Ontario Grade 11 Functions and Applications (MCF3M) curriculum and lessons

The course map includes Quadratic Functions, Exponential Functions, Trigonometric Functions. Follow the complete section list above for the full study path.

درس تابع‌ها و کاربردهای پایه یازدهم انتاریو (MCF3M) چه مباحثی دارد؟ از جمله مباحث این درس تابع‌های درجه دوم، تابع‌های نمایی، تابع‌های مثلثاتی است. فهرست کامل بخش‌ها در بالای صفحه قرار دارد.

53 of 53 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 تابع‌ها و کاربردهای پایه یازدهم انتاریو را از کجا پیدا کنم؟ اکنون 53 درس از 53 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.

A quadratic relationship can describe a quantity that rises and then falls, or falls and then rises. For example, the height of a…

An exponent does not have to be a whole number. A fraction used as an exponent is called a rational exponent. It connects two…

A right triangle has one angle of . If you know one acute angle and one side, you can often find another side. If you know two sides…

A situation can describe a quantity that changes. If the quantity depends on an unknown number, we can use a variable to represent…

An exponent tells how a base is used in a power. For example, means multiply four factors of . Some expressions use exponents that…

Some two-dimensional situations contain more than one right triangle. Each triangle can describe part of the situation, but the…

Factoring rewrites an expression as a product. For example, writing as is factoring a number. In this lesson, you will use that idea…

Suppose a savings balance grows by the same percentage each year. The amount added is not the same each year because it depends on…

Quadratic equations, representations, transformations, modelling, and applications.

• A1.1 · Pose and solve application problems from quadratic tables and graphs (published written lesson)
• A1.2 · Represent situations with quadratic expressions and simplify them (published written lesson)
• A1.3 · Factor quadratic expressions using an appropriate strategy (published written lesson)
• A1.4 · Solve quadratic equations by factoring (published written lesson)
• A1.5 · Connect factors with x-intercepts (published written lesson)
• A1.6 · Explore and apply the quadratic formula using technology (published written lesson)
• A1.7 · Connect roots, x-intercepts, and the discriminant (published written lesson)
• A1.8 · Solve quadratic equations and compare strategies (published written lesson)
• A2.1 · Distinguish functions from non-functions (published written lesson)
• A2.2 · Evaluate linear and quadratic functions in context (published written lesson)
• A2.3 · Describe domain and range of linear and quadratic functions (published written lesson)
• A2.4 · Explain contextual restrictions on quadratic domain and range (published written lesson)
• A2.5 · Investigate transformations in vertex form (published written lesson)
• A2.6 · Sketch quadratic graphs from vertex form (published written lesson)
• A2.7 · Convert vertex form to standard form (published written lesson)
• A2.8 · Complete the square to convert standard form to vertex form (published written lesson)
• A2.9 · Sketch a quadratic from factored form (published written lesson)
• A2.10 · Interpret information from standard, vertex, and factored forms (published written lesson)
• A2.11 · Sketch a quadratic from standard form and identify key features (published written lesson)
• A3.1 · Collect and graph data modelled by a quadratic function (published written lesson)
• A3.2 · Determine a quadratic model for a data set (published written lesson)
• A3.3 · Solve real-world problems from quadratic equations (published written lesson)

Exponents, exponential models, compound interest, and annuities.

• B1.1 · Interpret powers with rational exponents (published written lesson)
• B1.2 · Evaluate numerical expressions with integer and rational exponents (published written lesson)
• B1.3 · Graph and define exponential functions (published written lesson)
• B1.4 · Describe key properties of exponential functions (published written lesson)
• B1.5 · Develop and apply exponent rules (published written lesson)
• B1.6 · Distinguish exponential, linear, and quadratic functions (published written lesson)
• B2.1 · Collect and graph data modelled exponentially (published written lesson)
• B2.2 · Identify exponential growth and decay and contextual restrictions (published written lesson)
• B2.3 · Solve applications using exponential graphs and equations (published written lesson)
• B3.1 · Compare simple and compound interest (published written lesson)
• B3.2 · Calculate amount and principal with the compound-interest formula (published written lesson)
• B3.3 · Connect compound interest with exponential growth (published written lesson)
• B3.4 · Use technology to find interest rates or compounding periods (published written lesson)
• B3.5 · Explain annuities using numeric and graphical representations (published written lesson)
• B3.6 · Investigate how changing conditions affects an annuity (published written lesson)
• B3.7 · Solve ordinary simple annuity problems using technology (published written lesson)

Acute-triangle trigonometry, sine functions, periodic data, and applications.

• C1.1 · Solve right-triangle problems with primary trigonometric ratios (published written lesson)
• C1.2 · Solve two-dimensional problems involving two right triangles (published written lesson)
• C1.3 · Verify the sine law and cosine law using technology (published written lesson)
• C1.4 · Choose and apply the sine law or cosine law in acute triangles (published written lesson)
• C1.5 · Solve real-world acute-triangle problems (published written lesson)
• C2.1 · Describe properties of periodic functions in applications (published written lesson)
• C2.2 · Predict future behaviour from periodic data (published written lesson)
• C2.3 · Connect the sine ratio with the sine function (published written lesson)
• C2.4 · Sketch the sine graph and describe its properties (published written lesson)
• C2.5 · Connect changes in periodic situations with graph transformations (published written lesson)
• C2.6 · Investigate vertical and horizontal sine transformations (published written lesson)
• C2.7 · Sketch transformed sine functions and state domain and range (published written lesson)
• C3.1 · Collect and graph data modelled by a sine function (published written lesson)
• C3.2 · Identify periodic and sinusoidal functions and contextual restrictions (published written lesson)
• C3.3 · Pose and solve real-world sine-function problems (published written lesson)

Solve x² − 5x + 6 = 0 by factoring.

Worked method: (x − 2)(x − 3) = 0, so x = 2 or x = 3.

A value starts at 200 and grows by 5% each year. Write a model.

Worked method: Each year multiplies the value by 1.05, so after n years the model is A = 200(1.05)^n.

From 20 m away, the angle of elevation to a tree top is 35°. Find the height.

Worked method: tan 35° = h/20, so h = 20 tan 35° ≈ 14.0 m.

Convert y = (x − 2)² + 3 to standard form.

Find the amount after two years for CAD 500 at 4% compounded annually.