You will learn how to evaluate algebraic expressions by substitution.
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You will learn how to evaluate algebraic expressions by substitution.
For more instructional resources, CLICK me here! 👇👇👇
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! 👍👍👍
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
Creately offers many Venn diagram templates which you can use to instantly create your own Venn diagram. 3 set Venn diagrams, 2 set Venn diagrams or even 4 set Venn diagrams we got you covered. If you like a particular template just click on the use as templates button to immediately start modifying it using our online diagramming tools.
Sample of License Examination of Teachers and Educators in Philippines conducted by Philippines Regulatory Commission. Department of Education is accepting only if they pass BLEPT.
Click to have an interactive version of this reviewer
http://preofery.com/27lV
Sample of License Examination of Teachers and Educators in Philippines conducted by Philippines Regulatory Commission. Department of Education is accepting only if they pass BLEPT.
Program for investiture 2016 tagalog versionDaniel Bragais
Boy Scout of the Philippines Investiture ceremony is conducted in order to officially dedicates its new member in scouting organization all around the world. This Script or Spiel is in Tagalog or Filipino so that it can easily be understood by Pinoy or People of the Philippine Republic.
All students can learn and succeed but not all at the same day and at the same time. More than the awards they are receiving this afternoon; let us celebrate the effort your children have given to accomplish the school year. Howard Gardner of Harvard has identified seven distinct intelligences. This theory has emerged from recent cognitive research and "documents the extent to which students possess different kinds of minds and therefore learn, remember, perform, and understand in different ways," according to Gardner (1991).
A search warrant is a court order issued by a magistrate, judge or Supreme Court official that authorizes law enforcement officers to conduct a search of a person, location, or vehicle for evidence of a crime and to confiscate evidence if it is found. A search warrant cannot be issued in aid of civil process.
Jurisdictions that respect the rule of law and a right to privacy put constraints on the powers of police investigators, and typically require search warrants, or an equivalent procedure, for searches conducted as part of a criminal investigation. An exception is usually made for hot pursuit: if a criminal flees the scene of a crime and a police officer follows him, the officer has the right to enter a property in which the criminal has sought shelter. Conversely, in authoritarian regimes, the police typically have the right to search property and people without having to provide justification, or without having to secure the permission of a court.
K to 12 means Kindergarten and the 12 years of elementary and secondary education. K12 implemented by Deped in the Philippines
Presented During the opening of Casa Del Nino Science Highschool. www.casans.edu.ph
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
A Strategic Approach: GenAI in EducationPeter Windle
Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
This Gasta posits a strategic approach to integrating AI into HEIs to prepare staff, students and the curriculum for an evolving world and workplace. We will highlight the advantages of working with these technologies beyond the realm of teaching, learning and assessment by considering prompt engineering skills, industry impact, curriculum changes, and the need for staff upskilling. In contrast, not engaging strategically with Generative AI poses risks, including falling behind peers, missed opportunities and failing to ensure our graduates remain employable. The rapid evolution of AI technologies necessitates a proactive and strategic approach if we are to remain relevant.
June 3, 2024 Anti-Semitism Letter Sent to MIT President Kornbluth and MIT Cor...Levi Shapiro
Letter from the Congress of the United States regarding Anti-Semitism sent June 3rd to MIT President Sally Kornbluth, MIT Corp Chair, Mark Gorenberg
Dear Dr. Kornbluth and Mr. Gorenberg,
The US House of Representatives is deeply concerned by ongoing and pervasive acts of antisemitic
harassment and intimidation at the Massachusetts Institute of Technology (MIT). Failing to act decisively to ensure a safe learning environment for all students would be a grave dereliction of your responsibilities as President of MIT and Chair of the MIT Corporation.
This Congress will not stand idly by and allow an environment hostile to Jewish students to persist. The House believes that your institution is in violation of Title VI of the Civil Rights Act, and the inability or
unwillingness to rectify this violation through action requires accountability.
Postsecondary education is a unique opportunity for students to learn and have their ideas and beliefs challenged. However, universities receiving hundreds of millions of federal funds annually have denied
students that opportunity and have been hijacked to become venues for the promotion of terrorism, antisemitic harassment and intimidation, unlawful encampments, and in some cases, assaults and riots.
The House of Representatives will not countenance the use of federal funds to indoctrinate students into hateful, antisemitic, anti-American supporters of terrorism. Investigations into campus antisemitism by the Committee on Education and the Workforce and the Committee on Ways and Means have been expanded into a Congress-wide probe across all relevant jurisdictions to address this national crisis. The undersigned Committees will conduct oversight into the use of federal funds at MIT and its learning environment under authorities granted to each Committee.
• The Committee on Education and the Workforce has been investigating your institution since December 7, 2023. The Committee has broad jurisdiction over postsecondary education, including its compliance with Title VI of the Civil Rights Act, campus safety concerns over disruptions to the learning environment, and the awarding of federal student aid under the Higher Education Act.
• The Committee on Oversight and Accountability is investigating the sources of funding and other support flowing to groups espousing pro-Hamas propaganda and engaged in antisemitic harassment and intimidation of students. The Committee on Oversight and Accountability is the principal oversight committee of the US House of Representatives and has broad authority to investigate “any matter” at “any time” under House Rule X.
• The Committee on Ways and Means has been investigating several universities since November 15, 2023, when the Committee held a hearing entitled From Ivory Towers to Dark Corners: Investigating the Nexus Between Antisemitism, Tax-Exempt Universities, and Terror Financing. The Committee followed the hearing with letters to those institutions on January 10, 202
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Francesca Gottschalk - How can education support child empowerment.pptxEduSkills OECD
Francesca Gottschalk from the OECD’s Centre for Educational Research and Innovation presents at the Ask an Expert Webinar: How can education support child empowerment?
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
1. SUMMER COURSE OUTLINE IN LINEAR ALGEBRA
1. SETS AND ITS OPERATION
2. VENN-EULER DIAGRAM
3. APPLICATION OF SET
4. RELATIONS AND FUNCTIONS
5. COMPOSITION OF FUNCTIONS
6. REVIEW OF LONG METHOD DIVISION OF POLYNOMIALS
7. POLYNOMIAL THEOREMS
8. EXPONENTIAL EQUATIONS
9. LOGARITHMIC EQUATION
10. SOLVING LINEAR EQUATIONS IN TWO VARIABLES UNKNOWN
USING ELIMINATION AND SUBSTITUTION
11.WORDED PROBLEMS
A. INTEGER PROBLEM
B. AGE PROBLEM
C. MOTION PROBLEM
D. CLOCK PROBLEM
E. MIXTURE PROBLEM
F. MONEY PROBLEM
G. INVESTMENT PROBLEM
H. WORK PROBLEM
12.EXPONENTIAL GROWTH AND DECAY
13.MATRICES
A. GAUSSIAN ELIMINATION METHOD
B. DETERMINANTS AND CRAMERS‟ RULE
2. Module 1 : SETS and OPERATION
Set- a well-defined collection of objects, concrete or abstract of any kind.
TWO METHODS OF WRITING A SET
1. ROSTER METHOD
2. SET- BUILDER NOTATION
2 Major Type
1. Finite set- a set whose elements are limited or countable and the last element is
identifiable.
2. Infinite Set- a set whose elements are unlimited.
OTHER TYPE OF SET
1. EMPTY SET/ NULL SET or { }
2. UNIT SET {1}
3. UNIVERSAL SET U= {0,1,2,3,4,5,…20.}
4. SUBSET A= { 1,2,3,4,5,6,7,8,9,10.} B= { 2,3,4,6,8.} B A
5. EQUAL SET A= { L,I,S,T,E,N.} B= { S,I,L,E,N,T} B A
6. EQUIVALENT SET A= { 1,2,3,4} B= { A,B,C,D}
7. JOINT SET A={ 1,2,3,4,5,6,7,8,9,10.} B= { 2,3,4,6,8}
8. DISJOINT SET A={ 1,2,3,4,5,6,7,8,9,10.} B = { 0,11, 12,13,14…}
BASIC NOTATION
1. - INTERSECTION
2. - UNION
3. - NOT AN ELEMENT OF
4. - AN ELEMENT OF
5. - PROPER SUBSET OF
6. - IS EQUIVALENT TO
7. NULL SET
8. „ PRIME SYMBOL
4. MODULE 2: OPERATIONS ON SET
THERE ARE 5 OPERATIONS ON SET SYMBOL USED
1. UNION OF SET
2. INTERSECTION OF SET
3. CARTESIAN PRODUCT AXB
4. COMPLEMENT OF A SET A‟( PRIME)
5. DIFFERENCE OF A SET A-B
UNION OF SET
Combined elements found in a given set with the other set.
A= { 1,2,3,4,5,6,7,8,9,10} B= { 2,5,7,9} * +
ITERSECTION OF SET
Element(s) which that are common to both given sets.
A= { 1,2,3,4,5,6,7,8,9,10} B= { 2,5,7,9} * +
CARTESIAN PRODUCT
Each Element of a given set A are being paired with each elements found in Set B.
A= { 1,2,3} B= { 2,5,7,9}
AXB= { (1,2), (1,5) ,(1,7), (1,9),( 2,2).(2,5),(2,7),(2,9), (3,2),(3,5),(3,7),(3,9)}
COMPLEMENT OF A SET
Elements which are found in the universal set but not in the given set.
U= { 0,1,2,3,4,5,6,7,8,9,10…15} A‟ = { 2,4,5,7,8,10,11,12,13,14,15}
A= { 0,1,3,6,9}
6. NAME: _________________________________________
SCORE_____________
DATE: _________________
Exercises 1.3A VISUAL REPRESENTATION OF OPERATIONS ON SET
TAKE HOME QUIZ
DIRECTIONS: Given the sets below, give the elements of the following operations on set
using
Venn- Euler diagram and Shade the corresponding region where the
elements are found.
Given; U= {1,2,3,4,5,6,7} A= {1,3,5,7} B= { 2,4,6} C= {1,3,5}
1.
2. =
3. * + =
4.
5.
6. ( )
7. ( )
8.
9.
10.( )
EXAMPLE
U= { 1,2,3,4,5,…20}
A= {1,2,3,4,5,6}
B= { 4,6,9}
4
6
9
1
2
3
7 8 20
A B
10
11 5 19
12 13 14 15 16 17 18
U
7. NAME: _________________________________________ SCORE_____________
DATE: _________________
EXERCISES 1.3B APPLICATION OF SETS
VENN- EULER DIAGRAM
DIRECTIONS: Read and analyze the following problem s below and represent the
following set to solve
using the Venn- Euler diagram. Show your solution. (30 points)
1. A survey on subjects being taken by 250 college students in Metro Manila revealed
the following information; 90 likes Math; 88 English; 145 Filipino; 25 Math &
Filipino; 38 Filipino & English; 59 Math and English; 15 All. How many did not
take the survey?
2. There are 20 seniors serving the student council of CDNSHS. Of these, 3 have not
served before. 10 served on the council in their junior years, 9 in their sophomore
years, and 11 in their freshmen years. There are 5 who served during both their
sophomore and junior years, 6 during both freshman & junior years and 4 during
both freshman and sophomore years. How many seniors served in the student
council during each of the 4 years in high school?
3. In a survey involving 800 employees, it was found that 485 employees saves in
BDO , 550 save in Metro Bank , 540 save in BPI, 255 save in BDO and Metro
Bank. 270 save in BDO and BPI, and 325 save in Metro bank and BPI. All
employees save with at least one of these banks.
a. How many employees save in BPI but not in Metro Bank?
b. How many employees save in BDO but not in Metro Bank or BPI?
c. How many employees save in all three banks?
8. MODULE 3 RELATIONS AND FUNCTIONS
Definition of terms
A relation is any set of ordered pairs ( x,y), ( domain, range)
Relation = {x/x is any ( x,y)} i.e., { (1,2), (2,3), ( 4,5), ( 6,7)}
A relation S is a function if and only if (a,b) S and ( a,c) S implies that b=c
A function is a set of ordered pairs ( x,y) such that for each first component, there is
at most one value of the second component.
A function is a set of ordered pairs having the property that no two distinct
ordered pairs have the same first entry or domain.
NOTE:
All functions are relations but not all relations are functions.
A graph represents a function if and only if no vertical line intersects the graph
more than once.
y
0
1
2
3
3
3
10. NAME: _________________________________________
SCORE_____________
DATE: _________________
EXERCISES 1.4 RELATIONS AND FUNCTIONS
A. Directions: Determine whether the following relations are function or not. Write
F if it is a function and N if it is not a function.
______1. { ( 2,3), ( 4,4), ( 2,4), ( 3,2)}
______ 2. { ( 1,2), (2,3), (-1,2),( -2,3)}
______3. {0.2, 0.003), (0.002, .005), (2/10, 1/3)}
______4. { ( ), ( , ), ( ) }
_____5. { (1.5, -1.5), ( 2.5, -2.5), ( 3,3), ( -2,3)}
B. Directions: Determine the domain and range. Use the vertical line test to
determine whether the relation is a function or not.
Domain Range
1. _______ __________
2. _______ __________
3. _______ __________
4. _______ __________
5. _______ __________
C. Directions: In each of the following, indicate the values of x must be excluded from
the domain.
1. ( )
( )
2. ( )
( )
3. √
4. √
5. ( )
11. OPERATIONS ON FUNCTIONS (MDAS)
Let f and g be two functions with domains Df and Dg respectively. Then
1. ( )( ) ( ) ( )
2. ( )( ) ( ) ( )
3. ( )( ) ( ) ( )
4. ( ) ( )
( )
( )
COMPOSITE FUNCTIONS
Let f and g be functions. The composition of f on g is the function defined by ( )( )
( ( )) where its domain is dom ( ) * ( ) ( ) ( ) +
( ) ( ( ))
( ) ( ( ))
OPERATIONS ON FONCTIONS
LET f(x) = g(x) =
1. ( )( ) ( ) ( )
=
=
=
2. ( )( ) ( ) ( )
= ( )
=
3. ( )( ) ( ) ( )
= ( )( )
=
4. ( ) ( )
( )
( )
=
( )( )
=
12. MODULE 4: POLYNOMIAL THEOREMS
REMAINDER THEOREM
If a polynomial f(x) is divided by (x-r) until a remainder independent of x is
obtained then, the remainder is equal to P(r).
FACTOR THEOREM
If (x-r) is a factor of P(x), then r is a root of the equation P(x) =0.
FUNDAMENTAL THEOREM OF ALGEBRA
If P(x) is a polynomial with positive degree, then P(x) has at least one zero.
THE NUMBER OF ROOTS THEOREM
IF P(x) is a polynomial of degree n, then P(x) =0 will have n roots.
Descarte‟s rule of sign
This states that for every change in the sign in a given polynomial this corresponds to
the number of positive and negative roots.
Example
FUNDAMENTAL THEOREM OF ALGEBRA
Since the equation consist of a positive degree of n, therefore it has at least one zero.
THE NUMBER OF ROOTS THEOREM
In the above equation the highest degree of exponent is 2, then there exist 2 roots of
P(x)
Descarte‟s rule of sign
Consider the change in the sign of the first term and second term.
last term.
( ) There are 2 positive roots taken from the original equation
FACTOR THEOREM
( )( ) ?
( ) ( )
40-77+28=0 16-44+28=0
-28+28=0 -28+28=0
0=0 0=0
Then, 4 and 7 are the roots of
13. NAME: _________________________________________ SCORE_____________
DATE: _________________
EXERCISES 1.5 FINDING THE ROOTS OF A POLYNOMIAL
using the different Polynomial Theorems
Example
P(+) = 2 roots factor( x-7)(x-4)=0 then 4 and 7 are the roots.
P(-) 0
#of roots positive negative factors
roots
1.
2.
3. –
4.
5.
6.
7.
8.
9.
10.
11.If Is a factor of the given
equation?
12.Find the value of k such that when
13.Find the value of k such that when e
14.If (x+1) is a factor of ____.
15.Find the value of k such that when
( )
14. MODULE 5: EXPONENTIAL AND LOGARITHMIC EQUATION
PRE- REQUISITE TOPICS
LAWS OF RATIONAL EXPONENT
FACTORING
SOLVING POLYNOMIAL EQUATION
EXPONENTIAL AND LOGARITHMIC FUNCTIONS
EXPONENTIAL FUNCTIONS
If b is any positive number, then the expression b
x
=designates exactly one real
number for every real value of x. where b is no equal to zero.
f(x)= b
x
Properties of
Logarithms
1. Product rule:
2. Quotient rule: ( )
3. Power rule:
4. If and and = x
x -2 -1 0 1 2
y 0.25 0.5 1 2 4
f(x)=
2x
y
-2
-1
0
1
2
15. NAME: _________________________________________ SCORE_____________
DATE: _________________
EXERCIES 1.6 EXPONENTIAL AND LOGARITHMIC EQUATIONS
DIRECTIONS: Solve for x in the following equation below. Match Column A with the
correct value of x in
Column B. If the answer is not found in the selection, write the correct
answer.
Note: Calculator is allowed.
COLUMN A COLUMN B
1. A. x=4 P. x = 49/4
2. B. x= 5 Q. x = -8/3
3. C. x = -1/2 R. x = 6
4. ( )
D. x = 3 S. x = 0
5. E. x = 3/2 T. x = 4/49
6. F. x = ½
7. G.
8. H. x = 81
9. I. x = 16/9
10. J. x = 5/2
11. K. x = 19/6
12. L. x = -1
13. M. x = 2/21
14. N. x = 21/2
15. O. √
B. Directions: Solve each equation applying the different properties of Logarithm.
16.
17.
18.
19.
20. ( )
21. =
22.
23.
24.
25.
16. C. EXPONENTIAL EQUATIONS LEADING TO QUADRATIC EQUATION
26. ( )
27. ( )
28. ( ) ( )
29. ( )
30. ( ) ( )
31. = 4
y
32.
33.
34.
35.
17. INTEGER PROBLEM
Let x, x+1, x+2, x+3, x+4,… for a consecutive integer
Let x,x+2, x+4, x+6, x+8,… for a consecutive even/ odd integer
Age Problem
Past & ago implies subtraction from the present age.
Ex. A is one year younger than B means A‟s age is x-1 and B‟s age is x.
In n
th
year means that one needs to add the particular number to the
present age.
In a given problem sentence, when one sees the word “is” this implies
equal.
Mixture
The word” is/ must be added to “means add the two mixtures.
The word “must be reduced to” means deduct the amount of mixture from
the other.
The word “to make a mixture of” or “to have a result of” means add up the
two mixtures.
Ex.
A 5 gram of 20% SALT SOLUTION must be added to a pure concentration
of SALT solution must be added to make a 75% Salt solution.
5g( 20%) + x g ( 100%) = 75%(5g + x g)
WORK PROBLEM
SAME JOB TO BE DONE
X+Y = 1
RATE OF WORK= 1/X
MOTION PROBLEM
DISTANCE = RATE X TIME or d = rt
18. Over take problem
d1 = d2
Opposite Direction
d1+ d2= dt
d1-d2= difference on distance
Worded Problems
1. Trixie has 10 pieces of P100- bills and 35 pieces of P20-bills. How much money does
she have?
2. Mollie has a total of P 4,800 consisting of P50 and P100-bills. The number of P50-
bills is 16 less than twice the number of P 100-bills. How many P50-bills does she
have?
3. Jonas has a jar in his office that contains 39 coins. Some are 5 cents and the rest
are 10 cents. If the total value of the coins is P2.55, how many 5 cents does he
have?
4. In problem number 3, how many 10 cents does Jonas have in the jar?
5. Erick has a box of coins. The box currently contains 40 coins, consisting of 5 cents,
10 cents, and 25 cents. The number of 5 cents is equal to the number of 25 cents,
and the total value is P5.80 How many of 25 cents of coin does he have in the box?
6. Ruth has P1900 consisting of P50 and P10 bills. The number of P10 bills is 5 less
than the number of P 50 bills. How many P10 bill does she have?
7. Mildred can sew a dress in ten days. What part of the dress is finished after 6 days?
8. Glen is 3 years older than his brother. Three years ago, Four years from now, the
sum of their ages will be 33 years, how old are they now?
9. Mr. Sta. Maria is five years older than his wife. Five years ago, his age was 4/3 her
age. What will be their ages 8 years from now?
10.A man can wash the car in 120 minutes if he works alone. His son, working alone
can do the same job in 3 hours. How long will it take to take them to wash the car if
they work together?
19. 11. An inlet pipe can fill a tank in 9 minutes. A drain pipe can empty the tank in ten
minutes. If the tank is empty and both pipes are open, how long will it take before
the tank overflows?
12. Find three consecutive even integers such that four times the first less the
third is six more than twice the second.
13. Find three consecutive integers such that the sum of the first plus one-third
of the second plus three eights of the third is 25.
14. A paint that contains 21% green dye is mixed with a paint that contains
15% green dye. How many gallons of each must be used to make 60 gallons
of paint that is 19% green dye.
15. A chemist has 10 milliliters of a solution that contains a 30% solution of
acid. How many milliliters of pure acid must be added in order to increase the
concentration to 50%?
1. ( )
2. ( )
3. ( ) ( )
4. ( )
5. ( ) ( )
6. = 4
y