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Grade 11

Master Grade 11 Functions and Applications

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Find the right Ontario Grade 11 course

Grade 11 Functions, University Preparation (MCR3U)

Grade 11 Functions and Applications, University/College Preparation (MCF3M)

Grade 11 Foundations for College Mathematics, College Preparation (MBF3C)

Grade 11 Mathematics for Work and Everyday Life, Workplace Preparation (MEL3E)

Ontario Grade 11 Functions Help: Master MCF3M FastHelp

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ON.OE.11FA.A1.1

11FA.A1.1: 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

ON.OE.11FA.A1.2

11FA.A1.2: Represent situations using quadratic expressions in one variable, and expand and simplify quadratic expressions in one variable

ON.OE.11FA.A1.3

11FA.A1.3: Factor quadratic expressions in one variable, including those for which a ? 1, differences of squares, and perfect square trinomials, by selecting and applying an appropriate strategy

ON.OE.11FA.A1.4

11FA.A1.4: Solve quadratic equations by selecting and applying a factoring strategy

ON.OE.11FA.A1.5

11FA.A1.5: 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

ON.OE.11FA.A1.6

11FA.A1.6: Explore the algebraic development of the quadratic formula, and apply the formula to solve quadratic equations, using technology

ON.OE.11FA.A1.7

11FA.A1.7: 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

ON.OE.11FA.A1.8

11FA.A1.8: Determine the real roots of a variety of quadratic equations, and describe the advantages and disadvantages of each strategy

ON.OE.11FA.A2.1

11FA.A2.1: 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 using a variety of representations and strategies

ON.OE.11FA.A2.2

11FA.A2.2: Substitute into and evaluate linear and quadratic functions represented using function notation, including functions arising from real-world applications

ON.OE.11FA.A2.3

11FA.A2.3: Explain the meanings of the terms domain and range, through investigation using numeric, graphical, and algebraic representations of linear and quadratic functions, and describe the domain and range of a function appropriately

ON.OE.11FA.A2.4

11FA.A2.4: Explain any restrictions on the domain and the range of a quadratic function in contexts arising from real-world applications

ON.OE.11FA.A2.5

11FA.A2.5: 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 transformations on the graph of f(x) = x?

ON.OE.11FA.A2.6

11FA.A2.6: Sketch graphs of g(x) = a(x ? h)? + k by applying one or more transformations to the graph of f(x) = x?

ON.OE.11FA.A2.7

11FA.A2.7: 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

ON.OE.11FA.A2.8

11FA.A2.8: 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

ON.OE.11FA.A2.9

11FA.A2.9: 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

ON.OE.11FA.B1.1

11FA.B1.1: Determine, through investigation using a variety of tools and strategies, the value of a power with a rational exponent

ON.OE.11FA.B1.2

11FA.B1.2: Evaluate, with and without technology, numerical expressions containing integer and rational exponents and rational bases

ON.OE.11FA.B1.3

11FA.B1.3: Graph, with and without technology, an exponential relation, given its equation in the form y = a? (a > 0, a ? 1), define this relation as the function f(x) = a?, and explain why it is a function

ON.OE.11FA.B1.4

11FA.B1.4: Determine, through investigation, and describe key properties relating to domain and range, intercepts, increasing/decreasing intervals, and asymptotes for exponential functions represented in a variety of ways

ON.OE.11FA.B1.5

11FA.B1.5: Determine, through investigation using technology, the roles of a, c, and d in functions in the form f(x) = a?, f(x) = a? + c, and f(x) = a(???), and describe these roles in terms of transformations on the graph of f(x) = a? with angles expressed in degrees

ON.OE.11FA.B2.1

11FA.B2.1: Distinguish exponential functions from linear and quadratic functions by making comparisons in a variety of ways

ON.OE.11FA.B2.2

11FA.B2.2: Determine, through investigation using technology, that the equation of a given exponential function can be expressed using different bases, and explain the connections between the equivalent forms in a variety of ways

ON.OE.11FA.B3.1

11FA.B3.1: Collect data that can be modelled as an exponential function, through investigation with and without technology, from primary sources, using a variety of tools, or from secondary sources, and graph the data

ON.OE.11FA.B3.2

11FA.B3.2: Identify exponential functions, including those that arise from real-world applications involving growth and decay, given various representations, and explain any restrictions that the context places on the domain and range

ON.OE.11FA.B3.3

11FA.B3.3: Solve problems using given graphs or equations of exponential functions arising from a variety of real-world applications by interpreting the graphs or by substituting values for the exponent into the equations

ON.OE.11FA.C1.1

11FA.C1.1: Solve problems, including those that arise from real-world applications, by determining the measures of the sides and angles of right triangles using the primary trigonometric ratios

ON.OE.11FA.C1.2

11FA.C1.2: Solve problems involving two right triangles in two dimensions

ON.OE.11FA.C1.3

11FA.C1.3: Verify, through investigation using technology, the sine law and the cosine law

ON.OE.11FA.C1.4

11FA.C1.4: 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

ON.OE.11FA.C1.5

11FA.C1.5: Solve problems that require the use of the sine law or the cosine law in acute triangles, including problems arising from real-world applications

ON.OE.11FA.C2.1

11FA.C2.1: Describe key properties of periodic functions arising from real-world applications, given a numeric or graphical representation

ON.OE.11FA.C2.2

11FA.C2.2: Predict, by extrapolating, the future behaviour of a relationship modelled using a numeric or graphical representation of a periodic function

ON.OE.11FA.C2.3

11FA.C2.3: Make connections between the sine ratio and the sine function by graphing the relationship between angles from 0? to 360? and the corresponding sine ratios, with or without technology, defining this relationship as the function f(x) = sinx, and explaining why the relationship is a function

ON.OE.11FA.C2.4

11FA.C2.4: Sketch the graph of f(x) = sinx for angle measures expressed in degrees, and determine and describe its key properties

ON.OE.11FA.C2.5

11FA.C2.5: 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 corresponding graph

ON.OE.11FA.C2.6

11FA.C2.6: 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), and describe these roles in terms of transformations on the graph of f(x) = sinx with angles expressed in degrees

ON.OE.11FA.C2.7

11FA.C2.7: Sketch graphs of f(x) = a sinx, f(x) = sinx + c, and f(x) = sin(x ? d) by applying transformations to the graph of f(x) = sinx, and state the domain and range of the transformed functions

ON.OE.11FA.C3.1

11FA.C3.1: Collect data that can be modelled as a sine function, through investigation with and without technology, from primary sources, using a variety of tools, or from secondary sources, and graph the data

ON.OE.11FA.C3.2

11FA.C3.2: Identify periodic and sinusoidal functions, including those that arise from real-world applications involving periodic phenomena, given various representations, and explain any restrictions that the context places on the domain and range

ON.OE.11FA.C3.3

11FA.C3.3: 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
Complete Ontario Grade 11 Functions and Applications Coverage

Grade 11 Functions Lessons

60

Video Explanations

322

Practice Problems

570

Ontario Standards

100% Aligned

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Ontario Grade 11 Functions and Applications, University/College Preparation (MCF3M) Math FAQ

We’ve got answers to some popular questions.

What are the main topics covered in Grade 1 math in Alberta?

Grade 1 math in Alberta covers counting to 100, basic addition and subtraction within 20, introduction to fractions (halves), shape recognition, and simple data representation through concrete graphs.

How can I help my child transition from kindergarten to Grade 1 math?

Encourage counting during daily activities, practice simple addition with objects, and explore shapes in your environment. Maintaining a positive attitude towards math is crucial for a smooth transition.

Are there specific math skills my child should master by the end of Grade 1?

By the end of Grade 1, children should confidently count to 100, add and subtract within 20, recognize basic shapes, understand the concept of half, and create simple concrete graphs.

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