A. Functions

  1. Domain and range
  2. Identify functions
  3. Evaluate functions
  4. Find values using function graphs
  5. Complete a table for a function graph
  6. Find the slope of a linear function
  7. Graph a linear function
  8. Write the equation of a linear function
  9. Linear functions over unit intervals
  10. Add, subtract, multiply, and divide functions
  11. Composition of functions
  12. Identify inverse functions
  13. Find values of inverse functions from tables
  14. Find values of inverse functions from graphs
  15. Find inverse functions and relations

B. Families of functions

  1. Function transformation rules
  2. Translations of functions
  3. Reflections of functions
  4. Dilations of functions
  5. Transformations of functions
  6. Describe function transformations

C. Quadratic functions

  1. Find the maximum or minimum value of a quadratic function
  2. Characteristics of quadratic functions
  3. Graph a quadratic function
  4. Match quadratic functions and graphs
  5. Solve a quadratic equation using square roots
  6. Solve a quadratic equation by factoring
  7. Solve a quadratic equation by completing the square
  8. Solve a quadratic equation using the quadratic formula
    • New! Solve quadratic equations: word problems
  9. Using the discriminant

D. Polynomials

  1. Divide polynomials using long division
  2. Divide polynomials using synthetic division
  3. Evaluate polynomials using synthetic division
  4. Find the roots of factored polynomials
  5. Write a polynomial from its roots
  6. Rational root theorem
  7. Complex conjugate theorem
  8. Conjugate root theorems
  9. Descartes’ Rule of Signs
  10. Fundamental Theorem of Algebra
  11. Match polynomials and graphs
  12. Domain and range of polynomials
  13. Factor sums and differences of cubes
  14. Solve equations with sums and differences of cubes
  15. Factor using a quadratic pattern
  16. Solve equations using a quadratic pattern
  17. Pascal’s triangle
  18. Pascal’s triangle and the Binomial Theorem
  19. Binomial Theorem I
  20. Binomial Theorem II

E. Rational functions

  1. Rational functions: asymptotes and excluded values
  2. Solve rational equations
  3. Check whether two rational functions are inverses

F. Exponential and logarithmic functions

  1. Domain and range of exponential and logarithmic functions
  2. Convert between exponential and logarithmic form
  3. Solve exponential equations by rewriting the base
  4. Evaluate logarithms
  5. Change of base formula
  6. Product property of logarithms
  7. Quotient property of logarithms
  8. Power property of logarithms
  9. Evaluate logarithms using properties
    • New! Graph logarithmic functions
  10. Solve exponential equations using logarithms
  11. Solve logarithmic equations with one logarithm
  12. Solve logarithmic equations with multiple logarithms
  13. Exponential functions over unit intervals
  14. Identify linear and exponential functions
  15. Describe linear and exponential growth and decay
  16. Exponential growth and decay: word problems
  17. Compound interest: word problems

G. Radical functions

  1. Domain and range of radical functions
  2. Solve radical equations

H. Roots and rational exponents

  1. Roots of integers
  2. Roots of rational numbers
  3. Find roots using a calculator
  4. Evaluate rational exponents
  5. Operations with rational exponents
  6. Simplify radical expressions with variables
  7. Nth roots
  8. Simplify expressions involving rational exponents

I. Systems of equations

  1. Solve a system of equations by graphing
  2. Solve a system of equations by graphing: word problems
  3. Classify a system of equations
  4. Solve a system of equations using substitution
  5. Solve a system of equations using substitution: word problems
  6. Solve a system of equations using elimination
  7. Solve a system of equations using elimination: word problems
  8. Solve a system of equations using augmented matrices
  9. Solve a system of equations using augmented matrices: word problems
  10. Solve a system of equations in three variables using substitution
  11. Solve a system of equations in three variables using elimination
  12. Determine the number of solutions to a system of equations in three variables

J. Systems of inequalities

  1. Solve systems of linear inequalities by graphing
  2. Solve systems of linear and absolute value inequalities by graphing
  3. Find the vertices of a solution set
  4. Linear programming

K. Nonlinear inequalities

  1. Graph solutions to quadratic inequalities
  2. Solve quadratic inequalities
  3. Graph solutions to higher-degree inequalities
  4. Solve higher-degree inequalities

L. Matrices

  1. Matrix vocabulary
  2. Matrix operation rules
  3. Add and subtract matrices
  4. Multiply a matrix by a scalar
  5. Add and subtract scalar multiples of matrices
  6. Multiply two matrices
  7. Simplify matrix expressions
  8. Properties of matrices
  9. Solve matrix equations
  10. Determinant of a matrix
  11. Is a matrix invertible?
  12. Inverse of a 2 x 2 matrix
  13. Inverse of a 3 x 3 matrix
  14. Identify inverse matrices
  15. Solve matrix equations using inverses
  16. Identify transformation matrices
  17. Transformation matrices: write the vertex matrix
  18. Transformation matrices: graph the image

M. Trigonometry

  1. Convert between radians and degrees
  2. Radians and arc length
  3. Quadrants
  4. Coterminal and reference angles
  5. Find trigonometric ratios using right triangles
  6. Find trigonometric ratios using the unit circle
  7. Find trigonometric ratios of special angles
  8. Find trigonometric ratios using reference angles
  9. Inverses of trigonometric functions
  10. Inverses of trigonometric functions using a calculator
  11. Solve trigonometric equations
  12. Trigonometric ratios: find a side length
  13. Trigonometric ratios: find an angle measure
  14. Solve a right triangle
  15. Law of Sines
  16. Law of Cosines
  17. Solve a triangle
  18. Area of a triangle: sine formula
  19. Area of a triangle: Heron’s formula

N. Trigonometric functions

  1. Find properties of sine functions
  2. Write equations of sine functions from graphs
  3. Write equations of sine functions using properties
  4. Graph sine functions
  5. Graph translations of sine functions
  6. Find properties of cosine functions
  7. Write equations of cosine functions from graphs
  8. Write equations of cosine functions using properties
  9. Graph cosine functions
  10. Graph translations of cosine functions
  11. Graph sine and cosine functions
  12. Graph translations of sine and cosine functions

O. Trigonometric identities

  1. Complementary angle identities
  2. Symmetry and periodicity of trigonometric functions
  3. Trigonometric identities I
  4. Trigonometric identities II

P. Conic sections

  1. Find properties of parabolas
  2. Write equations of parabolas in vertex form
  3. Graph parabolas
  4. Find properties of circles
  5. Write equations of circles in standard form
  6. Graph circles
  7. Find properties of ellipses
  8. Find the eccentricity of an ellipse
  9. Write equations of ellipses in standard form
  10. Find properties of hyperbolas
  11. Find the eccentricity of a hyperbola
  12. Write equations of hyperbolas in standard form
  13. Convert equations of conic sections from general to standard form

Q. Real numbers

  1. Sort rational and irrational numbers
  2. Classify rational and irrational numbers
  3. Properties of operations on rational and irrational numbers

R. Complex numbers

  1. Add and subtract complex numbers
  2. Complex conjugates
  3. Multiply and divide complex numbers
  4. Add, subtract, multiply, and divide complex numbers
  5. Absolute values of complex numbers
  6. Powers of i

S. Complex plane

  1. Introduction to the complex plane
  2. Graph complex numbers
  3. Addition in the complex plane
  4. Subtraction in the complex plane
  5. Graph complex conjugates
  6. Absolute value in the complex plane
  7. Midpoints in the complex plane
  8. Distance in the complex plane

T. Polar form

  1. Find the modulus and argument of a complex number
  2. Convert complex numbers from rectangular to polar form
  3. Convert complex numbers from polar to rectangular form
  4. Convert complex numbers between rectangular and polar form
  5. Match polar equations and graphs

U. Two-dimensional vectors

  1. Find the magnitude of a vector
  2. Find the component form of a vector
  3. Find the direction angle of a vector
  4. Find the component form of a vector from its magnitude and direction angle
  5. Graph a resultant vector using the triangle method
  6. Graph a resultant vector using the parallelogram method
  7. Add vectors
  8. Subtract vectors
  9. Find the magnitude and direction of a vector sum
  10. Multiply a vector by a scalar
  11. Find the magnitude of a vector scalar multiple
  12. Determine the direction of a vector scalar multiple
  13. Find a unit vector
  14. Linear combinations of vectors

V. Three-dimensional vectors

  1. Find the magnitude of a three-dimensional vector
  2. Find the component form of a three-dimensional vector
  3. Add and subtract three-dimensional vectors
  4. Scalar multiples of three-dimensional vectors
  5. Find a three-dimensional unit vector
  6. Linear combinations of three-dimensional vectors

W. Sequences and series

  1. Find terms of a sequence
  2. Find terms of a recursive sequence
  3. Identify a sequence as explicit or recursive
  4. Find a recursive formula
  5. Find recursive and explicit formulas
  6. Convert a recursive formula to an explicit formula
  7. Convert an explicit formula to a recursive formula
  8. Convert between explicit and recursive formulas
  9. Identify arithmetic and geometric series
  10. Introduction to sigma notation
  11. Find the sum of an arithmetic series
  12. Find the sum of a finite geometric series
  13. Introduction to partial sums
  14. Partial sums of arithmetic series
  15. Partial sums of geometric series
  16. Partial sums: mixed review
  17. Convergent and divergent geometric series
  18. Find the value of an infinite geometric series
  19. Write a repeating decimal as a fraction

X. Probability

  1. Introduction to probability
  2. Calculate probabilities of events
  3. Combinations and permutations
  4. Find probabilities using combinations and permutations
  5. Find probabilities using two-way frequency tables
  6. Identify independent events
  7. Find conditional probabilities
  8. Independence and conditional probability
  9. Find conditional probabilities using two-way frequency tables
  10. Find probabilities using the addition rule

Y. Probability distributions

  1. Identify discrete and continuous random variables
  2. Write a discrete probability distribution
  3. Graph a discrete probability distribution
  4. Expected values of random variables
  5. Variance of random variables
  6. Standard deviation of random variables
  7. Write the probability distribution for a game of chance
  8. Expected values for a game of chance
  9. Choose the better bet
  10. Find probabilities using the binomial distribution
  11. Mean, variance, and standard deviation of binomial distributions
  12. Find probabilities using the normal distribution I
  13. Find probabilities using the normal distribution II
  14. Find z-values
  15. Find values of normal variables
  16. Distributions of sample means
  17. The Central Limit Theorem
  18. Use normal distributions to approximate binomial distributions

Z. Statistics

  1. Identify biased samples
  2. Variance and standard deviation
  3. Identify an outlier
  4. Identify an outlier and describe the effect of removing it
  5. Outliers in scatter plots
  6. Match correlation coefficients to scatter plots
  7. Calculate correlation coefficients
  8. Find the equation of a regression line
  9. Interpret regression lines
  10. Analyze a regression line of a data set
  11. Analyze a regression line using statistics of a data set
  12. Find confidence intervals for population means
  13. Find confidence intervals for population proportions
  14. Interpret confidence intervals for population means
  15. Experiment design
  16. Analyze the results of an experiment using simulations

AA. Limits

  1. Find limits using graphs
  2. Find one-sided limits using graphs
  3. Determine if a limit exists
  4. Find limits at vertical asymptotes using graphs
  5. Determine end behavior using graphs
  6. Find limits using addition, subtraction, and multiplication laws
  7. Find limits using the division law
  8. Find limits using power and root laws
  9. Find limits using limit laws
  10. Find limits of polynomials and rational functions
  11. Find limits involving factorization and rationalization

BB. Continuity

  1. Identify graphs of continuous functions
  2. Determine continuity using graphs
  3. Determine one-sided continuity using graphs
  4. Find and analyze points of discontinuity using graphs
  5. Determine continuity on an interval using graphs

CC. Introduction to derivatives

  1. Average rate of change I
  2. Average rate of change II
  3. Find instantaneous rates of change
  4. Velocity as a rate of change
  5. Find values of derivatives using limits
  6. Find the slope of a tangent line using limits
  7. Find equations of tangent lines using limits