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
Correlation last revised: 9/16/2020