MCR3U — Functions, Grade 11, University Preparation
The Grade 11 university-preparation functions course: the year students stop working with one equation at a time and start working with the object that produces them. Planned end to end before the first class, so every unit knows how many days it has.
| Course code | MCR3U |
|---|---|
| Course name | Functions, Grade 11, University Preparation |
| Credit value | 1.0 |
| Prerequisite | MPM2D — Principles of Mathematics, Grade 10, Academic |
| Instructor | Alina Yang, OCT |
| School | Lester B. Pearson C.I. · Toronto District School Board |
| School year | 2026–2027 · Semester 1 |
| Instructional days | 87 · September 8, 2026 to January 22, 2027 |
| Textbook | Nelson Functions 11 |
| Curriculum | The Ontario Curriculum, Grades 11 and 12: Mathematics |
Section 1 — Units of study
What the course covers
Seven units across the semester. Each one is sequenced before the course begins, so it knows how many days it has and what it has to leave behind.
Unit 1 Introduction to Functions
- Relations and functions; function notation
- Properties of the parent functions
- Domain and range, including in context
- The inverse function and its properties
- Translations, stretches, compressions, and reflections
- Combined transformations: y = af[k(x − d)] + c
Unit 2 Equivalent Algebraic Expressions
- Adding, subtracting, and multiplying polynomials
- Factoring: common factors, grouping, simple and complex trinomials, special products
- Simplifying rational expressions
- Multiplying, dividing, adding, and subtracting rational expressions
Unit 3 Quadratic Functions
- Properties of quadratic functions; completing the square
- Maximum and minimum problems, including projectile motion
- The inverse of a quadratic function
- Operations with radicals; rationalizing
- Solving quadratic equations; the discriminant and the nature of the roots
- Families of quadratic functions; linear–quadratic systems
Unit 4 Exponential Functions
- Integer and rational exponents
- Simplifying algebraic expressions involving exponents
- Properties and transformations of exponential functions
- Solving exponential equations
- Applications: growth, decay, and compound change
Unit 5 Trigonometric Ratios
- Trigonometric ratios of acute angles; special angles
- Ratios for any angle, including angles greater than 90°
- Exact values without a calculator
- Trigonometric identities
- The sine law and the ambiguous case; the cosine law
- Three-dimensional problems
Unit 6 Sinusoidal Functions
- Periodic functions and sinusoidal behaviour
- Interpreting sinusoidal functions
- Transformations of sinusoidal functions
- Building a model from a graph
- Problem solving with sinusoidal models: Ferris wheels, pendulums, tides
Unit 7 Discrete Functions — Sequences and Series
- Arithmetic and geometric sequences
- Arithmetic and geometric series
- Pascal’s triangle and binomial expansions
Section 2 — Evaluation
How the mark is earned
| Component | Share | Weight |
|---|---|---|
| Tests — seven unit tests Term work · 65% | 45% | |
| Quizzes — six mid-unit quizzes Term work · 65% | 20% | |
| Final written examination Final evaluation · 25% | 25% | |
| Attendance and participation Reported on its own | 10% |
Term work 65% · final evaluation 25% · attendance and participation 10%. Taken from the MCR3U course outline for 2026-2027, following the Growing Success update of September 2026 for Grades 11 and 12. The written examination is required by the Ministry for mathematics.
Section 3 — Shape of the semester
Where the days go
87 instructional days, allocated before the first class rather than discovered in December.
| Day type | Share | Days |
|---|---|---|
| Teaching | 59 | |
| Review | 13 | |
| Tests | 7 | |
| Quizzes | 6 | |
| Buffer | 2 | |
| Total | 87 |
Section 4 — Planning notes
Why it is built this way
Four decisions in the plan that are choices rather than defaults.
Every long unit gets a quiz before its test
Six of the seven units carry a mid-unit quiz, so a student who has lost the thread finds out with a week still left to fix it. Unit 7 is short and carries a test only.
Two days are held back on purpose
One after the Unit 3 test, one on the last day before Winter Break — days that assemblies, weather, and re-teaching reliably take. Unspent, they run as work periods.
The exam review package goes out early
Handed out on the Unit 7 test day rather than in the last week, so students who want to start early can, and three review days at the end are review rather than first contact.
The plan opens with a diagnostic, not with content
Two days on prerequisite skills before Unit 1 — the same principle as the get-to-know-you questionnaire, applied to what the class can already do algebraically.
Alina Yang, OCT