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COURSE: Grade 12U - Advanced Functions

CODE: MHF4U

PREREQUISITE: MCR3U, MCT4C

DESTINATION: Grade 12 Calculus and Vectors

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COURSE TOPICS

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  1. Polynomial and Rational Functions: describing key features of polynomial and rational functions, making connections between numeric, graphical and algebraic representations of these functions, solving problems involving polynomial and rational equations and inequalities. 

  2. Characteristics of Functions:  understanding average and instantaneous rates of change, determine functions that result in the manipulation of two function and its related problems by modeling and reasoning including problems with solutions that are not accessible by standard algebraic techniques.

  3. Trigonometric Functions:  understanding radian measure and its applications, making connections between all trigonometric ratios and the graphical and algebraic representations of corresponding trigonometric functions, solving problems involving trig. equations and proving trig. identities

  4. Exponential and Logarithmic Functions: understanding the relationship between exponential and logarithmic expressions, evaluating logarithms and applying the laws of logarithms, graphing exponential and logarithmic functions and solving exponential and logarithmic equations including those in problems arising from real-world applications.

Units:

  1. Factoring, Equations, Inequalities

  2. Trigonometry 1

  3. Trigonometry 2

  4. Curve Sketching

  5. Exponential and Logarithmic Functions and Equations

  6. Trigonometric Functions Evaluation:  

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COURSE: Grade 12U-Calculus and Vectors

CODE: MCV4U                              

Prerequisite: MHF4U

 

COURSE TOPICS:        

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  1. Rates of Change: demonstrate an understanding of rates 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 derivative of polynomial, sinusoidal and exponential functions and make connections between numeric, graphical and algebraic representations of a function and its derivative;  verify graphically and algebraically the rules for determining derivative; apply these rules to determine the derivatives of polynomials, sinusoidal, exponential, rational and radial functions, and simple combinations of functions; and solve related problems

 

   2. Derivatives and their Applications:  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.

 

    3. Geometry and Algebra of Vectors: 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. 

  1. Units:

    1. Limits

    2. Derivatives of Polynomials

    3. Application of Derivatives

    4. Trigonometric, Logarithmic & Exponential Derivatives

    5. Curve Sketching

    6. Optimization

    7. Geometric Vectors

    8. Algebraic Vectors

    9. Describing Lines and Planes using Linear, Scalar, Vector, and Parametric Equations

         Note:

          ​​a) The final assessments will be worth 30% of your grade.                  b) The summative assessment will take place over the last                     third of the course.  There will be two parts to this                               assessment: performance task(s) designed to assess your                 ability to problem solve and communicate your solutions                     and an exam that will assess your knowledge and                               understanding as well as your ability to apply your                               knowledge.                                                                                       c) Throughout this course you will be assessed using many                   of the following: quizzes, tests, assignments, journals,                         observations and performance tasks/problems.                               d) These assessments will be worth 70% of the final grade.

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