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Math
Grade 11 Math Courses - Ontario Curriculum
Discover Ontario's Grade 11 Math options, including Functions, Applications, and College Preparation. Explore course pathways and prepare for advanced studies in mathematics.
Ontario Grade 11 Math Curriculum - Functions and Applications Topics
OE_ID | Expectations | StudyPug Topic |
|---|---|---|
A. Characteristics of Functions : 1. Representing Functions | ||
OE.11F.A1.1 | 1.1: 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) |
OE.11F.A1.2 | 1.2: Represent linear and quadratic functions using function notation, given their equations, tables of values, or graphs, and substitute into and evaluate functions |
OE.11F.A1.3 | 1.3: 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 |
OE.11F.A1.4 | 1.4: Relate the process of determining the inverse of a function to their understanding of reverse processes |
OE.11F.A1.5 | 1.5: 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 |
OE.11F.A1.6 | 1.6: 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 |
OE.11F.A1.8 | 1.8: 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 |
OE.11F.A1.9 | 1.9: 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 |
A. Characteristics of Functions : 2. Solving Problems Involving Quadratic Functions | ||
OE.11F.A2.1 | 2.1: Determine the number of zeros of a quadratic function, using a variety of strategies |
OE.11F.A2.2 | 2.2: 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 |
OE.11F.A2.3 | 2.3: Solve problems involving quadratic functions arising from real-world applications and represented using function notation |
OE.11F.A2.4 | 2.4: 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 |
OE.11F.A2.5 | 2.5: Solve problems involving the intersection of a linear function and a quadratic function graphically and algebraically |
A. Characteristics of Functions : 3. Determining Equivalent Algebraic Expressions | ||
OE.11F.A3.1 | 3.1: Simplify polynomial expressions by adding, subtracting, and multiplying |
OE.11F.A3.2 | 3.2: 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 |
OE.11F.A3.3 | 3.3: Simplify rational expressions by adding, subtracting, multiplying, and dividing, and state the restrictions on the variable values |
B. Exponential Functions : 1. Representing Exponential Functions | ||
OE.11F.B1.1 | 1.1: 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 |
OE.11F.B1.2 | 1.2: Determine, through investigation using a variety of tools and strategies, the value of a power with a rational exponent |
OE.11F.B1.3 | 1.3: Simplify algebraic expressions containing integer and rational exponents, and evaluate numeric expressions containing integer and rational exponents and rational bases |
OE.11F.B2.2 | 2.2: 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) |
OE.11F.B2.4 | 2.4: 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 |
OE.11F.B2.5 | 2.5: Represent an exponential function with an equation, given its graph or its properties |
OE.11F.B3.2 | 3.2: 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 |
C. Discrete Functions : 1. Representing Sequences | ||
OE.11F.C1.1 | 1.1: Make connections between sequences and discrete functions, represent sequences using function notation, and distinguish between a discrete function and a continuous function |
OE.11F.C1.5 | 1.5: 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 |
OE.11F.C1.6 | 1.6: 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 |
C. Discrete Functions : 2. Investigating Arithmetic and Geometric Sequences and Series | ||
OE.11F.C2.1 | 2.1: Identify sequences as arithmetic, geometric, or neither, given a numeric or algebraic representation |
OE.11F.C2.3 | 2.3: 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 |
C. Discrete Functions : 3. Solving Problems Involving Financial Applications | ||
OE.11F.C3.1 | 3.1: Make and describe connections between simple interest, arithmetic sequences, and linear growth, through investigation with technology |
OE.11F.C3.2 | 3.2: Make and describe connections between compound interest, geometric sequences, and exponential growth, through investigation with technology |
OE.11F.C3.5 | 3.5: Explain the meaning of the term annuity, and determine the relationships between ordinary simple annuities, geometric series, and exponential growth, through investigation with technology |
D. Trigonometric Functions : 1. Determining and Applying Trigonometric Ratios | ||
OE.11F.D1.1 | 1.1: Determine the exact values of the sine, cosine, and tangent of the special angles: 0?, 30?, 45?, 60?, and 90? |
OE.11F.D1.3 | 1.3: Determine the measures of two angles from 0? to 360? for which the value of a given trigonometric ratio is the same |
OE.11F.D1.4 | 1.4: 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 |
OE.11F.D1.5 | 1.5: 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 |
OE.11F.D1.6 | 1.6: 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) |
D. Trigonometric Functions : 2. Connecting Graphs and Equations of Sinusoidal Functions | ||
OE.11F.D2.1 | 2.1: Describe key properties of periodic functions arising from real-world applications, given a numeric or graphical representation |
OE.11F.D2.5 | 2.5: 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 |
OE.11F.D2.8 | 2.8: Represent a sinusoidal function with an equation, given its graph or its properties |
OE.11F.D3.2 | 3.2: 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 |
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