United States · Common Core State Standards
12th Grade Mathematics
This course prepares students for college level calculus and statistics by focusing on the behavior of complex functions and real world data modeling. Students transition from procedural fluency to conceptual synthesis through rigorous proof and application.
The Language of Functions and Continuity
Explores the foundational properties of functions including transformations, composition, and the formal definition of limits.
Investigating how functions behave as they approach specific values or infinity.
Analyzing how nested functions interact and the conditions required for a function to be reversible.
Transitioning from average rate of change to the concept of the derivative at a point.
Transcendental Functions and Growth
Deep dive into exponential, logarithmic, and logistic models used to describe natural phenomena.
Using logarithms to linearize data and solve complex growth equations.
Investigating the origin and applications of the constant e in continuous compounding and growth.
Modeling growth that is constrained by environmental or physical factors.
Trigonometric Synthesis and Periodic Motion
Extending trigonometry to circular functions, identities, and the modeling of wave-like behavior.
Connecting geometric rotation to algebraic coordinates and the logic of radians.
Using algebraic manipulation to prove equivalence between complex trigonometric expressions.
Applying sine and cosine functions to model sound waves, tides, and pendulums.
Vectors, Matrices, and Systems
Utilizing linear algebra tools to solve multi dimensional problems and transform coordinates.
Performing operations on vectors to solve physics based problems involving force and velocity.
Using matrices to scale, rotate, and reflect geometric figures in a coordinate plane.
Solving large systems of linear equations using matrix row reduction techniques.
Probability and Inferential Statistics
Moving beyond descriptive statistics to make predictions and test hypotheses using data.
Analyzing binomial and normal distributions to determine the likelihood of outcomes.
Using p values and confidence intervals to evaluate the validity of experimental claims.
Calculating the probability of events based on prior knowledge of related conditions.
Series and Discrete Structures
Exploring patterns in sequences, the logic of mathematical induction, and summation.
Finding sums of finite and infinite sequences and applying them to financial models.
Proving that a statement holds true for all natural numbers using a recursive logic structure.
Expanding binomial expressions using Pascal's Triangle and combinatorics.