The suggested sequence of course unit delivery as well as the recommended number of hours to complete the respective unit. For complete details of targeted expectations within each unit and activity, please see each Unit Overview is listed below.

Unit 1: Introduction to Calculus

A variety of mathematical operations with functions are needed in order to do the 12 hours calculus of this course. This unit begins with students developing a better understanding of these essential concepts. Students will then deal with rates of change problems and the limit concept. While the concept of a limit involves getting close to a value but never getting to the value, Often the limit of a function can be determined by substituting the value of interest for the variable in the function. Students will work with several examples of this concept. 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.

Unit 2: Derivatives

the concept of a derivative is, in essence, a way of creating a short cut to determine the tangent line slope function that would normally require the concept of a limit. Once patterns are seen from the evaluation of limits, rules can be established to simplify what must be done to determine this slope function. This unit begins by examining those rules including: the power rule, the product rule, the quotient rule and the chain rule followed by a study of the derivatives of composite functions.

Unit 3 : Derivatives of Exponential, Logarithmic and Trigonometric Functions

In this unit, students will learn about the rates of change of exponents and Logarithms. Students will cover derivatives of exponential functions and its applications. Students will study derivatives of Logarithmic and Trigonometric Functions as well.

Unit 4: Curve Sketching

Determine maximum and minimum values of the graphs of polynomial functions using first derivative test; use the second derivative test to determine the intervals of concavity; sketch the graph of a polynomial function, given its equation, by using 5 steps. This unit will help you understand the fundamentals of using calculus to help us sketch curves, and solve some basic optimization problems

Unit 5: Derivative Applications and Related Rates

Students will learn about how to calculate Implicit and Logarithmic differentiation; apply the concepts of derivative to sketch the velocity-time and acceleration-time graph; solve problems arising from real world applications, such as population and rates of population change, volume and rates of flow, height and growth rates.

Unit 6: Introduction to Vectors

In this unit, students will learn to define a vector as a quantity with both magnitude and direction; distinguish between a scalar quantity and vector quantity; add, subtract vectors both graphically and algebraically; represent a vector in two-space using angle system, directional system, and bearing system and solve real world problems involving operations with vectors in two dimensions.

Unit 7: Vector Applications

Applications involving work and torque are used to introduce and lend context to the dot and cross products of Cartesian vectors. The vector and scalar projections of Cartesian vectors are written in terms of the dot product. The properties of vector products are investigated and proven. These vector products will be revisited to predict characteristics of the solutions of systems of lines and planes in the intersections of lines and planes.

Unit 8: Lines in Three-Space

A variety of types of problems exist in this unit and are generally grouped into the following categories: Pythagorean Theorem Problems (these include ladder and intersection problems), Volume Problems (these usually involve a 3-D shape being filled or emptied), Trough Problems, Shadow problems and General Rate Problems. During this unit students will look at each of these types of problems individually.

Unit 9: Planes

In this unit, students will recognize a normal to a plane geometrically and algebraically; identify the cases when two planes coincide or they are two distinct parallel planes and determine the equation of a plane that intersect with two other planes of planes in one point, or in more than one point.

Unit 10: Matrices and Linear Systems

This unit teach students to convert linear systems to matrix; add, subtract and multiply matrices and determine the points of intersections of three planes using operations with matrices. The unit ends, as in all other units, with an quiz and a unit test.

FINAL EXAM: Proctored Exam

30% of Final Grade

• This exam is the final evaluation of MCV4U. 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 ELITE HIGH SCHOOL CAMPUS: If you live close to Elite High School Campus, or if you attend Elite High School Campus, you can take your exam there. You will receive a confirmation email with next steps and exam information once your exam date is scheduled.The exam can be rescheduled or cancelled with a reasonable proof in case of a medical emergency.
• 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@elitehighschool.com if you need assistance.