Outline of Course Content
Unit | Title | Length |
Unit 1 | Functions and Transformations | 25 hours |
Unit 2 | Exponential Functions | 16 hours |
Unit 3 | Trigonometric Ratios | 15 hours |
Unit 4 | Sinusoidal Functions | 15 hours |
Unit 5 | Discrete Functions | 15 hours |
Unit 6 | Financial Applications | 15 hours |
Unit 7 | End of Term | 9 hours |
| Total: | 110 hours |
Unit Overviews
Unit 1: Functions and Transformations
Verify the multiplicative property of radicals. Simplifying radical expressions by multiplying binomials involving radicals terms. Properties of the quadraticfunction, including the vertex, axis of symmetry, zeros and y-intercept. Determining which form: standard, factored or vertex is best to solve problems. Determine the number of zero’s by calculating the discriminate, inspectinggraphs, or factoring equations. Find the max/min by completing the square, oraveraging the zeros. Solve problems involving profit and other real world problems. Simplify rational expressions by adding subtracting multiplying ordividing. State restrictions. Determine if two expressions are equivalent by simplifying or substituting values. Determine how transformations affect a family of quadratic functions. Solve problems involving linear and quadratic systems. Functions and relations. Function notation. Domain and Range. Finding the inverse using a graph, table of values or equation. Relating the domain and range of a function and its inverse. Transformations of the linear, quadratic, square root and reciprocal functions involving horizontal/ verticaltranslations, horizontal/vertical stretches or compressions and reflections inthe x-axis or y-axis. State the domain and range of a transformed function.
Unit 2: Exponential Functions
Simplify exponential expressions involving integer and rational exponents. Determine strategies for solving problems involving rational exponents.
Investigate real world problems modeled by exponential growth and decay. Make connections to how the graph changes if the starting value or rate changes. Investigate how base changes the graph in exponential functions. Determine keyfeatures, domain range, intercepts, increasing/decreasing intervals and asymptotes of exponential functions. Compare exponential, linear and quadraticfunctions by graphing, finite differences, inspection and equations. Determinethe roles of parameters a, k, c, and d, in and sketch transformations of exponential functions. Solve exponential equations, by writing terms in logarithmic form. Build exponential equations from real world problems using tables, or by finding key features.
Unit 3: Trigonometric Ratios
Exact values of sine and cosine for special angles 0°, 30°, 45°, 60° and 90°. Determine values of trigonometric ratios from 0° to 360°. Determine two angleswith the same trigonometric ratio. Define cosecant secant and cotangent. Provesimple trigonometric identities. Pose problems involving right and oblique triangles in three dimensions. Solve problems using the sine law and cosine law.
Unit 4: Sinusoidal Functions
Describe periodic functions and their properties, including cycle, amplitude, andperiod. Properties of sinusoidal functions including cycle, domain, range, intercepts, amplitude, period, maximum and minimum value, increasing/decreasingintervals. Interpreting sinusoidal functions in real world applications. Exploring transformations of sinusoidal functions with parameters a, k d and c. Sketching sinusoidal functions using their transformations. Modelling and solving problems with sinusoidal functions.
Unit 5: Discrete Functions
Arithmetic sequences. Geometric sequences. Fibonacci sequence and patterns involved in it. Pascal’s Triangle and binomial expansion. Arithmetic series. Geometric series. Recursion. Solve problems involving sequences and series.
Unit 6: Financial Applications
SimpleInterest. Compound Interest. Terminology for compounding periods, annually, semi-annually, quarterly, monthly, daily. Determine the better investment option. Solve problems involving future value, present value, interest rate and compounding periods. Annuities. Solve problems involving annuities, including, payment, future value, present value, total interest and make connections to real world problems.
Unit 7: End of Term
Final Task, Review of Course, Final Exam
