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