Ontario · Grade 11
Functions and Applications, Grade 11 (University/College)
- MCF3M
Ontario’s Grade 11 math course, from Quadratic Functions to Trigonometric Functions.
- Units
- 3
- Lessons
- 11
- Skills
- 53
- Provincial exam
- None
- Official curriculum
- Ontario Ministry of Education
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 22 skills
Quadratic Functions
Solving Quadratic Equations
Posing and solving real-world quadratic problems
I can pose and solve real-world problems involving quadratic relations.
Skill 1.1
Representing situations with quadratic expressions and expanding them
I can represent real-world situations with quadratic expressions and expand and simplify them.
Skill 1.2
Factoring quadratic expressions
I can factor quadratic expressions, including trickier cases.
Skill 1.3
Solving quadratic equations by factoring
I can solve quadratic equations by factoring.
Skill 1.4
Connecting factors to the graph's x-intercepts
I can connect the factors of a quadratic equation to the x-intercepts of its graph.
Skill 1.5
Exploring and applying the quadratic formula
I can explore how the quadratic formula was developed and use it to solve equations.
Skill 1.6
The discriminant and the number of real roots
I can use the discriminant to tell how many real roots a quadratic equation has.
Skill 1.7
Comparing strategies for finding real roots
I can compare the advantages and disadvantages of different strategies for finding real roots.
Skill 1.8
Understanding Functions, Domain, and Range
What makes a relation a function
I can explain what makes a relation a function and tell functions apart from non-functions.
Skill 1.9
Substituting into and evaluating function notation
I can substitute into and evaluate functions written in function notation.
Skill 1.10
What domain and range mean
I can explain what domain and range mean for linear and quadratic functions.
Skill 1.11
Domain and range restrictions in real-world contexts
I can explain how a real-world context restricts a quadratic function's domain and range.
Skill 1.12
Connecting Graphs and Equations of Quadratic Functions
What a, h, and k do to a parabola's graph
I can describe what a, h, and k do to the graph of a quadratic function in vertex form.
Skill 1.13
Sketching quadratic graphs using transformations
I can sketch quadratic graphs by applying transformations to f(x) = x².
Skill 1.14
Converting vertex form to standard form
I can convert a quadratic function from vertex form to standard form.
Skill 1.15
Converting standard form to vertex form by completing the square
I can convert a quadratic function from standard form to vertex form by completing the square.
Skill 1.16
Sketching a quadratic graph from factored form
I can sketch a quadratic graph from factored form using its x-intercepts.
Skill 1.17
Comparing what standard, vertex, and factored form each reveal
I can describe what the standard, vertex, and factored forms of a quadratic function each reveal.
Skill 1.18
Sketching a quadratic graph from standard form and identifying its key features
I can sketch a quadratic graph from standard form and identify its key features.
Skill 1.19
Solving Problems Involving Quadratic Functions
Collecting and graphing data that fits a quadratic model
I can collect and graph data that fits a quadratic model.
Skill 1.20
Finding the quadratic equation that best fits a data set
I can find the quadratic equation that best models a set of data.
Skill 1.21
Solving real-world problems from a quadratic function's equation
I can solve real-world problems using the algebraic representation of a quadratic function.
Skill 1.22
The official wording · 22 outcomes
- 1.1
- pose problems involving quadratic relations arising from real-world applications and represented by tables of values and graphs, and solve these and other such problems
- 1.2
- represent situations (e.g., the area of a picture frame of variable width) using quadratic expressions in one variable, and expand and simplify quadratic expressions in one variable
- 1.3
- factor quadratic expressions in one variable, including those for which a ≠ 1
- 1.4
- solve quadratic equations by selecting and applying a factoring strategy
- 1.5
- determine, through investigation, and describe the connection between the factors used in solving a quadratic equation and the x-intercepts of the graph of the corresponding quadratic relation
- 1.6
- explore the algebraic development of the quadratic formula
- 1.7
- relate the real roots of a quadratic equation to the x-intercepts of the corresponding graph, and connect the number of real roots to the value of the discriminant
- 1.8
- determine the real roots of a variety of quad- ratic equations
- 1.9
- explain the meaning of the term function, and distinguish a function from a relation that is not a function, through investigation of linear and quadratic relations
- 1.10
- substitute into and evaluate linear and quadratic functions represented using function notation
- 1.11
- explain the meanings of the terms domain and range, through investigation using numeric, graphical, and algebraic representations of lin- ear and quadratic functions
- 1.12
- explain any restrictions on the domain and the range of a quadratic function in contexts arising from real-world applications
- 1.13
- determine, through investigation using technology, the roles of a, h, and k in quadratic functions of the form f(x) = a(x – h) + k, and describe these roles in terms of transforma- tions on the graph of f(x) = x
- 1.14
- sketch graphs of g(x) = a(x – h) + k by applying one or more transformations to the graph of f(x) = x
- 1.15
- express the equation of a quadratic function in the standard form f(x) = ax + bx + c, given the vertex form f(x) = a(x – h) + k, and verify, using graphing technology, that these forms are equivalent representations
- 1.16
- express the equation of a quadratic function in the vertex form f(x) = a(x – h) + k, given the standard form f(x) = ax + bx + c, by completing the square
- 1.17
- sketch graphs of quadratic functions in the factored form f(x) = a(x – r)(x – s) by using the x-intercepts to determine the vertex
- 1.18
- describe the information (e.g., maximum, intercepts) that can be obtained by inspecting the standard form f(x) = ax + bx + c, the vertex form f(x) = a(x – h) + k, and the factored form f(x) = a(x – r)(x – s) of a quadratic function
- 1.19
- sketch the graph of a quadratic function whose equation is given in the standard form f(x) = ax + bx + c by using a suitable strategy
- 1.20
- collect data that can be modelled as a quad- ratic function, through investigation with and without technology, from primary sources, using a variety of tools
- 1.21
- determine, through investigation using a vari- ety of strategies
- 1.22
- solve problems arising from real-world appli- cations, given the algebraic representation of a quadratic function
Key ideas
A quadratic relation shows up in situations like the height of a thrown object over time — the graph is a parabola.
A function is a relation where each input has exactly one output.
In f(x) = a(x - h)² + k, h shifts the graph left/right, k shifts it up/down, and a stretches, compresses, or flips it.
Real data — from measurements, experiments, or online sources — can show a quadratic pattern when graphed.
Reading a table of values or a graph carefully lets you answer real questions, like 'how high did it start?' or 'when did it land?'.
Watch out for
- Assuming every real-world relationship is linear instead of checking if it curves like a parabola.
- Thinking any equation with x and y in it must automatically be a function.
- Thinking h shifts the graph in the same direction as its sign (e.g., (x - 3) shifts left instead of right).
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 16 skills
Exponential Functions
Rational Exponents and Evaluating Powers
What a power with a rational exponent means
I can figure out the value of a power with a rational exponent.
Skill 2.1
Evaluating expressions with integer and rational exponents
I can evaluate expressions with integer and rational exponents, with and without technology.
Skill 2.2
Exponent rules for multiplying, dividing, and powers of powers
I can use exponent rules for multiplying, dividing, and finding a power of a power.
Skill 2.3
Connecting Graphs and Equations of Exponential Functions
Graphing an exponential relation and defining it as a function
I can graph an exponential relation and explain why it is a function.
Skill 2.4
Key properties of exponential functions
I can describe the key properties of exponential functions.
Skill 2.5
Telling exponential, linear, and quadratic functions apart
I can tell exponential functions apart from linear and quadratic functions.
Skill 2.6
Solving Problems Involving Exponential Functions
Collecting and graphing data that fits an exponential model
I can collect and graph data that fits an exponential model.
Skill 2.7
Identifying exponential growth and decay in real-world contexts
I can identify exponential growth and decay situations and explain restrictions on domain and range.
Skill 2.8
Solving real-world problems with exponential graphs and equations
I can solve real-world problems using exponential graphs and equations.
Skill 2.9
Solving Financial Problems Involving Exponential Functions
Comparing simple and compound interest
I can compare simple and compound interest for the same investment.
Skill 2.10
Using the compound interest formula to find amount or principal
I can use the compound interest formula to find the amount or the principal.
Skill 2.11
Compound interest is exponential growth
I can show that compound interest is an example of exponential growth.
Skill 2.12
Using the TVM Solver to find interest rate or number of periods
I can use the TVM Solver to find an interest rate or number of compounding periods.
Skill 2.13
What an annuity is
I can explain what an annuity is.
Skill 2.14
How changing an annuity's conditions affects it
I can investigate how changing an annuity's conditions affects its growth.
Skill 2.15
Solving for an annuity's amount, present value, or payment
I can solve for an annuity's amount, present value, or regular payment.
Skill 2.16
The official wording · 16 outcomes
- 2.1
- determine, through investigation using a variety of tools (e.g., calculator, paper and pencil, graphing technology) and strategies
- 2.2
- evaluate, with and without technology, numerical expressions containing integer and rational exponents and rational bases
- 2.3
- determine, through investigation (e.g., by patterning with and without a calculator), the exponent rules for multiplying and dividing numeric expressions involving exponents
- 2.4
- graph, with and without technology, an expo- nential relation, given its equation in the form y = a
- 2.5
- determine, through investigation, and describe key properties relating to domain and range, intercepts, increasing/decreasing intervals, and asymptotes
- 2.6
- distinguish exponential functions from linear and quadratic functions by making comparisons in a variety of ways
- 2.7
- collect data that can be modelled as an exponential function, through investigation with and without technology, from primary sources
- 2.8
- identify exponential functions, including those that arise from real-world applications involving growth and decay
- 2.9
- solve problems using given graphs or equations of exponential functions arising from a variety of real-world applications
- 2.10
- compare, using a table of values and graphs, the simple and compound interest earned for a given principal
- 2.11
- solve problems, using a scientific calculator, that involve the calculation of the amount, A
- 2.12
- determine, through investigation (e.g., using spreadsheets and graphs), that compound interest is an example of exponential growth
- 2.13
- solve problems, using a TVM Solver on a graphing calculator or on a website, that involve the calculation of the interest rate per compounding period
- 2.14
- explain the meaning of the term annuity, through investigation of numeric and graphical representations using technology
- 2.15
- determine, through investigation using technology (e.g., the TVM Solver on a graph- ing calculator, online tools), the effects of changing the conditions
- 2.16
- solve problems, using technology (e.g., scien- tific calculator, spreadsheet, graphing calcula- tor), that involve the amount, the present value, and the regular payment of an ordinary simple annuity
Key ideas
A rational exponent like 1/2 or 1/3 is connected to roots: x^(1/n) means the nth root of x.
An exponential relation has the form y = aˣ, where the variable is the exponent.
Data from experiments (like a cooling liquid) or online sources can reveal an exponential pattern when graphed.
Simple interest earns the same dollar amount every period; compound interest earns interest on the interest already earned, so it grows faster.
Patterning with the exponent laws (like 4^(1/2) × 4^(1/2) = 4^1) helps discover what a fractional exponent must mean.
Watch out for
- Thinking a fractional exponent means dividing the base by the fraction.
- Confusing an exponential function (variable exponent) with a power function (variable base).
- Assuming decay data will hit zero instead of levelling off near a limiting value (like room temperature).
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 15 skills
Trigonometric Functions
Applying the Sine Law and the Cosine Law in Acute Triangles
Solving right-triangle problems with primary trig ratios
I can solve real-world right-triangle problems using the primary trig ratios.
Skill 3.1
Solving problems with two right triangles
I can solve problems involving two right triangles in two dimensions.
Skill 3.2
Verifying the sine law and the cosine law
I can verify the sine law and the cosine law using technology.
Skill 3.3
Choosing between the sine law and the cosine law
I can decide whether to use the sine law or the cosine law and use it to solve acute triangles.
Skill 3.4
Solving real-world problems with the sine or cosine law
I can solve real-world problems using the sine law or the cosine law.
Skill 3.5
Connecting Graphs and Equations of Sine Functions
Key properties of periodic functions
I can describe the key properties of periodic functions from real-world data.
Skill 3.6
Predicting future behaviour of a periodic relationship
I can predict the future behaviour of a periodic relationship by extrapolating.
Skill 3.7
Connecting the sine ratio to the sine function
I can connect the sine ratio to the sine function by graphing angles against their sine ratios.
Skill 3.8
Sketching f(x) = sin x and its key properties
I can sketch f(x) = sin x and describe its key properties.
Skill 3.9
Connecting real-world changes to graph transformations
I can connect changes in a real-world periodic situation to transformations of its graph.
Skill 3.10
What a, c, and d do to the sine function's graph
I can describe what a, c, and d do to the graph of the sine function.
Skill 3.11
Sketching sine function transformations and stating domain/range
I can sketch transformed sine functions and state their domain and range.
Skill 3.12
Solving Problems Involving Sine Functions
Collecting and graphing data that fits a sine model
I can collect and graph data that fits a sine model.
Skill 3.13
Identifying periodic and sinusoidal functions in real-world contexts
I can identify periodic and sinusoidal functions in real-world data and explain restrictions on domain and range.
Skill 3.14
Posing and solving problems with sine functions
I can pose and solve real-world problems involving sine functions.
Skill 3.15
The official wording · 15 outcomes
- 3.1
- solve problems, including those that arise from real-world applications (e.g., surveying, navigation), by determining the measures of the sides and angles of right triangles using the primary trigonometric ratios
- 3.2
- solve problems involving two right triangles in two dimensions
- 3.3
- verify, through investigation using technol- ogy (e.g., dynamic geometry software, spreadsheet), the sine law and the cosine law
- 3.4
- describe conditions that guide when it is appropriate to use the sine law or the cosine law, and use these laws to calculate sides and angles in acute triangles
- 3.5
- solve problems that require the use of the sine law or the cosine law in acute triangles, including problems arising from real-world applications
- 3.6
- describe key properties (e.g., cycle, amplitude, period) of periodic functions arising from real-world applications
- 3.7
- predict, by extrapolating, the future behaviour of a relationship modelled using a numeric or graphical representation of a periodic function
- 3.8
- make connections between the sine ratio and the sine function by graphing the relationship between angles from 0º to 360º and the corresponding sine ratios
- 3.9
- sketch the graph of f(x) = sinx for angle measures expressed in degrees, and determine and describe its key properties
- 3.10
- make connections, through investigation with technology, between changes in a real-world situation that can be modelled using a periodic function and transformations of the correspon- ding graph
- 3.11
- determine, through investigation using technology, the roles of the parameters a, c, and d in functions in the form f(x) = a sinx, f(x) = sinx + c, and f(x) = sin(x – d)
- 3.12
- sketch graphs of f(x) = a sinx, f(x) = sinx + c, and f(x) = sin(x – d) by applying transforma- tions to the graph of f(x) = sinx
- 3.13
- collect data that can be modelled as a sine function (e.g., voltage in an AC circuit, sound waves), through investigation with and without technology, from primary sources
- 3.14
- identify periodic and sinusoidal functions, including those that arise from real-world applications involving periodic phenomena
- 3.15
- pose problems based on applications involving a sine function, and solve these and other such problems by using a given graph or a graph generated with technology from a table of values or from its equation
Key ideas
Sine, cosine, and tangent connect the angles and side lengths of a right triangle.
A periodic function repeats the same pattern over and over — the length of one repeat is its period.
Real periodic phenomena, like AC circuit voltage or sound waves, can be measured and graphed to reveal a sine-shaped pattern.
Choosing the correct ratio depends on which sides and angle are known or wanted.
Amplitude measures how far the function swings above and below its middle value.
Watch out for
- Mixing up which sides are 'opposite' and 'adjacent' relative to the angle being used.
- Confusing amplitude (half the height of one swing) with the full height from max to min.
- Assuming any wavy-looking data must be a perfect sine wave without checking amplitude and period consistency.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Plan the term
Pick your term and the days you study. Each unit gets its share of the weeks and comes back a week later for a review. The last two weeks go over the whole course.
Which course?
Ontario has 4 math courses for Grade 11. Here they are side by side.
- Foundations for College Mathematics, Grade 11 (College)MBF3C4 units · 57 skillsNo provincial examWhat it coversMathematical Models · Personal Finance · Geometry and Trigonometry · Data Management
- Functions and Applications, Grade 11 (University/College)This courseMCF3M3 units · 53 skillsNo provincial examWhat it coversQuadratic Functions · Exponential Functions · Trigonometric Functions
- Functions, Grade 11 (University)MCR3U4 units · 68 skillsNo provincial examWhat it coversCharacteristics of Functions · Exponential Functions · Discrete Functions · Trigonometric Functions
- Mathematics for Work and Everyday Life, Grade 11 (Workplace)MEL3E3 units · 48 skillsNo provincial examWhat it coversEarning and Purchasing · Saving, Investing, and Borrowing · Transportation and Travel
What a university, college or program asks for is theirs to say: check its admission page, and your school’s course guide.
The official curriculum
This page follows Ontario’s own curriculum for Functions and Applications, Grade 11 (University/College).
Textbooks
The textbooks Ontario Ministry of Education lists for Functions and Applications, Grade 11 (University/College):
- McGraw-Hill Ryerson Functions and Applications 11
- Nelson Functions and Applications 11
From the Trillium List, read October 27, 2026. ontario.ca
Strands
| Strand | Outcomes | Taught in |
|---|---|---|
| AQuadratic Functions | Outcomes 22 | Taught in Unit 1 |
| BExponential Functions | Outcomes 16 | Taught in Unit 2 |
| CTrigonometric Functions | Outcomes 15 | Taught in Unit 3 |
Study it in MapleMind
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Course Companion
Your year in one workbook
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Questions about Functions and Applications, Grade 11 (University/College)
What is Functions and Applications, Grade 11 (University/College)?
Ontario’s Grade 11 math course: 3 units and 53 skills, from Quadratic Functions to Trigonometric Functions.
What units are in Functions and Applications, Grade 11 (University/College)?
1. Quadratic Functions, 2. Exponential Functions and 3. Trigonometric Functions.
Is there a provincial exam for Functions and Applications, Grade 11 (University/College)?
No. Ontario gives no provincial exam for Functions and Applications, Grade 11 (University/College).
What textbook does Functions and Applications, Grade 11 (University/College) use?
The textbooks Ontario Ministry of Education lists for Functions and Applications, Grade 11 (University/College): McGraw-Hill Ryerson Functions and Applications 11, McGraw-Hill Ryerson and Nelson Functions and Applications 11, Nelson Education Ltd.
What comes after Functions and Applications, Grade 11 (University/College)?
Advanced Functions, Grade 12 (University), Calculus and Vectors, Grade 12 (University), Mathematics of Data Management, Grade 12 (University), Foundations for College Mathematics, Grade 12 (College), Mathematics for College Technology, Grade 12 (College) and Mathematics for Work and Everyday Life, Grade 12 (Workplace).
Can MapleMind help with Functions and Applications, Grade 11 (University/College)?
Yes. MapleMind teaches every skill of Functions and Applications, Grade 11 (University/College), step by step, with practice and checks, and its tutor answers questions about any of them. It’s free with daily limits, on iPhone, Android and the web.
Get ready for Functions and Applications, Grade 11 (University/College)
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