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F.4 sum of roots
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what is sum of roots
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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] QAnswer1C2C3C4C5B6A7C8C9B10C11D12B13B14C15B16B17C18C19C20AGenerate all of these 25 questions Part A: Each correct answer is worth 5. 1. The regular pentagon shown has a side length of 2 cm. The perimeter of the pentagon is (A) 2 cm (B) 4 cm (C) 6 cm (D) 8 cm (E) 10 cm 2 cm 2. The faces of a cube are labelled with 1, 2, 3, 4, 5, and 6 dots. Three of the faces are shown. What is the total number of dots on the other three faces? (A) 6 (B) 8 (C) 10 (D) 12 (E) 15 3. The equation that best represents \a number increased by _ve equals 15" is (A) n 5 = 15 (B) n _ 5 = 15 (C) n + 5 = 15 (D) n + 15 = 5 (E) n _ 5 = 15 4. The line graph shows the number of bobbleheads sold at a store each year. The sale of bobbleheads increased the most between (A) 2016 and 2017 (B) 2017 and 2018 (C) 2018 and 2019 (D) 2019 and 2020 (E) 2020 and 2021 Number of 2016 2017 2018 2019 2020 Year Sale of Bobbleheads 2021 Bobbleheads 20 40 60 80 5. Starting at 72, Aryana counts down by 11s: 72; 61; 50; : : : . What is the last number greater than 0 that Aryana will count? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 6. In the diagram, \ABC = 90_. The value of x is (A) 68 (B) 23 (C) 56 (D) 28 (E) 26 Day of the Week 44° x° A B C x° 7. Which of the following values is closest to zero? (A) 1 (B) 5 4 (C) 12 (D) 4 5 (E) 0:9 Grade 8 8. A jar contains 267 quarters. One quarter is worth $0.25. How many quarters must be added to the jar so that the total value of the quarters is $100.00? (A) 33 (B) 53 (C) 103 (D) 133 (E) 153 9. A package of 8 greeting cards comes with 10 envelopes. Kirra has 7 cards but no envelopes. What is the smallest number of packages that Kirra needs to buy to have more envelopes than cards? (A) 3 (B) 4 (C) 5 (D) 6 (E) 7 10. For the points in the diagram, which statement is true? (A) e > c (B) b < d (C) f > b (D) a < e (E) a > c y x (e, f ) (a, b) (c, d ) Part B: Each correct answer is worth 6. 11. The 26 letters of the English alphabet are listed in an in_nite, repeating loop: ABCDEFGHIJKLMNOPQRSTUVWXY ZABC : : : What is the 258th letter in this sequence? (A) V (B) W (C) X (D) Y (E) Z 12. A public holiday is always celebrated on the third Wednesday of a certain month. In that month, the holiday cannot occur on which of the following days? (A) 16th (B) 22nd (C) 18th (D) 19th (E) 21st 13. A circular spinner is divided into three sections. An arrow is attached to the centre of the spinner. The arrow is spun once. The probability that the arrow stops on the largest section is 50%. The probability it stops on the next largest section is 1 in 3. The probability it stops on the smallest section is (A) 1 4 (B) 2 5 (C) 1 6 (D) 2 7 (E) 3 10 14. A positive number is divisible by both 3 and 4. The tens digit is greater than the ones digit. How many positive two-digit numbers have this property? (A) 4 (B) 5 (C) 6 (D) 7 (E) 8 15. A rectangular pool measures 20 m by 8 m. There is a 1 m wide walkway around the outside of the pool, as shown by the shaded region. The area of the walkway is (A) 56 m2 (B) 60 m2 (C) 29 m2 (D) 52 m2 (E) 50 m2 20 m 8 m 1 m Grade 8 16. The results of asking 50 students if they participate in music or sports are shown in the Venn diagram. What percentage of the 50 students do not participate in music and do not participate in sports? (A) 0% (B) 80% (C) 20% (D) 70% (E) 40% Music Sports 15 5 20 17. There are 2 3 as many golf balls in Bin F as in Bin G. If there are a total of 150 golf balls, how many fewer golf balls are in Bin F than in Bin G? (A) 15 (B) 30 (C) 50 (D) 60 (E) 90 18. In the sequence shown, Figure 1 is formed using 7 squares. Each _gure after Figure 1 has 5 more squares than the previous _gure. What _gure has 2022 squares? (A) Figure 400 (B) Figure 402 (C) Figure 404 (D) Figure 406 (E) Figure 408 Figure 1 Figure 2 Figure 3 19. Mateo's 300 km trip from Edmonton to Calgary passed through Red Deer. Mateo started in Edmonton at 7 a.m. and drove until stopping for a 40 minute break in Red Deer. Mateo arrived in Calgary at 11 a.m. Not including the break, what was his average speed for the trip? (A) 83 km/h (B) 94 km/h (C) 90 km/h (D) 95 km/h (E) 64 km/h 20. Equilateral triangle ABC has sides of length 4. The midpoint of BC is D, and the midpoint of AD is E. The value of EC2 is (A) 7 (B) 6 (C) 6:25 (D) 8 (E) 10 Part C: Each correct answer is worth 8. 21. The positive factors of 6 are 1, 2, 3, and 6. There are two perfect squares less than 100 that have exactly _ve positive factors. What is the sum of these two perfect squares? (A) 177 (B) 80 (C) 145 (D) 52 (E) 97 22. In the list p; q; r; s; t; u; v, each letter represents a positive integer. The sum of the values of each group of three consecutive letters in the list is 35. If q + u = 15, then p + q + r + s + t + u + v is (A) 85 (B) 70 (C) 80 (D) 90 (E) 75 Grade 8 23. The net shown is folded to form a cube. An ant walks from face to face on the cube, visiting each face exactly once. For example, ABCFED and ABCEFD are two possible orders of faces the ant visits. If the ant starts at A, how many possible orders are there? (A) 24 (B) 48 (C) 32 (D) 30 (E) 40 A D B C E F 24. The number 385 is an example of a three-digit number for which one of the digits is the sum of the other two digits. How many numbers between 100 and 999 have this property? (A) 144 (B) 126 (C) 108 (D) 234 (E) 64 25. Student A, Student B, and Student C have been hired to help scientists develop a new avour of juice. There are 4200 samples to test. Each sample either contains blueberry or does not. Each student is asked to taste each sample and report whether or not they think it contains blueberry. Student A reports correctly on exactly 90% of the samples containing blueberry and reports correctly on exactly 88% of the samples that do not contain blueberry. The results for all three students are shown below. Student A Student B Student C Percentage correct on samples 90% 98% (2m)% containing blueberry Percentage correct on samples 88% 86% (4m)% not containing blueberry Student B reports 315 more samples as containing blueberry than Student A. For some positive integers m, the total number of samples that the three students report as containing blueberry is equal to a multiple of 5 between 8000 and 9000. The sum of all such values of m is (A) 45 (B) 36 (C) 24 (D) 27 (E) 29The outdoor recreation industry represents a new economy. The leaders of this economy will need to have a deep understanding of our local natural resources and integrate the components of innovation, health, and wellness into a vision for what comes next. Everyone wins when you do the right things for the environment, the community, and the venture. We want to offer the young generation a chance to be part of the foundation we are building for adventure tourism in the emirates and the region. Adventure Tourism Is the Fastest-Growing Global Niche. What does this mean? It means that there’s plenty of room for young experts to enter the field. It’s not just the "guides" that the adventure tourism industry needs. It’s everything that goes with it, from adventure tourism accommodations to trip planners, event managers, marketing and finance directors, advertising, public relations, and communications. We want to highlight that adventure tourism requires more than just guides, and various careers within adventure tourism play a big role in attracting high-value customers, supporting local economies, and encouraging sustainable practices. The continued growth of this sector creates net positive impacts not only for tourism, but also for destination economies, their people, and their environment. 1) Understanding Tourism Tourism is one of the world’s fastest-growing industries and a major foreign exchange and employment generation for many countries. It is one of the most remarkable economic and social phenomena. 2) Understanding Adventure Tourism Adventure tourism is defined as the movement of the people from one to another place outside their comfort zone for exploration or travel to remote areas, exotic and possibly hostile areas. Adventure tourism is a type of tourism in which tourists engage in adventure activities such as trekking, climbing, rafting, scuba diving, or the likes. Adventure tourism gains much of its excitement by allowing the tourist to step outside their comfort zone. This may be from experiencing culture shock or through the performance of acts that required some degree of risk whether real or perceived. It is also about connecting with a new culture or a new landscape and being physically active at the same time. It is not only about being risky or pushing your boundaries. In fact, it is especially important to know and respect your limits while you are in an unfamiliar area. Adventure travel is a leisure activity that takes place in an unusual, exotic, remote, or wilderness destination. It tends to be associated with high levels of activity by the participant, most of it outdoors. Adventure tourists expect to experience various levels of risk, excitement, and tranquillity and be personally tested. In particular, they are explorers of unspoiled, exotic parts of the planet and also seek personal challenges. The main factor distinguishing adventure tourism from all other forms of tourism is the planning and preparation involved. 3) Definitions of Adventure Tourism Adventure tourism is a new concept in the tourism industry. The tourism industry adopted adventure tourism, but there is not any specific definition of adventure tourism. Most commentators concur that adventure tourism is a niche sector of the tourism industry, but there are many other niche sectors in tourism that have the same characteristics that overlap with adventure tourism such as ecotourism, activity tourism, or adventure travel. One of them can confuse. Adventure tourism is a complicated and ambiguous topic. Some important definitions of adventure tourism are as following: A) According to the Adventure Travel Trade Association (ATTA): “adventure tourism is a tourist activity that includes physical activity, cultural exchange, or activities in nature.” B) According to Muller and Cleaver: “Adventure tourism is characterized by its ability to provide the tourist with relatively high levels of sensory stimulation, usually achieved by including physically challenging experiential components with the tourist experience.” C) The Canadian Tourism Commission in 1995 defines adventure tourism as: “an outdoor leisure activity that takes place in an unusual, exotic, remote or wilderness destination, involves some form of unconventional means of transportation, and tends to be associated with low or high levels of activity.” D) According to Sung et al: “adventure tourism is the sum of the phenomena and relationships arising from the interactions of adventure touristic activities with the natural environment away from the participant’s usual place of residence area and containing elements of risk in which the outcome is influenced by the participation, setting, and the organizer of the tourist’s experience.” E) According to UNWTO: ” adventure tourism can be domestic or international, and like all travel, it must include an overnight stay, but not last longer than one year.” 4) Types of Adventure Tourism Adventure tourism has grown exponentially all over the world in recent years with tourists visiting destinations previously undiscovered. This allows for new destinations to market themselves as truly unique, appealing to those travellers looking for a rare, incomparable experience. Adventure tourism includes various activities like caving, hiking, sailing, trekking, etc. Adventure tourism is categorized into two categories: • Hard Adventure • Soft Adventure Hard Adventure Hard adventure refers to activities with high levels of risk, requiring intense commitment and advanced skills. Hard tourism includes the activities like climbing mountains/rock/ice, trekking, caving, etc. Hard adventure activities are highly risked in nature. Professional guides and advanced levels of skills are required to perform these activities. Many tourists died during climbing mountains, caving every day. Soft Adventure Soft adventure refers to activities with a perceived risk but low levels of risk, requiring minimal commitment and beginner skills; experienced guides lead most of these activities. Soft tourism includes the activities like backpacking, camping, hiking, kayaking, etc. Soft adventure activities are low-risk in nature. Professional guides lead these activities. Soft adventure is a popular category in adventure tourism as it caters to a wider audience. 5) Adventure Tourism Activities Adventure travellers are early adopters by nature, meaning they are generally more willing to try new destinations, activities, and travel products. Popular activities change rapidly, and it seems there is a new twist on an existing sport every year. Some activities have low risk and some have high. Adventure tourism activities are classified into two types: • Hard Adventure Activities • Soft Adventure Activities Hard Adventure Activities Hard adventure activities are highly risky and dangerous in nature. These activities are as the following: • Caving • Mountain Climbing • Rock Climbing • Ice Climbing • Trekking • Sky Diving Soft Adventure Activities These activities are less dangerous and risk as compared to hard adventure activities. These activities are mostly lead by professional guides. An example of these activities are: • Backpacking • Bird watching • Camping • Canoeing • Eco-tourism • Fishing • Hiking • Horseback riding • Hunting • Kayaking/sea/whitewater • Orienteering • Safaris • Scuba Diving • Snorkeling • Skiing • Snowboarding • Surfing Adventure tourism activities sit well with the environment because the natural world provides us with the resources for many of the activities that provide risk, challenge, sensory stimulus, novelty, discovery, and so on. 6) Characteristics and Features of Adventure Tourism The threefold combination of activity, nature, and culture marks adventure travel as an all-around challenge. Some unique characteristics and features of adventure tourism are as the following: • Physical activity, like involving physical exertion or psychomotor skills • Contact with nature, activities bringing contact with the natural world in general, or with specific wildlife • Contact with different cultures, i.e. people, faith, lifestyles • Journeys for example vehicle, animal, or human power • Uncertain outcomes • Danger and risk • Challenges • Anticipated rewards • Novelty • Stimulation and excitement • Exploration and discovery • Contrasting emotions 7) Adventure Tourism Supplier A tourism supply chain is the system of people, products, activities, and materials that get a product or service from its raw state through production and distribution to the consumer. As with any sector, volume discounts drive the mass price point, so major retailers primarily market select trips that sell in high volume. The supply chain for these mass tourism products is often very simple, comprising only transportation and accommodation elements. The adventure tourism supply chain is more complex. Niche products often require specializes in knowledge and operations. Adventure tourism’s supply chain linkages go very deep, and this is one of the key reasons that adventure tourism delivers greater benefits at the local level. Supply chains vary from destination to destination. Without a proper supply chain, the tourism sector cannot survive. Tourism suppliers are the backbone of the tourism industry. Adventure tourism suppliers work at a different, different level like as domestic as well international level. 8) Adventure Tourism Importance and Benefits Adventure tourism is one of the fastest-growing sectors of the tourism sector, attracting high-value customers, supporting local economies, and encouraging sustainable practices. The continued growth of this sector creates net positive impacts not only for tourism, but also for destination economies, their people, and their environment. Some importance and benefits of adventure tourism are: A) Employment Generation Adventure tourism generates jobs. Adventure tourism generates directs jobs to accommodation, transportation sector, and travel agencies or tour operators. Adventure tourism also provides indirect jobs to tourism suppliers. Adventure tourism plays an important role in the generation of employment in the economy. B) Foreign Exchange Adventure tourism attracts foreign tourists on a large scale, as a result, it helps in foreign exchange generation. When tourists travel to another country, they spend a large amount of money on accommodation, transportation, and shopping. Adventure tourism generates foreign exchange and supports the economy of the host country. C) Economy Development Adventure tourism helps in the development of the host country’s economy. Adventure tourism activities directly support the economy in various forms. The more tourists, the more economic growth. D) Support Local Communities Adventure tourism helps in the development of infrastructure and supports local communities. Adventure tourism activities directly contributed to the local economy of the communities and increase local people's living standards. E) Conservation of Natural Resources Adventure tourism activities are nature-based activities. Leaders in the adventure tourism industry are dedicated to making this tourism segment as sustainable as possible. They help in the conservation of natural resources as well as culture. F) Creating Business Opportunities Adventure tourism activities create new business opportunities. Several companies specialize in helping emerging adventure tourism operators market their products. Each new adventure tourism activity creates a new business opportunity. G) Local and Foreign Investment Adventure tourism creates business opportunities; as a result, it attracts local as well as international investors. Investors invest their money in accommodation, transportation, and travel trade organization. Adventure tourism plays an important role in the economy of the host country.F.4 Speaking -- Photos FirstF.4 Listening U1.1-1.5NCSCOS Grade 8 Math - Skill: NC.8.F.4 1 La cottura La cottura consiste nella trasmissione di calore da una sorgente a un alimento. In particolare, si parla di cottura quando si espone un alimento a una temperatura superiore a 40 °C. Molti alimenti devono essere cotti per: • diventare commestibili, oppure più digeribili e gradevoli; • prolungare la conservabilità; • diventare più sicuri dal punto di vista igienico e microbiologico. Con la cottura: • si applica una temperatura > 40 °C; • l’alimento si scalda; • le caratteristiche fisiche e chimiche dell’alimento si modificano definitivamente a seguito del rialzo termico. Ad esempio, l’acqua si trasforma in vapore a 100 °C alla pressione di 1 atm (mentre solidifica a 0 °C). Il burro fonde (ma non cuoce) al di sotto di 40 °C. Da che cosa dipendono la temperatura e il tempo di cottura? Con la cottura, l’alimento, scaldandosi, assorbe calore. La temperatura di cottura, cioè la quantità di calore da applicare nei processi di cottura, dipende: • dal peso dell’alimento (la temperatura di cottura aumenta proporzionalmente al peso dell’alimento); • dalla composizione dell’alimento, in particolare dal suo contenuto in acqua (per scaldare un alimento umido serve più calore). Il tempo di cottura (cioè la durata dell’esposizione al calore) varia in base: • alla tecnica di cottura applicata; • al recipiente di cottura (materiale, sagoma); • alla forma dell’alimento. A parità di condizioni, l’olio si riscalda più velocemente dell’acqua perché il calore specifico dei grassi è pari a circa la metà di quello dell’acqua. Calore È una forma di energia legata al moto disordinato delle molecole che si trasmette da un corpo più caldo a uno più freddo, 昀椀no al raggiungimento dell’equilibrio termico. L’unità di misura del calore è il joule (J). In cucina si usa la chilocaloria (kcal), un multiplo della caloria equivalente al calore necessario per aumentare di 1 °C la temperatura di un chilogrammo, ovvero un litro, di acqua (1 kcal = 4,184 kJ; 1 kJ = 0,239 kcal). Calore speci昀椀co È la quantità di calore che serve per aumentare di 1 °C la temperatura di un chilogrammo di un materiale.TEORIA / UDA 4 Le tecniche e le preparazioni di base 153 Come si trasmette il calore? Il calore si trasmette dal corpo più caldo a quello più freddo. Ciò può avvenire in diversi modi: per conduzione, per convezione e per irraggiamento. In tutte le tecniche di cottura una delle tre modalità risulta dominante, ma agisce combinandosi con le altre. Nelle cotture per conduzione e per convezione è sempre presente un mezzo di conduzione, che può essere l’acqua, il vapore acqueo, una sostanza grassa, l’aria o il recipiente di cottura. Conduzione • I due corpi (generalmente solidi) sono a contatto diretto e hanno temperature diverse (l’uno è caldo e l’altro è più freddo) • Non c’è spostamento di materia (il calore si trasmette attraverso la materia) • La quantità di calore trasferito dipende dalla composizione dei due corpi ed è proporzionale alla differenza di temperatura e alla superficie di contatto Esempio: cottura alla piastra o in padella Irraggiamento • I due corpi non sono a contatto diretto: il passaggio del calore avviene nel vuoto o nell’aria • Il corpo caldo emette onde elettromagnetiche (raggi infrarossi) che sono assorbite dal corpo freddo Esempio: cottura in forno, cottura in forno a microonde, cottura allo spiedo, cottura alla griglia Convezione • È presente un fluido, cioè un liquido (olio, acqua) o un gas (aria, vapore) • Si produce uno spostamento di materia: il fluido si riscalda, si espande verso l’alto e produce correnti convettive che, muovendosi, favoriscono lo scambio di calore Esempio: bollitura (in acqua), frittura (in olio) ESERCIZIO 1 Nella trasmissione per conduzione i due corpi sono a contatto diretto V F 2 Nella trasmissione per convezione si formano correnti convettive che favoriscono lo scambio di calore V F 3 Nella trasmissione per irraggiamento i due corpi non sono a contatto diretto V F 4 Nella trasmissione per irraggiamento è sempre presente un mezzo 昀氀uido V FF&E 4.2 Types of Energy