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Questions and Answers
Who is the Chairperson of the Commission on Higher Education?
Patricia B. Licuanan, Ph.D.
What license is the Teaching Guide for Senior High School under?
How can the material be shared under the Creative Commons license?
Share — copy and redistribute the material in any medium or format; Adapt — remix, transform, and build upon the material.
Define a parabola.
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What is the standard form of the equation of a parabola?
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Which of the following is an example of a conic section?
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The _____ barked.
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What is the core subject title discussed in the provided content?
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What are some of the topics covered in Unit 1: Analytic Geometry?
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The SHS for SHS Framework stands for 'Skills-Harmony-Strength' - True or False?
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In Lesson 2.4, students learn about Pascal's Triangle and the concept of __________.
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Match the following components with their meanings in the SHS for SHS Framework:
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What does the precalculus course aim to provide students who are planning to take courses in the STEM track?
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What is the primary aim of the Teaching Guide for Precalculus based on the Curriculum Guide for Precalculus of the Department of Education?
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What are some of the elements provided in the Teaching Guide to guide teachers?
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The equation of the curve that contains the possible location of the epicenter is $____ + (y + 3)^2 = 6^2$
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What are the dimensions of the window shown in the figure? (rounded off to 1 decimal place)
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Which of the following equations represents a parabola in a vertical orientation?
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A parabola with its vertex at the origin always opens upward.
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What are the four types of conic sections discussed in the lesson?
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Define a circle.
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What is the standard equation of a circle with center C(h, k) and radius r?
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A circle may also be considered a special kind of _____ for the special case when the tilted plane is horizontal.
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What are the coordinates of the center of a circle with equation (x + 2)^2 + (y + 1)^2 = 16?
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Match the following circle descriptions with their standard equations:
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Identify the center and radius of the circle with the equation x^2 + y^2 = 49. Sketch its graph and indicate the center.
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Identify the center and radius of the circle with the equation 4x^2 + 4y^2 = 25. Sketch its graph and indicate the center.
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Identify the center and radius of the circle with the equation x^2 + y^2 - 12x - 10y = 12. Sketch its graph and indicate the center.
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Identify the center and radius of the circle with the equation x^2 + y^2 + 8x - 9y = 6. Sketch its graph and indicate the center.
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Identify the center and radius of the circle with the equation 4x^2 + 4y^2 - 20x - 40y = 5. Sketch its graph and indicate the center.
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What is the shape formed by the collection of all points where the sum of distances from two distinct points is constant?
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What are the points called that are on the x-axis and are a certain distance away from the center of the ellipse?
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What are the points on the ellipse that are collinear with the center and foci?
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What is the segment through the center of the ellipse, perpendicular to the major axis, called?
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What is the part of the ellipse that the minor axis divides into two congruent parts?
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What is the directrix of the parabola in the given scenario?
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What is the axis of symmetry of the parabola in the given scenario?
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What is the standard form equation of the parabola in general form (y^2 + 8x + 8y - 24 = 0) in the provided context?
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What is the vertex of the parabola with the equation y^2 - 5x + 12y = 16?
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The standard equation for the parabola given by 5x^2 + 30x = 24y + 51 can be rewritten as __(x + 3)^2 = __(y - 4).
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Study Notes
Introduction to Teaching Guide for Senior High School Precalculus
- The Commission on Higher Education (CHED) developed this Teaching Guide in collaboration with the Philippine Normal University (PNU) for Senior High School Precalculus.
- The guide is designed to support teachers in implementing the K to 12 curriculum and promoting the vision and mission of the K to 12 program.
- The guide is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
SHS for SHS Framework
- The SHS for SHS Framework is a guiding principle for teaching and learning in Senior High School.
- The framework consists of three fundamental concepts:
- SAYSAY: Meaning (Why is this important?)
- HUSAY: Mastery (How will I deeply understand this?)
- SARILI: Ownership (What can I do with this?)
Precalculus Curriculum Guide
- The Precalculus course is a Core Subject for Grade 11 students in the Science, Technology, Engineering, and Mathematics (STEM) strand.
- The course consists of 80 hours of instruction per semester.
- The course covers the following topics:
- Analytic Geometry: conic sections, systems of nonlinear equations
- Mathematical Induction: series, summation, and mathematical induction
- Trigonometry: circular and trigonometric functions, trigonometric identities, and polar coordinate system
Analytic Geometry
- Conic sections: parabola, ellipse, hyperbola, and degenerate cases
- Key concepts: definition and equation of a circle, parabola, ellipse, and hyperbola
- Graphing conic sections in a rectangular coordinate system
- Solving situational problems involving conic sections
Learning Competencies
- The learners shall be able to:
- Illustrate the different types of conic sections
- Define and determine the standard form of equation of a circle, parabola, ellipse, and hyperbola
- Graph conic sections in a rectangular coordinate system
- Solve situational problems involving conic sections### STEM PC11: Pre-Calculus
- The course covers key concepts of Analytic Geometry, Series and Mathematical Induction, and Trigonometry.
- It aims to provide students with conceptual understanding and computational skills crucial for Basic Calculus and future STEM courses.
Analytic Geometry
- Solve systems of nonlinear equations using techniques such as substitution, elimination, and graphing.
- Solve situational problems involving systems of nonlinear equations.
Series and Mathematical Induction
- Illustrate a series and differentiate it from a sequence.
- Use the sigma notation to represent a series.
- 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 without expanding.
- Solve problems using mathematical induction and the Binomial Theorem.
Trigonometry
- Formulate and solve situational problems involving circular functions.
- 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 and use reference angles to find exact values of circular functions.
- Determine the domain and range of the different circular functions.
- Graph the six circular functions (amplitude, period, and phase shift).
- Solve problems involving circular functions.
- Apply appropriate trigonometric identities in solving situational problems.
- Derive the fundamental trigonometric identities and trigonometric identities involving sum and difference of angles.
- Derive the double and half-angle formulas and simplify trigonometric expressions.
- Prove other trigonometric identities and solve situational problems involving trigonometric identities.
- Illustrate the domain and range of the inverse trigonometric functions.
- Evaluate an inverse trigonometric expression and solve trigonometric equations.
- Solve situational problems involving inverse trigonometric functions and trigonometric equations.
- Locate points in polar coordinate system and convert the coordinates of a point from rectangular to polar systems and vice versa.
- Solve situational problems involving polar coordinate system.
Teaching Guide
- The guide is divided into three units: Analytic Geometry, Summation Notation and Mathematical Induction, and Trigonometry.
- Each unit is composed of lessons that bring together related learning competencies.
- Each lesson is further divided into sub-lessons that focus on one or two competencies for effective teaching and learning.
- Each sub-lesson is designed for a one-hour session, but teachers have the option to extend the time allotment to one-and-a-half hours for some sub-lessons.
- Each sub-lesson ends with a Seatwork/Homework, which consists of exercises related to the topic being discussed.
- Exercises can be used for short quizzes and long exams.
- Answers, solutions, or hints to most items in Seatwork/Homework and Exercises are provided to guide teachers.
About the Teaching Guide
- The guide is designed to be highly usable for teachers and contains classroom activities and pedagogical notes.
- It is integrated with innovative pedagogies.
- The guide is mapped and aligned to the DepEd SHS Curriculum.
DepEd Functional Skills and CHED's College Readiness Standards
- The DepEd articulated a set of 21st century skills that should be embedded in the SHS curriculum across various subjects and tracks.
- The skills are desired outcomes that K to 12 graduates should possess in order to proceed to either higher education, employment, entrepreneurship, or middle-level skills development.
- The Commission declared the College Readiness Standards that consist of the combination of knowledge, skills, and reflective thinking necessary to participate and succeed in entry-level undergraduate courses in college.
- The alignment of both standards prepares Senior High School graduates to the revised college curriculum which will initially be implemented by AY 2018-2019.### Civic Awareness and Responsibility
- A citizen of a multicultural Philippines and a diverse world should have clear appreciation of one's responsibility.
- Key aspects of civic awareness and responsibility include:
- Global awareness
- Scientific and economic literacy
- Critical thinking and problem-solving skills
- Risk-taking
- Flexibility and adaptability
- Initiative and self-direction
Analytic Geometry: Conic Sections and Circles
- Conic sections are a particular class of curves that appear in nature and have applications in other fields.
- The four conic sections are:
- Parabola: when the plane intersects only one cone to form an unbounded curve
- Ellipse: when the (tilted) plane intersects only one cone to form a bounded curve
- Circle: a special kind of ellipse (for the special case when the tilted plane is horizontal)
- Hyperbola: when the plane (not necessarily vertical) intersects both cones to form two unbounded curves
Properties of Circles
- Definition of a circle: a set of all points P having the same distance from a given point C (the center)
- Standard equation of a circle: (x - h)^2 + (y - k)^2 = r^2
- Properties:
- Radius: the distance from the center to a point on the circle
- Center: the point that is equidistant from every point on the circle
- Diameter: a line segment that passes through the center and connects two points on the circle
- Circumference: the distance around the circle
Solving Situational Problems Involving Circles
- Real-world applications of circle properties:
- Semircular tunnels
- Archaeological plates
- Techniques:
- Perpendicular bisectors
- Midpoints
- Distance formula
- Completing the square
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Description
Test your understanding of parabolas, conic sections, and math-related questions on education and licenses. Review the standard form of a parabola's equation and learn about Creative Commons licenses.
