Courses

Newfoundland & Labrador · Grade 12

Mathematics 3208 (Calculus)

Newfoundland & Labrador’s Grade 12 math course, from Pre-Calculus to Antidifferentiation and Integration.

Learn thisPractice test
Units
4
Lessons
13
Skills
34
Provincial exam
None
Official curriculum
gov.nl.ca

Unit by unit

Every skill in the course, numbered by unit.

Unit 1 · 5 skills

Pre-Calculus

Operations and Composition of Functions

Rational, Exponential and Logarithmic Functions

Inverse Trigonometric Functions

The official wording · 5 outcomes
1.1
Write a function h ( x ) as the sum, difference, product or quotient of two or more functions
1.2
Determine the equation of the composite function given the equations of two functions f ( x ) and g ( x )
1.3
Determine if the graph of a rational function will have an asymptote or a hole for a non-permissible value
1.4
Graph and analyze exponential and logarithmic functions y = e x and y = ln x
1.5
Explain why trigonometric functions must have their domains restricted to create inverse trigonometric functions

Key ideas

  1. Functions add, subtract, multiply, and divide value by value at each x.

  2. A non-permissible value gives a vertical asymptote unless the factor cancels, which gives a hole.

  3. A trig function is not one-to-one, so its domain is restricted before inverting.

  4. The domain of the result excludes any x outside a part's domain or where a divisor is zero.

  5. Near a vertical asymptote the function grows without bound.

Watch out for

  • Combining rules instead of function values.
  • Treating every non-permissible value as an asymptote.
  • Forgetting the restricted range of an inverse trig function.

Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit

Unit 2 · 8 skills

Limits and Continuity

The Concept of a Limit

Evaluating Limits

Limits at Infinity and Continuity

The official wording · 8 outcomes
2.1
Explore the concept of limit and the notation used in expressing the limit of a function
2.2
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
2.3
Apply the properties of limits including: Sum Rule Difference Rule Product Rule Constant Multiple Rule Quotient Rule Power Rule to solve problems
2.4
Determine the value of the limit of a function as the variable approaches a real number by substitution by algebraic manipulation
2.5
Determine limits that result in infinity (infinite limits)
2.6
Evaluate limits of functions as x approaches infinity (limits at infinity)
2.7
Determine whether a function is continuous at a point using the definition of continuity
2.8
Establish each of the following trigonometric limits, using informal methods

Key ideas

  1. A limit is the value a function approaches as x nears a point, whether or not the function is defined there.

  2. The limit of a sum, difference, product, or quotient is that operation on the limits (with a nonzero denominator).

  3. A limit at infinity describes the function's end behaviour.

  4. One-sided limits approach from the left or the right separately.

  5. These laws break a complicated limit into simple pieces.

Watch out for

  • Confusing the limit with the function's value at the point.
  • Applying the quotient rule when the denominator's limit is zero.
  • Comparing only leading coefficients without the degrees.

Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit

Unit 3 · 17 skills

Derivatives and Their Applications

The Derivative as a Limit

Differentiation Rules

Curve Sketching

Applications of Derivatives

Derivatives of Trigonometric, Exponential and Other Functions

The official wording · 17 outcomes
3.1
Identify the instantaneous rate of change of a function at a point as the limiting value of a sequence of average rates of change
3.2
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
3.3
Use alternate notation interchangeably to express derivatives
3.4
Sketch a graph of the derivative of a function, given the graph of a function
3.5
Determine derivatives of functions, using the Constant, Constant Multiple, Power, Sum, Difference, Product and Quotient Rules
3.6
Determine derivatives of functions using the Chain Rule
3.7
Determine the derivative of an implicit relation
3.8
For a polynomial function, use f ' ( x ) to identify the critical numbers, relative and absolute extrema, and intervals of increase and decrease
3.9
For a polynomial function, sketch the graph of f ( x ) using information obtained from the function and its derivatives
3.10
For a rational function, use the given function f ( x ) to determine its features such as intercepts, asymptotes, points of discontinuity and the domain
3.11
Solve problems involving derivatives drawn from a variety of applications, limited to tangent and normal lines, straight line motion and rates of change
3.12
Solve a problem involving related rates drawn from a variety of applications
3.13
Solve an optimization problem drawn from a variety of applications, using calculus techniques
3.14
Determine the derivative of expressions involving trigonometric functions
3.15
Determine the derivative of an inverse trigonometric function
3.16
Determine the derivative of an exponential function
3.17
Define tanh x , csch x , coth x , and sech x in terms of sinh x and cosh x

Key ideas

  1. The average rate of change is the slope of a secant line over an interval.

  2. The power rule differentiates a power by bringing down the exponent and reducing it by one.

  3. Critical numbers occur where the first derivative is zero or undefined.

  4. For straight-line motion, velocity is the derivative of position and acceleration is the derivative of velocity.

  5. The derivative of sine is cosine and of cosine is negative sine; the other four follow.

Watch out for

  • Confusing the secant slope with the tangent slope.
  • Differentiating a product as a product of derivatives.
  • Confusing a critical number with an extremum without a sign test.

Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit

Unit 4 · 4 skills

Antidifferentiation and Integration

Antiderivatives and Indefinite Integrals

Area and the Definite Integral

The official wording · 4 outcomes
4.1
Determine the general antiderivative of functions
4.2
Determine the indefinite integral of a function given extra conditions
4.3
Determine the area using the infinite Riemann sum
4.4
Using definite integrals, determine the area under a polynomial function from x = a to x = b

Key ideas

  1. An antiderivative F of f satisfies F prime equals f.

  2. A finite sum of rectangle areas approximates the area under a curve.

  3. The general antiderivative includes an arbitrary constant, written with the integral sign.

  4. Letting the number of rectangles grow without bound gives the exact area as an infinite Riemann sum.

  5. An initial condition pins down the constant, giving a particular antiderivative.

Watch out for

  • Forgetting the constant of integration.
  • Using too few rectangles and calling it exact.
  • Differentiating instead of antidifferentiating.

Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit

Which course?

Newfoundland & Labrador has 4 math courses for Grade 12. Here they are side by side.

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 Newfoundland & Labrador’s own curriculum for Mathematics 3208 (Calculus).

Government of Newfoundland and Labrador, Department of Education - Mathematics 3208 Calculusgov.nl.ca · Read August 7, 2026

Study it in MapleMind

MapleMind teaches Mathematics 3208 (Calculus) 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.

Mathematics 2201 (Academic) in the MapleMind app on a tablet: its units, Unit 1 open, and the skills done so far with their starsMathematics 2201 (Academic) in the MapleMind app on a phone: its units, Unit 1 open, and the skills done so far with their stars
Pictured: Mathematics 2201 (Academic), another Newfoundland & Labrador course, partway through Unit 1.

Practise it

Course Companion

Your year in one workbook

A fun way to keep Mathematics 3208 (Calculus) organized, get to know your child better and see early when they need a hand. Fill it in on a screen, or print it.

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Questions about Mathematics 3208 (Calculus)

What is Mathematics 3208 (Calculus)?

Newfoundland & Labrador’s Grade 12 math course: 4 units and 34 skills, from Pre-Calculus to Antidifferentiation and Integration.

What units are in Mathematics 3208 (Calculus)?

1. Pre-Calculus, 2. Limits and Continuity, 3. Derivatives and Their Applications and 4. Antidifferentiation and Integration.

Is there a provincial exam for Mathematics 3208 (Calculus)?

No. Newfoundland & Labrador gives no provincial exam for Mathematics 3208 (Calculus).

Can MapleMind help with Mathematics 3208 (Calculus)?

Yes. MapleMind teaches every skill of Mathematics 3208 (Calculus), 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.

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