<style>.lazy{display:none}</style> Grade 12 Math - Calculus and Vectors (MCV4U) - York Region Tutoring - Math, Science (Chemistry, Biology, Physics), English

Grade 12 Math - Calculus and Vectors (MCV4U)

What will you learn:  
Academic, IB, AP, Enriched

Subject Status:

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Overview of Grade 12 Math - Calculus and Vectors (MCV4U)

Grade 12 Calculus and Vectors builds on students’ 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 the modelling of real-world relationships. Students will also refine their use of the mathematical processes necessary for success in senior mathematics. This course 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.

Further information about this course can be found at the Ontario Ministry of Education Website: www.edu.gov.on.ca/

York Region Tutoring urges all students to complete the past tests that we have compiled specifically from YRDSB/YCDSB school teachers. Tests in the Grade 12 Maths and sciences tend to follow a very strict layout, and so completing them will give students the opportunity to assess their strengths and weaknesses as well as direct their attention to topics that require more attention. Completing past tests also allows students to approach school evaluations with more confidence as they are familiarized with the organization of the test & general nature of questions asked. *Please note: while there are clear trends in the types of questions asked on tests, it is not guaranteed that past test questions will map perfectly onto school evaluations, since test-making is ultimately a subjective endeavour, meaning teachers can and do exercise their creative liberties when writing tests.

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Grade 12 Calculus and Vectors (University) Breakdown

Rate of Change
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  • Demonstrate an understanding of rate of change by making connections between average rate of change over an interval and instantaneous rate of change at a point, using the slopes of secants and tangents and the concept of the limit.
  • Graph the derivatives of polynomial, sinusoidal, and exponential functions, and make connections between the numeric, graphical, and algebraic representations of a function and its derivative.
  • Verify graphically and algebraically the rules for determining derivatives; apply these rules to determine the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions, and simple combinations of functions; and solve related problems.
Derivatives and their Applications
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  • Make connections, graphically and algebraically, between the key features of a function and its first and second derivatives, and use the connections in curve sketching.
  • Solve problems, including optimization problems, that require the use of the concepts and procedures associated with the derivative, including problems arising from real-world applications and involving the development of mathematical models.
Geometry and Algebra of Vectors
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  • Demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications.
  • Perform operations on vectors in two-space and three-space, and use the properties of these operations to solve problems, including those arising from real-world applications.
  • Distinguish between the geometric representations of a single linear equation or a system of two linear equations in two-space and three-space, and determine different geometric configurations of lines and planes in three-space.
  • Represent lines and planes using scalar, vector, and parametric equations, and solve problems involving distances and intersections.

WHAT IS INCLUDED IN OUR LESSONS?

York Region Tutoring Provides

Write Past Tests

If a student is approaching a forthcoming test, we can provide them with a previous test to be completed at home before their upcoming session. Subsequently, during their next class, just before the exam, they can review the test with their tutor. These tests are exclusively sourced from high schools in York Region and other areas in Ontario, serving as the definitive benchmark for students to assess their readiness.

We Come To Class Prepared

York Region Tutors and are equipped with drawing tablets making collaboration simple, efficient and effective. We also offer drawing tablets at a discount for purchase to students who really take to the functionality of the product.

YRDSB-Minded Homework

At the parents' request, following each tutoring session, our tutors can assign homework tailored to address weaknesses and reinforce strengths in students. Additionally, we incorporate homework questions directly extracted from previous tests and quizzes administered by YRDSB school teachers, allowing students to familiarize themselves with potential test questions.

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