MCV4Ur Repeat Calculus and Vectors – Grade 12 (University)
PREREQUISITE: A final grade of 40% or higher in the same course
GRADE: 12 (Universty)
AVAILABILITY: Blyth Academy Online
THE ONTARIO CURRICULUM: Mathematics
MCV4Ur online builds on student’s previous experience with functions and their developing understanding of rates of change. Students will solve problems involving geometric and algebraic representations of vectors, and representations of lines and planes in three-dimensional space; broaden their understanding of rates of change to include the derivatives of polynomial, rational, exponential, and sinusoidal functions; and apply these concepts and skills to modelling of real-world relationships. MCV4Ur online is intended for students who plan to study mathematics in university and who may choose to pursue careers in fields such as physics and engineering.
UNIT ONERates of Change
- In this unit, students will revisit the ideas introduced in their Advanced Functions course: slopes of secants and tangents; limits; and applications involving rates of change. These basic ideas will be extended and expanded to be able to distinguish between average and instantaneous rates of change to help students solve problems arising in real-world applications and involving the development of mathematical models.
- In this unit, students will learn about derivatives of polynomials. Students will learn about the Product Rule as well as displacement, velocity and acceleration. Students will learn the Quotient Rule, about extreme values and the Chain Rule. Students will also practice different optimization problems.
UNIT THREECurve Sketching
- In this unit, students will learn how to decrease and increase functions, how to find Maximas and Minimas and concavity. Students will also learn about rational functions.
UNIT FIVEDerivatives of Exponential and Sinusoidal Functions
- In this unit, students will learn about the rates of change of ‘e’ and the Natural Logarithm. Students will cover derivatives of exponential functions as well as the applications of exponential functions. Students will study rates of change of sinusoidal F and derivatives of sinusoidal functions.
- In unit five, students will learn about the operations and applications of geometric vectors. We will learn about Cartesian vectors in R2 as well as vectors in R3. We will cover dot product and applications, scalar and vector projections and cross product and applications.
UNIT SIXLines and Planes
- In this unit, students will learn equations of lines in R2 and R3, they will cover planes as well as the intersection of lines and planes. Students will also learn strategies to determine the distance from a point to a line in R2 and R3.
FINAL EXAMProctored Exam
- This exam is the final evaluation of MCV4Ur online. Students need to arrange their final exam 10 days in advance. All coursework should be completed and submitted before writing the final exam, please be advised that once the exam is written, any outstanding coursework will be given a grade of zero. The exam will be two hours.
- Please consult our Frequently Asked Questions Page or the Exam section within your course for details on exam proctoring options.