Ontario Grade 11 Functions (MCR3U) curriculum and lessons

The course map includes Characteristics of Functions, Exponential Functions, Discrete Functions, and 1 other section. Follow the complete section list above for the full study path.

درس تابع‌های پایه یازدهم انتاریو (MCR3U) چه مباحثی دارد؟ از جمله مباحث این درس ویژگی‌های تابع‌ها، تابع‌های نمایی، تابع‌های گسسته است. فهرست کامل بخش‌ها در بالای صفحه قرار دارد.

67 of 67 written lessons are currently published and free to read. Open a linked lesson in the section map above. Check the official Ontario curriculum for exact requirements.

درس‌ها و برنامهٔ درسی تابع‌های پایه یازدهم انتاریو را از کجا پیدا کنم؟ اکنون 67 درس از 67 درس نوشتاری منتشر شده و خواندن آن‌ها رایگان است. درس‌های دارای پیوند را در نقشهٔ بخش‌های بالا باز کنید. برای شرایط دقیق به برنامهٔ درسی رسمی انتاریو مراجعه کنید.

Every time you type a value into a calculator and press a button, you expect exactly one answer. That idea — one input, one output —…

You already know how to evaluate powers like or . In previous grades you worked with linear functions (straight lines) and quadratic…

You have worked with functions before — rules that pair every input with exactly one output. In this lesson you will see that a…

When you press sin(30°) on a calculator, you get 0.5. That decimal is exact, but for many other angles the calculator gives a rounded…

You already know how to write equations like or from Grade 10. In this lesson, you will learn a more powerful way to write the same…

In Grade 10, you learned how to work with whole-number exponents and how to simplify square roots and other radicals. Those two ideas…

Have you ever followed a set of instructions where each new step depends on what you just did? That is exactly the idea behind a…

In Grade 10, you used sine, cosine, and tangent only for acute angles inside a right triangle. But angles in the real world — from…

Functions, inverses, transformations, quadratic problems, and equivalent algebraic expressions.

• A1.1 · Distinguish functions from non-functions using multiple representations (published written lesson)
• A1.2 · Represent and evaluate linear and quadratic functions using function notation (published written lesson)
• A1.3 · Describe domain and range and apply contextual restrictions (published written lesson)
• A1.4 · Connect inverse functions with reverse processes (published written lesson)
• A1.5 · Determine numeric and graphical representations of inverse relations (published written lesson)
• A1.6 · Relate the domain and range of a function and its inverse (published written lesson)
• A1.7 · Determine algebraic representations of inverse linear and quadratic relations (published written lesson)
• A1.8 · Investigate transformation parameters in y = af(k(x − d)) + c (published written lesson)
• A1.9 · Sketch transformed linear, quadratic, square-root, and reciprocal functions (published written lesson)
• A2.1 · Determine the number of zeros of a quadratic function (published written lesson)
• A2.2 · Find a quadratic maximum or minimum algebraically (published written lesson)
• A2.3 · Solve real-world problems involving quadratic functions (published written lesson)
• A2.4 · Determine a quadratic function from its roots and a point (published written lesson)
• A2.5 · Solve intersections of linear and quadratic functions (published written lesson)
• A3.1 · Simplify polynomial expressions by adding, subtracting, and multiplying (published written lesson)
• A3.2 · Simplify radical expressions using product relationships (published written lesson)
• A3.3 · Operate on rational expressions and state restrictions (published written lesson)
• A3.4 · Determine whether algebraic expressions are equivalent (published written lesson)

Rational exponents, exponential representations, transformations, growth, and decay.

• B1.1 · Graph and define exponential functions (published written lesson)
• B1.2 · Interpret powers with rational exponents (published written lesson)
• B1.3 · Simplify and evaluate expressions with integer and rational exponents (published written lesson)
• B1.4 · Describe domain, range, intercepts, intervals, and asymptotes of exponential functions (published written lesson)
• B2.1 · Distinguish exponential, linear, and quadratic functions (published written lesson)
• B2.2 · Investigate transformations of exponential functions (published written lesson)
• B2.3 · Sketch transformed exponential functions and state domain and range (published written lesson)
• B2.4 · Connect equivalent exponential equations written with different bases (published written lesson)
• B2.5 · Represent an exponential function from its graph or properties (published written lesson)
• B3.1 · Collect and graph data modelled by an exponential function (published written lesson)
• B3.2 · Identify exponential growth and decay models and contextual restrictions (published written lesson)
• B3.3 · Solve real-world problems using exponential graphs and equations (published written lesson)

Recursive sequences, arithmetic and geometric series, compound interest, and annuities.

• C1.1 · Connect sequences with discrete functions (published written lesson)
• C1.2 · Describe recursive procedures that generate sequences (published written lesson)
• C1.3 · Connect nth-term formulas with function notation (published written lesson)
• C1.4 · Represent sequences recursively, explicitly, and with function notation (published written lesson)
• C1.5 · Investigate recursive patterns in Fibonacci sequences and Pascal’s triangle (published written lesson)
• C1.6 · Use Pascal’s triangle to expand binomial powers (published written lesson)
• C2.1 · Classify arithmetic, geometric, and other sequences (published written lesson)
• C2.2 · Develop and use general-term formulas for arithmetic and geometric sequences (published written lesson)
• C2.3 · Develop and use finite arithmetic and geometric series formulas (published written lesson)
• C2.4 · Solve applications involving arithmetic and geometric sequences and series (published written lesson)
• C3.1 · Connect simple interest, arithmetic sequences, and linear growth (published written lesson)
• C3.2 · Connect compound interest, geometric sequences, and exponential growth (published written lesson)
• C3.3 · Calculate principal, amount, or interest rate in compound-interest problems (published written lesson)
• C3.4 · Determine the number of compounding periods using technology (published written lesson)
• C3.5 · Connect ordinary simple annuities with geometric series (published written lesson)
• C3.6 · Investigate how changing conditions affects an annuity (published written lesson)
• C3.7 · Solve ordinary simple annuity problems using technology (published written lesson)

Angles to 360°, identities, sinusoidal transformations, and periodic applications.

• D1.1 · Determine exact trigonometric ratios for special angles (published written lesson)
• D1.2 · Determine trigonometric ratios for angles from 0° to 360° (published written lesson)
• D1.3 · Find two angles with the same trigonometric ratio (published written lesson)
• D1.4 · Define and relate secant, cosecant, and cotangent (published written lesson)
• D1.5 · Prove simple trigonometric identities (published written lesson)
• D1.6 · Solve two-dimensional right and oblique triangle problems (published written lesson)
• D1.7 · Solve three-dimensional triangle problems (published written lesson)
• D2.1 · Describe properties of periodic functions in applications (published written lesson)
• D2.2 · Predict future behaviour from periodic data (published written lesson)
• D2.3 · Connect sine and cosine ratios with sine and cosine functions (published written lesson)
• D2.4 · Sketch sine and cosine graphs and describe their properties (published written lesson)
• D2.5 · Investigate transformations of sinusoidal functions (published written lesson)
• D2.6 · Determine amplitude, period, phase shift, domain, and range (published written lesson)
• D2.7 · Sketch transformed sine and cosine functions (published written lesson)
• D2.8 · Represent a sinusoidal function from a graph or properties (published written lesson)
• D3.1 · Collect and graph sinusoidal data (published written lesson)
• D3.2 · Identify periodic and sinusoidal models and contextual restrictions (published written lesson)
• D3.3 · Model periodic phenomena that do not involve angles (published written lesson)
• D3.4 · Predict how changing conditions changes a periodic model (published written lesson)
• D3.5 · Pose and solve real-world sinusoidal problems (published written lesson)

Does the relation {(1, 3), (2, 5), (1, 7)} define a function?

Worked method: No. The input 1 has two outputs, 3 and 7. A function assigns exactly one output to each input.

Find the fifth term of 3, 6, 12, 24, …

Worked method: The common ratio is 2. The next term is 24 × 2 = 48, so the fifth term is 48.

What is the amplitude of y = 4 sin x + 2?

Worked method: The amplitude is the absolute value of the coefficient of sine: |4| = 4. The +2 shifts the midline but does not change amplitude.

For f(x) = 2x² − 3, find f(2).

Classify 5, 15, 45, 135, … and find the next term.