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

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
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
4. Factor using a quadratic pattern
5. Factor by grouping
6. Factor sums and differences of cubes
7. Factor polynomials

1. Characteristics of quadratic functions: graphs
2. Characteristics of quadratic functions: equations
3. Complete a function table: quadratic functions
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
• 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
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

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
8. Simplify radical expressions involving fractions
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

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

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
3. Graphs of angles
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