Ontario · Grade 11
Foundations for College Mathematics, Grade 11 (College)
- MBF3C
Ontario’s Grade 11 math course, from Mathematical Models to Data Management.
- Units
- 4
- Lessons
- 11
- Skills
- 57
- Provincial exam
- None
- Official curriculum
- Ontario Ministry of Education
Unit by unit
Every skill in the course, numbered by unit.
Unit 1 · 19 skills
Mathematical Models
Connecting Graphs and Equations of Quadratic Relations
Building tables of values and graphing quadratic relations
I can build a table of values and graph a real-world quadratic relation.
Skill 1.1
Interpreting meaningful values from a quadratic graph
I can interpret meaningful values from a graph of a real-world quadratic relation.
Skill 1.2
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 relation.
Skill 1.3
Sketching quadratic graphs from vertex form
I can sketch a quadratic graph given its equation in vertex form.
Skill 1.4
Expanding and simplifying quadratic expressions
I can expand and simplify quadratic expressions involving binomials.
Skill 1.5
Converting vertex form to standard form
I can convert a quadratic relation from vertex form to standard form.
Skill 1.6
Factoring trinomials
I can factor trinomials of the form ax² + bx + c.
Skill 1.7
Connecting factors to the graph's x-intercepts
I can connect the factors of a quadratic expression to the graph's x-intercepts.
Skill 1.8
Solving real-world quadratic problems by factoring or graphing
I can solve real-world quadratic problems by factoring or graphing.
Skill 1.9
Understanding Exponents and Exponential Relations
What negative exponents and zero as an exponent mean
I can explain what negative exponents and zero as an exponent mean.
Skill 1.10
Evaluating expressions with integer exponents and rational bases
I can evaluate expressions with integer exponents and rational bases.
Skill 1.11
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 1.12
Graphing simple exponential relations by hand
I can graph simple exponential relations by hand.
Skill 1.13
Connecting numeric, graphical, and algebraic exponential representations
I can connect numeric, graphical, and algebraic representations of an exponential relation.
Skill 1.14
Telling exponential relations apart from linear and quadratic ones
I can tell exponential relations apart from linear and quadratic ones.
Skill 1.15
Solving Problems Involving Exponential Relations
Collecting and graphing data that fits an exponential model
I can collect and graph data that fits an exponential model.
Skill 1.16
Describing characteristics of real-world exponential relations
I can describe characteristics of real-world exponential relations.
Skill 1.17
Posing and solving problems using exponential graphs
I can pose and solve real-world problems using exponential graphs.
Skill 1.18
Solving problems using exponential equations
I can solve real-world problems using exponential equations.
Skill 1.19
The official wording · 19 outcomes
- 1.1
- construct tables of values and graph quadra- tic relations arising from real-world applica- tions
- 1.2
- determine and interpret meaningful values of the variables, given a graph of a quadratic relation arising from a real-world application
- 1.3
- determine, through investigation using technology, the roles of a, h, and k in quadratic relations of the form y = a(x – h) + k
- 1.4
- sketch graphs of quadratic relations repre- sented by the equation y = a(x – h) + k
- 1.5
- expand and simplify quadratic expressions in one variable involving multiplying binomials
- 1.6
- express the equation of a quadratic relation in the standard form y = ax + bx + c, given the vertex form y = a(x – h) + k, and verify, using graphing technology, that these forms are equivalent representations
- 1.7
- factor trinomials of the form ax + bx + c, where a = 1 or where a is the common factor, by various methods
- 1.8
- determine, through investigation, and describe the connection between the factors of a quadratic expression and the x-intercepts of the graph of the corresponding quadratic relation
- 1.9
- solve problems, using an appropriate strategy (i.e., factoring, graphing), given equations of quadratic relations, including those that arise from real-world applications
- 1.10
- determine, through investigation using a variety of tools and strategies (e.g., graphing with technology; looking for patterns in tables of values), and describe the meaning of nega- tive exponents and of zero as an exponent
- 1.11
- evaluate, with and without technology, numeric expressions containing integer exponents and rational bases
- 1.12
- determine, through investigation (e.g., by patterning with and without a calculator), the exponent rules for multiplying and dividing numerical expressions involving exponents
- 1.13
- graph simple exponential relations, using paper and pencil, given their equations
- 1.14
- make and describe connections between representations of an exponential relation
- 1.15
- distinguish exponential relations from linear and quadratic relations by making compar- isons in a variety of ways
- 1.16
- collect data that can be modelled as an exponential relation, through investigation with and without technology, from primary sources
- 1.17
- describe some characteristics of exponential relations arising from real-world applications
- 1.18
- pose problems involving exponential relations arising from a variety of real-world applica- tions
- 1.19
- solve problems using given equations of exponential relations arising from a variety of real-world applications
Key ideas
A quadratic relation shows up in situations like a dropped ball's height or a cube's changing surface area.
A negative exponent means taking the reciprocal of the positive-exponent power.
Data from experiments or online sources can reveal an exponential pattern when graphed.
Building a table of values first, then plotting the points, reveals the parabola's shape.
Any nonzero number raised to the exponent zero equals 1 — patterns in a table of values reveal why.
Watch out for
- Connecting the plotted points with straight line segments instead of a smooth curve.
- Thinking a negative exponent makes the result negative.
- Assuming any increasing set of data points must be exponential without checking the pattern.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 2 · 14 skills
Personal Finance
Solving Problems Involving Compound Interest
Compound interest as repeated simple interest
I can investigate compound interest using repeated simple interest calculations.
Skill 2.1
The link between compound interest and exponential growth
I can describe the relationship between compound interest and exponential growth.
Skill 2.2
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 2.3
Calculating total interest earned or paid
I can calculate the total interest earned or paid.
Skill 2.4
Using the TVM Solver to find interest rate or number of periods
I can use a TVM Solver to find an interest rate or number of compounding periods.
Skill 2.5
How changing time, rate, or period affects an investment or loan
I can investigate how changing the time, rate, or period affects an investment or loan.
Skill 2.6
Comparing Financial Services
Comparing savings alternatives and their costs
I can compare savings alternatives and their costs.
Skill 2.7
Comparing investment alternatives by risk and return
I can compare investment alternatives by risk and rate of return.
Skill 2.8
Comparing costs and incentives of credit and debit cards
I can compare the costs and incentives of credit and debit cards.
Skill 2.9
Credit card interest rates and the effect of delayed payments
I can investigate credit card interest rates and the effect of delayed payments.
Skill 2.10
Applying the compound interest formula to purchases on credit
I can apply the compound interest formula to find the cost of a purchase on credit.
Skill 2.11
Owning and Operating a Vehicle
Comparing vehicle insurance costs
I can compare vehicle insurance costs across drivers and vehicles.
Skill 2.12
Comparing the costs of buying versus leasing a vehicle
I can compare the costs of buying versus leasing a vehicle.
Skill 2.13
Solving problems with fixed and variable vehicle costs
I can solve problems involving the fixed and variable costs of owning a vehicle.
Skill 2.14
The official wording · 14 outcomes
- 2.1
- determine, through investigation using technol- ogy, the compound interest for a given invest- ment, using repeated calculations of simple interest
- 2.2
- determine, through investigation (e.g., using spreadsheets and graphs), and describe the relationship between compound interest and exponential growth
- 2.3
- solve problems, using a scientific calculator, that involve the calculation of the amount, A
- 2.4
- calculate the total interest earned on an invest- ment or paid on a loan by determining the difference between the amount and the princi- pal
- 2.5
- 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, i, or the number of com- pounding periods, n
- 2.6
- determine, through investigation using technology (e.g., a TVM Solver on a graphing calculator or on a website), the effect on the future value of a compound interest invest- ment or loan of changing the total length of time, the interest rate, or the compounding period
- 2.7
- gather, interpret, and compare information about the various savings alternatives com- monly available from financial institutions
- 2.8
- gather and interpret information about invest- ment alternatives
- 2.9
- gather, interpret, and compare information about the costs (e.g., user fees, annual fees, service charges, interest charges on overdue balances) and incentives
- 2.10
- gather, interpret, and compare information about current credit card interest rates and regulations, and determine, through investi- gation using technology, the effects of delayed payments on a credit card balance
- 2.11
- solve problems involving applications of the compound interest formula to determine the cost of making a purchase on credit
- 2.12
- gather and interpret information about the procedures and costs involved in insuring a vehicle (e.g., car, motorcycle, snowmobile) and the factors affecting insurance rates
- 2.13
- gather, interpret, and compare information about the procedures and costs (e.g., monthly payments, insurance, depreciation, mainte- nance, miscellaneous expenses) involved in buying or leasing a new vehicle or buying a used vehicle
- 2.14
- solve problems, using technology (e.g., calcu- lator, spreadsheet), that involve the fixed costs (e.g., licence fee, insurance) and variable costs (e.g., maintenance, fuel) of owning and oper- ating a vehicle
Key ideas
Compound interest is calculated by repeatedly applying simple interest to a growing balance, period after period.
Financial institutions offer different savings alternatives, like chequing accounts and term investments, each with its own fees and rules.
Insurance rates depend on factors like the driver's age, gender, and driving record, and the vehicle's model and use.
Compound interest earns more over time than simple interest on the same principal and rate.
Some strategies, like maintaining a minimum balance, can reduce or eliminate certain fees.
Watch out for
- Recalculating each year's interest based on the original principal instead of the growing balance.
- Assuming all savings accounts have the same fees and rules.
- Assuming insurance costs are the same for every driver regardless of their profile.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 3 · 8 skills
Geometry and Trigonometry
Representing Two-Dimensional Shapes and Three-Dimensional Figures
Recognizing real-world applications of geometric shapes
I can recognize and explain real-world applications of geometric shapes.
Skill 3.1
Representing 3D objects with drawing tools and software
I can represent three-dimensional objects using concrete materials and drawing software.
Skill 3.2
Creating nets, plans, and patterns from physical models
I can create nets, plans, and patterns from physical models.
Skill 3.3
Solving design problems with given constraints
I can solve design problems that satisfy given constraints.
Skill 3.4
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 3.5
Verifying the sine law and the cosine law
I can verify the sine law and the cosine law using technology.
Skill 3.6
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 3.7
Solving real-world triangle problems with metric and imperial measurements
I can solve real-world triangle problems that mix metric and imperial measurements.
Skill 3.8
The official wording · 8 outcomes
- 3.1
- recognize and describe real-world applications of geometric shapes and figures, through investigation
- 3.2
- represent three-dimensional objects, using concrete materials and design or drawing software, in a variety of ways
- 3.3
- create nets, plans, and patterns from physical models arising from a variety of real-world applications
- 3.4
- solve design problems that satisfy given con- straints (e.g., design a rectangular berm that would contain all the oil that could leak from a cylindrical storage tank of a given height and radius), using physical models
- 3.5
- 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
- 3.6
- verify, through investigation using technology (e.g., dynamic geometry software, spread- sheet), the sine law and the cosine law
- 3.7
- 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
- 3.8
- solve problems that arise from real-world applications involving metric and imperial measurements and that require the use of the sine law or the cosine law in acute triangles
Key ideas
Geometric shapes are chosen for real-world objects for practical reasons, like preventing a sewer cover from falling into the sewer.
Sine, cosine, and tangent connect the angles and side lengths of a right triangle.
Investigating shapes in product design, architecture, and fashion reveals these hidden reasons.
Choosing the correct ratio depends on which sides and angle are known or wanted.
3D objects can be represented in different ways: orthographic projections (front, side, top views), isometric drawings, or scale models.
Watch out for
- Assuming a shape was chosen only for looks, without a practical, geometric reason.
- Mixing up which sides are 'opposite' and 'adjacent' relative to the angle being used.
- Not connecting a shape's mathematical properties (like constant width for a circle) to its real-world use.
Every skill’s key ideas, worked examples and checks are in MapleMind.Practise this unit
Unit 4 · 16 skills
Data Management
Working With One-Variable Data
Designing questionnaires and experiments for one-variable data
I can design questionnaires or experiments to gather one-variable data.
Skill 4.1
Collecting one-variable data from secondary sources
I can collect and organize one-variable data from secondary sources.
Skill 4.2
Population versus sample and why sampling is necessary
I can explain the difference between population and sample and why sampling is necessary.
Skill 4.3
Sampling techniques and collecting primary data
I can describe sampling techniques and collect one-variable data from primary sources.
Skill 4.4
Types of one-variable data and graphical forms
I can identify types of one-variable data and represent it in appropriate graphs.
Skill 4.5
Properties of common data distributions
I can identify and describe properties of common data distributions.
Skill 4.6
Measures of Central Tendency and Spread
Calculating measures of central tendency and spread
I can calculate measures of central tendency and spread.
Skill 4.7
Choosing the appropriate measure of central tendency or spread
I can explain when to use each measure of central tendency and spread.
Skill 4.8
Comparing two or more data sets using central tendency and spread
I can compare two or more data sets using central tendency and spread.
Skill 4.9
Solving problems by interpreting and analysing secondary-source data
I can solve problems by interpreting and analysing one-variable data collected from secondary sources.
Skill 4.10
Applying Probability
Identifying probability in the media and its representations
I can identify examples of probability in the media and how it's represented.
Skill 4.11
Determining theoretical probability
I can determine the theoretical probability of an event.
Skill 4.12
Determining experimental probability
I can perform a probability experiment and determine experimental probability.
Skill 4.13
Comparing theoretical and experimental probability
I can compare theoretical and experimental probability and explain any difference.
Skill 4.14
How experimental probability approaches theoretical probability with more trials
I can show that experimental probability approaches theoretical probability as trials increase.
Skill 4.15
Connecting probability and statistics in the media
I can connect probability and statistics as they're used in the media.
Skill 4.16
The official wording · 16 outcomes
- 4.1
- identify situations involving one-variable data (i.e., data about the frequency of a given occurrence), and design questionnaires
- 4.2
- collect one-variable data from secondary sources (e.g., Internet databases), and organ- ize and store the data using a variety of tools
- 4.3
- explain the distinction between the terms population and sample, describe the charac- teristics of a good sample, and explain why sampling is necessary
- 4.4
- describe and compare sampling techniques (e.g., random, stratified, clustered, conven- ience, voluntary); collect one-variable data from primary sources
- 4.5
- identify different types of one-variable data (i.e., categorical, discrete, continuous), and represent the data, with and without techno- logy, in appropriate graphical forms
- 4.6
- identify and describe properties associated with common distributions of data
- 4.7
- calculate, using formulas and/or technology (e.g., dynamic statistical software, spread- sheet, graphing calculator), and interpret measures of central tendency
- 4.8
- explain the appropriate use of measures of central tendency (i.e., mean, median, mode) and measures of spread (i.e., range, standard deviation)
- 4.9
- compare two or more sets of one-variable data, using measures of central tendency and measures of spread
- 4.10
- solve problems by interpreting and analysing one-variable data collected from secondary sources
- 4.11
- identify examples of the use of probability in the media and various ways in which proba- bility is represented
- 4.12
- determine the theoretical probability of an event (i.e., the ratio of the number of favourable outcomes to the total number of possible outcomes, where all outcomes are equally likely)
- 4.13
- perform a probability experiment (e.g., toss- ing a coin several times), represent the results using a frequency distribution, and use the distribution to determine the experimental probability of an event
- 4.14
- compare, through investigation, the theoreti- cal probability of an event with the experi- mental probability, and explain why they might differ
- 4.15
- determine, through investigation using class- generated data and technology-based simula- tion models
- 4.16
- interpret information involving the use of probability and statistics in the media, and make connections between probability and statistics
Key ideas
One-variable data is data about the frequency of a single occurrence, like a favourite colour or a count.
Mean, median, and mode are measures of central tendency — they describe a 'typical' value.
Probability appears often in the media, like weather forecasts or sports statistics.
A well-designed questionnaire or experiment considers ethics, privacy, honesty, and possible bias.
Range and standard deviation are measures of spread — they describe how varied the data is.
Watch out for
- Writing a question that leads people toward a particular answer.
- Confusing mean (average) with median (middle value) when calculating by hand.
- Not recognizing a statement like '70% chance of rain' as a probability statement.
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)This courseMBF3C4 units · 57 skillsNo provincial examWhat it coversMathematical Models · Personal Finance · Geometry and Trigonometry · Data Management
- Functions and Applications, Grade 11 (University/College)MCF3M3 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 Foundations for College Mathematics, Grade 11 (College).
Textbooks
The textbooks Ontario Ministry of Education lists for Foundations for College Mathematics, Grade 11 (College):
- Pearson Math 11
- Foundations of College Mathematics 11
From the Trillium List, read October 27, 2026. ontario.ca
Strands
| Strand | Outcomes | Taught in |
|---|---|---|
| AMathematical Models | Outcomes 19 | Taught in Unit 1 |
| BPersonal Finance | Outcomes 14 | Taught in Unit 2 |
| CGeometry and Trigonometry | Outcomes 8 | Taught in Unit 3 |
| DData Management | Outcomes 16 | Taught in Unit 4 |
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Questions about Foundations for College Mathematics, Grade 11 (College)
What is Foundations for College Mathematics, Grade 11 (College)?
Ontario’s Grade 11 math course: 4 units and 57 skills, from Mathematical Models to Data Management.
What units are in Foundations for College Mathematics, Grade 11 (College)?
1. Mathematical Models, 2. Personal Finance, 3. Geometry and Trigonometry and 4. Data Management.
Is there a provincial exam for Foundations for College Mathematics, Grade 11 (College)?
No. Ontario gives no provincial exam for Foundations for College Mathematics, Grade 11 (College).
What textbook does Foundations for College Mathematics, Grade 11 (College) use?
The textbooks Ontario Ministry of Education lists for Foundations for College Mathematics, Grade 11 (College): Pearson Math 11, Pearson Education Canada and Foundations of College Mathematics 11, McGraw-Hill Ryerson.
What comes after Foundations for College Mathematics, Grade 11 (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 Foundations for College Mathematics, Grade 11 (College)?
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