Unlocking Mathematical Relationships

In this course, you’ll explore the powerful concept of functions, building on your previous experience with linear and quadratic relations.

You’ll dive into the properties of different types of functions, including:

Discrete and continuous functions
Trigonometric and exponential functions
How to represent functions in different ways, such as numerically, algebraically, and graphically
How to solve real-world problems using functions
Inverse functions and how they relate to original functions

How to simplify and manipulate algebraic expressions

Through a combination of problem-solving, critical thinking, and mathematical reasoning, you’ll develop your ability to tackle complex, multi-step problems and communicate your thinking effectively.

Prerequisite: Principles of Mathematics, Grade 10 (Academic)

Unit 1: Introduction to Functions

In this unit, students will learn to recognize functions in various representations and use function notation, explore the properties of some basic functions, apply transformations to those functions, and investigate the inverse of linear function and its properties. This unit will teach students to identify a function as a special type of relation.

Unit 2: Equivalent Algebraic Expressions

This unit will teach adding, subtracting, multiplying, and factoring polynomials. Students will learn to simplify rational expressions and add, subtract, multiply, and divide rational expressions. By the end of the unit, students will be able to determine whether algebraic expressions are equivalent.

Unit 3: Quadratic Functions

In this unit, students will learn to determine the zeros of quadratic functions, calculate their maximum or minimum values, and solve problems involving quadratic functions. By the unit’s end, students will be able to graph and analyze the properties of quadratic functions.

Unit 4: Exponential Functions

In this unit, students will learn to compare exponential functions with linear and quadratic functions, evaluate powers with integer and rational exponents, and simplify expressions involving them. Students will use exponential functions to solve problems involving exponential growth and decay. The unit will teach students to describe the characteristics of exponential functions and their graphs.

Unit 5: Trigonometric Ratios

In this unit, students will learn to relate the six trigonometric ratios to the unit circle and solve real-life problems by using trigonometric ratios, properties of triangles, and the sine and cosine laws. This unit will make students proficient in proving simple trigonometric identities.

Unit 6: Sinusoidal Functions

In this unit, students will understand the effect of applying transformations to the functions: fx = sin x and fx = cos x, where x is measured in degrees, and determine the equations of sinusoidal functions in real-world situations, using these equations to solve problems. The unit will teach students to identify situations that can be modeled using sinusoidal and other periodic functions and interpret the graphs of sinusoidal and other periodic phenomena.

Unit 7: Sequences and Series

In this unit, students will explore efficient ways to add the terms of a sequence and model real-life problems using sequences. By the end of the unit, students will be able to create functions for describing sequences, identify and classify sequences, and use them to make predictions.

Unit 8: Discrete Functions: Financial Applications

In the final unit, students will learn to solve problems about money invested at regular intervals and calculate payments that must be made when a purchase is financed over a period of time.

By the end, students will be able to determine how interest is earned and charged, and use the difference between future value and present value to solve problems.