Ontario, Canada · Curriculum spine

Grade 12

17 concepts across 1 subject. Codes follow the ministry's own expectation numbers; where a course is broken into bites (chapter.bite), each bite names the expectations it covers.

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Advanced Functions (MHF4U)

The Ontario Curriculum, Grades 11 and 12: Mathematics, 2007 · 17 concepts
Strand A

Exponential and Logarithmic Functions

Logarithms, their laws, and solving exponential and logarithmic equations.

4
  1. A1.1
    Logarithm as inverse of exponent
    Define a logarithm, convert between exponential and logarithmic form, and evaluate logarithms.
    function grapher
    Coming soon
  2. A1.2
    Laws of logarithms
    Use the product, quotient and power laws to simplify and evaluate.
    After A1.1balance
    Coming soon
  3. A2.1
    Graphs of log functions
    Sketch logarithmic functions and their transformations, and describe domain, range and asymptotes.
    After A1.1function grapher
    Coming soon
  4. A3.1
    Solving exponential and log equations
    Solve equations algebraically and graphically, including applications like half-life and pH.
    After A1.2balance
    Coming soon
Strand B

Trigonometric Functions

Radians, identities, and trigonometric equations.

5
  1. B1.1
    Radian measure
    Convert between degrees and radians and find exact values at special angles.
    unit circle
    Coming soon
  2. B1.2
    Graphs of trig functions in radians
    Sketch sine, cosine and tangent and their transformations, including reciprocal functions.
    After B1.1function grapher
    Coming soon
  3. B2.1
    Compound angle formulas
    Derive and apply compound angle and double angle formulas.
    After B1.1unit circle
    Coming soon
  4. B2.2
    Proving identities
    Prove trigonometric identities using known identities and algebra.
    After B2.1balance
    Coming soon
  5. B3.1
    Solving trig equations
    Solve linear and quadratic trigonometric equations over a domain, in radians.
    After B2.1unit circle
    Coming soon
Strand C

Polynomial and Rational Functions

Polynomial behaviour, factoring, rational functions, equations and inequalities.

5
  1. C1.1
    Polynomial functions and their graphs
    Connect degree, leading coefficient and zeros to the shape and end behaviour of a graph.
    function grapher
    Coming soon
  2. C1.2
    Remainder and factor theorems
    Divide polynomials and use the remainder and factor theorems to factor.
    After C1.1balance
    Coming soon
  3. C2.1
    Rational functions
    Sketch rational functions and identify asymptotes, holes and intercepts.
    After C1.1function grapher
    Coming soon
  4. C3.1
    Polynomial and rational equations
    Solve polynomial and rational equations algebraically and interpret the solutions.
    After C1.2balance
    Coming soon
  5. C4.1
    Inequalities
    Solve polynomial and rational inequalities graphically and algebraically.
    After C3.1function grapher
    Coming soon
Strand D

Characteristics of Functions

Rates of change, combining functions, and function behaviour.

3
  1. D1.1
    Average and instantaneous rate of change
    Estimate rates of change from graphs and tables and connect them to slope.
    function grapher
    Coming soon
  2. D2.1
    Combining functions
    Add, subtract, multiply, divide and compose functions and describe the results.
    function grapher
    Coming soon
  3. D3.1
    Choosing a model
    Select and justify a function model for a real situation and solve problems with it.
    After D2.1A3.1modelling canvas
    Coming soon