Expressions and Equations 3-9-16 HW

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

Here’Transformation,Ratio,Proportion, Fractions and Algebraic Expressions,Transformation 1. Translation 2. Reflection 3. Rotation 4. Enlargement 5. Transformation 6. Congruence 7. Similarity 8. Scale Factor 9. Image 10. Pre-image 11. Symmetry 12. Isometry 13. Ratio 14. Proportion 15. Equivalent Ratios 16. Simplify 17. Unit Ratio 18. Scale 19. Part-to-Part 20. Part-to-Whole 21. Rate 22. Comparison 23. Proportional Relationship 24. Cross Multiplication 25. Direct Proportion 26. Inverse Proportion 27. Constant of Proportionality 28. Golden Ratio 29. Linear Relationship 30. Equal Proportions 31. Proportional Constant 32. Scale Drawing 33. Word Problems 34. Unitary Method 35. Percentage 36. Double Number Line 37. Fraction 38. Numerator 39. Denominator 40. Improper Fraction 41. Proper Fraction 42. Mixed Number 43. Simplified Fraction 44. Reciprocal 45. Least Common Denominator (LCD) 46. Greatest Common Factor (GCF) 47. Equivalent Fractions 48. Decimal 49. Variable 50. Coefficient 51. Constant 52. Algebraic Term 53. Polynomial 54. Monomial 55. Binomial 56. Expression 57. Equation 58. Like Terms 59. Simplify 60. Substitution -

Select all the numbers that can be used as a common denominator to rewrite the fractions __ 2 6 and __ 1 2 . A 3 D 12 B 6 E 16 C 8 2 Aaron ran __ 5 8 mile to his friend’s house. Then he ran another __ 1 4 mile to the park. 1 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 8 1 4 Which equation shows how many miles Aaron ran? A __ 5 8 – __ 1 4 = __ 2 8 C __ 5 8 + __ 1 4 = __ 7 8 B __ 5 8 – __ 1 4 = __ 3 8 D __ 5 8 + __ 1 4 = __ 8 8 3 Select all the expressions that can be used to find the sum of __ 6 8 and ___9 12. A ___ 36 48 + ___ 36 48 D ___ 18 20 + ___ 17 20 B ___ 24 36 + ___ 27 36 E ___ 18 24 + ___ 18 24 C ___ 14 16 + ___ 13 16 4 Write a pair of equivalent fractions for __ 3 4 and __ 2 5 using a common denominator of 20. __ 3 4 = __ 2 5 = 5 Katie spent __ 4 5 hour painting and __ 1 2 hour drawing. ? 1 1 2 1 5 1 5 1 5 1 5 How much more time in hours did she spend painting than drawing? 6 Dave is planting a garden. He plants cucumbers in ___2 12 of his garden and tomatoes in __ 2 3 of his garden. What fraction of his garden does Dave plant with cucumbers and tomatoes? 7 Of the students in Maria’s class, __ 2 5 have dogs and __ 1 3 have cats. No students have both a dog and a cat. What fraction represents how many more students in Maria’s class have dogs? 52 © Houghton Mifflin Harcourt Publishing Company Module 6 • Form A Name Module Test DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-C 9 Mr. Gonzales used __ 3 4 quart of broth and __ 1 2 quart of milk to make soup. How many quarts of liquid did he use? Part A Complete the fraction model to represent the problem. 1 1 2 1 4 1 4 1 4 Part B Write an equation to show how many quarts of liquid Mr. Gonzales used to make soup. 10 A bowl of cereal contains __ 2 3 cup of oats and __ 2 8 cup of raisins. Write a numerical expression using equivalent fractions with a common denominator of 24 to model how many more cups of oats than raisins there are in the bowl. 11 Jessica read __ 1 6 of her book on Thursday, __ 2 9 of her book on Friday, and __ 1 2 of her book on Saturday. Part A Write a numerical expression using equivalent fractions to model how much of her book she has read so far. Part B What fraction of her book has Jessica read?

The expression 2 + 4 1 + 2 is equal to (A) 0 (B) 1 (C) 2 (D) 4 (E) 5 2. The ones (units) digit of 542 is 2. When 542 is multiplied by 3, the ones (units) digit of the result is (A) 9 (B) 3 (C) 5 (D) 4 (E) 6 3. Some of the 1 × 1 squares in a 3 × 3 grid are shaded, as shown. What is the perimeter of the shaded region? (A) 10 (B) 14 (C) 8 (D) 18 (E) 20 4. If 3x + 4 = x + 2, the value of x is (A) 0 (B) −4 (C) −3 (D) −1 (E) −2 5. Which of the following is equal to 110% of 500? (A) 610 (B) 510 (C) 650 (D) 505 (E) 550 6. Eugene swam on Sunday, Monday and Tuesday. On Monday, he swam for 30 minutes. On Tuesday, he swam for 45 minutes. His average swim time over the three days was 34 minutes. For how many minutes did he swim on Sunday? (A) 20 (B) 25 (C) 27 (D) 32 (E) 37.5 7. For which of the following values of x is x 3 < x2 ? (A) x = 5 3 (B) x = 3 4 (C) x = 1 (D) x = 3 2 (E) x = 2112 years, Janice will be 8 times as old as she was 2 years ago. How old is Janice now? (A) 4 (B) 8 (C) 10 (D) 2 (E) 6 10. In the diagram, pentagon T P SRQ is constructed from equilateral 4 P T Q and square P QRS. The measure of ∠ST R is equal to (A) 10◦ (B) 15◦ (C) 20◦ (D) 30◦ (E) 45◦ Q P R S T Part B: Each correct answer is worth 6. 11. In the diagram, which of the following points is at a different distance from P than the rest of the points? (A) A (B) B (C) C (D) D (E) E y A x 2 2 4 4 6 8 6 8 B C D E P 12. If x = 2 and y = x 2 − 5 and z = y 2 − 5, then z equals (A) −6 (B) −8 (C) 4 (D) 76 (E) −4 13. In the diagram, P QR is a straight line segment. If x + y = 76, what is the value of x? (A) 28 (B) 30 (C) 35 (D) 36 (E) 38 x° x° x° y° y° P Q R 14. The line with equation y = 2x − 6 is reflected in the y-axis. What is the x-intercept of the resulting line? (A) −12 (B) 6 (C) −6 (D) −3 (E) 0 15. Amy bought and then sold 15n avocados, for some positive integer n. She made a profit of $100. (Her profit is the difference between the total amount that she earned by selling the avocados and the total amount that she spent in buying the avocados.) She paid $2 for every 3 avocados. She sold every 5 avocados for $4. What is the value of n? (A) 100 (B) 20 (C) 50 (D) 30 (E) 8 16. If 3x = 5, the value of 3x+2 is (A) 10 (B) 25 (C) 2187 (D) 14 (E) 45

Electrostatics The section of CBSE Class 12 Physics electrostatic potential and capacitance notes mainly deals with the in-depth analysis of electromagnetic phenomena when they are not performing any movements. Additionally, it is divided into ten further sub-topics to study the companion processes of reaching the state. These are - 1. Electric charge In this section of Physics ch 2 Class 12 notes, you get to learn about the basic features of electric charge and its expression in Physics. Along with its basics, the sections help to understand the full potential of charge. Different aspects of Charge included in Class 12 Physics Chapter 2 notes are - Definition Type: Positive and Negative Charge Unit and dimensional formula Point Charge Properties of Charge Comparison of Charge and Mass Methods of Charging Electroscope 2. Coulomb's Law Force is created when charges of opposite signs attract each other, and they repulse if the signs are the same. Coulomb's law tries to define this phenomenon through a mathematical formula, explicitly mentioned in Physics Class 12 notes Chapter 2. Moreover, there is key information about the variation of the constant k and its effect on a medium. Coulomb's law's vector form and the principle of superimposition are also explained in ch 2 Physics Class 12 notes. (Image will be uploaded soon) 3. Electric Field As stated in Class 12 Physics Chapter 2 notes, every positively or negatively charged particle has their respective electric fields. It feels a force at the time of interaction which might be attraction or repulsion. As it arises from electric charge, it is crucial to know about its different parts like - Electric field intensity Relation between electric force and electric field Super imposition of electric field Point charge Continuous charge distributions Properties of Electric Field Lines Motion of Charged Particles in an Electric field Learning more about the electric field from electric potential and capacitance notes Class 12 helps a student to get a grasp of upcoming chapters. 4. Electric Potential Energy When energy helps a charge to move from an electric field, it is known as the Electric Potential Energy. This section of electrostatic chapter Class 12 notes requires a student to study the Electron volt (eV), and the potential energy that an n number of charges can hold. 5. Electric Potential This section of Class 12 Physics Chapter 2 notes focuses on in-depth learning of Electric Potential or Voltage. Basically, it defines the potential movement of energy. 6. Relation between Electric Field and Potential Apart from knowing more about the relationship between the two values, Physics Class 12 Chapter 2 notes also discuss equipotential surfaces. 7. Electric Dipole Essentially, 'Dipoles' are two opposite points of charge represented with q and –q, with their distance between each other being 2a. Electric Dipoles are crucial in your study of Physics Class 12 Chapter 2 notes to learn more about electric fields and their potential. Additionally, Class 12 Physics Chapter 2 notes focus on the influence of electric dipoles on a uniform electric field mainly through Force and Torque, Work, and Potential Energy. In the last part of Electrostatics, further focus is on using the formulas to their fullest potential. It includes subsections of Electric Field, Electric Potential Energy, Electric Potential, and Electric Dipole. In the notes for electrostatic potential and capacitance, you will find proper solutions accompanied by clear and crisp diagrams for better understanding. 8. Gauss's Law Apart from just discussing the Gauss's Law, in Physics Class 12 ch 2 notes there is a thorough explanation of its properties and applications. The Gauss' Law states that net electric flux passing through a hypothetical closed surface is equal to the net electric charge present within the same closed surface. Being a broad part of the whole chapter, you may need to spend a little more time on it. Moving forward, it starts discussing the properties of conductors in relation to Gauss's Law. The Class 12 Physics notes Chapter 2 perfectly defines the journey to Gauss' Law from Coulomb's Law. Here is the Gauss's Law present in the Class 12 Physics ch 2 notes, (image will be uploaded soon) 9. Capacitors There is a dedicated section about Capacitors in the Class 12 Physics Chapter 2 notes elucidating its functions and importance as storage of potential electric energy. After explaining the structure of a capacitor, it points out the different types, parallel plate, spherical and cylindrical. The section of Chapter 2 notes of Physics Class 12 is further divided into subheads like: Properties of an ideal battery Grouping of capacitors Simple circuits (Series and Parallel) Dielectric Van de Graaff generator Combination of drops Charge distribution method Wheatstone Bridge-based circuit Extended Wheatstone Bridge Infinite network of capacitors Redistribution of charge between two capacitors Vedantu prepares the Class 12 Physics Chapter 2 notes with help from subject matter experts. In the PDF, you get a comprehensive idea of the topic along with potential answers to the most asked questions. Furthermore, the detailed explanation on each section and subsections are written in a simple language allows a student to ace their exams with wholesome knowledge. These Physics Chapter 2 Class 12 notes are going to be one of the best supplementary study materials besides a student’s textbooks. Visit the Vedantu website or download the app to get your hands on all important notes! Important Questions A charge of 4 × 10–8C is uniformly distributed on the surface of a spherical conductor, having a radius of 15 cm. Determine the electric field just outside this sphere at a point that is 15 cm from the centre of this sphere. Determine the capacitance given that the distance between the two plates has been reduced by half and the parallel plate capacitor holds a capacitance of 20 pF (where 1pF = 10-12 F) having air between the two plates. What will be the total capacitance of a combination where three capacitors, each having a capacitance of 20 pF, are connected in series. A square having a side of 10 cm has a 500 µC charge at its centre. Determine the work done to move a charge of 10 µC between two points that are diagonally opposite each other on the square. At an equatorial point, what will be the electrostatic potential because of an electric dipole? Calculate the work done to move a test charge, q, through a length of 1 cm along the equatorial axis of an electric dipole? Polarisation A capacitor has its plates enclosed in a medium that can be filled by insulating substances. A net dipole moment is then induced by an electric field in the dielectric. This event causes the field in an opposite direction. Equipotential Surface An equipotential surface is a type of surface where the potential always has a constant value. If considered as a point charge, the concentric spheres that are centred at a particular area of this charge are basically equipotential surfaces. Advantages of Vedantu's Revision Notes: A Comprehensive Resource for Effective Learning There are several reasons why one may refer to Vedantu's revision notes for studying a subject like Electrostatic Potential and Capacitance. Here are some key points: Comprehensive Coverage: Vedantu's revision notes provide a comprehensive coverage of the entire topic, ensuring that all important concepts and subtopics are included. Concise and Organized: The notes are designed to be concise, focusing on the key points and core ideas. They are organized in a structured manner, making it easy for students to navigate and revise the content. Simplified Explanation: The revision notes offer simplified explanations of complex concepts, making them more accessible and easier to understand. This helps students grasp the material more effectively. Key Formulas and Equations: The notes highlight the key formulas and equations relevant to the topic, ensuring that students have a clear understanding of the mathematical aspects of Electrostatic Potential and Capacitance. Examples and Illustrations: Vedantu's revision notes often include examples and illustrations that help clarify concepts and provide practical applications, enabling students to better relate theory to real-world scenarios. Quick Recap: The revision notes serve as a quick recap of the important points, allowing students to review the material efficiently before exams or assessments. Exam-Oriented Approach: Vedantu's revision notes are designed with an exam-oriented approach, focusing on the topics and concepts that are frequently asked in examinations. This helps students prepare effectively and increase their chances of scoring well. Accessible Anytime: Vedantu's revision notes are easily accessible online, allowing students to study at their convenience and revise the material anytime, anywhere.

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