Algebra 8-3 Add and Subtract Polynomials

Q1. A teacher designs a lesson where students compute real-life percentages such as discounts and savings. 👉 A student calculates 15% of 200 to determine savings in a purchase. What is the correct result? A. 20 B. 25 C. 30 D. 35 Q2. In a classroom activity, learners compare numbers to find the highest common factor for grouping materials evenly. 👉 What is the GCF of 24 and 36? A. 6 B. 8 C. 12 D. 18 📘 FRACTIONS, DECIMALS, AND POWERS Q3. A learner converts fractions into percentages for data interpretation. 👉 What is 3/4 expressed as a percentage? A. 50% B. 60% C. 75% D. 80% Q4. A student models exponential growth using repeated multiplication. 👉 What is the value of 252^525? A. 25 B. 30 C. 32 D. 64 📘 ALGEBRA (EQUATIONS AND EXPRESSIONS) Q5. A teacher guides students to solve equations that represent real-life situations. 👉 Solve: 2x+8=202x + 8 = 202x+8=20 A. x = 4 B. x = 6 C. x = 8 D. x = 10 Q6. Students simplify expressions to understand relationships between quantities. 👉 Simplify: 3(x+4)−2x3(x + 4) - 2x3(x+4)−2x A. x + 12 B. x + 4 C. 5x + 4 D. 5x + 12 📘 FUNCTIONS AND GRAPHING Q7. A student analyzes a linear equation to determine its rate of change. 👉 What is the slope of y=3x−5y = 3x - 5y=3x−5? A. -5 B. -3 C. 3 D. 5 Q8. A learner evaluates functions to predict outcomes. 👉 If f(x)=2x+3f(x) = 2x + 3f(x)=2x+3, what is f(4)f(4)f(4)? A. 7 B. 9 C. 11 D. 14 📘 GEOMETRY Q9. Students explore geometric shapes and their properties through visual models. 👉 What is the sum of interior angles of a triangle? A. 90° B. 180° C. 270° D. 360° Q10. A student calculates the area of a classroom table with dimensions 8 cm by 5 cm. 👉 What is the area? A. 26 sq cm B. 30 sq cm C. 40 sq cm D. 48 sq cm 📘 MEASUREMENT AND FIGURES Q11. A learner determines the volume of a cube used in a science experiment. 👉 What is the volume of a cube with side 4 cm? A. 16 cubic cm B. 32 cubic cm C. 48 cubic cm D. 64 cubic cm Q12. Students identify shapes used in design projects. 👉 How many sides does a hexagon have? A. 5 B. 6 C. 7 D. 8 📘 STATISTICS AND PROBABILITY Q13. A teacher helps students interpret data sets using measures of central tendency. 👉 What is the mean of 4, 6, 8, 10, 12? A. 6 B. 8 C. 10 D. 12 Q14. A class experiment involves flipping a fair coin. 👉 What is the probability of getting heads? A. 1/4 B. 1/3 C. 1/2 D. 2/3 📘 WORD PROBLEMS (APPLICATION) Q15. A car travels 180 km in 3 hours during a learning task on speed. 👉 What is its average speed? A. 45 km/h B. 60 km/h C. 75 km/h D. 90 km/h Q16. Students analyze work efficiency in a project. 👉 If 5 workers complete a task in 12 days, how long will 10 workers take? A. 3 days B. 6 days C. 8 days D. 12 days Q17. A student solves a problem involving ratios in a classroom population. 👉 If the ratio of boys to girls is 3:2 and there are 30 students, how many boys are there? A. 12 B. 15 C. 18 D. 20 Q18. A learner determines the duration of a scheduled trip. 👉 A journey starts at 8:30 AM and ends at 11:15 AM. How long is the trip? A. 2 hrs 15 mins B. 2 hrs 30 mins C. 2 hrs 45 mins D. 3 hrs 15 mins Q19. A student computes simple interest for financial literacy. 👉 What is the simple interest on ₱1000 at 5% for 2 years? A. ₱50 B. ₱75 C. ₱100 D. ₱150 Q20. A learner solves a perimeter problem involving a rectangle. 👉 A rectangle has a length of 12 cm and perimeter of 34 cm. What is the width? A. 5 cm B. 7 cm C. 10 cm D. 11 cm ✅ ANSWER KEY (BASED ON YOUR REVIEWER) (All verified from your uploaded file) [ilide.info...002acd4e5a | PDF] QAnswer1C2C3C4C5B6A7C8C9B10C11D12B13B14C15B16B17C18C19C20A

Section 1: Numbers, Operations, and Relationships (15 marks) 1. Number Concepts (5 marks) 1.1. Decompose the following numbers into tens and ones: (2 marks) a. 34 b. 67 1.2. Count the objects in the pictures below and write the total number: (3 marks) [This section would need images of objects. You can provide images of groups of objects, e.g., 3 groups of 4 apples each and ask the students to count the total number.] 2. Solve Problems (5 marks) 2.1. Solve the following word problem using drawings: (3 marks) Samantha has 5 baskets. Each basket has 8 apples. How many apples does she have in total? Samantha has 5 × 8 = 40 5×8=40 apples. 2.2. Solve the following word problem by building up and breaking down numbers: (2 marks) There are 4 boxes. Each box has 6 chocolates. How many chocolates are there in total? There are 4 × 6 = 24 4×6=24 chocolates in total. 3. Calculations (5 marks) 3.1. Multiply the following numbers using drawings: (3 marks) a. 5 × 4 = 20 b. 4 × 5 = 20 3.2. Use a number line to solve: (2 marks) a. 3 × 5 = 15 b. 2 × 4 = 8 Section 2: Patterns, Functions, and Algebra (10 marks) 4. Number Patterns (10 marks) 4.1. Complete the number sequences: (5 marks) a. 180, 170, 160, 150, 140, 130, 120, 110, 100, 90 b. 150, 152, 154, 156, 158, 160, 162, 164, 166, 168 4.2. Count in twos and fill in the missing numbers: (5 marks) a. 102, 104, 106, 108, 110, 112, 114, 116 Section 3: Space and Shape (Geometry) (10 marks) 5. Position (10 marks) 5.1. Follow the directions to move around the classroom: (5 marks) Draw a path showing how you would move from your desk to the teacher's table by following these steps: Move 3 steps forward. Turn left and move 2 steps. Turn right and move 4 steps. [Students would draw a path based on these directions.] 5.2. Use the language of position to describe the following: (5 marks) a. The pencil is on the book. b. The chair is beside the desk. c. The bag is under the table. d. The ruler is next to the notebook. e. The eraser is inside the pencil case.

WHAT IS SCIENCE? - is a way in which answers related to NATURAL events are proposed. - a way in which people can learn and UNDERSTAND events in the NATURAL WORLD - based on OBSERVABLE EVENTS - a study of the NATURAL WORLD - a method of DISCOVERY and UNDERSTANDING by using a PROBLEM-SOLVING process called the?? - A systematic body of knowledge based on observation and experimentation. FOUR COMMON CHARACTERISTICS OF SCIENCE: 1. It focuses on the NATURAL WORLD. 2. Goes through experiment. 3. Relies on evidence. 4. Passes through the scientific community. WHAT IS TECHNOLOGY? Brian Arthur (2009) defined technology as: 1. a means to fulfill a human purpose 2. assemblage of practices and components 3. a collection of devices and engineering practices available to a culture. SOCIETY ST (Science Technology) would not exist without society. WHAT IS STS? Science and Technology and Society (STS) is the study of how society, politics and culture affect scientific research and technological innovation and how these, in turn affects society, politics and culture. EVENTS IN THE HISTORY OF SCIENCE AND TECHNOLOGY THAT TRANSFORMED THE SOCIETY (IN THE WORLD) ANCIENT PERIOD 3500 BC. - 500 AD EUROPE - use of fire by Homo Erectus CA 750,000 - Stone Headed Spears CA 45,000 - Wooden bow and arrow CA 20,000 - The Minoans build palaces in Crete CA 2,000 THE AMERICAS - The Folsom people living on eastern side of the Rocky Mountain developed sophisticated tools CA 8,000. - Pottery is made in South America CA 6,000 - Olmec sculpture carves figurines and giant human heads. CA 1200 ASIA AND OCEANA - Earliest known clay pots are made in Japan CA 11,000. - Bronze is first made in Thailand CA 4000 - A lunar calendar is developed in China CA 2950 - Chinese doctors begin using acupuncture CA 2500 - The Hindu calendar of 360 days was introduced in India CA 1000 AFRICA AND MIDDLE EAST - Homo erectus uses stone tools CA 1000000 - CA 15000 in Africa, bone harpoons are used for fishing. - Clay tokens are used for record keeping in Mesopotamia CA 7500 - Mesopotamian mathematicians discover the Pythagorean Theorem MEDIEVAL PERIOD CA 500 -1500 - Dark ages because few written records and evidences remained - Scholastic tradition was established by Charlemagne - Vertical windmills, spectacles, mechanical clock, water mills, gothic style were invented - Johannes Gutenberg invented the printing press RENAISSANCE PERIOD 14TH – 17TH CENTURY - Rebirth of revival - Printing with movable type allowed Bible, secular books made in large amount - Nicolas Copernicus presented a heliocentric theory - Galileo Galilei invented telescope INDUSTRIAL REVOLUTION 18TH CENTURY - Skilled workers were set aside because of the machines - Iron production, steam engine and textile flourished - Scottish James Watt improved steam engine Robert Fulton (steam boat) - The following were invented: Light bulb, telephone, first steam powered locomotive 19TH CENTURY - Age of machine and tools - Herman Helmholtz (law of conservation of energy) - James Clark Maxwell (light as electro-magnetic wave) - Henry Becquerel (radioactivity) - Marie and Pierre Curie (radium) - Hans Christian Oersted (electric current near the magnet) - Michael Faraday (magnet produces electricity) - Atomic Theory proposed by John Dalton - Electron discovered by JJ. Thomson - Telegraph developed by Samuel Morse 20TH CENTURY - Communication, transportation, military research were developed - Personal computer was created - Intel developed microprocessor - Apple was introduced by Steve Jobs and Steve Wozniak - Internet was created (ARPANET) - Henry Ford's mass production of cars - Artificial Intelligence was invented SCIENCE, TECHNOLOGY AND SOCIETY (PHILIPPINE HISTORY) Stone Age - Archeological findings show that modern man from Asian mainland first came over land on across narrow channels to live in Batangas and Palawan about 48,000 B.C. - Subsequently they formed settlement in Sulu, Davao, Zamboanga, Samar, Negros, Batangas, Laguna, Rizal, Bulacan and Cagayan. Inventions - They made simple tools and weapons of stone flakes and later developed method of sawing and polishing stones around 40,000 B.C. - By around 3,000 B.C. they were producing adzes ornaments of seashells and pottery. Pottery flourished for the next 2,000 years until they imported Chinese porcelain. Soon they learned to produce copper, bronze, iron, and gold metal tools and ornaments. Iron Age - The Iron Age lasted from the third century B.C. to 11th century A.D. During this period Filipinos were engaged in extraction smelting and refining of iron from ores, until the importation of cast iron from Sarawak and later from China. INVENTIONS AND DISCOVERIES - They learn to weave cotton, make glass ornaments, and cultivate lowland rice and dike fields of terraced fields utilizing spring water in mountain regions. - They also learned to build boats for trading purposes. - Spanish chronicles noted refined plank built warships called caracoa suited for interisland trade raids 10TH CENTURY A.D. - Filipinos from the Butuan were trading with Champa (Vietnam) and those from Ma-I (Mindoro) with China as noted in Chinese records containing several references to the Philippines. These archaeological findings indicated that regular trade relations between the Philippines, China and Vietnam had been well established from the 10th century to the 15th century A.D. TRADING - The People of Ma-I and San-Hsu (Palawan) traded bee wax, cotton, pearls, coconut heart mats, tortoise shell and medicinal betel nuts, panie cloth for porcelain, leads fishnets sinker, colored glass beads, iron pots, iron needles and tin. SOME PRESPANISH FILIPINO SCIENCE AND TECHNOLOGY - Curative values of plants extract use as medicine - Alphabet (Alibata) - Counting Methods - Weights - Measuring system (isang gatang) - Calendar based on the periods of moon - Banaue Rice Terraces SPANISH REGIME  Religion the Catholic Church - The latter part of the 16th Century Development of schools: - Colegio de San Ildefonso-Cebu-1595 - Colegio de San Ignacio-Manila-1595 - Colegio De Nuestra Senora del Rosario-Manila 1597 - Colegio De San Jose-Manila-1601  Colegio De San Ildefonso De Cebu - In 1863 the colonial authorities issued a royal degree to reform the existing educational system. In 1871 the school of medicine and pharmacy were opened to UST, after 15 years it had granted the degree Of Licenciado En Medicina to 62 graduates.  Medicine - Development of hospitals San Juan Lazaro hospital the oldest in the far east was founded in 1578.  Roads and Bridges Among other Spanish contributions: - Arithmetic - Algebra - Geometry - Trigonometry - Physics - Hydrography - Meteorology - Navigation - Pilotage American Period and Post Commonwealth Era - BUREAU OF GOVERNMENT LABORATORIES (1901) - BUREAU OF SCIENCE (1905) - INSTITUTE OF SCIENCE (1946) RA 2067 OTHERWISE KNOWN AS THE “SCIENCE ACT OF 1958”. - This was enacted to integrate, coordinate, and intensify scientific and technological research and development and to foster invention including allocation of funds and other purposes. NATIONAL RESEARCH COUNCIL WAS ESTABLISHED ON DECEMBER 8, 1933. - Its Mandate (Nrcp) Promotes And Supports Fundamental Or Basic Research For The Continuing Total Improvement Of The Research Capability Of Individual Scientists Or Group Of Scientists; Provides Advice On Problems And Issues Of National Interest; Promotes Scientific And Technological Culture To All Sectors Of Society; And Fosters Linkages With Local And International Scientific Organizations For Enhanced Cooperation In The Development And Sharing Of Information NATIONAL RESEARCH COUNCIL WAS ESTABLISHED IN DECEMBER 8, 1933. - Its Mandate (NRCP) promotes and supports fundamental or basic research for the continuing total improvement of the research capability of individual scientists or group of scientists; provides advice on problems and issues of national interest; promotes scientific and technological culture to all sectors of society; and fosters linkages with local and international scientific organizations for enhanced cooperation in the development and sharing of information. It was during the American Period when Science was inclined towards: - Agriculture - Food Processing - Forestry - Medicine - Pharmacy - Nursing

0:01 i pasticciotti presentano Federico II di 0:05 Sveia 0:07 Nel 0:09 1186 Costanza D'Alta Villa figlia del re 0:12 normno di Sicilia Ruggero II sposò ormai 0:16 trentenne Enrico VI di Svevia figlio 0:20 dell'imperatore Federico Barbarossa che 0:23 si servì di questo matrimonio per 0:26 stringere un'alleanza politica con la 0:28 monarchia siciliana 0:31 Purtroppo non fu un'unione felice sia 0:34 perché il marito aveva 10 anni in meno 0:37 della moglie sia perché lui non aveva un 0:40 bel carattere e pare che rinfacciasse 0:44 continuamente a costanza la sua età 0:47 avanzata temendo che ciò fosse causa di 0:50 sterilità 0:52 Alla morte di Federico Barbarossa nel 0:56 1190 Enrico VI ereditò dal padre il 1:00 titolo di imperatore del Sacro Romano 1:02 Impero ma era incapace di esercitare un 1:06 buon governo nei confronti dei sudditi 1:09 normanni che vivevano nel regno di 1:11 Sicilia portatogli in dote dalla moglie 1:14 Costanza 1:16 Così nel 1:18 1994 Enrico partì per una spedizione in 1:22 Sicilia senza la moglie al seguito e 1:25 fece in modo di essere incoronato re di 1:28 Sicilia il giorno di Natale nella 1:31 cattedrale di 1:33 Palermo Lo stesso giorno Costanza che 1:36 era in avanzato stato di gravidanza e 1:39 stava viaggiando in direzione di Palermo 1:42 per raggiungere il marito si rese conto 1:44 di essere prossima al 1:47 parto Se oggi nessuno più si meraviglia 1:50 della gravidanza di una quarantenne nel 1:52 Medioevo una gestazione a quell'età 1:55 sembrava una cosa praticamente 1:57 impossibile Pertanto si erano alimentate 2:01 voci malevoli sulla vera condizione di 2:04 costanza e neppure il marito pareva 2:07 realmente convinto della gravidanza 2:09 della moglie E dato che Costanza prima 2:12 di sposarsi era stata per un periodo in 2:16 monastero circolava addirittura la voce 2:19 che nel suo grembo ci fosse 2:21 l'anticristo che secondo una leggenda 2:24 medievale sarebbe nato dall'unione di 2:26 una vecchia monaca con un 2:29 frate Così Costanza decise di fermarsi 2:33 nella cittadina di Iesi e per fugare 2:36 ogni dubbio sulla sua gravidanza fece 2:39 allestire una tenda nella piazza 2:42 centrale della cittadina 2:44 marchigiana in modo da partorire al 2:47 cospetto di tutte le donne sposate del 2:50 paese Alcuni riferirono che il giorno 2:53 successivo al parto la regina lattò 2:56 pubblicamente il piccolo che poi fu 2:59 battezzato nella cattedrale di San 3:01 Ruffino di Assisi con il nome di 3:04 Federico 3:06 Ruggero Federico per indicare la 3:09 discendenza sveva quale nipote di 3:12 Federico 3:13 Barbarossa e Ruggero per sottolineare la 3:17 discendenza normanna dal primo re di 3:20 Sicilia Ruggero 3:23 d'Altavilla A soli 3 anni il piccolo 3:26 Federico rimase orfano e fu posto sotto 3:30 la tutela di Papa Innocenzo II da cui si 3:33 affrancò a 14 anni quando divenne prima 3:37 re di Sicilia e poi re di 3:41 Germania acquisendo il nome di Federico 3:44 II congiuntamente al titolo di 3:47 imperatore nel 1220 3:50 Ma Federico era più interessato 3:53 all'Italia che alla 3:54 Germania Così stabilì la sua corte in 3:57 Sicilia a 4:00 Palermo Federico II organizzò un regno 4:04 forte e 4:05 accentrato costruendo in tutta l'Italia 4:08 meridionale vari castelli dove collocò 4:11 le sue truppe che dovevano controllare 4:14 il territorio e sedare eventuali rivolte 4:18 Vanno menzionati in particolare il 4:21 castello di Melfi in Basilicata dove 4:25 furono promulgate le famose costituzioni 4:29 melfitane una raccolta di leggi scritte 4:32 rivolte a tutti gli abitanti del regno 4:35 con cui si limitavano i poteri dei 4:38 baroni locali e si vietava il ricorso 4:41 alla vendetta personale per affidarsi 4:44 invece alla giustizia stabilita dalle 4:47 leggi 4:48 C'era poi il castello di Trani che aveva 4:51 la funzione di sorvegliare l'ingresso 4:54 alla città e al porto E infine il 4:58 celeberrimo castel del Monte 5:01 caratterizzato da un'originale pianta 5:03 ottagonale attorniata da torri anch'esse 5:07 ottagonali che fungeva da dimora come 5:10 testimoniato dalla presenza di grandi 5:13 camini Uomo colto fine giurista 5:17 Amante dell'arte della letteratura 5:20 Federico II ospitò alla sua corte 5:22 studiosi e artisti provenienti da tutta 5:25 Europa Dialogò con intellettuali arabi e 5:29 fondò l'Università di Napoli che ancora 5:32 oggi porta il suo 5:35 nome Con l'editto di Salerno regolamentò 5:38 per la prima volta la professione del 5:41 farmacista separandola di fatto da 5:44 quella del medico scrisse anche un libro 5:48 un manuale sulla falconeria e sull'arte 5:52 venatoria chiamato de Arte venandi cum 5:57 avibus ossia l'arte di cacciare con gli 6:01 uccelli che fu uno dei primi manoscritti 6:04 con disegni a tema 6:08 naturalistico In una nota alla sua morte 6:11 il monaco Matteo Paris lo chiamerà 6:14 stupor Mundi cioè stupore del mondo Un 6:19 appellativo che racchiude l'essenza 6:21 della sua inestinguibile curiosità 6:25 intellettuale che lo portò ad 6:27 approfondire la filosofia l'astrologia 6:30 la matematica l'algebra la medicina e le 6:34 scienze naturali ha al punto da 6:37 impiantare a Palermo persino uno zoo 6:40 famoso ai suoi tempi per il gran numero 6:43 di animali esotici che conteneva anche 6:46 un 6:47 elefante I rapporti col papo però non 6:51 furono idiaci 6:53 Sia Papa Onorio II che Gregorio Io detto 6:57 anche il Papa Guerriero lo costrinsero a 7:00 intraprendere una nuova crociata in 7:02 Terra Santa minacciando di scomunicarlo 7:06 qualora non l'avesse 7:08 fatto Così dopo tanta insistenza da 7:11 parte del papato Federico si mise in 7:13 viaggio per la Terra Santa 7:16 Giunto in Oriente però non mosse guerra 7:19 ai musulmani ma preferì stringere 7:22 accordi con il sultano d'Egitto 7:25 ottenendo il controllo della città di 7:27 Gerusalemme e una tregua di 10 anni 7:32 Si trattava di conquiste importanti dal 7:34 punto di vista diplomatico ma al suo 7:37 ritorno Federico II fu accusato 7:40 duramente di essere sceso a patti con 7:42 gli 7:43 infedeli Nel suo programma di governo 7:47 Federico II era intenzionato a 7:49 riaffermare la sua autorità sui comuni 7:52 del Nord Italia fatto che preoccupava il 7:56 Papa il quale temeva il rafforzamento 7:59 del potere imperiale anche a nord dello 8:02 Stato Pontificio già confinante a sud 8:05 con il Regno di Sicilia 8:08 In pratica il Papa si sentiva 8:11 schiacciato sia a nord che a sud 8:14 dall'imperatore Così Papa Gregorio Io 8:18 appoggiò alcuni comuni che si riunirono 8:20 nella Lega Lombarda e che furono detti 8:24 guelfi A questi si contrapposero i 8:27 comuni ghibellini che decisero di 8:30 schierarsi a sostegno 8:33 dell'imperatore Iniziò così una 8:35 lunghissima contesa che avrebbe 8:38 dilaniato le città 8:41 italiane Tutto 8:43 chiaro ciao e al prossimo 8:49 video Se questo video ti è piaciuto ti 8:52 chiedo di fare mi piace cliccando 8:53 sull'icona qui sotto Per me è molto 8:55 importante quindi grazie in anticipo se 8:57 lo farai Per essere informato ogni volta 8:59 che pubblico un nuovo video ricorda di 9:01 cliccare anche sul grande pulsante rosso 9:02 Iscriviti e sulla campanella di fianco 9:05 [Musica]

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