A: Students use patterns to describe the world and to solve problems; represent algebraic expressions in multiple ways; and, use algebraic and graphical models to generalize patterns, make predictions, and solve problems.

A.1: derive and apply expressions to represent general terms for geometric growth and to solve problems

Geometric Sequences

A.4: solve exponential equations having bases that are powers of one another

Exponential Functions

A.5: solve and verify exponential and logarithmic equations

Exponential Functions

A.8: determine the exact and the approximate values of trigonometric ratios for any multiples of 0°, 30°, 45°, 60° and 90°, and 0 rad, pi / 6 rad, pi / 4 rad, pi / 3 rad, and pi / 2 rad

Cosine Function
Sine Function
Tangent Function

A.11: analyse trigonometric identities

A.11.1: graphically

Cosine Function
Sine Function
Tangent Function

A.12: use sum, difference, and double angle identities for sine and cosine to verify and simplify trigonometric expressions

Sum and Difference Identities for Sine and Cosine

A.14: model, graph, and apply exponential functions to solve problems

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

A.15: model, graph, and apply logarithmic functions to solve problems

Logarithmic Functions

A.16: describe the three primary trigonometric functions as circular functions with reference to the unit circle and an angle in standard position

Cosine Function
Sine Function
Tangent Function

A.17: sketch and analyse the graphs of sine, cosine, and tangent functions, for

A.17.1: amplitude, if defined

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

A.17.2: period

Cosine Function
Sine Function
Tangent Function
Translating and Scaling Sine and Cosine Functions

A.17.4: asymptotes, if any

Tangent Function

A.17.5: behaviour under transformations

Translating and Scaling Sine and Cosine Functions

A.18: use trigonometric functions to model and solve problems

Cosine Function
Sine Function

B: Students perform, analyse, and create transformations of functions and relations that are described by equations or graphs.

B.1: describe how vertical and horizontal translations of functions affect graphs and their related equations:

B.1.1: y = f(x − h)

Absolute Value with Linear Functions
Introduction to Exponential Functions
Rational Functions
Translating and Scaling Sine and Cosine Functions
Translations

B.1.2: y − k = f(x)

Absolute Value with Linear Functions
Introduction to Exponential Functions
Quadratics in Vertex Form
Rational Functions
Translating and Scaling Sine and Cosine Functions
Translations

B.2: describe how compressions and expansions of functions affect graphs and their related equations:

B.2.1: y = af(x)

Introduction to Exponential Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

B.2.2: y = f(kx)

Introduction to Exponential Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

B.3: describe how reflections of functions in both axes and in the line y = x affect graphs and their related equations:

B.3.1: y = f(−x)

Absolute Value with Linear Functions
Introduction to Exponential Functions
Quadratics in Vertex Form
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

B.3.2: y = −f(x)

Absolute Value with Linear Functions
Introduction to Exponential Functions
Quadratics in Vertex Form
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

B.3.3: y = f to the −1 power (x)

Absolute Value with Linear Functions
Introduction to Exponential Functions
Quadratics in Vertex Form
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions

B.4: using the graph and/or the equation of f(x), describe and sketch 1 / f(x)

Introduction to Exponential Functions

B.5: using the graph and/or the equation of f(x), describe and sketch |f(x)|

Absolute Value with Linear Functions
Translating and Scaling Functions

C: Students solve problems based on the counting of sets, using techniques such as the fundamental counting principle, permutations, combinations, and combining of simpler probabilities.

C.2: use factorial notation to determine different ways of arranging n distinct objects in a sequence

Permutations and Combinations

C.3: determine the number of permutations of n different objects taken r at a time, and use this to solve problems

Permutations and Combinations

C.4: determine the number of combinations of n different objects taken r at a time, and use this to solve problems

Binomial Probabilities
Permutations and Combinations

C.7: classify events as independent or dependent

Independent and Dependent Events

C.9: determine the conditional probability of two events

Independent and Dependent Events

C.10: solve probability problems involving permutations, combinations, and conditional probability

Binomial Probabilities
Independent and Dependent Events
Permutations and Combinations