The following tutorials are test reviews for the Mcgraw-Hill Ryerson Calculus &Vectors textbook in the province of Ontario, Canada.
This tutorial discusses (in detail) the solutions to a Calculus test on rates of change, limits and finding derivatives using the first principles definition of the derivative.
This tutorial was created for the Calculus & Vectors (MCV4U) course in the province of Ontario, Canada and aligns with the McGraw-Hill Ryerson Calculus & Vectors textbook.
A pdf copy of the review plus answers can be found at this link: Rates of Change
This tutorial discusses (in detail) the solutions to a Calculus test on differentiation. Topics include power rule, sum/difference rule, chain rule and the quotient rule. Examples include both multiple choice questions and long answer including tangent line questions, velocity and acceleration and a business profit - revenue - cost question.
This tutorial was created for the Calculus & Vectors (MCV4U) course in the province of Ontario, Canada and aligns with the McGraw-Hill Ryerson Calculus & Vectors textbook.
A pdf copy of the review plus answers can be found at this link: Derivatives .
This tutorial discusses (in detail) the solutions to a Calculus test on curve sketching and optimization. Topics include local maxima/minima, intervals of increase/decrease, concavity and points of inflection, sketching a curve using the aforementioned tools and three examples of optimization.
This tutorial was created for the Calculus & Vectors (MCV4U) course in the province of Ontario, Canada and aligns with the McGraw-Hill Ryerson Calculus & Vectors textbook.
A pdf copy of the review plus answers can be found at this link: Curve Sketching .
This tutorial discusses (in detail) the solutions to a Calculus test on differentiation of sinusoidal functions. Topics include differentiating sine and cosine functions and functions with sinusoidal functions in them. Differentiation examples include using the product, quotient and chain rules to differentiate these functions. Two examples also include modelling with sinusoidal functions with some derivatives questions included.
This tutorial was created for the Calculus & Vectors (MCV4U) course in the province of Ontario, Canada and aligns with the McGraw-Hill Ryerson Calculus & Vectors textbook.
A pdf copy of the review plus answers can be found at this link: Derivatives of Sinusoidal Functions.
This tutorial discusses (in detail) the solutions to a Calculus test on differentiation of exponential functions and also includes some questions relating to logarithmic functions (although no derivatives of logs). Differentiation examples include using the product, and chain rules to differentiate exponential functions. Examples include modelling with exponential functions with some derivatives questions included and finding equations of tangent lines to functions with exponential parts
This tutorial was created for the Calculus & Vectors (MCV4U) course in the province of Ontario, Canada and aligns with the McGraw-Hill Ryerson Calculus & Vectors textbook.
A pdf copy of the review plus answers can be found at this link: Exponential and Log Functions
This tutorial discusses (in detail) the solutions to a Calculus test on geometric vectors. Topics include properties of vectors and scalars, components, adding and subtracting vectors geometrically and some applications involving forces and velocities.
This tutorial was created for the Calculus & Vectors (MCV4U) course in the province of Ontario, Canada and aligns with the McGraw-Hill Ryerson Calculus & Vectors textbook.
A pdf copy of the review plus answers can be found at this link: Geometric Vectors
This tutorial discusses (in detail) the solutions to a Calculus test on Cartesian vectors. Topics include properties of vectors and scalars, components, adding and subtracting vectors algebraically and some applications the dot & cross product. An algebraic proof is also included.
This tutorial was created for the Calculus & Vectors (MCV4U) course in the province of Ontario, Canada and aligns with the McGraw-Hill Ryerson Calculus & Vectors textbook.
A pdf copy of the review plus answers can be found at this link: Cartesian Vectors
This tutorial discusses (in detail) the solutions to a Calculus test on equations of lines and planes. Topics include finding vector and parametric equations of lines given points and vectors parallel to the line and finding parametric, vector and Cartesian (or scalar) equations of planes from knowing a point on the plane and vectors parallel to the plane or three points in the plane.
Several questions also include fining intersections of lines with a plane or intersections of three planes.
This tutorial was created for the Calculus & Vectors (MCV4U) course in the province of Ontario, Canada and aligns with the McGraw-Hill Ryerson Calculus & Vectors textbook.
A pdf copy of the review plus answers can be found at this link: Equations of Lines and Planes