### A: Rate of Change

#### A.2: 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;

A.2.7: recognize that the natural logarithmic function f(x) = log base e of x, also written as f(x) = ln x, is the inverse of the exponential function f(x) = e to the x power , and make connections between f(x) = ln x and f(x) = e to the x power [e.g., f(x) = ln x reverses what f(x) = e to the x power does; their graphs are reflections of each other in the line y = x; the composition of the two functions, e to the lnx power or ln e to the x power , maps x onto itself, that is, e to the lnx power = x and ln e to the x power = x]

### C: Geometry and Algebra of Vectors

#### C.1: demonstrate an understanding of vectors in two-space and three-space by representing them algebraically and geometrically and by recognizing their applications;

C.1.1: recognize a vector as a quantity with both magnitude and direction, and identify, gather, and interpret information about real-world applications of vectors (e.g., displacement, forces involved in structural design, simple animation of computer graphics, velocity determined using GPS)

C.1.2: represent a vector in two-space geometrically as a directed line segment, with directions expressed in different ways (e.g., 320º; N 40º W), and algebraically (e.g., using Cartesian coordinates; using polar coordinates), and recognize vectors with the same magnitude and direction but different positions as equal vectors

C.1.4: recognize that points and vectors in three-space can both be represented using Cartesian coordinates, and determine the distance between two points and the magnitude of a vector using their Cartesian representations

#### C.2: 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;

C.2.1: perform the operations of addition, subtraction, and scalar multiplication on vectors represented as directed line segments in two-space, and on vectors represented in Cartesian form in two-space and three-space

C.2.3: solve problems involving the addition, subtraction, and scalar multiplication of vectors, including problems arising from real-world applications

C.2.4: perform the operation of dot product on two vectors represented as directed line segments (i.e., using vector a times vector b = (absolute value of vector a)(absolute value of vector b)(cos Theta)) and in Cartesian form (i.e., using vector a times vector b = (a base 1 of b base 1) + (a base 2 of b base 2) or (vector a times vector b) = (a base 1 of b base 1) + (a base 2 of b base 2) + (a base 3 of b base 3)) in two-space and three-space, and describe applications of the dot product (e.g., determining the angle between two vectors; determining the projection of one vector onto another)

C.2.5: determine, through investigation, properties of the dot product (e.g., investigate whether it is commutative, distributive, or associative; investigate the dot product of a vector with itself and the dot product of orthogonal vectors)

#### C.3: 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;

C.3.1: recognize that the solution points (x, y) in two-space of a single linear equation in two variables form a line and that the solution points (x, y) in two-space of a system of two linear equations in two variables determine the point of intersection of two lines, if the lines are not coincident or parallel

C.3.3: determine, through investigation using a variety of tools and strategies (e.g., modelling with cardboard sheets and drinking straws; sketching on isometric graph paper), different geometric configurations of combinations of up to three lines and/or planes in three-space (e.g., two skew lines, three parallel planes, two intersecting planes, an intersecting line and plane); organize the configurations based on whether they intersect and, if so, how they intersect (i.e., in a point, in a line, in a plane)

Correlation last revised: 8/18/2015

This correlation lists the recommended Gizmos for this province's curriculum standards. Click any Gizmo title below for more information.