\int_{ }^{ }\frac{dx}{\sqrt{a^2-x^2}}

\ \frac{1}{a}\sin^{-1}\left(\frac{x}{a}\right) + c

\ \frac{1}{a}\sin^{-1}\left(\frac{x}{a}\right)

\int_{ }^{ }\frac{dx}{x^2\ +\ 2x\ +\ 3}

\frac{1}{\sqrt{2}}\tan^{-1}\left(\frac{x+1}{\sqrt{2}}\right)+c

-\ \frac{1}{\sqrt{2}}\tan^{-1}\left(\frac{x+1}{\sqrt{2}}\right)+c

\tan^{-1}\left(\frac{x+1}{\sqrt{2}}\right)+c

Class 12/Math Test/Integration/2022

12MT-4/Det/240522

QUIZ ON INVERSE TRIG FUNCTIONS CONCEPTS

F2 Class Quiz 12 (week 18)

Area The amount of space inside a shape. We found the area of the rectangle. 面积 Volume The amount of space something takes up. The box has a volume of 12 cubic meters. 体积 Surface area The total area of all sides of a 3D shape. We calculated the surface area of the cube. 表面积 Coordinates Numbers that show a point’s location on a graph. The coordinates of the point are (2,3). 坐标 Polygon A flat shape with straight sides. A triangle is a polygon. 多边形 Prism A solid shape with two identical ends. We studied a rectangular prism in math class. 棱柱 Net (geometry) A flat pattern that can be folded into a 3D shape. We made a cube from its net. 展开图 Data Information or numbers collected for study. We used data from our survey. 数据 Representatio n A way to show something, like a graph or chart. The graph is a visual representation of data. 表示；图示 Model Something used to show or explain an idea. We built a model of a volcano.

Classroom Expectations and Policies Assessment 1. What should students bring to class every day? a. Only a positive attitude b. Charged Chromebook, writing utensil, and positive attitude c. Just their books d. Snacks and drinks 2. What is the consequence for bullying in the classroom? a. A warning b. A violation card c. Extra homework d. A meeting with the principal 3. If a student breaks a personal item, what must they do? a. Ignore it b. Apologize c. Buy a new one for the teacher d. Ask for forgiveness 4. How should students handle using the futon during class? a. Sit on it every day b. Use it without asking c. Ask first and only use it during work time d. Sit on it during lectures 5. Where will all assignments be posted? a. On the classroom wall b. On Canvas c. Only verbally d. In a textbook 6. What happens if an assignment is submitted late? a. It will be graded normally b. It will not be accepted c. It will drop a letter grade each day it is late d. It will be given extra credit 7. After how many days of lateness will a student receive only half credit for an assignment? a. 1 day b. 2 days c. 3 days d. 4 days 8. What is the policy for retaking tests? a. No retakes allowed b. Students must schedule the retake themselves c. Retakes are given automatically d. Only the teacher can decide on retakes 9. What constitutes cheating in this classroom? a. Asking for help b. Claiming credit for someone else's work c. Working with a partner d. Participating in study groups 10. What is the penalty for cheating? a. A warning b. A failing grade on the assignment and notification of parents c. Extra assignments d. A detention 11. How will grades be determined? a. By participation only b. By points, with tests and quizzes weighted more than classwork c. By effort d. By attendance 12. Where can students use their cell phones? a. In class anytime b. In the commons and hallways during passing time and lunch c. In the restroom d. In the cafeteria only 13. What happens if a student uses their phone during class? a. They will receive a warning b. The phone will be confiscated immediately c. They can keep it if they ask d. They will lose points on their grade 14. What should a student do if they know they will be absent? a. Ignore it and hope for the best b. Come to the teacher at least three days before c. Ask a friend for notes d. Just show up later 15. If a student is sick and cannot do work, what should they focus on? a. Completing all missed assignments b. Getting better c. Emailing the teacher every hour d. Asking for extra credit 16. What is the policy on bringing food or drinks to class? a. It's not allowed at all b. It’s allowed as long as it’s not a distraction c. Only water is allowed d. Students must share their food 17. How should students contact the teacher with questions? a. Only during class time b. Through social media c. By email or in person d. By sending a friend 18. What happens if a student emails after 9 PM? a. The teacher will respond immediately b. The teacher will respond the next day at 7:45 AM c. The email will be ignored d. The teacher will call the student 19. How do violations accumulate for cell phone use? a. They reset every trimester b. They accumulate throughout the school year c. They reset every week d. They do not count 20. What should students do if they have concerns while the teacher is on maternity leave? a. Contact the principal b. Contact the substitute teacher for assistance c. Wait until the teacher returns d. Handle it on their own Answer Key (Always review AI generated answers for accuracy - Math is more likely to be inaccurate) b. Charged Chromebook, writing utensil, and positive attitude b. A violation card c. Buy a new one for the teacher c. Ask first and only use it during work time b. On Canvas c. It will drop a letter grade each day it is late c. 3 days b. Students must schedule the retake themselves b. Claiming credit for someone else's work b. A failing grade on the assignment and notification of parents b. By points, with tests and quizzes weighted more than classwork b. In the commons and hallways during passing time and lunch b. The phone will be confiscated immediately b. Come to the teacher at least three days before b. Getting better b. It’s allowed as long as it’s not a distraction c. By email or in person b. The teacher will respond the next day at 7:45 AM b. They accumulate throughout the school year b. Contact the substitute teacher for assistance

Alright, Isti — here’s a longer and more detailed English version of the Isaac Newton text, still written at a level that’s accessible for Grade 4 students, but rich enough in information to meet PISA literacy expectations and EF A2-level vocabulary. I’ve kept sentences short, clear, and with explanations for new concepts so it’s easier for young learners to follow, while still including both famous facts and lesser-known stories. ⸻ Isaac Newton: The Man Who Changed the Way We See the World A Boy from a Small Village Isaac Newton was born on January 4, 1643, in Woolsthorpe, a small village in England. His life was not easy. His father died before he was born. When he was just a few months old, his mother remarried and left him to live with his grandmother. Isaac missed his parents, but he kept himself busy by making things and exploring the world around him. As a child, Isaac liked to build models and machines. He made a small windmill that could turn with the wind. He built a water clock that told the time by dripping water into a container. He even made a sundial — a clock that tells the time by using the shadow of the sun. 💡 Did you know? The sundial marks that Isaac carved as a boy can still be seen today on the wall of his old house. ⸻ School and Curiosity When Newton first went to school, he was not the top student. At first, he did not pay much attention in class. But one day, another boy teased him for not being smart. Newton decided to study hard to prove him wrong. Soon, he became the best in his class. Isaac loved asking questions. He wanted to know how and why things happened. He enjoyed watching the stars at night and thinking about how the world worked. ⸻ The Falling Apple and Gravity One of the most famous stories about Newton is the falling apple. One afternoon, Isaac sat in his mother’s garden and saw an apple drop from a tree. This made him think: “Why does the apple fall straight down? Why doesn’t it fly up into the sky?” From this question, Newton began to think about gravity — an invisible force that pulls objects toward each other. Gravity is what keeps our feet on the ground. It’s also what keeps the Moon moving around the Earth and the planets moving around the Sun. 💡 Fun fact: The apple did not hit Newton’s head. That’s just a story people made up later to make the tale more exciting. ⸻ Newton’s Three Laws of Motion Newton studied movement and wrote three important rules: 1. Objects stay still or keep moving unless something makes them change. • Example: A ball will not roll unless you push it. 2. The bigger the push, the bigger the movement. • Example: If you kick a ball harder, it will go faster and farther. 3. Every action has an equal and opposite reaction. • Example: When you jump off a boat, the boat moves backward as you move forward. These three laws are still used today to understand how cars, rockets, and even roller coasters work. ⸻ Discoveries in Light and Color Newton also studied light. He found that white light is not just one color — it is made of many colors. He used a glass prism to split sunlight into a rainbow. This helped scientists understand how colors work. ⸻ Inventions and New Ideas Newton made a special telescope that used mirrors instead of lenses. This type of telescope made images of planets and stars much clearer. It is still called the Newtonian telescope today. He also worked in mathematics and helped create a new type of math called calculus, which is used to study changes and movement. ⸻ Strange Experiments Newton was so curious that he sometimes tested ideas on himself. Once, he put a thin needle, called a bodkin, beside his eye to see how it would change his vision. It was very dangerous, but luckily he did not go blind. 💡 Did you know? Newton also studied alchemy — an old kind of science where people tried to turn metal into gold. He never succeeded, but it showed how wide his interests were. ⸻ Later Life and Work At the age of 27, Newton became a professor at Cambridge University. He later worked for the Royal Mint, making sure coins were made safely and stopping people from making fake money. He was very strict, and some criminals were sent to prison because of his work. Newton never married. He spent most of his life reading, writing, and doing experiments. ⸻ The End of His Life Isaac Newton died in 1727 at the age of 84. He was buried in Westminster Abbey, a famous place in London where great people of Britain are honored. His work changed the world forever. Even today, scientists, engineers, and students still use Newton’s laws and ideas. 💬 Newton once said: “If I have seen further, it is by standing on the shoulders of giants.” This means we can make new discoveries by learning from the work of others who came before us. give 10 questions to each passage with PISA literacy standard for kid 10 years, 1. Nikola Tesla: The Man Who Dreamed of Lightning Born: July 10, 1856 Died: January 7, 1943 When Nikola Tesla was a boy in Croatia, he saw a flash of lightning and asked his mother, “Can we catch the light?” That question never left him. As he grew older, Tesla became a brilliant inventor, especially fascinated by electricity. He believed in a future where energy could be sent wirelessly through the air—like music through the radio! Tesla invented the alternating current (AC) system, which became the foundation of modern electricity. At the time, Thomas Edison promoted direct current (DC), and the two men had a fierce competition. Many laughed at Tesla's bold ideas, but he never gave up. He dreamed of wireless communication, flying machines, and even free energy for everyone. Though he died alone and poor, today the world honors his vision. Think About It: Why do you think people didn’t believe Tesla at first? What can we learn from Tesla’s courage to dream big? 2. Charles Darwin: The Man Who Studied the World’s Weirdest Creatures Born: February 12, 1809 Died: April 19, 1882 When young Charles Darwin got on a ship called HMS Beagle, he didn’t know he would change science forever. He sailed around the world for five years, collecting plants, animals, and fossils. On the Galápagos Islands, he noticed something curious: finches had different beaks depending on their island. Why? Darwin’s observations led him to write the theory of evolution by natural selection. It explained how animals adapt and survive. But his ideas shocked many people because they seemed to challenge religious beliefs. Despite the controversy, Darwin continued his work. His book On the Origin of Species changed how we see life on Earth. Think About It: Should scientists share their ideas even if they go against what others believe? How did traveling help Darwin make new discoveries? 3. Marie Curie: The Woman Who Glowed in the Dark Born: November 7, 1867 Died: July 4, 1934 Marie Curie was born in Poland at a time when girls were not allowed to study science. But that didn’t stop her. She moved to France, worked day and night, and discovered radioactivity, a powerful energy hidden inside atoms. She and her husband, Pierre Curie, found two new elements: polonium and radium. She became the first woman to win a Nobel Prize, and the only person to win in two different sciences: physics and chemistry. Even when Pierre died in an accident, Marie continued their work. Her discoveries helped doctors treat cancer—but working with radioactive materials also harmed her health. She died from radiation exposure, but her legacy lives on. Think About It: What challenges did Marie Curie face as a woman in science? Why is it important to balance discovery with safety? 4. Galileo Galilei: The Star Watcher Who Defied the Church Born: February 15, 1564 Died: January 8, 1642 Galileo loved looking at the stars. He built one of the first powerful telescopes and made stunning discoveries: mountains on the Moon, moons around Jupiter, and that the Earth orbits the Sun—not the other way around. This idea, called heliocentrism, went against the teachings of the Church. He was put on trial and forced to say he was wrong. But he wasn’t. He spent his last years under house arrest, quietly writing. Today, Galileo is called the father of modern science for daring to question what others blindly believed. Think About It: Why do you think Galileo was punished for telling the truth? Should science always follow evidence, even if it goes against powerful beliefs? 5. Isaac Newton: The Man Who Asked “Why?” When an Apple Fell Born: January 4, 1643 Died: March 31, 1727 One day, an apple fell from a tree, and Isaac Newton began to wonder: Why did it fall down, not sideways or up? This simple question led to his theory of gravity. Newton also invented calculus, described the laws of motion, and changed physics forever. But Newton wasn’t just a genius—he was curious, quiet, and often worked alone. He believed everything in nature followed rules, and it was our job to discover them. Thanks to him, we understand how planets move, how rockets launch, and why you fall when you trip. Think About It: How did Newton’s curiosity lead to great discoveries? Do you think working alone helped or hurt Newton? 6. Ada Lovelace: The First Computer Programmer Before Computers Existed Born: December 10, 1815 Died: November 27, 1852 Ada Lovelace was the daughter of the famous poet Lord Byron, but she didn’t love poetry—she loved numbers! At a time when girls were expected to sew, Ada studied mathematics. She met Charles Babbage, who designed an early computer called the Analytical Engine. Ada imagined the machine could do more than just math—it could create music, art, and even write! She wrote what is now considered the first computer program, long before real computers were built. Think About It: How did Ada imagine something that didn’t exist yet? Why do we call her a pioneer in technology? 7. Albert Einstein: The Man Who Brought Time and Space Together Born: March 14, 1879 Died: April 18, 1955 Albert Einstein wasn’t always a good student. In fact, his teachers thought he was slow. But Einstein thought deeply. He asked big questions like, “What if you could ride a beam of light?” His theories of relativity changed how we see space, time, and gravity. He also warned the world about the dangers of nuclear weapons, even though his ideas helped create them. Einstein believed science should help people, not harm them. With his messy hair, kind smile, and brilliant mind, he remains a symbol of genius. Think About It: Can someone be bad in school but still be brilliant? Should scientists be responsible for how their inventions are used? 8. Pythagoras: The Musician Who Loved Math Born: Around 570 BC Died: Around 495 BC Long ago in ancient Greece, Pythagoras believed the universe followed numbers. He discovered the Pythagorean Theorem, a rule about triangles that helps us build houses, design computers, and navigate space. He also believed that music had math inside it—that certain notes made perfect harmony because of mathematical ratios. Pythagoras started a secret school and taught his students to search for truth through numbers, shapes, and sound. Think About It: Why do you think Pythagoras saw math in everything? How does music relate to math? 9. Rosalind Franklin: The Woman Behind the DNA Discovery Born: July 25, 1920 Died: April 16, 1958 Rosalind Franklin loved looking closely at things. She used a special machine called X-ray crystallography to photograph molecules. One of her greatest photos, called Photo 51, showed the shape of DNA, the molecule that carries life’s instructions. But her work was taken without credit. Two men, Watson and Crick, used her photo to build their famous model of DNA and won the Nobel Prize. Rosalind died young and never knew how important her work became. Think About It: Why is it important to give credit in science? What can we learn from Rosalind’s quiet strength? 10. Carl Linnaeus: The Man Who Gave Names to Everything Born: May 23, 1707 Died: January 10, 1778 Have you ever wondered why a tiger is called Panthera tigris? That’s thanks to Carl Linnaeus, a Swedish scientist who created a way to name and organize every living thing. His system is still used today in biology. Linnaeus loved nature and spent his life collecting plants, animals, and even rocks. He believed that by organizing life, we could better understand it. Thanks to him, we now have a global “dictionary of nature.” Think About It: Why is it important to name and organize living things? How does order help us understand the world?

Class 12

Class/12/1MCQ Test/Matrices-Determinants/2022

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