MCV4U Practice Tests: Grade 12 Calculus and Vectors

Limits

What a limit is, evaluating limits algebraically and from a graph, one-sided limits, and continuity.

Derivatives

The derivative as a rate of change and as the slope of a tangent. First principles, then the power, product, quotient, and chain rules.

Curve Sketching

Using the first and second derivatives to find intervals of increase and decrease, maximum and minimum points, concavity, points of inflection, and asymptotes, then putting them together into a graph.

Optimization

Building a model from a word problem, finding the maximum or minimum on an interval, and related rates.

Derivatives of Trig, Exp and Log

Derivatives of sine, cosine, and tangent, of exponential functions, and of logarithms, and combining them with the product, quotient, and chain rules.

Geometric Vectors

Vectors as magnitude and direction. Adding and subtracting them, scalar multiples, and resolving forces and velocities into components.

Cartesian Vectors

Vectors in component form in two and three dimensions, the dot product and the cross product, projections, and the angle between two vectors.

Lines and Planes

Vector, parametric, symmetric, and scalar equations of lines and planes, and finding where they intersect.