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, in the order I teach them. Unit 2 comes first so the algebra and factoring are fresh for everything that follows. Open a unit for its topics, its dates and places to practise.
Unit 2 Equivalent Algebraic Expressions Sep 10 – 23
- 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
10 classes · Quiz Wed, Sep 16 · Test Wed, Sep 23
Practice
- Factoring trinomials with a non-1 leading coefficient by grouping Video · Khan Academy · 5:39
- Polynomial special products: difference of squares Video · Khan Academy · 4:06
- Factoring Quadratics — algebra tiles Activity · Mathigon Polypad
- How To Factor Polynomials The Easy Way! Video · The Organic Chemistry Tutor · 11:54
- Simplifying rational expressions introduction Video · Khan Academy · 7:28
- Simplifying Rational Expressions — original vs simplified graph Activity · Desmos graph
- MCR3U — Multiplying Rational Expressions Video · JensenMath · 13:05
- Multiply & divide rational expressions Activity · Desmos graph
- Adding rational expressions: unlike denominators Video · Khan Academy · 5:10
- Adding and Subtracting Rational Expressions (Desmos Classroom, Julia Anker) Activity · Desmos Classroom
- Operations with Rational Expressions — Add, Subtract, Multiply, Divide Video · MooMooMath and Science · 13:34
Unit 1 Introduction to Functions Sep 24 – Oct 13
- 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
13 classes · Quiz Thu, Oct 1 · Test Tue, Oct 13
Practice
- MCR3U (1.1) — Relations vs Functions Video · AllThingsMathematics · 8:47
- The Vertical Line Test Activity · GeoGebra
- 1.2 Function Notation f(x)= Video · JensenMath · 13:31
- Function Notation Activity · GeoGebra
- Parent Functions Explained Video · Arun's Math Lab · 3:23
- Parent Functions (GeoGebra Book) Activity · GeoGebra
- How to find the domain and the range of a function given its graph Video · Khan Academy · 3:34
- Domain and range of a function given a formula Video · Khan Academy · 8:07
- Domain and Range Activity · GeoGebra
- Domain and Range Word Problems Video · Tom Teaches Math · 12:24
- Domain and Range in Context (Desmos Classroom, Karen McPherson) Activity · Desmos Classroom
- Introduction to function inverses Video · Khan Academy · 9:05
- The Inverse of a Function Activity · GeoGebra
- Shifting functions introduction Video · Khan Academy · 5:38
- Transformations of Functions Discovery Activity · GeoGebra
- Scaling functions introduction Video · Khan Academy · 6:03
- Parent functions and Transformations — y = a f(b(x − c)) + d Activity · Desmos graph
- MCR3U1 1.8 Using Transformations to Graph Functions — Part 1 Video · Tzeng Academy · 10:46
- Transformations af(b(x−c))+d — three applets Activity · GeoGebra
- MCR3U1 1.8 Using Transformations to Graph Functions — Part 2 Video · Tzeng Academy · 7:05
- Marbleslides: Parabolas Activity · Desmos Classroom
- MCR3U — Unit 1 Review Video · Jonathan Baker · 14:10
Unit 3 Quadratic Functions Oct 14 – Nov 5
- 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
17 classes · Quiz Fri, Oct 23 · Test Wed, Nov 4
Unit 4 Exponential Functions Nov 6 – 18
- Integer and rational exponents
- Simplifying algebraic expressions involving exponents
- Properties and transformations of exponential functions
- Solving exponential equations
- Applications: growth, decay, and compound change
9 classes · Quiz Wed, Nov 11 · Test Wed, Nov 18
Unit 5 Trigonometric Ratios Nov 19 – Dec 14
- 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
17 classes · Quiz Tue, Dec 1 · Test Mon, Dec 14
Unit 6 Sinusoidal Functions Dec 15 – Jan 8
- 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
9 classes · Quiz Tue, Jan 5 · Test Fri, Jan 8
Unit 7 Discrete Functions — Sequences and Series Jan 11 – 19
- Arithmetic and geometric sequences
- Arithmetic and geometric series
- Pascal’s triangle and binomial expansions
7 classes · Test Tue, Jan 19
Section 2 — Assessment calendar
Every quiz and test date
Six quizzes, seven tests and the final exam, all dated before the first class so studying can be planned ahead.
| Date | Type | Covers |
|---|---|---|
| Wed, Sep 16 | Quiz | Sections 2.1–2.3 |
| Wed, Sep 23 | Test | Unit 2 · Equivalent Algebraic Expressions |
| Thu, Oct 1 | Quiz | Sections 1.1–1.4 (approx. 45 min) |
| Tue, Oct 13 | Test | Unit 1 · Introduction to Functions |
| Fri, Oct 23 | Quiz | Sections 3.1–3.4 |
| Wed, Nov 4 | Test | Unit 3 · Quadratic Functions |
| Wed, Nov 11 | Quiz | Sections 4.2–4.4 (exponent laws) |
| Wed, Nov 18 | Test | Unit 4 · Exponential Functions |
| Tue, Dec 1 | Quiz | Sections 5.1–5.4 |
| Mon, Dec 14 | Test | Unit 5 · Trigonometric Ratios |
| Tue, Jan 5 | Quiz | Sections 6.1–6.5 |
| Fri, Jan 8 | Test | Unit 6 · Sinusoidal Functions |
| Tue, Jan 19 | Test | Unit 7 · Discrete Functions (Sequences and Series) |
| Thu, Jan 28 | Exam | Final written examination · the whole course |
Section 3 — 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.
Every quiz and test is marked against the four categories of the Ontario achievement chart — Knowledge and Understanding, Thinking, Communication, and Application — and reported as a percentage and an achievement level. Part marks are given for the steps a student gets right, so a paper shows what is already secure, not only what is missing.
Attendance and participation
This part of the mark reflects being in class and taking part. Excused absences — illness, unavoidable circumstances such as bad weather, and approved cultural or holy days — do not reduce it.
| Level | Classes missed without an excuse |
|---|---|
| Level 4 | About 2 or fewer in the semester, and consistently takes part |
| Level 3 | About 2.5 to 4.5 classes, and generally takes part |
| Level 2 | About 5 to 7 classes, and occasionally takes part |
| Level 1 | About 7.5 to 9 classes, and infrequently takes part |
Section 4 — 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 5 — 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 the first unit — the same principle as the get-to-know-you questionnaire, applied to what the class can already do algebraically.
Alina Yang, OCT