithmic equations I
- Solve logarithmic equations II
- Identify linear and exponential functions
- Exponential functions over unit intervals
- Describe linear and exponential growth and decay
- Exponential growth and decay: word problems
- Compound interest: word problems
- Continuously compounded interest: word problems

**Radical functions**

- Domain and range of radical functions
- Solve radical equations

**Roots and rational exponents**

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

**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 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

**Systems of inequalities**

- Solve systems of inequalities by graphing
- Find the vertices of a solution set
- Linear programming
- Graph solutions to quadratic inequalities
- Solve quadratic inequalities

**Matrices**

- Matrix vocabulary
- Matrix operation rules
- Add and subtract matrices
- Multiply a matrix by a scalar
- Linear combinations of matrices
- Multiply two matrices
- Simplify matrix expressions
- 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

**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 using reference angles
- Inverses of trigonometric functions
- 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

**Trigonometric functions**

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

**Trigonometric identities**

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

**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

**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

**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

**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

**Two-dimensional vectors**

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

**Three-dimensional vectors**

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

**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
- Introduction to sigma notation
- Identify arithmetic and geometric series
- Find the sum of a finite arithmetic or 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

**Logic**

- Identify hypotheses and conclusions
- Counterexamples
- Conditionals
- Negations
- Converses, inverses, and contrapositives
- Biconditionals

**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

**Probability distributions**

- Identify discrete and continuous random variables
- Write a discrete probability distribution
- Graph a discrete probability distribution
- Expected values of random variables
- Variance and 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
- Use normal distributions to approximate binomial distributions

**Statistics**

- Identify biased samples
- Variance and standard deviation
- Linear regression

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