OntarioGrade 11
ON Grade 11 Functions (MCR3U) Curriculum
Video lessons and practice for every Grade 11 Functions topic. Aligned to what Ontario schools teach in MCR3U, University Preparation.
ON Grade 11 Functions MCR3U Curriculum | StudyPugHelp
OE_ID | Expectations | StudyPug Topic |
|---|---|---|
ON.OE.11F.A1.1 | 11F.A1.1: 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 (i.e., tables of values, mapping diagrams, graphs, function machines, equations) and strategies (e.g., identifying a one-to-one or many-to-one mapping; using the vertical-line test) |
ON.OE.11F.A1.2 | 11F.A1.2: Represent linear and quadratic functions using function notation, given their equations, tables of values, or graphs, and substitute into and evaluate functions |
ON.OE.11F.A1.3 | 11F.A1.3: Explain the meanings of the terms domain and range, through investigation using numeric, graphical, and algebraic representations of the functions f(x) = x, f(x) = x^2, f(x) = ?x, and f(x) = 1/x; describe the domain and range of a function appropriately; and explain any restrictions on the domain and range in contexts arising from real-world applications |
ON.OE.11F.A1.4 | 11F.A1.4: Relate the process of determining the inverse of a function to their understanding of reverse processes |
ON.OE.11F.A1.5 | 11F.A1.5: Determine the numeric or graphical representation of the inverse of a linear or quadratic function, given the numeric, graphical, or algebraic representation of the function, and make connections between the graph of a function and the graph of its inverse |
ON.OE.11F.A1.6 | 11F.A1.6: Determine the relationship between the domain and range of a function and the domain and range of the inverse relation, and determine whether or not the inverse relation is a function |
ON.OE.11F.A1.8 | 11F.A1.8: Determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y = af(k(x ? d)) + c, and describe these roles in terms of transformations on the graphs of f(x) = x, f(x) = x^2, f(x) = ?x, and f(x) = 1/x |
ON.OE.11F.A1.9 | 11F.A1.9: Sketch graphs of y = af(k(x ? d)) + c by applying one or more transformations to the graphs of f(x) = x, f(x) = x^2, f(x) = ?x, and f(x) = 1/x, and state the domain and range of the transformed functions |
ON.OE.11F.A2.1 | 11F.A2.1: Determine the number of zeros of a quadratic function, using a variety of strategies |
ON.OE.11F.A2.2 | 11F.A2.2: Determine the maximum or minimum value of a quadratic function whose equation is given in the form f(x) = ax^2 + bx + c, using an algebraic method |
ON.OE.11F.A2.3 | 11F.A2.3: Solve problems involving quadratic functions arising from real-world applications and represented using function notation |
ON.OE.11F.A2.4 | 11F.A2.4: Determine, through investigation, the transformational relationship among the family of quadratic functions that have the same zeros, and determine the algebraic representation of a quadratic function, given the real roots of the corresponding quadratic equation and a point on the function |
ON.OE.11F.A2.5 | 11F.A2.5: Solve problems involving the intersection of a linear function and a quadratic function graphically and algebraically |
ON.OE.11F.A3.1 | 11F.A3.1: Simplify polynomial expressions by adding, subtracting, and multiplying |
ON.OE.11F.A3.2 | 11F.A3.2: Verify, through investigation with and without technology, that ?ab = ?a ? ?b, a ? 0, b ? 0, and use this relationship to simplify radicals and radical expressions obtained by adding, subtracting, and multiplying |
ON.OE.11F.A3.3 | 11F.A3.3: Simplify rational expressions by adding, subtracting, multiplying, and dividing, and state the restrictions on the variable values |
ON.OE.11F.B1.1 | 11F.B1.1: Graph, with and without technology, an exponential relation, given its equation in the form y = a^x (a > 0, a ? 1), define this relation as the function f(x) = a^x, and explain why it is a function |
ON.OE.11F.B1.2 | 11F.B1.2: Determine, through investigation using a variety of tools and strategies, the value of a power with a rational exponent |
ON.OE.11F.B1.3 | 11F.B1.3: Simplify algebraic expressions containing integer and rational exponents, and evaluate numeric expressions containing integer and rational exponents and rational bases |
ON.OE.11F.B2.2 | 11F.B2.2: Determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y = af(k(x ? d)) + c, and describe these roles in terms of transformations on the graph of f(x) = a^x (a > 0, a ? 1) |
ON.OE.11F.B2.4 | 11F.B2.4: 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.11F.B2.5 | 11F.B2.5: Represent an exponential function with an equation, given its graph or its properties |
ON.OE.11F.B3.2 | 11F.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.11F.C1.1 | 11F.C1.1: Make connections between sequences and discrete functions, represent sequences using function notation, and distinguish between a discrete function and a continuous function |
ON.OE.11F.C1.5 | 11F.C1.5: Determine, through investigation, recursive patterns in the Fibonacci sequence, in related sequences, and in Pascal's triangle, and represent the patterns in a variety of ways |
ON.OE.11F.C1.6 | 11F.C1.6: Determine, through investigation, and describe the relationship between Pascal's triangle and the expansion of binomials, and apply the relationship to expand binomials raised to whole-number exponents |
ON.OE.11F.C2.1 | 11F.C2.1: Identify sequences as arithmetic, geometric, or neither, given a numeric or algebraic representation |
ON.OE.11F.C2.3 | 11F.C2.3: Determine the formula for the sum of an arithmetic or geometric series, through investigation using a variety of tools and strategies, and apply the formula to calculate the sum of a given number of consecutive terms |
ON.OE.11F.C3.1 | 11F.C3.1: Make and describe connections between simple interest, arithmetic sequences, and linear growth, through investigation with technology |
ON.OE.11F.C3.2 | 11F.C3.2: Make and describe connections between compound interest, geometric sequences, and exponential growth, through investigation with technology |
ON.OE.11F.C3.5 | 11F.C3.5: Explain the meaning of the term annuity, and determine the relationships between ordinary simple annuities, geometric series, and exponential growth, through investigation with technology |
ON.OE.11F.D1.1 | 11F.D1.1: Determine the exact values of the sine, cosine, and tangent of the special angles: 0?, 30?, 45?, 60?, and 90? |
ON.OE.11F.D1.3 | 11F.D1.3: Determine the measures of two angles from 0? to 360? for which the value of a given trigonometric ratio is the same |
ON.OE.11F.D1.4 | 11F.D1.4: Define the secant, cosecant, and cotangent ratios for angles in a right triangle in terms of the sides of the triangle, and relate these ratios to the cosine, sine, and tangent ratios |
ON.OE.11F.D1.5 | 11F.D1.5: Prove simple trigonometric identities, using the Pythagorean identity sin^2 x + cos^2 x = 1; the reciprocal identities secx = 1/cosx, cscx = 1/sinx, and cotx = 1/tanx; the quotient identity tanx = sinx/cosx; and the Pythagorean identities 1 + tan^2 x = sec^2 x and 1 + cot^2 x = csc^2 x |
ON.OE.11F.D1.6 | 11F.D1.6: Pose problems involving right triangles and oblique triangles in two-dimensional settings, and solve these and other such problems using the primary trigonometric ratios, the cosine law, and the sine law (including the ambiguous case) |
ON.OE.11F.D2.1 | 11F.D2.1: Describe key properties of periodic functions arising from real-world applications, given a numeric or graphical representation |
ON.OE.11F.D2.5 | 11F.D2.5: Determine, through investigation using technology, the roles of the parameters a, k, d, and c in functions of the form y = af(k(x ? d)) + c, where f(x) = sinx or f(x) = cosx with angles expressed in degrees, and describe these roles in terms of transformations on the graphs of f(x) = sinx and f(x) = cosx |
ON.OE.11F.D2.8 | 11F.D2.8: Represent a sinusoidal function with an equation, given its graph or its properties |
ON.OE.11F.D3.2 | 11F.D3.2: 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 |
Grade 11 Functions (MCR3U) in Ontario
MCR3U is a University Preparation course that builds the mathematical foundation students need for Grade 12 and beyond. The course covers five main areas: characteristics of functions, exponential functions, discrete functions (sequences and series), financial applications, and trigonometric functions. Each strand develops new skills while connecting to concepts from Grades 9 and 10.
Functions and Their Properties
Students begin MCR3U by learning what a function is and how to distinguish it from a general relation. Topics include function notation, domain and range, inverse functions, and transformations. Understanding how parameters like a, k, d, and c affect the graph of a function is a core skill that appears throughout the course.
Exponential Functions
The exponential functions strand introduces graphs of the form y = ax, rational exponents, and key properties such as asymptotes and increasing or decreasing intervals. Students also explore real-world applications including population growth and radioactive decay, and learn to represent exponential relationships using equations and graphs.
Sequences, Series, and Financial Applications
Discrete functions connect arithmetic and geometric sequences to linear and exponential growth. Students derive formulas for the general term and the sum of arithmetic and geometric series. Financial applications extend these ideas to simple interest, compound interest using A = P(1 + i)n, and ordinary simple annuities.
- Arithmetic sequences and series
- Geometric sequences and series
- Compound interest and future value
- Present value and annuity calculations
- Pascal's triangle and the binomial expansion
Trigonometric Functions
The trigonometry strand starts with the primary ratios for special angles (0°, 30°, 45°, 60°, 90°) and extends to angles from 0° to 360°. Students prove trigonometric identities, apply the sine law and cosine law to two- and three-dimensional problems, and graph sinusoidal functions of the form f(x) = a sin(k(x − d)) + c. Real-world periodic phenomena such as tides and sound waves are modelled using sinusoidal functions.
How StudyPug Supports MCR3U Students
StudyPug provides video lessons and practice problems for every MCR3U expectation listed in the Ontario curriculum. Students can search by topic, watch a lesson, and immediately try practice problems with worked solutions. This makes it easy to get unstuck on homework or review before a test.