Course Title: Functions
Course Code: MCR3U
Grade: 11
Course Type: University Preparation
Credit Value: 1
Prerequisite: MPM2D
Department: Mathematics

Course Description

This course introduces the mathematical concept of function by extending the students’ knowledge with linear and quadratic relations. Students will investigate properties of discrete and continuous functions, including trigonometric and exponential functions. Students will further learn how to 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.

Course Outline
  • MCR3U Unit 1 Overview
  • Accessibility to MCR3U Unit1 Assignment
  • U1L1 Meaning of the function (A1.1)
  • U1L2 Introduce linear function (A1.2)
  • U1L3 Introduce quadratic function (A1.2)
  • U1L4 Domain of Functions (A1.3)
  • U1L5 Range of functions (A1.3)
  • U1L6 Inverse function (part 1) (A1.4)
  • U1L7 Inverse function (part 2) (A1.4)
  • U1L8 Numeric representation of the inverse (A1.5)
  • U1L9 Graphical representation of the inverse (A1.5)
  • U1L10 Domain of the inverse (A1.6)
  • U1L11 Range of the inverse (A1.6)
  • U1L12 Relationship between the inverse and the original function (A1.6)
  • U1L13 Function notations (A1.7)
  • U1L14 Algebraic Representation of a Function and Its Inverse (A1.7)
  • U1L15 Determine functions using technology (A1.8)
  • U1L16 Roles of the parameters (A1.8)
  • U1L17 Function transformation (A1.9)
  • U1L18 Transformation graphs (A1.9)
  • U1L19 Simplify polynomial expressions (A3.1)
  • U1L20 Graph of polynomial expressions (A3.1)
  • U1L21 Simplify rational expressions (A3.3)
  • U1L22 Restrictions on the variable values (A3.3)
  • U1L23 Algebraic expressions (A3.4)
  • U1L24 Equivalent expressions (A3.4)
  • Finish and Hand in MCR3U Unit1 Assignment at the end of lesson
  • MCR3U Unit1 Online Test
  • MCR3U Unit2 Overview
  • Accessibility to MCR3U Unit2 Assignment
  • U2L1 Maximum or minimum value of a quadratic function (A2.2)
  • U2L2 Number of zeros (A2.1)
  • U2L3 Simplify radicals and radical expressions (A3.2)
  • U2L4 Solve problems involving quadratic functions (A2.3)
  • U2L5 Determain maximum or minimum values (A2.2)
  • U2L6 Intersection of a linear function and a quadratic function (A2.5)
  • U2L7 Real roots (A2.4)
  • U2L8 The transformational relationship (A2.4 B1.1)
  • U2L9 Graph an exponential relation (B1.1)
  • U2L10 Value of a power with a rational exponent (B1.2)
  • U2L11 Investigate powers involving rational exponents (B1.3)
  • U2L12 Investigate exponential functions (B1.4)
  • U2L13 Simplify algebraic expressions involving powers and radicals (B1.3)
  • U2L14 Distinguish exponential functions from linear and quadratic (B2.1)
  • U2L15 Transformations on the graph (B2.2)
  • U2L16 Applying one or more transformations to the graph (B2.3)
  • U2L17 connections between the equivalent forms (B2.4)
  • U2L18 Represent an exponential function with an equation (B2.5)
  • U2L19 Domain and range of the transformed functions (B2.3)
  • U2L20 Model an exponential function (B3.1)
  • U2L21 Identify exponential functions (B3.2)
  • U2L22 Solve questions by interpreting the graphs (B3.3)
  • U2L23 Real-world applications of exponential functions (B3.3)
  • U2L24 Represent an exponential function with an equation by graphing (B2.5)
  • Accessibility to MCR3U Unit2 Assignment
  • MCR3U Unit2 Online Test
  • MCR3U Unit3 Overview
  • Accessibility to MCR3U Unit3 Assignment
  • U3L1 Sequences and discrete functions (C1.1)
  • U3L2 Recursive procedure (C1.2)
  • U3L3 nth term of a sequence (C1.3)
  • U3L4 Represent a sequence algebraically (C1.4)
  • U3L5 Formula for the nth term (C1.4)
  • U3L6 Recursive patterns in the Fibonacci sequence (C1.5)
  • U3L7 Pascal’s triangle (C1.6)
  • U3L8 Expansion of binomials (C1.6)
  • U3L9 Identify sequences as arithmetic, geometric, or neither (C2.1)
  • U3L10 Determine the formula for the general term (C2.2)
  • U3L11 Determine the formula for the sum of an arithmetic series (C2.3)
  • U3L12 Determine the formula for the sum of a geometric series (C2.3)
  • U3L13 Solve problems involving geometric sequences and series (C2.4)
  • U3L14 Solve problems involving arithmetic sequences and series (C2.4)
  • U3L15 Investigation with technology (C3.1)
  • U3L16 Use arithmetic sequences to calculate simple interest (C2.4)
  • U3L17 Compound interest (C3.2)
  • U3L18 Future value (C3.3)
  • U3L19 Compounding periods (C3.4)
  • U3L20 Annuity (C3.5)
  • U3L21 Different types of annuity (C3.5)
  • U3L22 Changing the conditions of ordinary simple annuities (C3.6)
  • U3L23 Real world tasks of simple annuity (C3.7)
  • U3L24 Use technology solve annuity (C3.7)
  • Finish and Hand in MCR3U Unit3 Assignment at the end of lesson
  • MCR3U Unit3 Online Test
  • MCR3U Unit4 Overview
  • Accessibility to MCR3U Unit4 Assignment
  • U4L1 Exact values (D1.1)
  • U4L2 Determine the values using a variety of tools and strategies (D1.2)
  • U4L3 Measures of two angles (D1.3)
  • U4L4 secant, cosecant, and cotangent ratios (D1.4)
  • U4L5 Prove simple trigonometric identities (D1.5)
  • U4L6 Right triangles and oblique triangles (D1.6)
  • U4L7 Cosine law and the sine law (D1.6)
  • U4L8 Right triangles in three-dimensional settings (D1.7)
  • U4L9 Oblique triangles in three-dimensional settings (D1.7)
  • U4L10 Key properties of periodic functions (D2.1)
  • U4L11 Predict the future behavior of a relationship (D2.2)
  • U4L12 Make connections between the trig ratio and the trig function (D2.3)
  • U4L13 Sketch the graphs (D2.4)
  • U4L14 Roles of the parameters (D2.5)
  • U4L15 Elements in sinusoidal functions (D2.6)
  • U4L16 Sketch graphs of one or more transformations (D2.7)
  • U4L17 Model data in sinusoidal function (D2.8)
  • U4L18 Determine the equation of the function (D2.8)
  • U4L19 Collect data that can be modelled as a sinusoidal function (D3.1)
  • U4L20 Identify periodic and sinusoidal functions (D3.2)
  • U4L21 Model periodic phenomena (D3.3)
  • U4L22 Predict the changes on a mathematical model (D3.4)
  • U4L23 Applications involving a sinusoidal function (D3.5)
  • U4L24 Real world tasks of sinusoidal function (D3.5)
  • Finish and Hand in MCR3U Unit4 Assignment at the end of lesson
  • MCR3U Final Project
  • MCR3U Final Exam
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