FIRST SEMESTER SYLLABUS IN PRE CALCULUS FIRST QUARTER · Grade 11: First Semester Syllabus in PRE -...

Grade 11: First Semester Syllabus in PRE - CALCULUS | 1

SENIOR HIGH SCHOOL

BASIC EDUCATION DEPARTMENT

Holy Angel University

Angeles City

FIRST SEMESTER SYLLABUS IN PRE – CALCULUS

FIRST QUARTER

CORE SUBJECT DESCRIPTION

The learner must be able to apply concepts and solve problems involving conic sections, systems

of nonlinear equations, series and mathematical induction, circular and trigonometric functions,

trigonometric identities, and polar coordinate system.

CONTENT STANDARD The learner demonstrates understanding of key concepts of problems involving conic sections,

systems of nonlinear equations, series and mathematical induction.

PERFORMANCE STANDARD

The learner is able to model situations appropriately and solve problems accurately using conic

sections and systems of nonlinear equations and; keenly observe and investigate patterns, and

formulate appropriate mathematical statements and prove them using mathematical induction

and/or Binomial Theorem.

TIME

FRAME TOPICS LEARNING COMPETENCIES ASSESSMENT

WEEK 1

Rectangular Coordinate System

o Distance Formula

o Midpoint Formula

o Slope

Values:

Socially Responsive Community

Leader. The concepts of the

Midpoint formula and Slope

The learner…

1. ENRICHMENT

uses the distance formula

2. ENRICHMENT

applies the midpoint formula

3. ENRICHMENT

recognize slope

Formative:

Recitation: How Far Can You

Go?

Board work: What’s the Point?

Reflect: Anong Hugot Mo?

Summative:

LAS 1 (Applications of

Distance Formula, Midpoint


illustrate the concept of equality

versus justice in the current society.

4. ENRICHMENT

applies skills in distance formula,

midpoint formulas and slope in

solving situational problems

Formula and Slope)

Quiz 1 – 1 (Rectangular

Coordinate System)

WEEK 2

Systems of Linear and Non-

Linear Equations

Techniques in Solving Systems

of Linear and Non-Linear

Equations

o Substitution

o Elimination

o Graphing

Solving Situational Problems

Values:

Critical thinker. In any problem that

man encounters, there will always

be different ways on how to

approach it and solve it. This is the

concept shown by the various

techniques in solving systems of

linear and nonlinear systems.

The learner…

1. STEM_PC11AG-If-1

illustrates systems of linear and

nonlinear equations.

2. STEM_PC11AG-If-g-1

determines the solutions of systems

of linear and nonlinear equations

using techniques such as

substitution, elimination, and

graphing.

3. STEM_PC11AG-Ig-2

solves situational problems involving

systems of linear and nonlinear

equations.

Formative:


Go?



Summative:

LAS 2 (Finding the Solutions

of Systems of Linear and

Nonlinear Equations using

Substitution, Elimination and

Graphing)

LAS 3 (Solving Situational

Problems Involving Systems of

Linear and Nonlinear

Equations)

Quiz 1 – 2 (Systems of Linear

and Nonlinear Equations)

WEEK 3

Introduction to Conics

Circle

o Standard Equation

o General Equation

The learner…

1. STEM_PC11AG-Ia-1

illustrates the different types of conic

sections: parabola, ellipse, circle,

hyperbola, and degenerate cases.

Formative:


Go?



o Graphing

Parabola

o Equation

o Graphing

Values:

Emotionally stable individual and

Balance. A journey towards

success should be a balance from

the point of achieving and the point

of giving up, in order have the right

amount of enthusiasm. Such

balance is shown in the concept of

locus as a path traveled by a point

with equal distance from

references.

Life - long learner. The center of a

circle is likened to the core values

of a person, and the radius as one’s

knowledge and abilities. Given

these variables, one can determine

the equation of a circle, which, in

real life, is finding one’s purpose in

life.

Effective communicator. Thoughts

can be expressed in various ways,

depending on the situation, but will

still possess the same meaning.

This is implicit in the lesson on

transforming the standard form of

an equation of a parabola to its

2. STEM_PC11AG-Ia-2

defines a circle.

3. STEM_PC11AG-Ia-3

finds the equation of a circle, given

its center and radius and vice versa.

4. STEM_PC11AG-Ia-4

graphs a circle in a rectangular

coordinate system.

5. STEM_PC11AG-Ia-5

defines a parabola.

6. STEM_PC11AG-Ib-1

determines the standard form of

equation of a parabola.

7. ENRICHMENT

finds the general form of the

equation of a parabola.

8. STEM_PC11AG-Ib-2

graphs a parabola in a rectangular

coordinate system.

9. STEM_PC11AG-Ie-2

solves situational problems

involving circles and parabolas.


Summative:

LAS 4 (Equations and Graphs

of Circles)


of Parabolas)

Quiz 1 – 3 (Circle and

Parabola)


general form.

WEEK 4

Ellipse

o Equation

o Graphing

Hyperbola

o Equation

o Graphing

Values:

Christ – centered individual.

Ellipses with vertex at the center is

like having God as the center of

one’s life, which makes things feel

lighter and easier, because He is

always there.

Life – long learner. The figure of a

hyperbola itself is a constant

reminder that there will always be

opposites, whether it be positive or

negative. Life becomes a mirror of

one’s dreams and aspirations

versus one’s achievements, where

the axis of symmetry is determined

by hard work and prayer.

The learner…

1. STEM_PC11AG-Ic-1

defines an ellipse.

2. STEM_PC11AG-Ic-2


equation of an ellipse.

3. STEM_PC11AG-Ic-3

graphs an ellipse with center at the

origin in a rectangular coordinate

system.

4. STEM_PC11AG-Id-1

defines a hyperbola.

5. STEM_PC11AG-Id-2


equation of a hyperbola.

6. ENRICHMENT

find the vertices, foci and

asymptotes of a hyperbola given an

equation

7. STEM_PC11AG-Id-3

graphs a hyperbola in a rectangular

Formative:


Go?



Summative:


of Ellipse)


of Hyperbola)

Quiz 1 – 4 (Ellipse and

Hyperbola)

Performance Task 1: Conic

sections on Earth!


coordinate system.

8. STEM_PC11AG-Ie-2

solves situational problems

involving ellipse and hyperbolas.

9. STEM_PC11AG-Ie-1

recognizes the equation and

important characteristics of the

different types of conic sections.

WEEK 5

Examination Week

1ST Mid - Quarter Exam

WEEK 6

Sequence

Series

o Sigma notation

Values:

Critical and systematic thinker.

Sequence is a continuous or

connected series that comes one

after the other. The idea conveys

that man should have an organized

and structured mind set to have a

smooth pace of life and an untangled

life path.

The learner…

1. STEM_PC11SMI-Ih-1

illustrates a series.


differentiates a series from a

sequence.

3. ENRICHMENT

find the general and nth term of

the sequence


uses the sigma notation to

represent a series.

5. ENRICHMENT

state the difference between

Formative:


Go?



Summative:

LAS 8 (Sequence)

LAS 9 (Sigma Notation for

Series)

Quiz 1 – 5 (Sequence and

Series)


arithmetic, geometric and

harmonic sequence and series.

WEEK 7

Pascal’s Triangle

Binomial Theorem

Values:

Life – long learner. Pascal’s triangle

has “1” on its peak and it is the

foundation of everything and the

triangle is made accumulatively

starting from the peak. Hence, man

should always look back before

moving forward in life. He has to use

his past experience to pass through

the challenges that comes along his

way.

The learner…

1. STEM_PC11SMI-Ii-2

illustrates Pascal’s Triangle in the

expansion of 𝑥 + 𝑦 𝑛 for small positive

integral values of 𝑛.

2. STEM_PC11SMI-Ii-3

proves the Binomial Theorem.

Formative:


Go?



Summative:

LAS 10 (Pascal’s Triangle)

Quiz 1 – 6 (Pascal’s Triangle)

WEEK 8

Mathematical Induction

Values:

Gender sensitive and Person with

High integrity. Mathematical

induction shows that a sigma

notation is equal to its expanded

form. In life, man should not be

blinded of the differences of man

physically. Man should treat

everybody else fairly.

The learner…


illustrates the Principle of

Mathematical Induction.

2. STEM_PC11SMI-Ih-i-1

applies mathematical induction in proving

identities.

Formative:


Go?



Summative:

LAS 11 (Mathematical

Induction)

Quiz 1 – 7 (Mathematical

Induction)


WEEK 9

Expanding Binomial Theorem

Solving Problems using

Mathematical Induction and

Binomial Theorem

Values:

Critical thinker and Life – long

learner. Binomial Theorem is solved

using combination and its quite

complex in appearance but on the

latter it’s as easy as pie. Man

shouldn’t be afraid to face the

challenges in his life because not

everything that looks difficult is

difficult at all. Man should also learn

to limit or control himself. He

shouldn’t do everything that he can

do but only those what he is ask to.

The learner…

1. STEM_PC11SMI-Ij-1

determines any term of (𝑥+𝑦)𝑛,

where 𝑛 is a positive integer,

without expanding.

2. STEM_PC11SMI-Ij-2

solves problems using

mathematical induction and the

Binomial Theorem.

Formative:


Go?



Summative:

LAS 12 (Expand me!)

LAS 13 (Mathematical

Induction and Binomial

Theorem in the Present!)

Quiz 1 – 8 (Problem solving in

Mathematical Induction and

Binomial Theorem)

Performance Task 2

WEEK 10 Examination Week

1st Quarter Examination


SENIOR HIGH SCHOOL

BASIC EDUCATION DEPARTMENT

Holy Angel University

Angeles City

FIRST SEMESTER SYLLABUS IN PRE – CALCULUS

SECOND QUARTER

CORE SUBJECT DESCRIPTION

The learner must be able to apply concepts and solve problems involving conic sections, systems of nonlinear equations, series and mathematical induction, circular and trigonometric functions, trigonometric identities, and polar coordinate system.

CONTENT STANDARD

The learner demonstrates understanding of key concepts of circular and trigonometric functions, trigonometric identities, inverse trigonometric functions and the polar coordinate system.

PERFORMANCE STANDARD

The learner is able to formulate and solve situational problems involving circular functions, trigonometric identities, trigonometric functions and the polar coordinate system.

TIME

FRAME TOPICS LEARNING COMPETENCIES ASSESSMENT

WEEK 11

Unit Circle

Conversion of Degree and Radian Measure

Angles o Standard Position o Co-terminal Angles

Circular Functions o Reference Angles

Values Life – long learner. The unit circle,

conversion of degree measure to radian measure, co-terminal angles,

The learner… 1. STEM_PC11T-IIa-1

illustrates the unit circle and the relationship between the linear and angular measures of a central angle in a unit circle.

2. STEM_PC11T-IIa-2 converts degree measure to radian measure and vice versa.

3. STEM_PC11T-IIa-3 illustrates angles in standard position

Formative:


Go?

Board work: What’s the

Point?


Summative:

LAS 1 (Applications of unit circle, conversion of degree to radian measure and vice versa)


and reference angles are the foundation of trigonometry. These lessons serve as a gateway to more trigonometry and other mathematical topics that will be studied more in depth as the class proceeds. All of us started learning the basic skills we needed to survive each day. Weak foundation results to a chaotic and unorganized living. Whereas, a life established with a strong foundation yields a harmonious cycle of living.

and co-terminal angles.

4. STEM_PC11T-IIb-1 illustrates different circular functions.

5. STEM_PC11T-IIb-2 uses reference angles to find exact values of circular functions.

LAS 2 (Basic Circular Functions)

Quiz 2 – 1 (Unit Circle and Conversion)

WEEK 12

Circular Functions

o Domain and Range Six Circular Functions

o Amplitude o Period o Phase Shift

Problem Solving involving Circular Functions

Values: Life – long learner. The circular

functions, also being repetitive, are very useful in analyzing such periodic phenomena.

In the circle of life, certain behaviors must be practiced repeatedly in order for them to be reinforced.

The learner… 1. STEM_PC11T-IIc-1

determines the domain and range of different circular functions.

2. STEM_PC11T-IIc-d-1 graphs the six circular functions (a) amplitude, (b) period and, (c) phase shift.

3. STEM_PC11T-IId-2 solves problems involving circular functions.

Formative:


Go?


Point?


Summative:

LAS 3 (Circular Functions and Problem Solving)

Quiz 2 – 2 (Circular Functions)

WEEK 13

Conditional Equations

Fundamental Trigonometric

The learner… 1. STEM_PC11T-IIe-1

Formative:



Identities o Sum and Difference of Angles o Double and Half-Angle

Formulas Values: Critical thinker and Globally

competitive. Trigonometric expressions are non-routine appearing problems. They are unfamiliar because the language of trigonometry looks foreign and complicated. In order to learn how to simplify or reduce the complexity of trigonometric expressions, we first need to examine the identities we need to utilize. Part of the history and story of a mankind are unfamiliar situations that may either be treated as struggles or challenges that can define a person’s future. In life, we always have to face these foreign circumstances for these can be tools for the betterment of one’s life.

determines whether an equation is an identity or a conditional equation.

2. STEM_PC11T-IIe-2 derives the fundamental trigonometric identities.

3. STEM_PC11T-IIe-3

derives trigonometric identities involving sum and difference of angles.

4. STEM_PC11T-IIf-1 derives the double and half-angle formulas.

Go?


Point?

Reflect: Anong Hugot Mo? Summative:

LAS 4 (Fundamental Trigonometric Identities)

Quiz 2 – 3 (Conditional; Equations and Fundamental Trigonometric Identities)

WEEK 14

Trigonometric Expressions o Simplifying o Proving

Problem Solving Values: Creative and Innovative Individual.

Simplifying trigonometric expressions is comparable to

The learner... 1. STEM_PC11T-IIf-2

simplifies trigonometric expressions.

2. STEM_PC11T-IIf-g-1 proves other trigonometric identities.

3. STEM_PC11T-IIg-2 solves situational problems involving

Formative:


Go?


Point?



making life easier. Simplified living means creating peace and harmony in one’s life and making each day as easy as possible; not escaping from the complexities of life but facing difficulties with enthusiasm resulting to a well-evaluated life.

trigonometric identities. LAS 5 (Trigonometric Expressions and Problem Solving)

Quiz 2 – 4 (Trigonometric Expressions)

Performance Task 3

WEEK 15

Examination Week 2nd Mid - Quarter Examination

WEEK 16

Inverse Trigonometric Functions o Domain and Range o Evaluating Expressions

Values: Emotionally stable Individual. Inverse

trigonometric functions are used to find the unknown measure of an angle when two side lengths are known. This concept is similar to the story of Sadness in the movie Inside Out. She may be negative in nature but she still has an important purpose in her world. Likewise in life, unnecessary events happen for a certain purpose. They may be in the form of struggles, but still, these can make a person wiser.

The learner... 1. STEM_PC11T-IIh-1

illustrates the domain and range of the inverse trigonometric functions.

2. STEM_PC11T-IIh-2 evaluates an inverse trigonometric expression.

Formative:


Go?


Point?


LAS 6 (Inverse Trigonometric Functions)

Quiz 2 – 5 (Inverse Trigonometric Functions)

WEEK 17

Trigonometric Equations

Problem Solving Values:

The learner... 1. STEM_PC11T-IIh-i-1

solves trigonometric equations.

Formative:


Go?


Critical thinker. Solving trigonometric equations include a method of simplification for each side of the equation. This is true in life, wherein, people must know how to simplify complicated situations in order to reach a balanced life.

2. STEM_PC11T-IIi-2 solves situational problems involving inverse trigonometric functions and trigonometric equations.


Point?


Summative:

LAS 7 (Trigonometric Equations and Problem Solving)

Quiz 2 – 6 (Trigonometric Equations)

WEEK 18

Polar Coordinate System

Converting Coordinates from Rectangular to Polar

Values: Socially responsive Community

leader. Polar coordinate system is a rule in mapping pair of points. This is magnified in the philosophy that “No man is an island.” where the need for interdependence is implied. Every person needs another, because there will always come a time that there will be a need from another person and vice versa.

The learner... 1. STEM_PC11T-IIj-1

locates points in polar coordinate system.

2. STEM_PC11T-IIj-2

converts the coordinates of a point from rectangular to polar system and vice versa.

Formative:


Go?


Point?


LAS 8 (Rectangular Coordinates to Polar Coordinates)

Quiz 2 – 7 (Polar Coordinate System)

WEEK 19

Problem Solving involving Polar Coordinate System

Values: Person with high Integrity and

Effective communicator. The points of a polar coordinate system are distance and angle. These pairs of

The learner... 1. STEM_PC11T-IIj-3

solve situational problems involving polar coordinate system.

Formative:


Go?


Point?



concepts are applied to real life as reminders that too much distance from other people will not allow you to see the perspectives or angles of others.

Summative:

LAS 9 (Problem Solving Involving Polar Coordinate System)

Quiz 2 – 8 (Problem solving in Polar Coordinate System)

Performance Task 4

WEEK 20 Examination Week

2nd Quarter Examination

Prepared by: Checked by:

Mr. Jeric Arrevado Ms. Brielene T. Nacpil Coordinator, S.T.E.M.

Ms. Cindy R. Dizon

Ms. Rachel Anne T. Medina

Ms. Helen Mae S. Moreno Teachers, Pre - Calculus

FIRST SEMESTER SYLLABUS IN PRE CALCULUS FIRST QUARTER · Grade 11: First Semester Syllabus in PRE -...

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