Introduction to Calculus, Grade 12 (40S)
Manitoba · Grade 12 · Mathematics — the complete curriculum-aligned outline, taught skill by skill by MapleMind's AI tutor.
4Units
12Lessons
19Skills
Unit 1: Limits
The concept of a limit, evaluating limits to analyze functions, and applying limits to continuity.
The Concept of a Limit
- Understanding limits graphically
- One-sided limits and existence
Evaluating Limits
- Evaluating limits algebraically
- Limits at infinity
Limits and Continuity
- Continuity of a function
Unit 2: Derivatives
The derivative as the slope of a curve, the differentiation rules, and implicit differentiation.
The Derivative as a Slope
- From secant slope to tangent slope
- The limit definition of the derivative
Differentiation Rules
- Power, constant, and sum rules
- Product and quotient rules
- The chain rule
Implicit Differentiation
- Implicit differentiation
Unit 3: Applications of Derivatives
Using derivatives for the motion of particles, for curve sketching, and for optimization and related rates.
Motion of Particles
- Velocity and acceleration
Curve Sketching
- Increasing, decreasing, and extrema
- Concavity and sketching the curve
Optimization and Related Rates
- Optimization
- Related rates
Unit 4: Integration (Integrals)
Antidifferentiation and integration, the definite integral, and applying integration to solve problems.
Antidifferentiation
- Antiderivatives and integration
The Definite Integral
- Understanding the definite integral
Applying Integration
- Solving problems with integration
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