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Competencies
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Illustrate the different types of conic sections: parabola, ellipse, circle, hyperbola, and degenerate cases.
Define a circle.
Determine the standard form of equation of a circle.
Graph a circle in a rectangular coordinate system.
Define a parabola.
Determine the standard form of equation of a parabola.
Graph a parabola in a rectangular coordinate system.
Define an ellipse.
Determine the standard form of equation of an ellipse.
Graph an ellipse in a rectangular coordinate system.
Define a hyperbola.
Determine the standard form of equation of a hyperbola.
Graph a hyperbola in a rectangular coordinate system.
Recognize the equation and important characteristics of the different types of conic sections.
Solve situational problems involving conic sections.
Illustrate systems of nonlinear equations.
Determine the solutions of systems of nonlinear equations using techniques such as substitution, elimination, and graphing.
Solve situational problems involving systems of nonlinear equations.
Illustrate a series.
Differentiate a series from a sequence.
Use the sigma notation to represent a series.
Illustrate the principle of mathematical induction.
Apply mathematical induction in proving identities.
Illustrate pascal’s triangle in the expansion of (x + y)n for small positive integral values of n
Prove the binomial theorem
Determine any term of (x + y)n, where n is a positive integer, without expanding
Solve problems using mathematical induction and the binomial
theorem
Illustrate the unit circle and the relationship between the linear and angular measures of a central angle in a unit circle
Convert degree measure to radian measure and vice versa
Illustrate angles in standard position and coterminal angles
Illustrate the different circular functions
Uses reference angles to find exact values of circular functions
Determine the domain and range of the different circular functions
Graph the six circular functions (a) amplitude, (b) period, and (c) phase shift
Solve problems involving circular functions
Determine whether an equation is an identity or a conditional equation
Derive the fundamental trigonometric identities
Derive trigonometric identities involving sum and difference of angles
Derive the double and half-angle formulas
Simplify trigonometric expressions
Prove other trigonometric identities
Solve situational problems involving trigonometric identities
Illustrate the domain and range of the inverse trigonometric functions.
Evaluate an inverse trigonometric expression.
Solve trigonometric equations.
Solve situational problems involving inverse trigonometric functions and trigonometric equations
Locate points in polar coordinate system
Convert the coordinates of a point from rectangular to polar
systems and vice versa
Solve situational problems involving polar coordinate system
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