Students solve simple radical equations and understand the possibility of extraneous solutions. They understand that care must be taken with the role of square roots so as to avoid apparent paradoxes.
Students explain and justify the steps taken in solving simple radical equations.

Students develop facility with graphical interpretations of systems of equations and the meaning of their solutions on those graphs. For example, they can use the distance formula to find the distance between the centers of two circles and thereby determine whether the circles intersect in 0, 1, or 2 points.
By completing the squares, students can convert the equation of a circle in general form to the center-radius form and, thus, find the radius and center. They can also convert the center-radius form to the general form by removing parentheses and combining like terms.
Students understand how to solve and graph a system consisting of two quadratic equations in two variables.

Students understand the possibility that an equation—or a system of equations—has no real solutions. Students identify these situations and make the appropriate geometric connections.

Students define a complex number in the form a + bi, where a and b are real numbers and the imaginary unit i satisfies i 2 = −1. Students geometrically identify i as a multiplicand effecting a 90° counterclockwise rotation of the real number line. Students locate points corresponding to complex numbers in the complex plane.
Students understand complex numbers as a superset of the real numbers; i.e., a complex number a + bi is real when b = 0. Students learn that complex numbers share many similar properties of the real numbers: associative, commutative, distributive, addition/subtraction, multiplication, etc.

Students solve quadratic equations with real coefficients that have complex solutions. They recognize when the quadratic formula gives complex solutions and write them as a + bi for real numbers a and b.

Students solve quadratic equations with real coefficients that have complex solutions. Students extend polynomial identities to the complex numbers.
Students note the difference between solutions to the equation and the x-intercepts of the graph of said equation.

Students understand the Fundamental Theorem of Algebra; that all polynomial expressions factor into linear terms in the realm of complex numbers. Consequences, in particular, for quadratic and cubic equations are understood.

Students apply geometric concepts in modeling situations. Specifically, they find distances between points of a circle and a given line to represent the height above the ground of a passenger car on a Ferris wheel as it is rotated a number of degrees about the origin from an initial reference point.
Students sketch the graph of a nonlinear relationship between variables

Students observe identities from graphs of sine and cosine basic trigonometric identities and relate those identities to periodicity, even and odd properties, intercepts, end behavior, and the fact that cosine is a horizontal translation of sine.

Students explore the historical context of trigonometry as motion of celestial bodies in a presumed circular arc.
Students describe the position of an object along a line of sight in the context of circular motion.
Students understand the naming of the quadrants and why counterclockwise motion is deemed the positive direction of turning in mathematics.

Students will define sine and cosine as functions for all real numbers measured in degrees.
Students will evaluate the sine and cosine functions at multiples of 30 and 45.

Students define the tangent function and understand the historic reason for its name.
Students use special triangles to determine geometrically the values of the tangent function for 30°, 45°, and 60°.

Students define the secant function and the co-functions in terms of points on the unit circle. They relate these names for these functions to the geometric relationships among lines, angles, and right triangles in a unit circle diagram.
Students use reciprocal relationships to relate the trigonometric functions and use these relationships to evaluate trigonometric functions for multiples of 30, 45, and 60 degrees.

Students graph the sine and cosine functions and analyze the shape of these curves.
For the sine and cosine functions, students sketch graphs showing key features, which include intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maxima and minima; symmetries; end behavior; and periodicity.

Students explore horizontal scalings of the graph of y =sin(x).
Students convert between degrees and radians.