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The official Newfoundland and Labrador Mathematics 3208 (Calculus) curriculum
Newfoundland and Labrador defines Mathematics 3208 (Calculus) 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 Newfoundland and Labrador's official curriculumRead it on the government site — gov.nl.ca ↗| Official strand | Outcomes | Where MapleMind teaches it |
|---|---|---|
| PAR | 5 | Pre-Calculus |
| Strand C | 29 | Limits and Continuity · Derivatives and Their Applications · Antidifferentiation and Integration |
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How MapleMind teaches Mathematics 3208 (Calculus) — every unit, lesson, and skill
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Unit 1Pre-CalculusOfficial strand · PAR
Combining and composing functions, rational functions and their asymptotes, exponential and logarithmic functions, and inverse trigonometric functions - the function theory calculus builds on.
Operations and Composition of Functions
- Combining functionsPAR.1.1 — Write a function h(x) as the sum, difference, product, or quotient of two or more functions, sketch the graph of such a combined function from the graphs of its parts, and determine its domain and range.
- Composition of functionsPAR.1.5 — Determine the value of a composition of functions at a point, determine the equation of a composite function from the equations of two functions, sketch the composite graph with its domain and range, and recover the original functions from a composition.
Rational, Exponential and Logarithmic Functions
- Rational functions, asymptotes and holesPAR.1.9 — Explain the behaviour of a rational function's graph near a non-permissible value, determine whether a non-permissible value gives an asymptote or a hole, and sketch the graph of a rational function.
- Exponential and logarithmic functionsPAR.1.11 — Graph and analyze the exponential function y = e^x and the logarithmic function y = ln x, including their domains, ranges, and asymptotes.
Inverse Trigonometric Functions
- Inverse trigonometric functionsPAR.1.13 — Explain the relationship between the trigonometric functions and their inverses, explain why the domains must be restricted to create inverses, sketch the graph of an inverse trigonometric function, and determine the exact value of an expression involving an inverse trigonometric function.
The official wording — 5 outcomes in this unit
- PAR.1.1
Write a function h ( x ) as the sum, difference, product or quotient of two or more functions
- PAR.1.5
Determine the equation of the composite function given the equations of two functions f ( x ) and g ( x )
- PAR.1.9
Determine if the graph of a rational function will have an asymptote or a hole for a non-permissible value
- PAR.1.11
Graph and analyze exponential and logarithmic functions y = e x and y = ln x
- PAR.1.13
Explain why trigonometric functions must have their domains restricted to create inverse trigonometric functions
Unit 2Limits and ContinuityOfficial strand · Strand C
The concept of a limit, one-sided and infinite limits, evaluating limits algebraically, limits at infinity and asymptotes, continuity, and trigonometric and exponential limits.
The Concept of a Limit
- The idea and notation of a limitC.2.3 — Explore the concept of a limit informally, including one-sided limits and the notation for the limit of a function as x approaches a from the right, from the left, and from both sides.
- Limits from graphs and tablesC.2.4 — Determine the value of a limit as the variable approaches a real number from a provided graph, including piecewise functions, and from a table of values, and evaluate one-sided limits from a graph.
Evaluating Limits
- The properties of limitsC.2.6 — Apply the properties of limits, including the sum, difference, product, constant-multiple, quotient, and power rules, to solve problems, and establish that the limit of 1/x as x approaches infinity is zero.
- Evaluating limits algebraicallyC.2.7 — Determine the value of a limit as the variable approaches a real number by direct substitution and by algebraic manipulation such as factoring or rationalizing.
- Infinite limits and vertical asymptotesC.2.8 — Determine limits that result in infinity (infinite limits) and investigate the behaviour of a function at a vertical asymptote using limits.
Limits at Infinity and Continuity
- Limits at infinity and end behaviourC.2.10 — Evaluate limits of functions as x approaches infinity (limits at infinity) and investigate the end behaviour of a function using limits to identify possible horizontal and oblique asymptotes.
- Continuity and discontinuitiesC.2.16 — Distinguish continuity from discontinuity, identify types of discontinuity such as removable, infinite, jump, and oscillating, determine continuity at a point from a graph and from the definition of continuity, determine continuity on a closed interval, and rewrite removable discontinuities.
- Trigonometric and exponential limitsC.2.19 — Establish the trigonometric limits (limit of sin x, cos x, sin x over x, and (cos x - 1) over x as x approaches 0) using informal methods, evaluate limits involving trigonometric expressions, and establish the exponential limit (e^h - 1)/h as h approaches 0.
The official wording — 8 outcomes in this unit
- C.2.3
Explore the concept of limit and the notation used in expressing the limit of a function
- C.2.4
Determine the value of the limit of a function as the variable approaches a real number by using a provided graph, including piecewise functions by using a table of values
- C.2.6
Apply the properties of limits including: Sum Rule Difference Rule Product Rule Constant Multiple Rule Quotient Rule Power Rule to solve problems
- C.2.7
Determine the value of the limit of a function as the variable approaches a real number by substitution by algebraic manipulation
- C.2.8
Determine limits that result in infinity (infinite limits)
- C.2.10
Evaluate limits of functions as x approaches infinity (limits at infinity)
- C.2.16
Determine whether a function is continuous at a point using the definition of continuity
- C.2.19
Establish each of the following trigonometric limits, using informal methods
Unit 3Derivatives and Their ApplicationsOfficial strand · Strand C
The derivative as a limit and a rate of change, differentiability, the differentiation rules, curve sketching, related rates and optimization, and the derivatives of the trigonometric, inverse-trigonometric, exponential, logarithmic, and hyperbolic functions.
The Derivative as a Limit
- Average and instantaneous rate of changeC.3.3 — Describe geometrically a secant line and a tangent line at a point, determine the average rate of change of a function over an interval, and identify the instantaneous rate of change at a point as the limiting value of average rates of change.
- The definition of the derivativeC.3.4 — Define and evaluate the derivative at x = a as a limit and define the derivative of a function using the limit of the difference quotient, limited to polynomials of degree three, square-root, and rational functions with linear terms.
- Tangent lines, notation, and differentiabilityC.3.7 — Determine the equation of the tangent and normal line at a point, use alternate derivative notations interchangeably, determine whether a function is differentiable at a point, and explain non-differentiability at corners, cusps, discontinuities, and vertical tangents.
- Graphs of a function and its derivativeC.3.11 — Determine all values for which a function is differentiable from its graph, sketch the graph of the derivative given the graph of a function, and sketch the graph of a function given the graph of its derivative.
Differentiation Rules
- The basic differentiation rulesC.3.14 — Derive the constant, constant-multiple, sum, difference, product, and quotient rules, determine derivatives using the power, sum, difference, product, and quotient rules, and determine second and higher-order derivatives.
- The chain ruleC.3.16 — Determine derivatives of composite functions using the chain rule.
- Implicit differentiationC.3.18 — Determine the derivative of an implicit relation, determine the equation of the tangent and normal line to a relation at a point, and determine the second derivative of a relation using implicit differentiation.
Curve Sketching
- First-derivative analysis of curvesC.3.21 — For a polynomial function, use the first derivative to identify critical numbers, relative and absolute extrema, and intervals of increase and decrease.
- Concavity and sketchingC.3.23 — For a polynomial function, use the second derivative to identify points of inflection and intervals of concavity, and sketch the graph using information from the function and its derivatives, including intercepts and domain.
- Sketching rational functionsC.3.28 — For a rational function, use the first and second derivatives to identify critical numbers, extrema, concavity, and points of inflection, sketch the graph, and determine features such as intercepts, asymptotes, points of discontinuity, and domain.
Applications of Derivatives
- Motion and rates of changeC.3.17 — Solve problems involving derivatives drawn from a variety of applications, limited to tangent and normal lines, straight-line motion, and rates of change.
- OptimizationC.3.33 — Determine the function to be optimized and any parameter equations in an optimization problem, solve the optimization problem using calculus, and interpret the solution.
Derivatives of Trigonometric, Exponential and Other Functions
- Derivatives of trigonometric functionsC.3.36 — Derive the derivatives of sine, cosine, tangent, cotangent, secant, and cosecant, determine the derivative of expressions involving trigonometric functions, and solve problems involving them.
- Derivatives of inverse trigonometric functionsC.3.39 — Derive the inverse trigonometric derivatives, determine the derivative of an inverse trigonometric function, and solve problems involving them.
- Derivatives of exponential and logarithmic functionsC.3.42 — Derive the derivatives of exponential functions and logarithmic functions, determine the derivative of an exponential or logarithmic function, solve problems involving them, and use logarithmic differentiation.
- Hyperbolic functionsC.3.47 — Define the hyperbolic functions sinh x and cosh x in terms of the exponential function, define the remaining hyperbolic functions in terms of sinh x and cosh x, and determine the derivative of a hyperbolic function.
The official wording — 17 outcomes in this unit
- C.3.3
Identify the instantaneous rate of change of a function at a point as the limiting value of a sequence of average rates of change
- C.3.4
Define and evaluate the derivative at x = a as: lim h → 0 f ( a + h ) - f ( a ) h and lim x → a f ( x ) - f ( a ) x - a
- C.3.7
Use alternate notation interchangeably to express derivatives
- C.3.11
Sketch a graph of the derivative of a function, given the graph of a function
- C.3.14
Determine derivatives of functions, using the Constant, Constant Multiple, Power, Sum, Difference, Product and Quotient Rules
- C.3.16
Determine derivatives of functions using the Chain Rule
- C.3.18
Determine the derivative of an implicit relation
- C.3.21
For a polynomial function, use f ' ( x ) to identify the critical numbers, relative and absolute extrema, and intervals of increase and decrease
- C.3.23
For a polynomial function, sketch the graph of f ( x ) using information obtained from the function and its derivatives
- C.3.28
For a rational function, use the given function f ( x ) to determine its features such as intercepts, asymptotes, points of discontinuity and the domain
- C.3.17
Solve problems involving derivatives drawn from a variety of applications, limited to tangent and normal lines, straight line motion and rates of change
- C.3.29
Solve a problem involving related rates drawn from a variety of applications
- C.3.33
Solve an optimization problem drawn from a variety of applications, using calculus techniques
- C.3.36
Determine the derivative of expressions involving trigonometric functions
- C.3.39
Determine the derivative of an inverse trigonometric function
- C.3.42
Determine the derivative of an exponential function
- C.3.47
Define tanh x , csch x , coth x , and sech x in terms of sinh x and cosh x
Unit 4Antidifferentiation and IntegrationOfficial strand · Strand C
Antiderivatives and indefinite integrals, applications to motion, area by Riemann sums, and the definite integral and area between curves.
Antiderivatives and Indefinite Integrals
- Antiderivatives and notationC.4.2 — Explain the meaning of an antiderivative, determine the general antiderivative of functions, use antiderivative (integral) notation appropriately, and identify the properties of antidifferentiation.
- Particular antiderivatives and motionC.4.5 — Determine the indefinite integral of a function given extra conditions, and use antidifferentiation to solve motion problems, computing displacement and velocity from suitable initial conditions and acceleration or velocity as functions of time.
Area and the Definite Integral
- Area by Riemann sumsC.4.8 — Estimate an area using a finite sum, determine an area using the infinite Riemann sum, and convert a Riemann sum to a definite integral.
- Definite integrals and area between curvesC.4.10 — Use definite integrals to determine the area under a polynomial function from x = a to x = b, calculate the definite integral of a function over an interval, and determine the area between two polynomial functions.
The official wording — 4 outcomes in this unit
- C.4.2
Determine the general antiderivative of functions
- C.4.5
Determine the indefinite integral of a function given extra conditions
- C.4.8
Determine the area using the infinite Riemann sum
- C.4.10
Using definite integrals, determine the area under a polynomial function from x = a to x = b
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The official source is linked on this page — Newfoundland and Labrador'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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