Ontario Grade 11 University/College Preparation math (MCF3M)

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

• A1.1 · Pose and solve application problems from quadratic tables and graphs (written lesson not published)
• A1.2 · Represent situations with quadratic expressions and simplify them (written lesson not published)
• A1.3 · Factor quadratic expressions using an appropriate strategy (written lesson not published)
• A1.4 · Solve quadratic equations by factoring (written lesson not published)
• A1.5 · Connect factors with x-intercepts (written lesson not published)
• A1.6 · Explore and apply the quadratic formula using technology (written lesson not published)
• A1.7 · Connect roots, x-intercepts, and the discriminant (written lesson not published)
• A1.8 · Solve quadratic equations and compare strategies (written lesson not published)
• A2.1 · Distinguish functions from non-functions (written lesson not published)
• A2.2 · Evaluate linear and quadratic functions in context (written lesson not published)
• A2.3 · Describe domain and range of linear and quadratic functions (written lesson not published)
• A2.4 · Explain contextual restrictions on quadratic domain and range (written lesson not published)
• A2.5 · Investigate transformations in vertex form (written lesson not published)
• A2.6 · Sketch quadratic graphs from vertex form (written lesson not published)
• A2.7 · Convert vertex form to standard form (written lesson not published)
• A2.8 · Complete the square to convert standard form to vertex form (written lesson not published)
• A2.9 · Sketch a quadratic from factored form (written lesson not published)
• A2.10 · Interpret information from standard, vertex, and factored forms (written lesson not published)
• A2.11 · Sketch a quadratic from standard form and identify key features (written lesson not published)
• A3.1 · Collect and graph data modelled by a quadratic function (written lesson not published)
• A3.2 · Determine a quadratic model for a data set (written lesson not published)
• A3.3 · Solve real-world problems from quadratic equations (written lesson not published)

Exponents, exponential models, compound interest, and annuities.

• B1.1 · Interpret powers with rational exponents (written lesson not published)
• B1.2 · Evaluate numerical expressions with integer and rational exponents (written lesson not published)
• B1.3 · Graph and define exponential functions (written lesson not published)
• B1.4 · Describe key properties of exponential functions (written lesson not published)
• B1.5 · Develop and apply exponent rules (written lesson not published)
• B1.6 · Distinguish exponential, linear, and quadratic functions (written lesson not published)
• B2.1 · Collect and graph data modelled exponentially (written lesson not published)
• B2.2 · Identify exponential growth and decay and contextual restrictions (written lesson not published)
• B2.3 · Solve applications using exponential graphs and equations (written lesson not published)
• B3.1 · Compare simple and compound interest (written lesson not published)
• B3.2 · Calculate amount and principal with the compound-interest formula (written lesson not published)
• B3.3 · Connect compound interest with exponential growth (written lesson not published)
• B3.4 · Use technology to find interest rates or compounding periods (written lesson not published)
• B3.5 · Explain annuities using numeric and graphical representations (written lesson not published)
• B3.6 · Investigate how changing conditions affects an annuity (written lesson not published)
• B3.7 · Solve ordinary simple annuity problems using technology (written lesson not published)

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

• C1.1 · Solve right-triangle problems with primary trigonometric ratios (written lesson not published)
• C1.2 · Solve two-dimensional problems involving two right triangles (written lesson not published)
• C1.3 · Verify the sine law and cosine law using technology (written lesson not published)
• C1.4 · Choose and apply the sine law or cosine law in acute triangles (written lesson not published)
• C1.5 · Solve real-world acute-triangle problems (written lesson not published)
• C2.1 · Describe properties of periodic functions in applications (written lesson not published)
• C2.2 · Predict future behaviour from periodic data (written lesson not published)
• C2.3 · Connect the sine ratio with the sine function (written lesson not published)
• C2.4 · Sketch the sine graph and describe its properties (written lesson not published)
• C2.5 · Connect changes in periodic situations with graph transformations (written lesson not published)
• C2.6 · Investigate vertical and horizontal sine transformations (written lesson not published)
• C2.7 · Sketch transformed sine functions and state domain and range (written lesson not published)
• C3.1 · Collect and graph data modelled by a sine function (written lesson not published)
• C3.2 · Identify periodic and sinusoidal functions and contextual restrictions (written lesson not published)
• C3.3 · Pose and solve real-world sine-function problems (written lesson not published)

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.