Slope (rate of change) and Y-Intercept (Initial Value)

Slope as Rate of Change, Direct Variation and Arithmetic Sequence

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

Continental Drift Theory. From the discussion of the rock cycle, it has been pointed out that through Earth's external and internal processes. Earth's surface is constantly changing. However, this idea of a changing environment did not conform with the belief of earlier scientists. Rather, they thought that the geographic positions of ocean basins and continents have been static since the beginning of time. It was around the 1500s when Leonardo da Vinci, upon his discovery of fossil seashells found at the high mountains of Italy, first thought of the idea that the areas where mountains are located may have been oceans in the past. Through time, other fossils of marine organisms found far above the current sea level further supported the idea that mountains were uplifted and weathering wore them down. At around the 1800s, most scientists have accepted the idea that Earth's crust is undergoing large vertical movements or uplifting. There was also evidence of possible horizontal movements, but the scientists then were not convinced about it. Alfred Wegener showed evidence of horizontal or lateral movement of the continents in his continental drift theory. According to him, the continents have drifted around the world and have once formed a giant landmass or supercontinent called Pangaea. To support his theory, Alfred Wegener presented a set of geographical, biological, and climatic evidence.Wegener's geographical evidence included the jigsaw puzzle fit of the current continents. He pointed out that the coastlines of South America and Africa seem to fit together. He also pointed the presence of mountain ranges having similar rock types and age but separated by vast oceans, like that of the folded rocks of the Caledonian mountains. The same folded rocks run through West Africa, North America, Newfoundland, Ireland, Wales, Scotland, Greenland, and Norway, all of which are now separated by the Atlantic Ocean. A geographical evidence on the similar rock types in West Africa, North America, Greenland, and Europe is found. The biological evidence came in the discovery of similar plant and animal fossils in different continents separated by oceans. The animal fossils of Mesosaurus and Lystrosaurus indicate that they were not capable of crossing the oceans to reach the other continents. If they were, the fossils should have been more widely distributed Africa, Australia, India, and South America were too large to be carried by wind. This indicates that the areas where the fossils were found were closely linked. It has also been found out that the plant only grew in areas with subpolar climate, which would indicate that the landmasses were located near the South Pole.Lastly, for his climatic evidence, Wegener discovered that a glacial period occurred during the late Paleozoic era in Southern Africa, South America, Australia, and India. The initial explanation for this event was global cooling, but it was rejected because large tropical swamps with so much vegetation were found at the same time in the Northern Hemisphere. This further supported the idea that the supercontinent was indeed near the South Pole, and the continents in Northern Hemisphere were once near the equator. The glacial period also left glacial striations, or the scratches glaciers make as they move across on the underlying bedrock, on the aforementioned continents. For such an event to happen, the continents would have to be connected. SCIENCE PIONEER. Alfred Wegener (1880-1930). Alfred Wegener was a German polar researcher, geophysicist, and meteorologist. He was known for his work on the continental drift theory. In his effort to defend his work, he went to the Greenland ice sheet where he died.Even with all the compelling evidence, the continental drift theory hardly convinced the scientific community at that time because Wegener was unable to identify a credible mechanism that drives the continental drift. He was unable to clearly explain how the continents moved and how the larger continents broke through the ocean floor. Eventually, critics of the continental drift began to accept the theory when new evidence supporting the theory was discovered. The new evidence led to a more encompassing theory the theory of plate tectonics. This theory provided a more convincing explanation as to how the continents moved. The evidence that paved the way for the theory of plate tectonics was the idea of wandering poles. Scientists began studying volcanic rocks to determine the location of the magnetic poles. When volcanic rocks crystallize, the minerals with magnetic properties align themselves parallel to Earth's magnetic field at the time the minerals were formed. This finding allowed scientists to determine the polarity of Earth's magnetic field and the magnetic inclination that showed the location of the poles. Upon studying the paleomagnetism of the rocks, geophysicists found out that rocks from various locations point to different magnetic north poles, suggesting that the poles have wandered. Since movement of magnetic poles is very unlikely, scientists have accepted the idea that the continents are indeed moving. And if the continents are moving, scientists thought that maybe the ocean basins are moving too. They also discovered that some rocks showed magnetic reversals, which led them to believe that the magnetic north pole now was not always the magnetic north pole. Seafloor Spreading. After World War II, exploration on the ocean floor became the focus of many geologic studies. It was only then that the ocean ridge system was discovered. A geologist in Princeton University named Harry Hess, along with other scientists, studied this ocean ridge system and hypothesized that the oceanic crust was moving away from the ridge. His hypothesis, known as seafloor spreading, showed that the ocean floor is split along the ridge where the magma rises to form the new ocean floor.Because of this, rocks located near the ridge are younger than those that are located magnetic polarity of Earth is also preserved in those rocks. Withe ridge scientists were able to see the magnetic reversals in the ocean floor, and they were able to make use of information to determine that the ocean floor is moving at a rate of about 10 cm per year. Plate Tectonics. Confirmation of the seafloor spreading hypothesis proved that continents are not moving above the ocean floor. Rather, it is the fragments of the lithosphere. The lithosphere is the rigid layer that is composed of the uppermost mantle and the crust that carry the continents and the ocean basins along. These fragments of the lithosphere are called plates. Underneath the lithosphere is a weaker region in the mantle known as asthenosphere that behaves like a fluid. Thus, the lithosphere floats above the asthenosphere, making it detached and free to move. This became the basis of the theory of plate tectonics. Now that it has been made clear that it is the plates which are moving, the question as to how they move remained. Sir Arthur Holmes proposed the driving force for this plate movement in 1919. He suggested that the movement in the mantle carries the plates along. It was previously discussed that Earth's interior is very hot due to the heat produced by radioactive decay. Convection takes place in the mantle, keeping the asthenosphere hot and weak. The convection currents produced in the asthenosphere are the ones carrying the lithospheric plates and making them move. However, convection currents are not enough. Mechanisms such as ridge push and slab pull aid the convection currents to slowly move the lithospheric plates. Ridge push occurs at mid ocean ridges which are higher in elevation than the surrounding trenches and abyssal plains. The new ocean floor from the ridge is hot and relatively thin. As it moves away from the ridge, it cools down and gets denser, heavier, and thicker. Below this cooling ocean floor is the asthenosphere, which is less dense. This area becomes a massive shear zone and the new ocean floor will effectively slide down the slope of the asthenosphere. When the plate collides with another plate with lesser density, the denser plate sinks and a subduction zone is formed. When the subducting plate sinks, it pulls on the rest of the plate behind it. These mechanisms explain the movement of the plates.Earth has seven major lithospheric plates that account for 94% of Earth's surface. These are the North American Plate, South American Plate, Pacific Plate, African Plate, Eurasian Plate, Indo-Australian Plate, and Antarctic Plate. These plates are constantly moving relative to the other plates. Thus, the interaction of plates occurs mostly along the boundaries. These movements are plotted using information from earthquakes and volcanic activities. There are three main types of plate boundaries: convergent, divergent, and transform boundaries Convergent boundaries are boundaries where two plates move towards each other A convergent boundary is also known as destructive margin since this is where the collision between two plates occhins. There are three types of convergence-oceanic oceanic, oceanic-continental, and continental-continental. Trenches are features of the ocean floor that are present in both oceanic-oceanic boundary and oceanic-continental boundary. Subduction occurs at the trenches, therefore, these are characterized as the deepest parts of Earth. A divergent boundary is the opposite of convergent boundary: two plates move away from each other. Divergent boundaries create new crust; thus, they are also known as constructive margins. The ocean ridge system is a divergent boundary where new ocean floor is produced as magma rises, pushing the older rocks aside.Transform boundary is also known as conservative plate margin since two plates just move past one another, neither creating nor destroying land. Earthquake epicenters are usually detected at transform boundaries because the rocks tend to break and not fold or sink, like in convergent boundaries. Evolution of the Ocean Basins. Both the movement of the plates and seafloor are responsible for the evolution of ocean basins. Along the divergent boundary where ocean ridge systems are found, magma is released and new ocean floor is created. Along convergent boundaries, the ocean floor is being destroyed. The evolution of the ocean basins started during the time when Pangaea was still present and was surrounded by the vast ocean or superocean known as Panthalassa, also called Paleo-Pacific or "old Pacific." Upon the initial break up of Pangaea into Laurasia and Gondwanaland, the Tethys Sea began to form. Then, the Eurasian and North about, forming the North Atlantic. The South Atlantic only started to form when the African Plate and South American Plate separated. The continued movement of the plates created the Himalayas at one side and separated the Pacific Ocean and Atlantic Ocean at the other side, which consequently formed the current ocean basins. Both the movement of the plates and seafloor are responsible for the evolution of ocean basins. Along the divergent boundary where ocean ridge systems are found, magma is released and new ocean floor is created. Along convergent boundaries, the ocean floor is being destroyed. The evolution of the ocean basins started during the time when Pangaea was still present and was surrounded by the vast ocean or superocean known as Panthalassa, also called Paleo-Pacific or "old Pacific." Upon the initial break up of Pangaea into Laurasia and Gondwanaland, the Tethys Sea began to form. Then, the Eurasian and North about, forming the North Atlantic. The South Atlantic only started to form when the African Plate and South American Plate separated. The continued movement of the plates created the Himalayas at one side and separated the Pacific Ocean and Atlantic Ocean at the other side, which consequently formed the current ocean basins.Continents do not immediately end at the point where the ocean meets the land. They may extend slightly into the oceans. The portion of the continent that is submerged is called continental margin. There are two types of continental margin: passive margin and active margin. A passive continental margin consists of a continental shelf, continental slope, and continental rise. It is not associated with plate boundaries; thus, there are very little tectonic activities. An active continental margin only has a continental shelf and a continental slope. It is associated with plate boundaries; thus, a main feature of this boundary is a trench. The different features of a continental margin are the following: 1. The continental shelf is the gently-sloping submerged portion of the continent. 2. The continental slope is the steep slope after the continental shelf. It is still part of the continent. 3. The continental rise is the gently-sloping area after the continental slope and before the ocean floor. 4. The trenches are the deepest parts of the ocean. These are narrow depressions caused by the subduction of the ocean floor along the convergent boundaries. 5. The mid-oceanic ridge is the mountain range system in the ocean. It is responsible for the production of new ocean floor. This is the region where new magma constantly emerges from. SCIENCE CAREER. A scientific illustrator uses art to inform and communicate complex details and concepts of science. He/She makes use of scientifically informed observations and research along with his/her technical art and aesthetic skills to make accurate representations. In Natural History, the scientific illustrators recreate how the extinct species look like by working with scientists and fossil records. Moreover, with the advances in technology, illustrators are now into 3D modelling, animation, and video making. Earth's History. All the processes that have been discussed require long periods of time to create a noticeable change on Earth's surface. You can just imagine how long it would take to create an oceanas vast as the Pacific Ocean if the ocean floor moves only at about 10 cm/year. It is then important to know the history of Earth to learn the complexities of its past and be able to use it to understand the present. Just like learning the history of a country that requires one to read a lot of books, learning the history of Earth involves studying a lot of rocks. Rocks, especially sedimentary rocks, contain a lot of information about Earth's past. It holds the key to most of the geologic processes that happened on Earth and the key to uncovering how life on Earth evolved. But these discoveries are worthless if there is no time perspective. Thus, one of the most important contributions of geologists to mankind is the geologic time scale, which holds a history that is exceedingly long.

Weathering describes the breaking down or dissolving of rocks and minerals on the surface of the Earth. Water, ice, acids, salts, plants, animals, and changes in temperature are all agents of weathering. Once a rock has been broken down, a process called erosion transports the bits of rock and mineral away. No rock on Earth is hard enough to resist the forces of weathering and erosion. Together, these processes carved landmarks such as the Grand Canyon, in the U.S. state of Arizona. This massive canyon is 446 kilometers (277 miles) long, as much as 29 kilometers (18 miles) wide, and 1,600 meters (1 mile) deep. Weathering and erosion constantly change the rocky landscape of Earth. Weathering wears away exposed surfaces over time. The length of exposure often contributes to how vulnerable a rock is to weathering. Rocks, such as lavas, that are quickly buried beneath other rocks are less vulnerable to weathering and erosion than rocks that are exposed to agents such as wind and water, As it smoothes rough, sharp rock surfaces, weathering is often the first step in the production of soils. Tiny bits of weathered minerals mix with plants, animal remains, fungi, bacteria, and other organisms. A single type of weathered rock often produces infertile soil, while weathered materials from a collection of rocks is richer in mineral diversity and contributes to more fertile soil. Soils types associated with a mixture of weathered rock include glacial till, loess, and alluvial sediments. Weathering is often divided into the processes of mechanical weathering and chemical weathering. Biological weathering, in whichliving or once-living organisms contribute to weathering, can be a part of both processes. Mechanical Weathering Mechanical weathering, also called physical weathering and disaggregation, causes rocks to crumble. Water, in either liquid or solid form, is often a key agent of mechanical weathering. For instance, liquid water can seep into cracks and crevices in rock. If temperatures drop low enough, the water will freeze. When water freezes, it expands. The ice then works as a wedge. It slowly widens the cracks and splits the rock. When ice melts, liquid water performs the act of erosion by carrying away the tiny rock fragments lost in the split. This specific process (the freeze-thaw cycle) is called frost weathering or cryofracturing. Figure 4.3 Frost Wedging Temperature changes can also contribute to mechanical weathering in a process called thermal stress. Changes in temperature cause rock to expand (with heat) and contract (with cold). As this happens over and over again. the structure of the rock weakens. Over time, it crumbles. Rocky desert landscapes are particularly vulnerable to thermal stress. The outer layer of desert rocks undergo repeated stress as the temperature changes from day Eventually, Lo outer night. layersflake off in thin sheets, a process called exfoliation. Exfoliation contributes to the formation of bornhardts, one of the most dramatic features in landscapes formed by weathering and erosion. Bornhardts are tall, domed, isolated rocks often found areas. in tropical Sugarloaf Mountain, an iconic landmark in Rio de Janeiro, Brazil, is bornhardt. a Salt also works to weather rock in a process called haloclasty. Saltwater sometimes gets into the cracks and pores of rock. If the saltwater evaporates, salt crystals are left behind. As the crystals grow, they put pressure on the rock, slowly breaking it apart. Plants and animals can be agents of mechanical weathering. The seed of a tree may sprout in soil that has collected in a cracked rock. As the roots grow, they widen the cracks, eventually breaking the rock into pieces. Over time, trees can break apart even large rocks. Even small plants, such as mosses, can enlarge tiny cracks as they grow. Animals that tunnel underground, such as moles and prairie dogs, also work to break apart rock and soil. Other animals dig and trample rock aboveground, causing rock to slowly crumble. Chemical Weathering Chemical weathering changes the molecular structure of rocks and soil.For instance, carbon dioxide from the air or soil sometimes combines with water in a process called carbonation. This produces a weak acid, called carbonic acid, that can dissolve rock. Carbonic acid is especially effective at dissolving limestone. When carbonic acid seeps through limestone underground, it can open up huge cracks or hollow out vast networks of caves. Carlsbad Caverns National Park, in the U.S. state of New Mexico, includes more than 119 limestone caves created by weathering and erosion. The largest is called the Big Room.. With an area of about 33,210 square meters (357,469 square feet), the Big Room is the size of six football fields. Another type of chemical weathering works on rocks that contain iron. These rocks turn to rust in a process called oxidation. Rust is a compound created by the interaction of oxygen and iron in the presence of water. As rust expands, it weakens rock and helps break it apart. Another familiar form of chemical weathering is hydrolysis. In the process of hydrolysis, a new solution (a mixture of two or more substances) is formed as chemicals in rock interact with water. In many rocks, for example, sodium minerals interact with water to form a saltwater solution. Hydration and hydrolysis contribute to flared slopes, another dramatic example of a landscape formed by weathering and erosion. Flared slopes are sometimes nicknamed "wave rocks." Their c-shape is largely concave rock formations a result of subsurface weathering, in which hydration and hydrolysis wear away rocks beneath the landscape's surfaceWeathering and People Weathering is a natural process, but human activities can speed it up. For example, certain kinds of air pollution increase the rate of weathering Burning coal, natural and petroleum releases chemicals such as nitrogen oxide and gas, sulfur dioxide into the atmosphere. When these chemicals combine with sunlight and moisture, they change into acids. They then fall back to Earth as acid rain. Acid rain rapidly weathers limestone, marble, and other kinds of stone. The effects of acid rain can often be seen on gravestones, making names and other inscriptions impossible to read. Acid rain has also damaged many historic buildings and monuments. For example, at 71 meters (233 feet) tall, the Leshan Giant Buddha at Mount Emei, China is the world's largest statue of the Buddha. It was carved 1,300 years ago and sat unharmed for centuries. An innovative drainage system mitigates the natural process of erosion But in recent years, acid rain has turned the statue's nose black and made some of its hair crumble and fall.

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