Calculus 12
British Columbia · Grade 12 · Mathematics — the complete curriculum-aligned outline, taught skill by skill by MapleMind's AI tutor.
4Units
4Lessons
11Skills
Unit 1: Functions for Calculus
The function toolkit calculus assumes: parent functions, piecewise functions, and inverse trigonometric functions.
Parent, Piecewise & Inverse Trig Functions
- Parent functions and piecewise functions
- Inverse trigonometric functions
Unit 2: Limits & Continuity
The idea calculus is built on: limits from tables, graphs, and algebra; one-sided limits; limits at infinity; and continuity with the intermediate value theorem.
Limits, One-Sided Limits & Continuity
- Evaluating limits: tables, graphs, algebra
- Limits at infinity, continuity, and the IVT
Unit 3: Differentiation
The derivative from definition through rules to applications: curve analysis, related rates, and optimization.
The Derivative: Definition & Rate of Change
- Average vs instantaneous rate and the definition of the derivative
- Differentiation rules: power, product, quotient, chain, transcendentals
- Curve analysis: f, f', f'' and the mean value theorem
- Related rates and optimization
Unit 4: Integration
From Riemann sums through the fundamental theorem to methods and applications: areas, volumes, and differential equations.
The Integral & the Fundamental Theorem
- Riemann sums and the definition of the integral
- The fundamental theorem and methods of integration
- Applications: areas, volumes, and differential equations
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