Ontario Grade 11 University Preparation math (MCR3U)

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

• A1.1 · Distinguish functions from non-functions using multiple representations (written lesson not published)
• A1.2 · Represent and evaluate linear and quadratic functions using function notation (written lesson not published)
• A1.3 · Describe domain and range and apply contextual restrictions (written lesson not published)
• A1.4 · Connect inverse functions with reverse processes (written lesson not published)
• A1.5 · Determine numeric and graphical representations of inverse relations (written lesson not published)
• A1.6 · Relate the domain and range of a function and its inverse (written lesson not published)
• A1.7 · Determine algebraic representations of inverse linear and quadratic relations (written lesson not published)
• A1.8 · Investigate transformation parameters in y = af(k(x − d)) + c (written lesson not published)
• A1.9 · Sketch transformed linear, quadratic, square-root, and reciprocal functions (written lesson not published)
• A2.1 · Determine the number of zeros of a quadratic function (written lesson not published)
• A2.2 · Find a quadratic maximum or minimum algebraically (written lesson not published)
• A2.3 · Solve real-world problems involving quadratic functions (written lesson not published)
• A2.4 · Determine a quadratic function from its roots and a point (written lesson not published)
• A2.5 · Solve intersections of linear and quadratic functions (written lesson not published)
• A3.1 · Simplify polynomial expressions by adding, subtracting, and multiplying (written lesson not published)
• A3.2 · Simplify radical expressions using product relationships (written lesson not published)
• A3.3 · Operate on rational expressions and state restrictions (written lesson not published)
• A3.4 · Determine whether algebraic expressions are equivalent (written lesson not published)

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

• B1.1 · Graph and define exponential functions (written lesson not published)
• B1.2 · Interpret powers with rational exponents (written lesson not published)
• B1.3 · Simplify and evaluate expressions with integer and rational exponents (written lesson not published)
• B1.4 · Describe domain, range, intercepts, intervals, and asymptotes of exponential functions (written lesson not published)
• B2.1 · Distinguish exponential, linear, and quadratic functions (written lesson not published)
• B2.2 · Investigate transformations of exponential functions (written lesson not published)
• B2.3 · Sketch transformed exponential functions and state domain and range (written lesson not published)
• B2.4 · Connect equivalent exponential equations written with different bases (written lesson not published)
• B2.5 · Represent an exponential function from its graph or properties (written lesson not published)
• B3.1 · Collect and graph data modelled by an exponential function (written lesson not published)
• B3.2 · Identify exponential growth and decay models and contextual restrictions (written lesson not published)
• B3.3 · Solve real-world problems using exponential graphs and equations (written lesson not published)

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

• C1.1 · Connect sequences with discrete functions (written lesson not published)
• C1.2 · Describe recursive procedures that generate sequences (written lesson not published)
• C1.3 · Connect nth-term formulas with function notation (written lesson not published)
• C1.4 · Represent sequences recursively, explicitly, and with function notation (written lesson not published)
• C1.5 · Investigate recursive patterns in Fibonacci sequences and Pascal’s triangle (written lesson not published)
• C1.6 · Use Pascal’s triangle to expand binomial powers (written lesson not published)
• C2.1 · Classify arithmetic, geometric, and other sequences (written lesson not published)
• C2.2 · Develop and use general-term formulas for arithmetic and geometric sequences (written lesson not published)
• C2.3 · Develop and use finite arithmetic and geometric series formulas (written lesson not published)
• C2.4 · Solve applications involving arithmetic and geometric sequences and series (written lesson not published)
• C3.1 · Connect simple interest, arithmetic sequences, and linear growth (written lesson not published)
• C3.2 · Connect compound interest, geometric sequences, and exponential growth (written lesson not published)
• C3.3 · Calculate principal, amount, or interest rate in compound-interest problems (written lesson not published)
• C3.4 · Determine the number of compounding periods using technology (written lesson not published)
• C3.5 · Connect ordinary simple annuities with geometric series (written lesson not published)
• C3.6 · Investigate how changing conditions affects an annuity (written lesson not published)
• C3.7 · Solve ordinary simple annuity problems using technology (written lesson not published)

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

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

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.