MCF3M introduces basic features of the function by extending students’ experiences with quadratic relations. Throughout MCF3M, students will explore three fundamental function types: quadratic, trigonometric, and exponential. Students will represent functions numerically, graphically, and algebraically; simplify expressions; solve equations; and solve problems relating to applications. Students in MCF3M will reason mathematically and communicate their thinking as they solve multi-step problems.
Course curriculum
Inside %course-code%: functions, with the applications attached
Two Grade 12 doors stay open
MCF3M is accepted as the prerequisite for MCT4C (college technology math) and MAP4C (college foundations math), and follows either Grade 10 academic or applied math.
The function concept, properly
Relations versus functions, domain and range, inverses, and the numeric, graphical and algebraic representations of quadratic, exponential and sine functions.
Trigonometry beyond right triangles
The sine and cosine laws for oblique triangles in two and three dimensions, then periodic functions: cycle, amplitude and period from real-world data.
Compound interest and annuities
Exponential functions applied to money: compound interest, the future value of regular payments, and comparing financial options, with a midterm and exit conference with your teacher.
MCF3M Course outline
Full unit-by-unit breakdown.
Distinguish functions from relations and express domain and range, apply those ideas to linear, quadratic and radical functions, find the inverse of a linear or quadratic function, and expand, simplify and factor quadratic expressions, solve quadratic equations and relate their roots to the graph.
Key topics
Functions and relations · domain and range · inverses · expanding and factoring · solving quadratic equations · roots and the graph · applications
Assessed by
Quadratics and polynomials assignment · factored form application · functions and quadratics assignment · Unit 1–2 problem set (25% combined)
Express and investigate exponential functions with calculators, paper and pencil and graphing technology, compare them with functions studied earlier, connect representations through graphing and transformations, and model real-world growth and decay.
Key topics
Exponent laws · exponential functions and their graphs · transformations · growth and decay models · comparing function families
Assessed by
Unit 2 mini assignment · midterm conference with your teacher · Unit 2 assignment 2 (25% combined)
Describe key properties of periodic functions arising from real-world applications, such as cycle, amplitude and period, connect the sine and cosine functions to the unit circle, and pose and solve problems involving right and oblique triangles in two and three dimensions using the primary ratios, the sine law and the cosine law.
Key topics
Sine law and cosine law · oblique triangles in 2D and 3D · periodic functions · cycle, amplitude and period · the sine function and the unit circle
Assessed by
Unit 3 assignment (10%)
Apply exponential functions to money: compare simple and compound interest, calculate compound interest and the future value of annuities using formulas and technology, and solve problems comparing financial options. Review the course ahead of the final exam.
Key topics
Compound interest · annuities and future value · comparing financial options · course review
Assessed by
Unit 4 assignment · exit conference with your teacher (5%)
