Level 30

SK Grade 12 Calculus 30 Curriculum

Video lessons and practice for every Calculus 30 topic. Aligned to what Saskatchewan schools teach. Master limits, derivatives, and integration with step-by-step explanations.

Workplace and Apprenticeship Mathematics 30

Foundations of Mathematics 30

Pre-Calculus 30

Calculus 30

SK Grade 12 Calculus 30 Curriculum | StudyPugHelp

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SO_ID	Outcome	StudyPug Topic
C30.1	Identify functions as algebraic, transcendental, piecewise from graphs and equations	Function notation (advanced) Composite functions Combining transformations of functions Adding functions Subtracting functions Multiplying functions Dividing functions Inverse functions Transformations of functions: Horizontal translations Transformations of functions: Vertical translations Reflection across the y-axis: y = f(-x) Reflection across the x-axis: y = -f(x) Transformations of functions: Horizontal stretches Transformations of functions: Vertical stretches Operations with functions Even and odd functions One to one functions

C30.2

Extend factoring to include negative and rational exponents, solve inequalities with rational expressions

Solving rational equations

Factor by taking out the greatest common factor

Factor by grouping

Factoring difference of squares:

x^2 - y^2

Factoring trinomials

Simplifying rational expressions and restrictions

Adding and subtracting rational expressions

Multiplying rational expressions

Dividing rational expressions

Applications of rational equations

Graphing reciprocals of linear functions

Simplifying complex fractions

Graphing reciprocals of quadratic functions

Factoring difference of cubes

Factoring sum of cubes

Partial fraction decomposition

C30.3

Develop meaning of limit, determine limit values, analyze continuity

Intermediate value theorem

Finding limits from graphs

Finding limits algebraically - direct substitution

Finding limits algebraically - when direct substitution is not possible

Infinite limits - vertical asymptotes

Limits at infinity - horizontal asymptotes

Squeeze theorem

l'Hospital's rule

C30.4

Develop definition of derivative, apply differentiation rules, determine tangent lines

Slope and equation of tangent line

Derivative of inverse trigonometric functions

Definition of derivative

Derivative of trigonometric functions

Derivative of exponential functions

Derivative of logarithmic functions

Implicit differentiation

Higher order derivatives

Estimating Derivatives from a table

C30.5

Use derivatives to determine critical points, extrema, and sketch function graphs

Critical number & maximum and minimum values

Position velocity acceleration

Curve sketching

C30.6

Solve optimization, rate of change, and related rates problems

Mean value theorem

Linear approximation

C30.7

Develop derivatives of exponential, logarithmic, trigonometric functions, apply to sketching

Continuous growth and decay

Demand, revenue, cost & profit

Marginal revenue, and maximizing revenue & average revenue

Marginal cost, and minimizing cost & average cost

Marginal profit, and maximizing profit & average profit

Elasticity of demand

C30.8

Distinguish between indefinite and definite integration, apply Fundamental Theorem of Calculus

Antiderivatives

Trigonometric substitution

Areas between curves

Integration of rational functions by partial fractions

Volumes of solids of revolution - Disc method

Volumes of solid with known cross-sections

Volumes of solid of revolution - Shell method

Average value of a function

Fundamental theorem of calculus

Improper integrals

Integration by parts

Integration using trigonometric identities

Definite integral

Numerical integration