Algebra I
Fundamentals:
- Real Numbers and Their Operations: Understanding different types of numbers (integers, rational, irrational, etc.) and performing operations with them.
- Variables and Expressions: Working with variables to represent unknown values and forming algebraic expressions.
- Evaluating Expressions: Substituting values for variables and simplifying expressions.
Linear Equations and Inequalities:
- Linear Equations: Solving for the unknown variable in equations with one variable.
- Graphing Linear Equations: Representing linear equations on a coordinate plane.
- Linear Inequalities: Solving and graphing inequalities with one variable.
- Systems of Linear Equations: Solving for multiple unknowns in a system of equations
Functions:
- Introduction to Functions: Understanding the concept of functions and how they relate to equations.
- Linear Functions: Analyzing and graphing linear functions, including slope and y-intercept.
- Function Notation: Using function notation (e.g., f(x)) to represent relationships.
Polynomials:
- Polynomials and Their Operations: Adding, subtracting, multiplying, and dividing polynomials.
- Factoring Polynomials: Breaking down polynomials into simpler expressions.
Exponents and Radicals:
- Exponents and Exponential Functions: Understanding exponents and their properties.
- Radical Expressions and Equations: Working with radicals and solving equations involving them.
Quadratic Equations:
- Solving Quadratic Equations: Using factoring, the quadratic formula, or graphing to solve quadratic equations.
- Graphing Parabolas: Understanding the shape and properties of parabolas.
Data Analysis and Probability:
- Data Analysis: Analyzing data using measures of central tendency (mean, median, mode) and spread (range, standard deviation).
- Probability: Understanding basic probability concepts.
Algebra II
- Functions and Relations:
- Linear, quadratic, polynomial, exponential, and logarithmic functions
- Function notation and evaluation
- Graphing functions
- Transformations of functions
- Composition of functions
- Equations and Inequalities:
- Solving linear, quadratic, and polynomial equations
- Solving systems of equations and inequalities
- Polynomials and Radical Expressions:
- Operations with polynomials
- Factoring polynomials
- Simplifying radical expressions
- Exponents and Exponential Functions:
- Properties of exponents
- Exponential growth and decay
- Graphing exponential functions
- Logarithms:
- Properties of logarithms
- Solving logarithmic equations
- Converting between logarithmic and exponential forms
- Quadratic Functions and Equations:
- Graphing quadratic functions
- Solving quadratic equations (factoring, quadratic formula, completing the square)
- The discriminant
- Conic Sections:
- Circles, ellipses, parabolas, and hyperbolas
- Graphing conic sections
- Standard forms of equations for conic sections
- Matrices:
- Matrix operations (addition, subtraction, multiplication)
- Solving systems of equations using matrices
- Determinants
- Data Analysis and Probability:
- Descriptive statistics (mean, median, mode, standard deviation)
- Probability (basic and conditional)
- Data visualization (histograms, box plots)
- Trigonometry:
- Trigonometric functions (sine, cosine, tangent)
- Angles and their measures
- Trigonometric identities
- Solving trigonometric equations
- Sequences and Series:
- Arithmetic and geometric sequences and series
- Finding the nth term and sum of a sequence or series
- Permutations and Combinations:
- Understanding and applying permutations and combinations
Precalculus
Functions:
- Types of Functions: Linear, quadratic, polynomial, rational, exponential, logarithmic, trigonometric
- Function Notation and Operations: Evaluating functions, function composition, transformations (shifts, stretches, reflections)
- Graphs of Functions: Interpreting graphs, finding intercepts, asymptotes, symmetry
- Inverse Functions: Finding and graphing inverse functions
Algebra:
- Polynomials: Factoring, solving polynomial equations, graphing polynomials
- Rational Functions: Simplifying, solving rational equations, graphing rational functions
- Systems of Equations and Inequalities: Solving systems of linear and nonlinear equations and inequalities
- Matrices: Operations with matrices, solving systems of equations using matrices
Trigonometry:
- Trigonometric Functions: Sine, cosine, tangent, cotangent, secant, cosecant
- Trigonometric Identities: Pythagorean identities, sum and difference formulas, double-angle formulas
- Solving Trigonometric Equations: Finding solutions to trigonometric equations
- Trigonometric Graphs: Graphing trigonometric functions, understanding amplitude, period, and phase shift
- Inverse Trigonometric Functions: Finding inverse trigonometric functions
- Trigonometry in Triangles: Law of Sines, Law of Cosines
Other Topics:
- Conic Sections: Circles, ellipses, parabolas, hyperbolas
- Vectors: Vector operations, dot product, applications
- Parametric Equations: Converting to and from parametric equations
- Polar Coordinates: Converting to and from polar coordinates
- Sequences and Series: Arithmetic and geometric sequences and series
- Introduction to Calculus: Limits, derivatives, and integrals (briefly)
Calculus
Limits and Continuity:
- limit laws
- continuous functions
- limits involving infinity
- Derivative and its meaning
- Tangent lines
Differentiation Rules:
- Linearity
- Product rule
- Quotient rule
- Chain rule
Other examples of derivatives:
- trigonometric functions
- inverse functions
- implicit derivatives
- logarithmic differentiation
Applications of differentiation:
- related rates
- max/min problems
- derivatives and shapes of curves
Techniques of integration:
- “u”-substitution
- integration by parts
- Partial fractions
Applications of integration:
- volumes (revolution)
- arc length
- average value
Sequences and Series:
- limits of sequences and series
- convergence tests for series,
- Taylor Polynomials