Havergal's Uncalendar, 2017-18 Academic Year

MCR3U – Functions, Grade 11, University Preparation 1 CREDIT This course explores the characteristics and properties of functions. You will investigate and apply transformations, similar to those that you applied to quadratic functions in MPM2D, to a variety of different functions including square root, absolute value, reciprocal, inverse, polynomial, exponential, logarithmic and trigonometric functions. You will develop some understanding of the mathematics associated with the financial applications of sequences and series. As well, you will refine your use of mathematical processes necessary for success in problem-solving. You will apply these skills to various real- life situations, such as how to maximize the area created with a certain amount of fencing, minimize the cost of producing products or determining simple interest and many other applications. This MCR3U course serves as a prerequisite for Grade 12 Mathematics courses; those students who excel in MCR3U may also consider AP Stats or AP Calculus. It is recommended that most students wishing to enrol in Calculus and Vectors do so in their Senior Year. Students wishing to select this course prior to Senior Year must consult with the Mathematics Department and must have the required prerequisite courses. Prerequisite: MPM2D – Principles of Mathematics, Grade 10, Academic GRADE 12 MCV4U – Calculus and Vectors, Grade 12, University Preparation 1 CREDIT The first part of this course introduces students to algebraic and geometric vectors. You will explore vector properties in two and three dimensions, properties of lines and planes, and you will 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. 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 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 ext . . .) • Unit 11- Introduction to Vectors (MCV4U) • Unit 12 – Vector Applications (MCV4U) • 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 properties of lines and planes and apply your knowledge Board) syllabus. Program content: •

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