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if and then mathematics, Cheat Sheet of Mathematical Methods

Mariano Marcos State University (MMSU)Mathematical Methods

If and then documents for students learning

Typology: Cheat Sheet

2022/2023

Uploaded on 05/01/2024

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bg1
9
WEEKLY LEARNING PLAN
SUBJECT: MATHEMATICS 8
TEACHER: SHERWIN P. MANALANSAN
SCHOOL YEAR: 2023 – 2024
GRADE GRADE 8 WEEK NUMBER: WEEK 2
QUARTER 3rd QUARTER TEACHING DATE: JANUARY 26-29 2024
I. OBJECTIVES
A. Content Standard The learner demonstrates understanding of key concepts of factors of polynomials,
rational algebraic expressions, linear equations and inequalities in two variables, systems
of linear equations and inequalities in two variables and linear functions.
B. Performance
Standard
The learner is able to communicate mathematical thinking with coherence and clarity in
formulating and analyzing
arguments.
The learner is able to formulate real-life problems involving factors of polynomials, rational
algebraic expressions, linear equations and inequalities in two variables, systems of linear
equations and inequalities in two variables and linear functions and solve these problems
accurately using a variety of strategies.
C. Learning Competencies
he learner determines
the relationship between
the hypothesis and the
conclusion of an if-then
statement
he learner determines
the relationship between
the hypothesis and the
conclusion of an if-then
statement
Finds the domain and range of a function. (M8AL-IId-1)
D. Learning Objectives
Identify the domain and range of a function given equation
Describe the domain and range of a function given the equation.
Appreciate the concept of domain and range in real-life situation.
II. CONTENT
A. Unit Topic Content DOMAIN AND RANGE OF A FUNCTION
B. Lesson Topic DOMAIN AND RANGE OF A FUNCTION
III. TEACHING STRATEGIES
Inquiry-Based
Lecture-Based
IV. LEARNING RESOURCES
A. References
http://www.montereyinstitute.org/courses/DevelopmentalMath/
COURSE_TEXT2_RESOURCE/U17_L2_T3_text_final.html
B. Teacher’s Guide
A. Learner’s Guide
B. Instructional Materials PowerPoint Presentation, TV, Laptop, Whiteboard
V. PROCEDURES
Daily Routine
JUNIOR HIGH SCHOOL DEPARTMENT School Year 2023 - 2024
pf3
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WEEKLY LEARNING PLAN

SUBJECT: MATHEMATICS 8

TEACHER: SHERWIN P. MANALANSAN

SCHOOL YEAR: 2023 – 2024

GRADE GRADE 8 WEEK NUMBER: WEEK 2

QUARTER 3 rd^ QUARTER TEACHING DATE:^ JANUARY 26-29 2024 I. OBJECTIVES

A. Content Standard

The learner demonstrates understanding of key concepts of factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions.

B. Performance

Standard The learner is able to communicate mathematical thinking with coherence and clarity in formulating and analyzing arguments. The learner is able to formulate real-life problems involving factors of polynomials, rational algebraic expressions, linear equations and inequalities in two variables, systems of linear equations and inequalities in two variables and linear functions and solve these problems accurately using a variety of strategies.

C. Learning Competencies

he learner determines the relationship between the hypothesis and the conclusion of an if-then statement he learner determines the relationship between the hypothesis and the conclusion of an if-then statement  Finds the domain and range of a function. (M8AL-IId-1)

D. Learning Objectives

 Identify the domain and range of a function given equation  Describe the domain and range of a function given the equation.  Appreciate the concept of domain and range in real-life situation. II. CONTENT A. Unit Topic Content (^) DOMAIN AND RANGE OF A FUNCTION B. Lesson Topic (^) DOMAIN AND RANGE OF A FUNCTION III. TEACHING STRATEGIES  Inquiry-Based  Lecture-Based IV. LEARNING RESOURCES A. References http://www.montereyinstitute.org/courses/DevelopmentalMath/ COURSE_TEXT2_RESOURCE/U17_L2_T3_text_final.html B. Teacher’s Guide A. Learner’s Guide B. Instructional Materials PowerPoint Presentation, TV, Laptop, Whiteboard V. PROCEDURES Daily Routine

● Opening Prayer (First Subject/Homeroom) ● Checking the attendance ● Reminding the house rules ● Closing Prayer (Last Subject/Homeroom) A. Drill or Review of past lesson Identify the domain and range of the following:

  1. {(-1,3), (0,1), (1, -1), (2, -3), (3, -5)}
  2. {(0,2), (1,3), (2,4), (3,5), (4,6)}

B. Establishing a purpose for the lesson (Motivation)

  1. How do you identify domain and range?
  2. How will you identify domain and range of equations? C. Presenting the lesson Given the rule, we can find the domain and range of a function algebraically. Examples:
  3. Consider the function f ( x )  x  1. We can substitute x with any real number that does not make the function undefined. Therefore, the domain is the set of real numbers. To find range, we let y  f ( x )  x  1 and solve for x in terms of y. Thus,  x  y  1 or x  y  1 ; which can be defined for any real number y. Therefore, the range of f ( x ) is the set of real numbers.
  4. If the function is in the form of a quotient like.We have to take note that rational expression should not have the denominator zero, therefore, 𝑥 here should not be equal to 4, but other real numbers can be possible value of 𝑥. , To find the range, let and then solve for 𝑥 in terms of 𝑦. Solving, which is undefined for 𝑦 = 0. Therefore, the range consists of nonzero real numbers.
  5. If the function is in the form of radical with an even number index as in f ( x )  x + 3, Since the radicand must not be negative, we set x + 3 0. This will give x 3. Therefore, D  x / x  3 = 3 ,. For the range, we solve the equation, y  x  3 for 𝑥 in terms of y 0,(y)^2 = (x+3)^2 y^2 x  3 Therefore, x= y^2 -3. The resulting equation tells that y^2 - 3 will always be defined for any real number 𝑦, but the original equation y = x + 3 means that 𝑦 is the principal square root of 𝑥 + 3, so 𝑦 is never negative. Therefore, the range is R  y / y  0 , 0, . f ( x )= (^) x −^44

x =

4 y + 4

y

f ( x ) 4 x^2  1

f x x

J. Additional activities for application or remediation (Assignment) Review Follow Up: Give 5 relations that are function. You may express them as ordered pairs, mapping, graph, or rule or equation. Determine the domain and range of the functions you have made. Find the domain and range of each function.

1. f(x)= x- 7

PREPARED BY: MR. SHERWIN P. MANALANSAN CHECKED AND APPROVED

BY:

MR. RONEL T. BORBON

MATHEMATICS INSTRUCTOR ACADEMIC

COORDINATOR

DATE: _____________________________ DATE: ______________________ _____

SUBMITTED TO: MR. DAVENH A. ADDURU NOTED BY: MR. ALEXANDER N.

IGNACIO

HEAD TEACHER, JUNIOR HIGH SCHOOL SCHOOL PRINCIPAL

DATE: _____________________________ DATE: ______________________

_____

f ( x )= 3 x x − 1