This MCT4C course enables students to extend their knowledge of functions. Students will investigate and apply properties of polynomial, exponential, and trigonometric functions; continue to represent functions numerically, graphically, and algebraically; develop facility in simplifying expressions and solving equations; and solve problems that address applications of algebra, trigonometry, vectors, and geometry. Students will reason mathematically and communicate their thinking as they solve multi-step problems. This MCT4C course prepares students for a variety of college technology programs.
Course curriculum
Inside %course-code%: functions for technology programs
The math credit for college technology
The Grade 12 math most engineering technician, technologist and trades-technology programs ask for, extending functions rather than the finance-and-statistics route of MAP4C.
Exponential, logarithmic and polynomial functions
Model growth and decay, use the laws of logarithms to solve equations, then sketch polynomials from factored form and find their real roots.
Trigonometry in degrees and radians
Periodic functions, the unit circle and special triangles, transformations of sine and cosine, and solving trigonometric equations, applied to real problems.
Projects, learning logs and video conferences
Applied projects such as modelling a zombie outbreak with exponentials and a vector treasure map, plus a learning log and a video conference with your teacher each unit.
MCT4C Course outline
Full unit-by-unit breakdown.
Investigate the properties of exponential functions with graphing technology and by hand, including domain and range, and use them to model growth and decay situations.
Key topics
Exponential functions and notation · domain and range · growth and decay models · graphing technology
Explore the relationship between exponential and logarithmic functions algebraically and graphically, and use the laws of logarithms to simplify expressions, evaluate logarithms and solve problems.
Key topics
Logarithms as inverses · laws of logarithms · solving exponential and logarithmic equations · applications
Assessed by
Learning log · Project: History of Springfield
Graph polynomial functions and connect degree, coefficients, intercepts and symmetry to their shape. Sketch from factored form and determine real roots of factorable and non-factorable polynomial equations graphically and algebraically.
Key topics
Degree, intercepts and end behaviour · curve sketching from factored form · polynomial equations and real roots · real-world polynomial models
Assessed by
Learning log · unit test · video conference with your teacher
Investigate the periodic nature of the primary trigonometric functions, convert between degrees and radians, use the unit circle and special triangles, apply transformations, and model and solve triangles with the sine and cosine laws.
Key topics
Radian measure and the unit circle · graphs of sine, cosine and tangent · transformations · sine law and cosine law · trigonometric equations
Assessed by
Learning log · unit test · video conference with your teacher
Represent vectors in two and three dimensions, solve real-world problems involving vectors, and apply circle geometry and related properties to practical situations.
Key topics
Vectors in two and three dimensions · vector applications · circle geometry
Assessed by
Learning log · Project: Treasure Map · video conference with your teacher
