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The official Manitoba Introduction to Calculus, Grade 12 (40S) curriculum
Manitoba defines Introduction to Calculus, Grade 12 (40S) by strands and outcomes. MapleMind teaches the same curriculum reorganized for one-skill-at-a-time tutoring — the table shows exactly where every official strand lands, and the ministry's own wording is quoted under each unit below.
Official source Manitoba's official curriculumRead it on the government site — edu.gov.mb.ca ↗| Official strand | Outcomes | Where MapleMind teaches it |
|---|---|---|
| Strand 1 | 3 | Limits |
| Strand 2 | 3 | Derivatives |
| Strand 3 | 3 | Applications of Derivatives |
| Strand 4 | 3 | Integration (Integrals) |
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How MapleMind teaches Introduction to Calculus, Grade 12 (40S) — every unit, lesson, and skill
Every skill below runs as a short session: a plain-words lesson, a worked example, solving it together, then a five-question skill check that earns up to three stars. Guided Mode keeps it teaching instead of answer-handing — turning it off needs a parent's password.
Unit 1LimitsOfficial strand · Strand 1
The concept of a limit, evaluating limits to analyze functions, and applying limits to continuity.
The Concept of a Limit
- Understanding limits graphically1C.1.1 — Demonstrate an understanding of the concept of a limit by estimating the value a function approaches near a point, using graphs and tables of values, and writing it in limit notation.
- One-sided limits and existence1C.1.1 — Demonstrate an understanding of the concept of a limit through left-hand and right-hand one-sided limits, and determine whether a two-sided limit exists.
Evaluating Limits
- Evaluating limits algebraically1C.1.2 — Evaluate limits to analyze functions using direct substitution and, for indeterminate forms, algebraic techniques such as factoring and rationalizing.
- Limits at infinity1C.1.2 — Evaluate limits to analyze functions as x approaches positive or negative infinity, and use these limits to describe end behaviour and horizontal asymptotes.
Limits and Continuity
- Continuity of a function1C.1.3 — Apply the concept of a limit to the continuity of a function, testing continuity at a point and classifying discontinuities.
The official wording — 3 outcomes in this unit
- 1C.1.1
Demonstrate an understanding of the concept of the limit.
- 1C.1.2
Evaluate limits to analyze functions.
- 1C.1.3
Apply the concept of limit to the continuity of a function.
Unit 2DerivativesOfficial strand · Strand 2
The derivative as the slope of a curve, the differentiation rules, and implicit differentiation.
The Derivative as a Slope
- From secant slope to tangent slope1C.2.1 — Develop the idea of the slope of a curve at a point as the limit of the slopes of secant lines, connecting average rate of change to instantaneous rate of change.
- The limit definition of the derivative1C.2.1 — State the definition of the derivative as a limit, f'(x) = lim as h approaches 0 of (f(x + h) - f(x)) over h, and compute a derivative from first principles.
Differentiation Rules
- Power, constant, and sum rules1C.2.2 — Develop and apply the power rule, constant multiple rule, and sum and difference rules to differentiate polynomial functions.
- Product and quotient rules1C.2.2 — Develop and apply the product rule and the quotient rule to differentiate products and quotients of functions.
- The chain rule1C.2.2 — Develop and apply the chain rule to differentiate composite functions.
Implicit Differentiation
- Implicit differentiation1C.2.3 — Demonstrate an understanding of implicit differentiation by differentiating a relation that is not solved for y and finding dy/dx.
The official wording — 3 outcomes in this unit
- 1C.2.1
Develop the definition of the derivative as the slope of a curve at a point.
- 1C.2.2
Develop and apply differentiation rules.
- 1C.2.3
Demonstrate an understanding of implicit differentiation.
Unit 3Applications of DerivativesOfficial strand · Strand 3
Using derivatives for the motion of particles, for curve sketching, and for optimization and related rates.
Motion of Particles
- Velocity and acceleration1C.3.1 — Apply derivatives to solve problems involving the motion of particles, finding velocity as the derivative of position and acceleration as the derivative of velocity.
Curve Sketching
- Increasing, decreasing, and extrema1C.3.2 — Determine features of a function using the first derivative — where it is increasing or decreasing and its local maximum and minimum points — to help sketch the function.
- Concavity and sketching the curve1C.3.2 — Determine features of a function using the second derivative — concavity and inflection points — and combine all features to sketch the function accurately.
Optimization and Related Rates
- Optimization1C.3.3 — Apply derivatives to solve optimization problems by modelling a quantity, finding its critical points, and identifying the maximum or minimum.
The official wording — 3 outcomes in this unit
- 1C.3.1
Apply derivatives to solve problems involving the motion of particles.
- 1C.3.2
Determine features of a function using derivatives to sketch the function
- 1C.3.3
Apply derivatives to solve optimization and related rates problems.
Unit 4Integration (Integrals)Official strand · Strand 4
Antidifferentiation and integration, the definite integral, and applying integration to solve problems.
Antidifferentiation
- Antiderivatives and integration1C.4.1 — Demonstrate an understanding of the relationship between antidifferentiation and integration, finding indefinite integrals and including the constant of integration.
The Definite Integral
- Understanding the definite integral1C.4.2 — Demonstrate and apply an understanding of the definite integral as the accumulated area under a curve, evaluating it using antiderivatives and the Fundamental Theorem of Calculus.
Applying Integration
- Solving problems with integration1C.4.3 — Apply integration to solve problems, such as finding the area between curves or recovering a quantity from its rate of change.
The official wording — 3 outcomes in this unit
- 1C.4.1
Demonstrate an understanding of the relationship between anti- differentiation and integration of functions.
- 1C.4.2
Demonstrate and apply an understanding of the definite integral.
- 1C.4.3
Apply integration to solve problems.
Printable workbook · A keepsake of the year
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Can MapleMind help me with Introduction to Calculus, Grade 12 (40S)?
Yes. MapleMind's AI tutor covers all 19 skills in Manitoba's Introduction to Calculus, Grade 12 (40S) — you pick the exact skill, and the tutor teaches it step by step: a short lesson, a worked example, solving together, then a skill check to show it stuck.
Is MapleMind aligned to Manitoba's official curriculum?
Yes. Every skill in this course maps to an official outcome code from Manitoba's Grade 12 Mathematics curriculum, and the ministry's own wording is quoted under each unit on this page — with the official government source linked so you can check it yourself.
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That's the point of skill-level tutoring: open Introduction to Calculus, Grade 12 (40S) in the app, tap the exact skill from the list on this page, and the tutor teaches just that — no wading through lessons you don't need.
Does MapleMind work in French or other languages?
Yes — 14 languages, including French. Both the app and the tutor's explanations switch to the language you choose.
Where can I see the official Manitoba curriculum for Introduction to Calculus, Grade 12 (40S)?
The official source is linked on this page — Manitoba's official curriculum. The outline here follows it: every MapleMind skill carries its official outcome code, and the ministry's own wording is quoted under each unit.
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