# Functions – Grade 11

This course introduces the mathematical concept of the function by extending students’ experiences with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions; represent functions numerically, algebraically, and graphically; solve problems involving applications of functions; investigate inverse functions; and develop facility in determining equivalent algebraic expressions. Students will reason mathematically and communicate their thinking as they solve multi-step problems.

$990.00

### Overall Curriculum Expectations

**Characteristics of Functions**

By the end of this course the student will:

1. Demonstrate an understanding of functions, their representations, and their inverses, and make connections between the algebraic and graphical representations of functions using transformations.

2. Determine the zeros and the maximum or minimum of a quadratic function, and solve problems involving quadratic functions, including problems arising from real-world applications.

3. Demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical, and rational expressions.

**Exponential Functions**

By the end of this course the student will:

1. Evaluate powers with rational exponents, simplify expressions containing exponents, and describe properties of exponential functions represented in a variety of ways.

2. Make connections between the numeric, graphical, and algebraic representations of exponential functions.

3. Identify and represent exponential functions, and solve problems involving exponential functions, including problems arising from real-world applications.

**Discrete Functions**

By the end of this course the student will:

1. Demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways, and make connections to pascal’s triangle.

2. Demonstrate an understanding of the relationships involved in arithmetic and geometric sequences and series and solve related problems.

3. Make connections between sequences, series, and financial applications, and solve problems involving compound interest and ordinary annuities.

**Trigonometric Functions**

By the end of this course the student will:

1. Determine the values of the trigonometric ratios for angles less than 360º; prove simple trigonometric identities; and solve problems using the primary trigonometric ratios, the sine law, and the cosine law.

2. Demonstrate an understanding of periodic relationships and sinusoidal functions, and make connections between the numeric, graphical, and algebraic representations of sinusoidal functions.

3. Identify and represent sinusoidal functions, and solve problems involving sinusoidal functions, including problems arising from real-world applications.

### Course Details

Course Code | MCR3U |

Course Type | University Preperation |

Format | Online School Course |

Prerequisite | MPM2D |

Tuition Fee | 650 – 1300 |

Department | Mathematics |

Course Title | Principles of Mathematics |

Grade | Grade 11 |

Credit Value | 1.0 |

### Outline of Course Content

Unit |
Title |
Time |

1 | Functions | 16 hours |

2 | Transformations of Functions | 17 hours |

3 | Exponential Functions | 14 hours |

4 | Trigonometry | 15 hours |

5 | Trigonometric Functions | 15 hours |

6 | Discrete Functions | 17 hours |

7 | Financial Applications | 14 hours |

Final Examination |
2 hours | |

Total |
110 hours |

### Course Details

Course Code | MPM2D |

Course Type | Academic |

Format | Online School Course |

Prerequisite | MPM1D or MFM1P |

Tuition Fee | 650 – 1300 |

Department | Mathematics |

Course Title | Principles of Mathematics |

Grade | Grade 10 |

Credit Value | 1.0 |

### Overall Curriculum Expectations

**Quadratic Relations of the Form y = ax2 bx c**

By the end of this course the student will:

- Determine the basic properties of quadratic relations.
- Relate transformations of the graph of y = x2 to the algebraic representation y = a (x – h)2 k.
- Solve quadratic equations and interpret the solutions with respect to the corresponding relations.
- Solve problems involving quadratic relations.

**Analytic Geometry**

By the end of this course the student will:

- Model and solve problems involving the intersection of two straight lines.
- Solve problems using analytic geometry involving properties of lines and lines segments.
- Verify geometric properties of triangles and quadrilaterals, using analytic geometry.

**Trigonometry**

By the end of this course the student will:

- Use their knowledge of ratio and proportion to investigate similar triangles and solve problems related to similarity.
- Solve problems involving right triangles, using the primary trigonometric ratios and the Pythagorean theorem.
- Solve problems involving acute triangles, using the sine law and the cosine law.

### Outline of Course Content

Unit |
Title |
Time |

1 | Linear Systems | 13 hours |

2 | Analytic Geometry | 11 hours |

3 | Geometric Properties | 14 hours |

4 | Quadratic Relations | 15 hours |

5 | Quadratic Expressions | 15 hours |

6 | Quadratic Equations | 15 hours |

7 | Trigonometry of Right Triangles | 13 hours |

8 | Trigonometry of Acute Triangles | 12 hours |

Final Examination |
2 hours | |

Total |
110 hours |