In the MCR3U course online, students embark on a deep dive into mathematical functions, transitioning from linear and quadratic basics to the complexities of trigonometric and exponential functions. MCR3U’s curriculum is designed to challenge students with real-life problem-solving, pushing them to enhance their critical thinking and communication. As MCR3U learners engage with a variety of representations—numerical, algebraic, and graphical—they tackle complex problems, fostering an appreciation for mathematics’ role in real-world applications. This comprehensive approach ensures that students in MCR3U not only build a robust mathematical foundation but are also prepared for further academic pursuits and professional success.
Course curriculum
Inside %course-code%: where functions begin
The prerequisite for Grade 12 university math
MCR3U is required for Advanced Functions (MHF4U) and Mathematics of Data Management (MDM4U). Students planning any Grade 12 university math take this course first.
What a function is
The difference between a function and a relation, domain and range, inverses and transformations — applied across linear, quadratic, radical, exponential and trigonometric functions.
Growth, decay and cycles
Exponential functions with real-world growth and decay applications, then periodic functions — cycle, amplitude, period — and the connection between sine, cosine and the unit circle.
Money math with real stakes
Sequences and series lead to simple and compound interest and annuities — the financial applications the course ends on.
MCR3U Course outline
Full unit-by-unit breakdown.
Explore the difference between a function and a relation, express domain and range, and apply these ideas to linear, quadratic and radical functions. Determine the inverse of a linear or quadratic function from its numeric, graphical or algebraic representation.
Key topics
Function vs. relation · function notation · domain and range · inverses · transformations
Assessed by
Quiz · end-of-unit conversation · proctored unit test
Develop facility in determining equivalent algebraic expressions: simplify rational expressions, state restrictions, and work with the algebraic forms functions take.
Key topics
Simplifying rational expressions · restrictions · equivalent algebraic expressions
Assessed by
Quiz · end-of-unit conversation · proctored unit test
Extend Grade 10 quadratics: solve problems involving quadratic functions, connect their forms, and apply domain, range and inverse ideas to them.
Key topics
Forms of a quadratic · maximum and minimum problems · quadratic equations · inverse of a quadratic
Assessed by
Quiz · end-of-unit conversation · proctored unit test
Express and investigate exponential functions using calculators, paper and pencil and graphing technology, compare them with functions studied earlier, and connect graphing and transformations — with an emphasis on real-world growth and decay.
Key topics
Exponent laws · graphs and transformations of exponential functions · growth and decay applications
Assessed by
Quiz · end-of-unit conversation · proctored unit test
Solve problems involving right and oblique triangles in two- and three-dimensional settings using the primary trigonometric ratios, the sine law and the cosine law.
Key topics
Primary trigonometric ratios · sine law and cosine law · 2D and 3D triangle problems
Assessed by
Quiz · end-of-unit conversation · proctored unit test
Describe the key properties of periodic functions arising from real-world applications — cycle, amplitude, period — and make connections between the sine and cosine functions and the unit circle, with and without technology.
Key topics
Periodic functions · amplitude and period · the unit circle · sinusoidal models
Assessed by
Quiz · end-of-unit conversation · proctored unit test
Build on patterning to express sequences and series, then apply them to financial problems based on simple investments and investments in a compound period.
Key topics
Arithmetic and geometric sequences and series · simple and compound interest · annuities
Assessed by
Quiz · end-of-unit conversation · proctored unit test
