Saskatchewan · Grade 12
Calculus 30
Saskatchewan’s Grade 12 math course, from Functions and Limits to Integration.
- Units
- 3
- Lessons
- 9
- Skills
- 19
- Provincial exam
- None
- Official curriculum
- Saskatchewan Ministry of Education
Unit by unit
Every skill in the course, with its official code.
Unit 1 · 7 skills
Functions and Limits
Extending Functions
Classifying and analyzing functions
I can classify a function and state its domain and range in interval notation.
Official code: C30.1
Rational functions: asymptotes, holes, and end behaviour
I can find the asymptotes, holes, and end behaviour of a rational function.
Official code: C30.1
Factoring and Inequalities
Extending factoring
I can factor sums and differences of cubes and use GCF with rational exponents.
Official code: C30.2
Solving rational, double, and absolute-value inequalities
I can solve rational, double, and absolute-value inequalities.
Official code: C30.2
Limits and Continuity
The meaning of a limit
I can explain what a limit is and read one from a graph.
Official code: C30.3
Evaluating limits
I can evaluate a limit using the right algebraic strategy.
Official code: C30.3
Continuity and discontinuity
I can decide if a function is continuous and classify any discontinuity.
Official code: C30.3
The official wording · 7 outcomes
- C30.1
- functions including: • algebraic functions (polynomial, rational, power) • transcendental functions (exponential, logarithmic, trigonometric) • piecewise functions, including absolute value.
- C30.1
- functions including: • algebraic functions (polynomial, rational, power)
- C30.2
- factoring, absolute value, and solving inequalities to include: • rational expressions
- C30.2
- • double inequalities • absolute value inequalities.
- C30.3
- limits and continuity.
- C30.3
- limits and continuity.
- C30.3
- limits and continuity.
Key ideas
Algebraic (polynomial, rational, power), transcendental (exponential, logarithmic, trigonometric), and piecewise (including absolute value) are the function families.
Sum of cubes: a³ + b³ = (a + b)(a² − ab + b²); difference of cubes swaps the sign.
The limit of f as x → a is the value f approaches, which may differ from f(a) or exist where f(a) doesn't.
A function is even if f(−x) = f(x) (symmetric about the y-axis), odd if f(−x) = −f(x) (symmetric about the origin).
GCF factoring extends to negative and rational exponents.
Watch out for
- Assuming every function is even or odd.
- Getting the middle-term signs wrong in the cube factorizations.
- Assuming lim(x→a) f(x) always equals f(a).
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 9 skills
Differentiation
The Derivative
The derivative from first principles
I can find a derivative from the limit definition.
Official code: C30.4
Rules of differentiation
I can differentiate using the power, product, quotient, and chain rules.
Official code: C30.4
Implicit differentiation, tangents, and notation
I can use implicit differentiation and find a tangent line.
Official code: C30.4
Curve Sketching
First-derivative analysis
I can use the first derivative to find where a function rises, falls, and peaks.
Official code: C30.5
Second-derivative analysis and sketching
I can use the second derivative and limits to sketch a complete curve.
Official code: C30.5
Applications of Derivatives
Optimization
I can solve an optimization problem using derivatives.
Official code: C30.6
Rates of change and related rates
I can solve a related-rates problem by relating changing quantities.
Official code: C30.6
Derivatives of Transcendental Functions
Defining e and differentiating transcendental functions
I can differentiate exponential, logarithmic, and trigonometric functions.
Official code: C30.7
Sketching and applying transcendental derivatives
I can sketch and solve problems with transcendental-function derivatives.
Official code: C30.7
The official wording · 9 outcomes
- C30.4
- differentiation based on slope as a rate of change.
- C30.4
- differentiation based on slope as a rate of change.
- C30.4
- differentiation based on slope as a rate of change.
- C30.5
- curve sketching by applying differentiation and limits.
- C30.5
- curve sketching by applying differentiation and limits.
- C30.6
- the application of derivatives to solve problems including: • optimization
- C30.6
- • rates of change • related rates.
- C30.7
- transcendental function derivatives and their applications.
- C30.7
- transcendental function derivatives and their applications.
Key ideas
Average rate of change is the slope of a secant line between two points; instantaneous rate of change is the slope of the tangent at one point.
Critical points occur where f'(x) = 0 or is undefined.
Optimization finds a maximum or minimum by setting the derivative of the quantity to zero.
e is defined by a limit and makes d/dx(eˣ) = eˣ.
The tangent slope is the limit of secant slopes as the second point approaches the first.
Watch out for
- Confusing average rate of change (secant) with instantaneous (tangent).
- Assuming every critical point is an extremum (some are neither).
- Optimizing before reducing to a single variable using the constraint.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 3 skills
Integration
Indefinite Integration
Indefinite integrals by sight and substitution
I can find an indefinite integral by sight and by substitution.
Official code: C30.8
The Fundamental Theorem of Calculus
The FTC and definite integrals
I can evaluate a definite integral using the Fundamental Theorem of Calculus.
Official code: C30.8
Area under and between curves
I can find the area under a curve and between two curves with a definite integral.
Official code: C30.8
The official wording · 3 outcomes
- C30.8
- indefinite and definite integration: • by sight • by substitution
- C30.8
- indefinite and definite integration: • by sight • by substitution • as used in the Fundamental Theorem of Calculus.
- C30.8
- indefinite and definite integration: • by sight • by substitution
Key ideas
An indefinite integral is the family of antiderivatives, written with + C; a definite integral is a number.
The FTC: ∫ₐᵇ f(x) dx = F(b) − F(a), where F is any antiderivative of f.
By sight: reverse the power rule, ∫xⁿ dx = xⁿ⁺¹/(n+1) + C (n ≠ −1).
Find an antiderivative, then subtract its values at the two limits.
Substitution reverses the chain rule: let u be the inner function, replace dx accordingly.
Watch out for
- Forgetting the + C on an indefinite integral.
- Forgetting to change the limits when substituting in a definite integral.
- Choosing a substitution whose derivative isn't present in the integrand.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Plan the term
Pick your term and the days you study. Each unit gets its share of the weeks and comes back a week later for a review. The last two weeks go over the whole course.
Which course?
Saskatchewan has 4 math courses for Grade 12. Here they are side by side.
- Calculus 30This course3 units · 19 skillsNo provincial examWhat it coversFunctions and Limits · Differentiation · Integration
- Foundations of Mathematics 306 units · 23 skillsNo provincial examWhat it coversFinancial Mathematics · Logical Reasoning · Set Theory · Probability · Modelling Data with Functions · Research and Presentation Project
- Pre-Calculus 303 units · 29 skillsNo provincial examWhat it coversTrigonometry · Functions and Transformations · Permutations, Combinations, and the Binomial Theorem
- Workplace and Apprenticeship Mathematics 303 units · 23 skillsNo provincial examWhat it coversReasoning and Measurement · Financial and Business Mathematics · Linear Relations and Statistics
What a university, college or program asks for is theirs to say: check its admission page, and your school’s course guide.
The official curriculum
This page follows Saskatchewan’s own curriculum for Calculus 30.
Study it in MapleMind
MapleMind teaches Calculus 30 one skill at a time. Each skill gets a short lesson, practice as you go and a check worth up to three stars. It remembers where you stopped.
Course Companion
Your year in one workbook
A fun way to keep Calculus 30 organized, get to know your child better and see early when they need a hand. Fill it in on a screen, or print it.
- Pages
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- Fillable fields
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Questions about Calculus 30
What is Calculus 30?
Saskatchewan’s Grade 12 math course: 3 units and 19 skills, from Functions and Limits to Integration.
What units are in Calculus 30?
1. Functions and Limits, 2. Differentiation and 3. Integration.
Is there a provincial exam for Calculus 30?
No. Saskatchewan gives no provincial exam for Calculus 30.
Can MapleMind help with Calculus 30?
Yes. MapleMind teaches every skill of Calculus 30, step by step, with practice and checks, and its tutor answers questions about any of them. It’s free with daily limits, on iPhone, Android and the web.
Get ready for Calculus 30
Practise every skill of Calculus 30 in MapleMind, free with daily limits.
