Havergal's Uncalendar, 2021-22 Academic Year

GRADE 12 MCV4U – Calculus and Vectors, Grade 12, University Preparation 1 CREDIT This course consists of two distinct parts: • In Calculus, you will explore the idea of finding the slope of a curve. Your ability to predict the rate of change along a curve will allow you to represent and solve problems using the derivative. Such problems include finding the maximum profit, minimum cost, ideal shape, least time, as well as locating the critical points such as turns and inflections along a graph efficiently. • In Vectors, you will develop algebraic techniques to represent and analyze lines and surfaces in three- dimensional space. Vectors will also allow you to represent and solve problems involving velocity, physical forces and business conundrums involving multiple criteria. This course is intended for students who choose to pursue careers in fields such as science, engineering, economics and some areas of business, including those students who will be required to take a university-level calculus, linear algebra or physics course. This course can only be taken after or concurrently with MHF4U Advanced Functions. Prerequisite: MCR3U – Functions, Grade 11, University Preparation; MHF4U – Advanced Functions, Grade 12, University Preparation must be taken prior to or concurrently with MCV4U – Calculus And Vectors, Grade 12, University Preparation Advanced Placement Calculus (AB) MCV4UP – Calculus And Vectors, Grade 12, University Preparation (Advanced Placement) 1 CREDIT MHF4UP – Advanced Functions, Grade 12, University Preparation (Advanced Placement) 1 CREDIT This two-section course prepares students to write the AP Calculus (College Board, Calculus AB) standardized exam in May. Due to the amount of content learned in a relatively short period of time, this course is fast-paced. It is recommended for students who are strong independent learners and love math. The course is taught similar to that of a first-year university course. Many colleges and universities (especially in the United States) will offer a math credit to students who score well on the College Board’s AP Calculus exam. The Calculus section of this course addresses concepts taught in MHF4U (Advanced Functions), the Calculus

concepts taught in MCV4U (Calculus and Vectors), along with all Calculus concepts from the AP Calculus (College

Board) syllabus. Program content:

• Unit 1 – Characteristics of Functions (MHF4U) • Unit 2 – Trigonometric Functions (MHF4U) • Unit 3 – Exponential and Logarithmic Functions (MHF4U) • Unit 4 - Rates of Change and Limits (MCV4U) • Unit 5 – Introduction to Derivatives (MCV4U) • Units 6 & 7 – Applications of Derivatives (MCV4U) • Unit 8 – Derivatives of Exponential and Logarithmic Functions (MCV4U) • Units 9 & 10 – Integration (AP exam & MHF4U) • Unit 13 – Equations of Lines and Planes (MCV4U) • Unit 14 – Intersection of Lines and Planes (MCV4U) The Vectors section of this course introduces students to algebraic and geometric vectors. You will explore vector properties in two and three dimensions, learn about the properties of lines and planes and apply your knowledge to solve a wide variety of vector problems in two and three dimensions. These applications involve velocity and force, the concept of deductive proof, for example, with a strong focus on the strategies involved in solving problems. The second part of this course builds on your knowledge of a variety of functions to explore rates of change, derivatives and the application of derivatives. You will learn how to apply derivatives to solve problems involving motion, optimization problems (involving, for example, maximum volume, minimum cost, least time) and sketching curves. Program content: Unit 1 Introduction to Vectors; Unit 2 Vector Applications; Unit 3 Equations of Lines and Planes; Unit 4 Points Lines and Planes. This course is intended for students who choose to pursue careers in fields such as science, mathematics, engineering, economics and some areas of business, including those students who will be required to take a university-level Calculus, Linear Algebra or Physics course. Prerequisite: MCR3U – Functions, Grade 11, University Preparation Corequisite: MHF4UP – Advanced Functions, Grade 12, University Preparation (Advanced Placement) • Unit 11- Introduction to Vectors (MCV4U) • Unit 12 – Vector Applications (MCV4U)

30 HAVERGAL COLLEGE | Uncalendar 2021–22