New BrunswickNB Grade 12 Calculus 120 Curriculum
Video lessons and practice for every Calculus 120 topic. Aligned to what New Brunswick Grade 12 schools teach. Get help with derivatives, integrals, and more.
NB Grade 12 Calculus 120 Curriculum | StudyPugHelp
SCO_ID | Curriculum Outcome - Elaborations | StudyPug Topic |
|---|---|---|
NB.SCO.C120.C1 | Explore the concepts of average and instantaneous rate of change: Determine average rate of change and instantaneous rate of change of a function |
NB.SCO.C120.C2 | Determine the derivative of a function by applying the definition of derivative: Use limit definition to find derivative and explore non-differentiable functions |
NB.SCO.C120.C3 | Apply derivative rules to determine the derivative of a function: Apply Constant, Power, Constant Multiple, Sum, Difference, Product, and Quotient Rules |
NB.SCO.C120.C4 | Find derivatives of trigonometric functions: Derive and apply derivatives of sine, cosine, and other trigonometric functions |
NB.SCO.C120.C5 | Apply the Chain Rule to determine the derivative of a function: Use Chain Rule for composite functions and implicit differentiation |
NB.SCO.C120.C6 | Solve problems involving inverse trigonometric functions: Find and apply derivatives of inverse trigonometric functions |
NB.SCO.C120.C7 | Find limits and derivatives of exponential and logarithmic functions: Establish exponential limit, find derivatives, and apply to growth and decay problems |
NB.SCO.C120.C8 | Use calculus techniques to sketch the graph of a function: Determine critical points, intervals, concavity, and asymptotic behavior to sketch graphs |
NB.SCO.C120.C9 | Use calculus techniques to solve optimization problems: Apply derivatives to find maximum and minimum values in applied contexts |
NB.SCO.C120.C10 | Use linearization to solve problems: Use linear approximations of functions to estimate function values near a point |
NB.SCO.C120.C11 | Solve problems involving related rates: Apply implicit differentiation to solve problems with related changing quantities |
NB.SCO.C120.C12 | Determine the definite integral of a function: Use Riemann sums and Fundamental Theorem of Calculus to evaluate definite integrals |
NB.SCO.C120.C13 | Determine the antiderivative of a function: Find indefinite integrals of various functions and apply integration techniques |
NB.SCO.C120.C14 | Solve problems that involve the application of the integral of a function: Apply integration to solve problems involving area, volume, motion, and other applications |
New Brunswick Grade 12 Calculus 120 — Topic Overview
Calculus 120 is the senior mathematics course for New Brunswick Grade 12 students. It introduces the foundational ideas of calculus — limits, derivatives, and integrals — that form the basis for university-level mathematics, physics, and engineering. StudyPug covers every unit in the course with clear video lessons and practice problems.
Rates of Change and Limits
The course begins with average and instantaneous rates of change. Students learn how to use the limit definition of a derivative and identify where functions are non-differentiable. These ideas underpin everything that follows in the course.
Differentiation Rules
Students apply the Constant, Power, Constant Multiple, Sum, Difference, Product, and Quotient Rules to differentiate a wide range of functions. Derivatives of sine, cosine, and other trigonometric functions are introduced, along with the Chain Rule for composite functions and implicit differentiation.
Inverse Trigonometric and Exponential Functions
Calculus 120 covers derivatives of inverse trigonometric functions and establishes the exponential limit. Students apply exponential derivatives to growth and decay problems — a key application for science and economics.
Curve Sketching and Optimization
Using derivatives, students find critical points, intervals of increase and decrease, concavity, and asymptotic behaviour to sketch accurate graphs. Optimization problems ask students to find maximum and minimum values in real-world applied contexts.
Linear Approximation and Related Rates
Students use linear approximations to estimate function values near a point. Related rates problems apply implicit differentiation to situations where two or more quantities change together over time.
Integration
The final units introduce Riemann sums, the Fundamental Theorem of Calculus, and techniques for finding indefinite integrals. Applications include area, volume, motion problems, and other real-world contexts.
- Limits and instantaneous rate of change
- Differentiation rules including Product, Quotient, and Chain Rules
- Trigonometric, inverse trigonometric, and exponential derivatives
- Curve sketching and optimization
- Related rates and linear approximation
- Definite and indefinite integrals with applications