1: Transformations of Functions

1.1: Describe how various translations of functions affect graphs and their related equations:

1.1.1: y = f(x − h)

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

1.1.2: y − k = f(x).

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

1.2: Describe how various stretches of functions (compressions and expansions) affect graphs and their related equations:

1.2.1: y = af(x)

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

1.2.2: y = f(kx).

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

1.3: Describe how reflections of functions in both axes and in the line y = x affect graphs and their related equations:

1.3.1: y = f(−x)

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

1.3.2: y = −f(x)

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

1.3.3: y = f −1(x).

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

1.5: Describe and perform single transformations and combinations of transformations on functions and relations.

Absolute Value with Linear Functions
Exponential Functions
Introduction to Exponential Functions
Radical Functions
Rational Functions
Translating and Scaling Functions
Translating and Scaling Sine and Cosine Functions
Translations
Zap It! Game

2: Exponents, Logarithms and Geometric Series

2.1: Derive and apply expressions to represent general terms and sums for geometric growth and to solve problems.

Geometric Sequences

2.3: Solve exponential equations having bases that are powers of one another.

Exponential Functions

2.5: Graph and analyze an exponential function, using technology.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

2.6: Model, graph and apply exponential functions to solve problems.

Compound Interest
Exponential Functions
Introduction to Exponential Functions
Logarithmic Functions

2.7: Change functions from exponential form to logarithmic form and vice versa.

Logarithmic Functions

2.10: Graph and analyze logarithmic functions with and without technology.

Logarithmic Functions
Logarithmic Functions: Translating and Scaling

3: Trigonometry

3.1: Distinguish between degree and radian measure, and solve problems using both.

Sine Function

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

Sine Function
Tangent Function

3.6: Describe sine, cosine and tangent as circular functions, with reference to the unit circle and an angle in standard position.

Cosine Function
Sine Function
Tangent Function

3.7: 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

3.8: Draw (using technology), sketch and analyze the graphs of sine, cosine and tangent functions, for:

3.8.1: amplitude, if defined

Translating and Scaling Sine and Cosine Functions

3.8.2: period

Sine Function
Translating and Scaling Sine and Cosine Functions

3.8.5: behaviour under transformations.

Translating and Scaling Sine and Cosine Functions

3.10: Use sine and cosine functions to model and solve problems.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Sum and Difference Identities for Sine and Cosine
Translating and Scaling Sine and Cosine Functions

4: Conic Sections

4.2: Classify conic sections according to a given equation in general or standard (completed square) form (vertical or horizontal axis of symmetry only).

Circles

5: Permutations and Combinations

5.2: Determine the number of linear permutations of n objects taken r at a time, and use this to solve problems.

Permutations and Combinations

5.3: Determine the number of combinations of n distinguishable objects taken r at a time, and use this to solve problems.

Binomial Probabilities
Permutations and Combinations

5.7: Solve probability problems using either permutations and combinations or the fundamental counting principle.

Binomial Probabilities
Permutations and Combinations

6: Statistics

6.1: Find the population standard deviation of a data set, using technology.

Polling: City
Real-Time Histogram

6.2: Solve probability problems, using the binomial distribution.

Binomial Probabilities