Course Title: Calculus and Vectors
Course Code: MCV4U
Grade: 12
Course Type: University Preparation
Credit Value: 1
Prerequisite: MHF4U (Note: MHF4U may be taking concurrently)
Department: Mathematics

Course Description

This course builds on students’ previous experience with functions and their 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 spaces. This will broaden their understanding of rates of change, including the derivatives of polynomial, sinusoidal, exponential, rational, and radical functions by applying these concepts and skills to the modeling 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 choose to pursue careers in fields such as science, engineering, economics, and in some areas of business, including those students who will be required to take a university-level calculus, linear algebra, or physics course.

Course Outline
  • MCV4U Unit1 Overview
  • Accessibility to MCV4U Unit1 Assignment
  • U1L1 Radical expressions (A1.1)
  • U1L2 Slope of a tangent at a given point on a curve (A1.2)
  • U1L3 Slope of a tangent to functions (A1.2)
  • U1L4 Introduce rate of change (A1.3)
  • U1L5 Rate of change – real world application (A1.1)
  • U1L6 Average and instantaneous rates of change (A1.3)
  • U1L7 Introducing limits (A1.4)
  • U1L8 Determine limits from graphs (A1.4)
  • U1L9 Properties of limits (A1.4)
  • U1L10 Rate of change over interval (A1.5)
  • U1L11 Instantaneous rates of change at a point (A1.6)
  • U1L12 Rate of change calculation (A1.5 A1.6)
  • U1L13 Instantaneous rates of change (A2.1)
  • U1L14 Derivatives of functions (A2.2)
  • U1L15 Calculation of Derivatives (A2.2 A2.3)
  • U1L16 Determine the derivatives of polynomial functions (A3.3)
  • U1L17 Solve the derivatives of various functions (A3.3)
  • U1L18 Derivatives of composite function (A3.4)
  • U1L19 Second derivatives (B1.3)
  • U1L20 Displacement, velocity, and acceleration (Part 1) (B2.1)
  • U1L21 Displacement, velocity, and acceleration (Part 2) (B2.1)
  • U1L22 Second derivatives application (B1.2)
  • U1L23 Derivatives – real world application (Part 1) (B2.3 B2.5)
  • U1L24 Derivatives – real world application (Part 2) (B2.3 B2.5)
  • Finish and hand in MCV4U Unit1 Assignment at the end of lesson
  • MCV4U Unit2 Overview
  • Accessibility to MCV4U Unit2 Assignment
  • U2L1 Intervals of increase and decrease (Part 1) (B1.1)
  • U2L2 Intervals of increase and decrease (Part 2) (D1.8)
  • U2L3 Critical points and local extrema (B1.4)
  • U2L4 The power rule for functions (A3.1)
  • U2L5 Key features of a polynomial function (Part 1) (B1.4)
  • U2L6 Key features of a polynomial function (Part 2) (B1.5)
  • U2L7 The rules of derivative (A3.2)
  • U2L8 Continuity of a function (A3.5)
  • U2L9 Graph polynomial functions accroding to features (B1.5)
  • U2L10 Derivative of exponential functions (Part 1) (A2.5 A2.6)
  • U2L11 Derivative of exponential functions (Part 2) (A2.6 A2.7)
  • U2L12 Derivative of exponential functions (Part 3) (A2.8)
  • U2L13 Graphical and algebraic representations of derivatives (B2.2)
  • U2L14 Optimization of funtions (B2.4)
  • U2L15 Solving real-world problems (B2.2 B2.4)
  • U2L16 Derivatives of sinusoidal functions – sine (A2.4)
  • U2L17 Derivatives of sinusoidal functions – cosine (A2.4)
  • U2L18 Derivatives of sinusoidal functions – exercise (A2.4)
  • U2L19 Derivative of tangent function (Part 1) (A2.4)
  • U2L20 Derivative of tangent function (Part 2) (A2.4)
  • U2L21 Connections between the graphical or algebraic representations (B2.2)
  • U2L22 Real-world applications (B2.4)
  • U2L23 Solve optimization problems (B2.4)
  • U2L24 Review and exercise (A2.4)
  • Finish and hand in MCV4U Unit2 Assignment at the end of lesson
  • MCV4U Unit2 Online Test
  • MCV4U Unit3 Overview
  • Accessibility to MCV4U Unit3 Assignment
  • U3L1 Introduce vector (C1.1)
  • U3L2 Recursive procedure (C1.2)
  • U3L3 Vector calculation (Part 1) (C2.1)
  • U3L4 Vector calculation (Part 2) (C2.1)
  • U3L5 Graph operations on vectors (C2.2)
  • U3L6 Properties of the operations (C2.2)
  • U3L7 Vector calculation – practice (C1.3)
  • U3L8 Points in 2D and 3D space (C1.3 C1.4)
  • U3L9 Cartesian representation for a vector in 2D space (Part 1) (C1.3)
  • U3L10 Cartesian representation for a vector in 2D space (Part 2) (C1.3)
  • U3L11 Cartesian representation for a vector in 3D space (Part 1) (C1.4)
  • U3L12 Cartesian representation for a vector in 3D space (Part 2) (C1.4)
  • U3L13 Force and vector (C2.3)
  • U3L14 Solve force problems (C2.3)
  • U3L15 Real-world investigation of force problems (C2.3)
  • U3L16 Use arithmetic sequences to calculate simple interest (C2.4)
  • U3L17 Computation of dot product (Part 1) (C2.4)
  • U3L18 Computation of dot product (Part 2) (C2.4 C2.5)
  • U3L19 Real-world investigation of dot product (C2.4)
  • U3L20 Scalar and vector projections of a vector (Part 1) (C2.5)
  • U3L21 Scalar and vector projections of a vector (Part 2) (C2.5)
  • U3L22 Introduce cross product (C2.6)
  • U3L23 Properties of the cross product (C2.7)
  • U3L24 Solve problems involving the dot product and cross product (C2.8)
  • Finish and hand in MCV4U Unit3 Assignment at the end of lesson
  • MCV4U Unit4 Overview
  • Accessibility to MCV4U Unit4 Assignment
  • U4L1 Vector and parametric equations (C4.1)
  • U4L2 Vector and parametric equations – practice (C4.1)
  • U4L3 Relationship between direction vectors and slope (C4.1)
  • U4L4 Logarithmic equations (Part 1) (C4.2)
  • U4L5 Relationship between vector equations in 3D space (C4.2)
  • U4L6 Solve exponential and logarithmic functions using graphs (C4.2)
  • U4L7 Geometric properties of a plane (C4.3)
  • U4L8 Equations of a plane (C4.5)
  • U4L9 Sketch a plane (C4.4)
  • U4L10 Intersection between a line and a plane (C3.1)
  • U4L11 Intersection between two lines in 2D and 3D space (C3.3)
  • U4L12 Systems of equations (C3.1)
  • U4L13 Intersection of two planes (C3.2)
  • U4L14 Intersections of three planes (Part 1) (C3.3)
  • U4L15 Intersections of three planes (Part 2) (C3.3)
  • U4L16 Distance form a point to a line – intro (C4.7)
  • U4L17 Distance form a point to a line – practice (C4.7)
  • U4L18 Distance form a point to a line – real-world problems (C4.7)
  • U4L19 Scalar equation for a plane (C4.6)
  • U4L20 Connections between the algebraic solution and the geometric configuration (C4.6)
  • U4L21 Properties of parametric equations (C4.5)
  • U4L22 Parametric equations of a plane (C4.5)
  • U4L23 Real word problem solving (C4.3)
  • U4L24 Review
  • Finish and hand in MCV4U Unit4 Assignment at the end of lesson
  • MCV4U Unit4 Online Test
  • MCV4U Final Project
  • MCV4U Final Exam
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