Precalculus and trigonometry
- advanced functions
- unit-circle trigonometry
- vectors
- limits readiness
Grade 12 / advanced pathways · typical sequence
Grade 12 pathways and capstones
Choose a goal-directed route through precalculus, statistics, calculus readiness, or practical quantitative reasoning.
Statistics and probability
- study design
- distributions
- inference foundations
- simulation
Calculus readiness and applied mathematics
- rate of change
- accumulation foundations
- financial math
- discrete modeling
Practice inventory
18 deterministic activities are available now.
Convert degrees and radians
Use a half-turn as the anchor relating 180 degrees and pi radians.
Read a unit-circle coordinate
Use reference angles and quadrant signs to identify exact coordinates.
Read a sinusoidal model
Read vertical scale and center from a periodic function rule or graph.
Use a trigonometric identity
Use sine squared plus cosine squared equals one and select the sign from the quadrant.
Find vector components
Subtract initial coordinates from terminal coordinates in a fixed order.
Add vectors by components
Add corresponding components while preserving magnitude-and-direction meaning.
Standardize a data value
Subtract the mean and divide by the standard deviation with attention to sign.
Use a normal-distribution benchmark
Connect one, two, and three standard deviations with the empirical-rule proportions.
Estimate probability by simulation
Divide simulated successes by total trials and distinguish an estimate from a guarantee.
Interpret a confidence interval
Describe a plausible range for a population parameter without assigning probability to a fixed parameter.
Explain random assignment
Separate random sampling for generalization from random assignment for treatment comparison.
Critique a statistical claim
Match the strength of a conclusion to sampling, assignment, measurement, and possible confounders.
Find average rate of change
Compute output change over input change and interpret it over an interval.
Estimate a limit from a table
Track values approaching from both sides without requiring the function value at the point.
Differentiate a power function
Multiply by the exponent and reduce the exponent by one.
Approximate accumulation
Multiply each rate by its interval width and sum the signed contributions.
Model compound growth
Distinguish principal, periodic rate, number of periods, and accumulated value.
Apply a matrix transformation
Multiply each matrix row by the vector column and interpret the new vector.