A. Variable expressions

  1. Evaluate variable expressions involving integers
  2. Evaluate variable expressions involving rational numbers
  3. Simplify variable expressions using properties
  4. Sort factors of single-variable expressions
  5. Sort factors of multi-variable expressions

B. Equations

  1. Solve linear equations
  2. Solve one-step and two-step equations: word problems
  3. Solve equations: complete the solution
  4. Solve absolute value equations
  5. Graph solutions to absolute value equations
  6. Solve multi-variable equations

C. Inequalities

  1. Graph a linear inequality in one variable
  2. Write inequalities from graphs
  3. Write a linear inequality: word problems
  4. Solve linear inequalities
  5. Graph solutions to linear inequalities
  6. Solve absolute value inequalities
  7. Graph solutions to absolute value inequalities
  8. Graph a two-variable linear inequality
  9. Graph solutions to two-variable absolute value inequalities
  10. Graph solutions to quadratic inequalities
  11. Solve quadratic inequalities

D. 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
    • New! Identify graphs: word problems
  6. Find solutions using a table
  7. Approximate solutions using a table
  8. Find the slope of a linear function
  9. Graph a linear function
  10. Write the equation of a linear function
  11. Linear functions over unit intervals
  12. Average rate of change
  13. Graph an absolute value function
  14. Domain and range of absolute value functions: graphs
  15. Domain and range of absolute value functions: equations
  16. Transformations of absolute value functions
  17. Graph piecewise-defined functions

E. Systems of equations

  1. Is (x, y) a solution to the system of equations?
  2. Solve a system of equations by graphing
  3. Solve a system of equations by graphing: word problems
  4. Find the number of solutions to a system of equations
  5. Classify a system of equations
  6. Solve a system of equations using substitution
  7. Solve a system of equations using substitution: word problems
  8. Solve a system of equations using elimination
  9. Solve a system of equations using elimination: word problems
  10. Solve a system of equations using any method
  11. Solve a system of equations using any method: word problems
  12. Solve a system of equations in three variables using substitution
  13. Solve a system of equations in three variables using elimination
  14. Determine the number of solutions to a system of equations in three variables
  15. Solve a system of linear and quadratic equations by graphing: parabolas
  16. Solve a system of linear and quadratic equations: parabolas
  17. Solve a system of linear and quadratic equations: circles
  18. Solve a nonlinear system of equations

F. Systems of inequalities

  1. Is (x, y) a solution to the system of inequalities?
  2. Solve systems of linear inequalities by graphing
  3. Solve systems of linear and absolute value inequalities by graphing
  4. Find the vertices of a solution set
  5. Linear programming

G. 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 matrix
  13. Identify inverse matrices
  14. Solve matrix equations using inverses
  15. Identify transformation matrices
  16. Transformation matrices: write the vertex matrix
  17. Transformation matrices: graph the image
  18. Solve a system of equations using augmented matrices
  19. Solve a system of equations using augmented matrices: word problems

H. Real numbers

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

I. Complex numbers

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

J. Factoring

  1. Factor out a monomial
  2. Factor quadratics using algebra tiles
  3. Factor quadratics
  4. Factor using a quadratic pattern
  5. Factor by grouping
  6. Factor sums and differences of cubes
  7. Factor polynomials

K. Quadratic functions

  1. Characteristics of quadratic functions: graphs
  2. Characteristics of quadratic functions: equations
  3. Complete a function table: quadratic functions
  4. Transformations of quadratic functions
  5. Graph a quadratic function
  6. Solve a quadratic equation using square roots
  7. Solve a quadratic equation using the zero product property
  8. Solve a quadratic equation by factoring
  9. Complete the square
  10. Solve a quadratic equation by completing the square
  11. Solve a quadratic equation using the quadratic formula
    • New! Solve quadratic equations: word problems
  12. Using the discriminant
  13. Write a quadratic function in vertex form
  14. Match quadratic functions and graphs
    • New! Domain and range of quadratic functions: graphs
  15. Domain and range of quadratic functions: equations
  16. Write a quadratic function from its zeros
  17. Write a quadratic function from its vertex and another point
    • New! Interpret parts of quadratic expressions: word problems

L. Polynomials

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

M. Radical functions and expressions

  1. Roots of integers
  2. Roots of rational numbers
  3. Find roots using a calculator
  4. Simplify radical expressions with variables I
  5. Simplify radical expressions with variables II
  6. Nth roots
  7. Multiply radical expressions
  8. Simplify radical expressions involving fractions
  9. Add and subtract radical expressions
  10. Simplify radical expressions using the distributive property
  11. Simplify radical expressions using conjugates
  12. Domain and range of radical functions
  13. Graph square root functions
  14. Solve radical equations

N. Rational exponents

  1. Evaluate rational exponents
  2. Multiplication with rational exponents
  3. Division with rational exponents
  4. Power rule
  5. Simplify expressions involving rational exponents I
  6. Simplify expressions involving rational exponents II

O. Rational functions and expressions

  1. Rational functions: asymptotes and excluded values
  2. Evaluate rational expressions I
  3. Evaluate rational expressions II
  4. Simplify rational expressions
  5. Multiply and divide rational expressions
  6. Add and subtract rational expressions
  7. Solve rational equations

P. Function operations

  1. Add and subtract functions
  2. Multiply functions
  3. Divide functions
  4. Composition of linear functions: find a value
  5. Composition of linear functions: find an equation
  6. Composition of linear and quadratic functions: find a value
  7. Composition of linear and quadratic functions: find an equation
  8. Identify inverse functions
  9. Find values of inverse functions from tables
  10. Find values of inverse functions from graphs
  11. Find inverse functions and relations

Q. 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

R. Variation

  1. Write and solve direct variation equations
  2. Write and solve inverse variation equations
  3. Classify variation
  4. Write joint and combined variation equations I
  5. Find the constant of variation
  6. Write joint and combined variation equations II
  7. Solve variation equations

S. Logarithms

  1. Convert between exponential and logarithmic form: rational bases
  2. Convert between natural exponential and logarithmic form
  3. Convert between exponential and logarithmic form: all bases
  4. Evaluate logarithms
  5. Evaluate natural logarithms
  6. Change of base formula
  7. Evaluate logarithms using a calculator
  8. Identify properties of logarithms
  9. Product property of logarithms
  10. Quotient property of logarithms
  11. Power property of logarithms
  12. Properties of logarithms: mixed review
  13. Evaluate logarithms using properties

T. Exponential and logarithmic functions

  1. Domain and range of exponential and logarithmic functions
  2. Evaluate exponential functions
    • New! Write exponential functions: word problems
  3. Graph exponential functions
  4. Match exponential functions and graphs
    • New! Graph logarithmic functions
  5. Solve exponential equations by rewriting the base
  6. Solve exponential equations using common logarithms
  7. Solve exponential equations using natural logarithms
  8. Solve logarithmic equations I
  9. Solve logarithmic equations II
  10. Exponential functions over unit intervals
  11. Identify linear and exponential functions
  12. Describe linear and exponential growth and decay
  13. Exponential growth and decay: word problems
  14. Compound interest: word problems
  15. Continuously compounded interest: word problems

U. Parabolas

  1. Identify the direction a parabola opens
  2. Find the vertex of a parabola
  3. Find the focus or directrix of a parabola
  4. Find the axis of symmetry of a parabola
  5. Write equations of parabolas in vertex form from graphs
  6. Write equations of parabolas in vertex form using properties
  7. Convert equations of parabolas from general to vertex form
  8. Find properties of a parabola from equations in general form
  9. Graph parabolas

V. Circles

  1. Find the center of a circle
  2. Find the radius or diameter of a circle
  3. Write equations of circles in standard form from graphs
  4. Write equations of circles in standard form using properties
  5. Convert equations of circles from general to standard form
  6. Find properties of circles from equations in general form
  7. Graph circles

W. Ellipses

  1. Find the center, vertices, or co-vertices of an ellipse
  2. Find the length of the major or minor axes of an ellipse
  3. Find the foci of an ellipse
  4. Write equations of ellipses in standard form from graphs
  5. Write equations of ellipses in standard form using properties
  6. Convert equations of ellipses from general to standard form
  7. Find properties of ellipses from equations in general form

X. Hyperbolas

  1. Find the center of a hyperbola
  2. Find the vertices of a hyperbola
  3. Find the length of the transverse or conjugate axes of a hyperbola
  4. Find the equations for the asymptotes of a hyperbola
  5. Find the foci of a hyperbola
  6. Write equations of hyperbolas in standard form from graphs
  7. Write equations of hyperbolas in standard form using properties
  8. Convert equations of hyperbolas from general to standard form
  9. Find properties of hyperbolas from equations in general form

Y. Angle measures

  1. Convert between radians and degrees
  2. Radians and arc length
  3. Graphs of angles
  4. Quadrants
  5. Coterminal angles
  6. Reference angles

Z. Trigonometry

  1. Pythagorean Theorem and its converse
  2. Special right triangles
  3. Trigonometric ratios: sin, cos, and tan
  4. Trigonometric ratios: csc, sec, and cot
  5. Trigonometric ratios in similar right triangles
  6. Find trigonometric ratios using the unit circle
  7. Sin, cos, and tan of special angles
  8. Csc, sec, and cot of special angles
  9. Find trigonometric ratios using reference angles
  10. Find trigonometric functions using a calculator
  11. Inverses of sin, cos, and tan: degrees
  12. Inverses of sin, cos, and tan: radians
  13. Inverses of csc, sec, and cot
  14. Solve trigonometric equations I
  15. Solve trigonometric equations II
  16. Trigonometric ratios: find a side length
  17. Trigonometric ratios: find an angle measure
  18. Solve a right triangle
  19. Law of Sines
  20. Law of Cosines
  21. Solve a triangle
  22. Area of a triangle: sine formula
  23. Area of a triangle: Law of Sines

AA. 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. Find properties of sine and cosine functions
  12. Write equations of sine and cosine functions from graphs
  13. Write equations of sine and cosine functions using properties
  14. Graph sine and cosine functions
  15. Graph translations of sine and cosine functions

BB. Trigonometric identities

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

CC. Sequences and series

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

DD. Probability

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

EE. 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. Find probabilities using the normal distribution I
  12. Find probabilities using the normal distribution II
  13. Find z-values
  14. Find values of normal variables
  15. Distributions of sample means

FF. 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
    • New! Match correlation coefficients to scatter plots
    • New! Calculate correlation coefficients
  6. Find the equation of a regression line
  7. Interpret regression lines
  8. Analyze a regression line of a data set
  9. Find confidence intervals for population means
  10. Find confidence intervals for population proportions
  11. Interpret confidence intervals for population means
  12. Experiment design
  13. Analyze the results of an experiment using simulations