# K to 12 Senior High School STEM Specialized Subject – Pre-Calculus Curriculum Guide

Curriculum Guide  |  PDF

Published on 2018 September 21st

Description
Curriculum Guide of K to 12 Senior High School STEM Specialized Subject – Pre-Calculus for Grade 11
Objective

#### Curriculum Information

 Education Type K to 12 Grade Level Grade 11 Learning Area Content/Topic Analytic Geometry Series and Mathematical Induction Trigonometry Intended Users Educators Competencies 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