Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles.
Determine the equation of a circle that is described geometrically in the coordinate plane and, given equations for a circle and a line, determine the coordinates of their intersection(s).
Explain and perform constructions related to the circle.
Derive and apply formulas for arc length and area of a sector of a circle.
SCI.9-12.1.9-12 SYSA.1: Science
Give examples of a positive feedback system and explain its regulatory mechanism (e.g., global warming causes Earth's ice caps to melt, reflecting less energy to space, increasing temperatures).
SCI.9-12.1.9-12 SYSA.2: Science
Give examples of a negative feedback system and explain its regulatory mechanism (e.g., when a human body overheats, it produces sweat that cools the body by evaporation).
SCI.9-12.1.9-12 SYSB.1: Science
Determine if a systems approach will be helpful in answering a question or solving a problem.
SCI.9-12.1.9-12 SYSB.2: Science
Represent the system with a diagram specifying components, boundaries, flows, and feedbacks.
SCI.9-12.1.9-12 SYSB.3: Science
Describe relevant subsystems and the larger system that contains the system being analyzed.
SCI.9-12.1.9-12 SYSB.4: Science
Determine how the system functions with respect to other systems.
SCI.9-12.1.9-12 SYSC.1: Science
Create a simplified model of a complex system. Trace the possible consequences of a change in one part of the system and explain how the simplified model may not be adequate to reliably predict consequences.
SCI.9-12.1.9-12 SYSD.1: Science
Analyze whether or not a system (e.g., population) is changing or in equilibrium.
SCI.9-12.1.9-12 SYSD.2: Science
Determine whether a state of equilibrium is static or dynamic (e.g., inflows equal outflows).