Circle and its part, calculation about inscribed and central angle

1. What is the meaning of the word "Izhaar"? A) To hide the sound B) To make it clear C) To change the sound D) To merge two letters 2. Which part of the body is used to pronounce Izhaar Halqi letters? A) The lips B) The tongue only C) The throat D) The nose 3. How many letters are there for Izhaar Halqi? A) 4 letters B) 6 letters C) 15 letters D) 2 letters 4. When do we apply the rule of Izhaar Halqi? A) When any letter comes after Meem Sakinah B) When an Izhaar letter comes after Noon Sakinah or Tanween C) When we see a Shaddah D) Only at the end of a Surah 5. Which of the following is NOT an Izhaar Halqi letter? A) Hamzah (أ) B) Haa (هـ) C) Baa (ب) D) 'Ayn (ع) 6. Which pair of letters comes from the deepest part of the throat (closest to the chest)? A) ع and ح B) غ and خ C) ء and هـ D) ق and ك 7. When you do Izhaar, do you make a long Ghunnah (nasal sound)? A) Yes, a very long one B) No, we pronounce the Noon clearly without extra Ghunnah C) Only if we want to D) Yes, for 2 counts 8. Which letter comes from the top part of the throat (closest to the mouth)? A) Khaad (خ) B) Haa (ح) C) Hamzah (أ) D) Meem (م) 9. What are the middle throat letters? A) ء and هـ B) ع and ح C) غ and خ D) ت and د 10. In the phrase "مَنْ عَمِلَ" (Man 'Amila), which rule is applied? A) Idghaam B) Ikhfaa C) Izhaar Halqi D) Iqlaab 11. Why do we do Izhaar in "مَنْ عَمِلَ"? A) Because the letter 'Ayn (ع) comes after Noon Sakinah B) Because it is easy to say C) Because Meem has a Fathah D) Because the Noon has a Shaddah 12. What does "Noon Sakinah" mean? A) A Noon with a Fathah B) A Noon with a Kasrah C) A Noon with no vowel (has a Sukoon) D) A double Noon 13. What is Tanween? A) A double vowel sign (Fathatain, Kasratain, Dammatain) at the end of a word D) A small Meem on top of a letter C) A stretching sign D) A stop sign 14. Can Izhaar Halqi happen within a single word? A) No, never B) Yes, it can happen in one word or between two words C) Only in short words D) Only in Surah Al-Fatihah 15. Look at the word "وَانْحَرْ" (Wanhar). What is the Izhaar letter here? A) Waw (و) B) Noon (ن) C) Haa (ح) D) Raa (ر) 16. In the Quran, what sign is usually placed on the Noon Sakinah to show it is Izhaar? A) A small circle or head of a Khaa (Sukoon sign) B) A Shaddah C) Nothing at all D) A little Meem 17. What happens to the Tanween vowels when there is Izhaar? A) They are written far apart from each other B) They are aligned perfectly parallel above/below each other C) One vowel is deleted D) They change color 18. Which of the following words contains an Izhaar Halqi rule? A) أَنْعَمْتَ B) مَنْ يَقُولُ C) مِنْ بَعْدِ D) كُنْتُمْ 19. Choose the group that contains ONLY Izhaar Halqi letters: A) ي ، ر ، م ، ل B) ء ، هـ ، ع ، ح ، غ ، خ C) ك ، ق ، ج ، د D) ب ، ت ، ث 20. In the phrase "عَذَابٌ أَلِيمٌ" ( 'Adhaabun Aleem), why is there Izhaar? A) Because Tanween is followed by Hamzah (أ) B) Because it ends with Meem C) Because the word is long D) Because of the letter Laam 21. What is the correct way to read "مِنْ حَكِيمٍ"? A) Mi---hakeem (hide the Noon) B) Min Hakeem (read Noon clearly and quickly) C) Mih-hakeem (mix them together) D) Mim-hakeem (change Noon to Meem) 22. "Ghain" (غ) and "Khaa" (خ) come from which part of the throat? A) Deep throat B) Middle throat C) Top throat D) The lips 23. If a Noon Sakinah is followed by the letter "هـ" (Haa), how do we pronounce it? A) Clear Noon B) Hidden Noon C) Double Noon D) Silent Noon 24. Which of these is a middle throat letter? A) ء B) خ C) ح D) هـ 25. Complete the sentence: Izhaar Halqi means to pronounce the Noon Sakinah or Tanween cleanly from its articulation point without any ________. A) Breathing B) Vowel (Harakah) C) Extra Ghunnah (nasalization) D) Stopping

Understanding Quantum Theory of Electrons in Atoms The goal of this section is to understand the electron orbitals (location of electrons in atoms), their different energies, and other properties. The use of quantum theory provides the best understanding to these topics. This knowledge is a precursor to chemical bonding. As was described previously, electrons in atoms can exist only on discrete energy levels but not between them. It is said that the energy of an electron in an atom is quantized, that is, it can be equal only to certain specific values and can jump from one energy level to another but not transition smoothly or stay between these levels. The energy levels are labeled with an n value, where n = 1, 2, 3, …. Generally speaking, the energy of an electron in an atom is greater for greater values of n. This number, n, is referred to as the principal quantum number. The principal quantum number defines the location of the energy level. It is essentially the same concept as the n in the Bohr atom description. Another name for the principal quantum number is the shell number. The shells of an atom can be thought of concentric circles radiating out from the nucleus. The electrons that belong to a specific shell are most likely to be found within the corresponding circular area. The further we proceed from the nucleus, the higher the shell number, and so the higher the energy level (Figure 9.4.1). The positively charged protons in the nucleus stabilize the electronic orbitals by electrostatic attraction between the positive charges of the protons and the negative charges of the electrons. So the further away the electron is from the nucleus, the greater the energy it has. This quantum mechanical model for where electrons reside in an atom can be used to look at electronic transitions, the events when an electron moves from one energy level to another. If the transition is to a higher energy level, energy is absorbed, and the energy change has a positive value. To obtain the amount of energy necessary for the transition to a higher energy level, a photon is absorbed by the atom. A transition to a lower energy level involves a release of energy, and the energy change is negative. This process is accompanied by emission of a photon by the atom. The following equation summarizes these relationships and is based on the hydrogen atom: The values nf and ni are the final and initial energy states of the electron. The principal quantum number is one of three quantum numbers used to characterize an orbital. An atomic orbital, which is distinct from an orbit, is a general region in an atom within which an electron is most probable to reside. The quantum mechanical model specifies the probability of finding an electron in the three-dimensional space around the nucleus and is based on solutions of the Schrödinger equation. In addition, the principal quantum number defines the energy of an electron in a hydrogen or hydrogen-like atom or an ion (an atom or an ion with only one electron) and the general region in which discrete energy levels of electrons in a multi-electron atoms and ions are located. Another quantum number is l, the angular momentum quantum number. It is an integer that defines the shape of the orbital, and takes on the values, l = 0, 1, 2, …, n – 1. This means that an orbital with n = 1 can have only one value of l, l = 0, whereas n = 2 permits l = 0 and l = 1, and so on. The principal quantum number defines the general size and energy of the orbital. The l value specifies the shape of the orbital. Orbitals with the same value of l form a subshell. In addition, the greater the angular momentum quantum number, the greater is the angular momentum of an electron at this orbital. Orbitals with l = 0 are called s orbitals (or the s subshells). The value l = 1 corresponds to the p orbitals. For a given n, p orbitals constitute a p subshell (e.g., 3p if n = 3). The orbitals with l = 2 are called the d orbitals, followed by the f-, g-, and h-orbitals for l = 3, 4, 5, and there are higher values we will not consider. There are certain distances from the nucleus at which the probability density of finding an electron located at a particular orbital is zero. In other words, the value of the wavefunction ψ is zero at this distance for this orbital. Such a value of radius r is called a radial node. The number of radial nodes in an orbital is n – l – 1. Consider the examples in Figure 9.4.2. The orbitals depicted are of the s type, thus l = 0 for all of them. It can be seen from the graphs of the probability densities that there are 1 – 0 – 1 = 0 places where the density is zero (nodes) for 1s (n = 1), 2 – 0 – 1 = 1 node for 2s, and 3 – 0 – 1 = 2 nodes for the 3s orbitals. The s subshell electron density distribution is spherical and the p subshell has a dumbbell shape. The d and f orbitals are more complex. These shapes represent the three-dimensional regions within which the electron is likely to be found. Principal quantum number (n) & Orbital angular momentum (l): The Orbital Subshell: https://youtu.be/ms7WR149fAY If an electron has an angular momentum (l ≠ 0), then this vector can point in different directions. In addition, the z component of the angular momentum can have more than one value. This means that if a magnetic field is applied in the z direction, orbitals with different values of the z component of the angular momentum will have different energies resulting from interacting with the field. The magnetic quantum number, called ml, specifies the z component of the angular momentum for a particular orbital. For example, for an s orbital, l = 0, and the only value of ml is zero. For p orbitals, l = 1, and ml can be equal to –1, 0, or +1. Generally speaking, ml can be equal to –l, –(l – 1), …, –1, 0, +1, …, (l – 1), l. The total number of possible orbitals with the same value of l (a subshell) is 2l + 1. Thus, there is one s-orbital for ml = 0, there are three p-orbitals for ml = 1, five d-orbitals for ml = 2, seven f-orbitals for ml = 3, and so forth. The principal quantum number defines the general value of the electronic energy. The angular momentum quantum number determines the shape of the orbital. And the magnetic quantum number specifies orientation of the orbital in space, as can be seen in Figure 9.4.3. Figure 9.4.4 illustrates the energy levels for various orbitals. The number before the orbital name (such as 2s, 3p, and so forth) stands for the principal quantum number, n. The letter in the orbital name defines the subshell with a specific angular momentum quantum number l = 0 for s orbitals, 1 for p orbitals, 2 for d orbitals. Finally, there are more than one possible orbitals for l ≥ 1, each corresponding to a specific value of ml. In the case of a hydrogen atom or a one-electron ion (such as He+, Li2+, and so on), energies of all the orbitals with the same n are the same. This is called a degeneracy, and the energy levels for the same principal quantum number, n, are called degenerate energy levels. However, in atoms with more than one electron, this degeneracy is eliminated by the electron–electron interactions, and orbitals that belong to different subshells have different energies. Orbitals within the same subshell (for example ns, np, nd, nf, such as 2p, 3s) are still degenerate and have the same energy. While the three quantum numbers discussed in the previous paragraphs work well for describing electron orbitals, some experiments showed that they were not sufficient to explain all observed results. It was demonstrated in the 1920s that when hydrogen-line spectra are examined at extremely high resolution, some lines are actually not single peaks but, rather, pairs of closely spaced lines. This is the so-called fine structure of the spectrum, and it implies that there are additional small differences in energies of electrons even when they are located in the same orbital. These observations led Samuel Goudsmit and George Uhlenbeck to propose that electrons have a fourth quantum number. They called this the spin quantum number, or ms. The other three quantum numbers, n, l, and ml, are properties of specific atomic orbitals that also define in what part of the space an electron is most likely to be located. Orbitals are a result of solving the Schrödinger equation for electrons in atoms. The electron spin is a different kind of property. It is a completely quantum phenomenon with no analogues in the classical realm. In addition, it cannot be derived from solving the Schrödinger equation and is not related to the normal spatial coordinates (such as the Cartesian x, y, and z). Electron spin describes an intrinsic electron “rotation” or “spinning.” Each electron acts as a tiny magnet or a tiny rotating object with an angular momentum, even though this rotation cannot be observed in terms of the spatial coordinates. The magnitude of the overall electron spin can only have one value, and an electron can only “spin” in one of two quantized states. One is termed the α state, with the z component of the spin being in the positive direction of the z axis. This corresponds to the spin quantum number ms=12. The other is called the β state, with the z component of the spin being negative and ms=−12. Any electron, regardless of the atomic orbital it is located in, can only have one of those two values of the spin quantum number. The energies of electrons having ms=−12 and ms=12 are different if an external magnetic field is applied. Figure 9.4.5 illustrates this phenomenon. An electron acts like a tiny magnet. Its moment is directed up (in the positive direction of the z axis) for the 12 spin quantum number and down (in the negative z direction) for the spin quantum number of −12. A magnet has a lower energy if its magnetic moment is aligned with the external magnetic field (the left electron) and a higher energy for the magnetic moment being opposite to the applied field. This is why an electron with ms=12 has a slightly lower energy in an external field in the positive z direction, and an electron with ms=−12 has a slightly higher energy in the same field. This is true even for an electron occupying the same orbital in an atom. A spectral line corresponding to a transition for electrons from the same orbital but with different spin quantum numbers has two possible values of energy; thus, the line in the spectrum will show a fine structure splitting. The Pauli Exclusion Principle An electron in an atom is completely described by four quantum numbers: n, l, ml, and ms. The first three quantum numbers define the orbital and the fourth quantum number describes the intrinsic electron property called spin. An Austrian physicist Wolfgang Pauli formulated a general principle that gives the last piece of information that we need to understand the general behavior of electrons in atoms. The Pauli exclusion principle can be formulated as follows: No two electrons in the same atom can have exactly the same set of all the four quantum numbers. What this means is that electrons can share the same orbital (the same set of the quantum numbers n, l, and ml), but only if their spin quantum numbers ms have different values. Since the spin quantum number can only have two values (±12), no more than two electrons can occupy the same orbital (and if two electrons are located in the same orbital, they must have opposite spins). Therefore, any atomic orbital can be populated by only zero, one, or two electrons. The properties and meaning of the quantum numbers of electrons in atoms are briefly

LARGE CARBON MOLECULES Many carbon compounds are built up from smaller, simpler molecules known as monomers (MAH-ne-mers), such as the ones shown in Figure 3-3. As you can also see in Figure 3-3, monomers can bond to one another to form polymers (PAWL-eh-mer). A polymer is a molecule that consists of repeated, linked units. The units may be identical or structurally related to each other. Large polymers are called macromolecules. There are many types of macromolecules, such as carbohydrates, lipids, proteins and nucleic acids. Monomers link to form polymers through a chemical reaction called a condensation reaction. Each time a monomer is added to a polymer, a water molecule is released. In the condensation reac- tion shown in Figure 3-4, two sugar molecules, glucose and fruc- tose, combine to form the sugar sucrose, which is common table sugar. The two sugar monomers become linked by a C—O—C bridge. In the formation of that bridge, the glucose molecule releases a hydrogen ion, H, and the fructose molecule releases a hydroxide ion, OH. The OH and H ions that are released then combine to produce a water molecule, H2O. In addition to building polymers through condensation reac- tions, living organisms also have to break them down. The break- down of some complex molecules, such as polymers, occurs through a process known as hydrolysis (hie-DRAHL-i-sis). In a hydrolysis reaction, water is used to break down a polymer. The water molecule breaks the bond linking each monomer. Hydrolysis is the reverse of a condensation reaction. The addition of water to some complex molecules, including polymers, under certain con- ditions can break the bonds that hold them together. For example, in Figure 3-4 reversing the reaction will result in sucrose breaking down into fructose and glucose. 2H2O Monomers Polymer C C O H OH C OH H CH2OH C H CH2OH C HO H C O H C OH H C CH2OH H C H OH O Sucrose C C O H OH C OH H CH2OH C H CH2OH C HO H C OH OH H C OH H C CH2OH H C H OH O Glucose Fructose H2O The condensation reaction below shows how glucose links with fructose to form sucrose. One water molecule is produced each time two monomers form a covalent bond. FIGURE 3-4 monomer from the Greek mono, meaning “single or alone,” and meros, meaning “a part” Word Roots and Origins A polymer is the result of bonding between monomers. In this example, each monomer is a six-sided carbon ring. The starch in potatoes is an example of a molecule that is a polymer. FIGURE 3-3 Copyright © by Holt, Rinehart and Winston. All rights reserved. 54 CHAPTER 3 ENERGY CURRENCY Life processes require a constant supply of energy. This energy is available to cells in the form of certain compounds that store a large amount of energy in their overall structure. One of these com- pounds is adenosine (uh-DEN-uh-SEEN) triphosphate, more commonly referred to by its abbreviation, ATP. The left side of Figure 3-5 shows a simplified ATP molecule struc- ture. The 5-carbon sugar, ribose, is represented by the blue carbon ring. The nitrogen-containing compound, adenine, is represented by the 2 orange rings. The three linked phosphate groups, —PO4 , are represented by the blue circles with a “P.” The phospate groups are attached to each other by covalent bonds. The covalent bonds between the phosphate groups are more unstable than the other bonds in the ATP molecule because the phosphate groups are close together and have negative charges. Thus, the negative charges make the bonds easier to break. When a bond between the phosphate groups is broken, energy is released. This hydrolysis of ATP is used by the cell to provide the energy needed to drive the chemical reactions that enable an organism to function.

CIRCLE, ITS PARTS AND CIRCUMFERENCE

Short Quiz in Math 10 determines the center and radius of a circle given its equation

Bacterial Cell One of the very first organisms to evolve on earth was probably a unicellular organism, like modern bacteria. Ever since then, life has evolved into a multitude of life forms over many millennia. However, we can still trace our ancestry back to this single-celled organism. Bacteria Definition “Bacteria are unicellular organisms belonging to the prokaryotic group where the organisms lack a few organelles and a true nucleus”. Internal Structures • Cytoplasm: A gel-like substance that fills the cell, containing water, enzymes, nutrients, and waste, where metabolic activities occur. • Nucleoid: A region within the cytoplasm that houses the bacterial chromosome, a single, continuous circle of DNA. • Ribosomes: Responsible for synthesizing proteins within the cell. • Plasmids: Small, circular, extra-chromosomal DNA molecules that can provide advantageous traits, such as antibiotic resistance. • Mesosomes: (Optional, less prominent in some views) Folds in the plasma membrane that are believed to be involved in cell division and respiration. Outer Structures & Layers • Cell Wall: A rigid outer layer composed of peptidoglycan that provides structural support, maintains cell shape, and protects against osmotic lysis. Capsule: (Optional) A sticky outer layer of polysaccharide that can help the bacteria adhere to surfaces, protect against phagocytosis by the immune system, and serve as a food reserve. • Plasma Membrane: A selectively permeable barrier that regulates the passage of nutrients and waste products into and out of the cell. Appendages • Flagella: Long, whip-like structures that provide motility, allowing the bacterium to move through its environment. • Pili (and Fimbriae): Hair-like protein appendages. Pili are longer and involved in bacterial conjugation (transfer of genetic material), while the shorter, more numerous fimbriae primarily function in attachment to host cells or surfaces.

Alexander Hamilton, a key figure in the founding of the United States, served as the first Secretary of the Treasury under President George Washington. Aaron Burr, on the other hand, was the sitting Vice President under Thomas Jefferson at the time of the duel. The animosity between Hamilton and Burr was well-documented, stemming from political disagreements and personal slights over the years. The Duel Date and Location: The duel took place on July 11, 1804, in Weehawken, New Jersey, a common site for duels due to its less strict enforcement of anti-dueling laws compared to New York. Cause: The immediate cause of the duel was a series of letters and meetings between intermediaries after Hamilton allegedly insulted Burr at a dinner, which was later reported in a newspaper. Burr demanded an apology; Hamilton refused, leading to the challenge. The Event: On the morning of the duel, both men, along with their seconds and a doctor, rowed across the Hudson River to the dueling ground. The exact events are a matter of historical debate, but it is generally believed that Hamilton fired his shot into the air, adhering to a principle of honor without intent to kill. Burr, however, aimed directly at Hamilton, hitting him in the abdomen. Outcome: Hamilton was severely wounded and transported back to New York City, where he died the following day, surrounded by family and friends5. Aftermath Public Reaction: The news of Hamilton's death caused widespread grief and indignation. Angelica Schuyler Church, Hamilton's sister-in-law, expressed the communal sorrow in a letter, highlighting the shock and consternation that gripped the town5. Impact on Burr: Although Burr was never tried for the duel, his political career suffered greatly. He became a pariah in many circles and faced various legal and financial troubles in the years that followed. Historical Significance: The duel is often cited as a turning point in American political culture, highlighting the dangers of political rivalry and the need for civility in discourse. Conclusion The duel between Alexander Hamilton and Aaron Burr remains a poignant reminder of the intense personal and political conflicts that shaped the early years of the United States. It underscores the tragic potential of unchecked animosity and the importance of reconciliation and dialogue in a democratic society.

A Clown Face How does a clown put on a face? Where does she start? First, she puts on white face paint. What comes next? How does a clown put on a face? Next, she puts paint around her mouth. She paints a big, red smile. What is next? How does a clown put on her face? Next, she paints her eyelids. What does she put on next? How does a clown put on her face? Next, she puts on big, fuzzy eyebrows. What comes after that? Then she paints big, pink circles on her cheeks. What comes next? How does a clown put on her face? Next, she puts on her red nose. It honks if you squeeze it. What does she do next? How does a clown put on her face? After putting on a red nose, she puts on a silly wig. What does she do next? Then she gets dressed. She puts on a polka-dot jacket and striped pants. And she puts on big, floppy shoes. At last the clown leaves the dressing room. Now it's time to make kids laugh.

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