# MCV4UR Repeat Calculus And Vectors – Grade 12 (University)

• Repeat

PREREQUISITE: A final grade of 40% or higher in the same course

THE ONTARIO CURRICULUM: Mathematics

## Course Overview

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 FOUR 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.

Please consult our Frequently Asked Questions Page or the Exam section within your course for more details on final exams and the exam fee. More information can also be found in our Student Handbook

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