Grade 12‎ > ‎


Some Online Resources for Extra Help

Unit 1 Review and Properties of Functions

What is a function, domain and range

12 basic functions

Odd and Even functions

Inverse relations:

Unit 2: Rates of Change

2.1 Average Rate of Change:

2.2 Finding the Instantaneous Rate of Change

From a Table:

From an equation (difference quotient):

2.3 Finding the Instantaneous Rate of Change from a graph

2.5 Finding maximum and minimum values with the derivative

Unit 3: Polynomial Functions, Polynomial equations and inequalities:

3.1 Exploring polynomials

What is a Polynomial?

Using Finite Differences

3.2 Characteristics of polynomials, 3.3 Multiplicities of zeroes (5 pages, comprehensive)

3.4 Transformations of cubics and quartics

3.5 division of functions

long division:

synthetic division:

3.6 factoring polynomials

The Remainder and Factor Theorems:

3.7 Solving Higher Degree Polynomials:

synthetic method:

3.8 Solving linear inequalities

3.9 Solving Polynomial Inequalities


Using a table:

3.10 Rates of change in polynomial functions

see rates of change section

Unit 4: Rational functions:

4.1 Graphing Reciprocal Functions

4.2 Introduction to Rational Functions

4.3 Graphs of Rational Functions


Finding asymptotes:

4.4 Rational Equations

Solving rational equations:

4.5 Rational Inequalities

Rational inequalities: (he uses testing points, using a table is often easier)

4.6 Rates of Change in Rational Functions

See Rates of Change Unit

Unit 5: Trigonometric functions:

5.1 Introduction to radians:

5.2 Radian measure on the Cartesian plane and special triangles

5.3 Graphing the primary trigonometric functions

5.4 Transformations of trigonometric functions:

Sine function:

All 6 basic functions:

5.5 Graphs of the reciprocal trigonometric functions:


Arithmetic series review:

5.6 Modelling with Trigonometric Functions

5.7 Rates of Change in Trigonometric Functions

See Rates of Change Unit

Unit 6: Logarithmic Functions:

Unit 7: Trigonometric Identities:


7.1 Equivalent trigonometric functions


7.2 Compound angle formulas


7.3 Double Angle Formulas


7.4 Proving Trig Identities


7.5 and 7.6 SolvingTrig Equations

Unit 8: Combined Functions:


8.1 Introduction to Logarithms


8.2 Transformations of logarithmic functions


8.3 Simplifying Logarithms


8.4 Laws of logarithms


8.5 Solving Exponential Equations


8.6 Solving Logarithmic Equations


8.7 Solving Problems with Exponential and Logarithmic Functions


8.8 Rate of Change in Logarithmic Functions

See rate of change unit. Note that we can only approximate an IROC for logarithms and exponentials at this time.


Unit 9: Combining Functions


9.1 Exploring function combinations


9.2 Sums and Differences of Functions


9.3 Product of functions


9.4 Quotients of Functions


9.5 Composition of Functions


9.6 Solving Function Equalities and 9.7 Modelling With Functions

These sections use skills developed over the entire course, hence there are no easy resources available.