MCF3M

Grade 11, University/College Preparation
 * MCF3M - Functions and Applications**

toc **Overall Course Description** This course introduces basic features of the function by extending students’ experiences with quadratic relations. It focuses on quadratic, trigonometric, and exponential functions and their use in modeling real-world situations. Students will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve problems relating to applications. Students will reason mathematically and communicate their thinking as they solve multi-step problems. (The Ontario Curriculum - Mathematics - Grades 11 and 12, page 57)

Prerequisite:
Principles of Mathematics, Grade 10, Academic OR Foundations of Mathematics, Grade 10, Applied

Units:
These units are based on the McGraw – Hill Ryerson Functions and Applications 11 textbook.

Unit 1 – Quadratic Formulas

 * Goals:**
 * Define function and identify a function from a relation that is not a function
 * Evaluate linear and quadratic functions
 * Define and identify restrictions domain and range by investigating numerical, graphical and algebraic representations
 * Investigate quadratic functions in vertex form, describe the roles of variables in the translations of f(x) = x² and sketch.
 * Collect data that represents a quadratic relations and determine the equations of curves of best fit where applicable

Unit 2 – Factor Quadratic Expressions

 * Goals:**
 * Expand and simplify, solve, and factor quadratic expressions in one variable using a variety of strategies (i.e. perfect square and difference of squares)
 * Connect factored form, standard form, and vertex form through investigation of the key variables.
 * Describe and sketch the intercepts, the maximum and minimum and other key features of a quadratic function.

Unit 3 – Represent Quadratic Functions

 * Goals:**
 * Find the real roots of a quadratic equation using various methods, including the quadratic formula
 * Use the discriminant to determine the number of real roots of a quadratic equation
 * Complete the square
 * Solve real world applications of quadratic functions

Unit 4 – Trigonometry

 * Goals:**
 * Use primary trigonometry ratios to determine measures of sides and angles of right triangles
 * Solve problems using two triangles
 * Use the sine law and cosine law to determine the measures of sides and angles in acute triangle

Unit 5 – Sine Functions

 * Goals:**
 * Describe key properties of periodic functions
 * Graph the sine function and make connections to the sine ratio
 * Determine the roles of a, c, and d in f(x) = a sin (x - d) + c and sketch the resulting graphs
 * Identify periodic and sinusoidal functions and restrictions of domain and range

Unit 6 – Exponential Functions

 * Goals:**
 * Evaluate expressions containing integer and rational exponents and rational bases
 * Graph exponential relations and explain why it is a function
 * Describe key properties of exponential relations
 * Identify functions as linear, quadratic or exponential
 * Collect data and solve problems with real-world applications that can be modeled as an exponential function

Unit 7 – Compound Interest

 * Goals:**
 * Compare simple and compound interest for a given principle and fixed interest rate over a certain period of time
 * Solve problems for any unknown using simple and compound interest and investigate compound interest as an example of exponential growth

Unit 8 – Annuities

 * Goals:**
 * Define and explore annuity through numerical and graphical representations
 * Explore the affects of changing the conditions of ordinary simple annuities
 * Solve annuity problems involving amount, present value and regular payment

Textbooks:
Functions and Relations Publisher: Addison - Wesley ISBN: 0-201-72657-2

McGraw-Hill Ryerson Functions and Applications 11 Publisher: McGraw-Hill Ryerson ISBN: 0-070-72596-9

Nelson Functions and Applications 11 Publisher: Nelson Education Ltd. ISBN: 0-176-33204-9

Online Resources:
OAME - Ontario Association for Mathematics Education

Ontario Ministry of Education:
The Ontario Curriculum - Mathematics - Grades 11 and 12 (Page 57) The Ontario Curriculum Exemplars, Grade 11, Mathematics (Section: Functions University/College Preparation)