MCV4Ur Repeat Calculus and Vectors – Grade 12 (University)
PREREQUISITE: Advanced Functions course (MHF4U) must be taken prior to or concurrently with Calculus and Vectors (MCV4U)
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 ONE
Rates of Change Essential Question: What is a 'limit' to a function? When does a limit not exist?
- 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.
UNIT TWO
Derivatives Essential Question: What is the limit of an average rate of change between two points on a graph as the distance between the points diminishes to zero?
- 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 THREE
Curve Sketching Essential Question: How can we find the maximum or minimum value of a function?
- 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 FIVE
Derivatives of Exponential and Sinusoidal Functions Essential Question: Why is the derivative of the sin function the cosine function? Why is the derivative of the natural logarithmic function equal to the natural logarithmic function?
- 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.
UNIT FIVE
Vectors Essential Question: How do you calculate combined velocities from relative velocities in two different directions?
- 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 SIX
Lines and Planes Essential Question: A plane can be defined by 1) three points, 2) two lines, or 3) by a point in the plane and a normal to the plane through the point. How can you write an equation for a plane given each of these sets of information?
- 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 EXAM
Proctored Exam 30% of Final Grade
- 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. There are two options for taking the exam:
- WRITE EXAM AT BLYTH ACADEMY CAMPUS: If you live close to a Blyth Academy Campus, or if you attend a Blyth Academy Campus, you can take your exam there. Once inside the exam scheduling interface, please click Login/Create Account. Check for an available time and date at the campus of your choosing. The earliest available date will be open within the next 3-5 business days. You cannot book an exam in more than one campus or multiple times at the same campus. You will receive an automatic confirmation email with next steps and exam information. You can cancel and reschedule anytime using the same link.
- USE EXAMITY PROCTORING SERVICE: For a fee of 22 USD*, students can arrange to take their exam in the comfort of their own home, at any time, on any day. Please select Examity Exam in the exam section of your course to set up your Examity profile and schedule your exam. Exams must be scheduled at least 24 hours in advance. *Price is subject to change.
- Please email exams@blythacademyonline.com if you need assistance.