30 free lessons · Worked examples and practice
Grade 12 math
Explore the transition to university mathematics through calculus, probability, and careful reasoning. Connect rates, accumulation, and statistical models to their meaning rather than using formulas in isolation.
Your study guide
What you will explore.
- Interpret rates, accumulation, and related models
- Examine assumptions in probability and statistics
- Explain multi-step arguments and limitations
Before you begin
Check your fluency with functions, graphs, algebra, and trigonometry. Calculus lessons assume the relevant introductory derivative or integral rules listed on the page.
Review Grade 11How to study these lessons
Write a short interpretation after each result. Check units, domain restrictions, and any assumptions about continuity, independence, or the model being used.
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Your Grade 12 lesson collection.
The lessons appear in their suggested study order. Choose the first lesson for a starting point, or use the search and subject filters to review a particular skill. Read the prerequisites whenever you change topics.
Showing 12 of 30 matching lessons · All free
AlgebraGrade 12 · Advanced 15 min
Read distant graph behavior from the leading term
Compare a polynomial with its highest-degree term as input magnitude grows.
Read, practice, and reflectAlgebraGrade 12 · Advanced 15 min
Recognize a power law on logarithmic axes
Separate power-law fitting from exponential fitting.
Read, practice, and reflectAlgebraGrade 12 · Advanced 15 min
Find the line a rational graph approaches
Use a vanishing remainder to identify a slant asymptote.
Read, practice, and reflectAlgebraGrade 12 · Advanced 15 min
Undo a shifted exponential and state the recovered domain
Use logarithms to invert an exponential transformation.
Read, practice, and reflectAlgebraGrade 12 · Advanced 15 min
Control the tail of an infinite geometric sum
Check convergence and quantify how much a finite truncation misses.
Read, practice, and reflectAlgebraGrade 12 · Advanced 15 min
Solve a recurrence with two independent growth modes
Use a characteristic equation for a second-order linear recurrence.
Read, practice, and reflectAlgebraGrade 12 · Advanced 15 min
Find all complex roots using equally spaced angles
Apply polar powers while retaining every angular branch.
Read, practice, and reflectGeometryGrade 12 · Advanced 15 min
Recognize a circle hidden in a polar equation
Translate a polar curve into a Cartesian equation.
Read, practice, and reflectGeometryGrade 12 · Advanced 15 min
Eliminate a parameter without losing traversal information
Distinguish a curve's equation from how it is traced.
Read, practice, and reflectTrigonometryGrade 12 · Advanced 15 min
Solve a polynomial equation in a trigonometric value
Separate algebraic roots from angle solutions and range checks.
Read, practice, and reflectTrigonometryGrade 12 · Advanced 15 min
Derive a tangent difference from sine and cosine
Form a quotient identity and retain denominator restrictions.
Read, practice, and reflectCalculusGrade 12 · Advanced 15 min
Diagnose a jump through unequal one-sided limits
Separate a function's assigned value from its nearby behavior.
Read, practice, and reflect