This document is a student project on price indexes. It includes an acknowledgements section thanking various people for their support. The objectives are to apply problem solving strategies and improve mathematical communication. Part 1 defines key terms like index number, weightage, and composite index. Part 2 shows a family's monthly expenditures for 2013 and calculates price indexes. Part 3 surveys television prices and chooses a Sony TV to purchase. Part 4 adjusts the family's budget to afford the TV and includes the student's own budget after getting a job. The conclusion reflects on learning about indexes in daily life.
Additional Mathematics Project (form 5) 2016Teh Ming Yang
This document is a math project submitted by Teh Ming Yang for class 5C. It examines volume and surface area calculations for different shapes like cylinders and cones. Through experiments using cylinders made of paper, it demonstrates that cylinders with larger radii hold more popcorn even if they are shorter in height. This is because radius has a greater impact on volume than height due to how it is calculated in the volume formula. The project also explores maximizing volume for a given surface area, comparing cones and cubes. The objectives are to apply math concepts to solve problems and appreciate the importance and beauty of mathematics.
Additional Mathematics Project Work Form 5 2014Oliver Louise
There are tons of grammar mistakes I had found in this project work, so please don't mind about the mistakes and use the layout of this assignment only as your reference for Add Math project work and good luck!
This document contains information about using scale drawings and scale factors to solve geometry problems involving real-world objects and distances. It includes examples of using scale drawings of maps to find actual distances between locations by setting up proportions from the scale. It also demonstrates how to find the actual size of an object drawn on a scale drawing or model by again using proportions and scale factors. The document emphasizes that geometry helps describe real-world objects by allowing accurate representations using scale drawings and conversions between actual sizes and scaled sizes.
MEASURES OF CENTRAL TENDENCY AND VARIABILITYMariele Brutas
The document introduces focus questions about norms, standards, and how data is analyzed using descriptive statistics. It then provides an overview of different measures used to analyze ungrouped and grouped data, including measures of central tendency (mean, median, mode) and measures of variability (range, standard deviation). Finally, it includes sample pre-assessment questions about these concepts.
Six students presented on the importance of mathematics in daily life. They discussed how mathematics originated from words meaning "what is learnt" and how it has been defined as the science of quantity and figures. They provided examples of how mathematics is used in areas like commerce, banking, foreign exchange, and more. Famous mathematicians from India and other parts of the world were discussed along with their contributions. In conclusion, the presentation emphasized that mathematics is essential for both educated and uneducated people in their daily lives and activities.
This lesson discusses the normal distribution and its key properties. A normal distribution is symmetrical and bell-shaped, with the mean, median, and mode occurring at the center. It extends indefinitely in both directions but never touches the x-axis. The standard deviation determines the width of the curve. The total area under the curve is 1, representing the total probability. The z-table can be used to find the exact probability or area associated with a given z-score.
This document summarizes key concepts about proportional reasoning. It defines proportional reasoning as a mathematical relationship between two quantities that involves a constant multiplicative relationship. It discusses proportional reasoning as developing between concrete and formal operations. It also provides examples of using proportional relationships to solve problems and discusses research on how to best teach proportional reasoning concepts to students.
This document discusses how math is used in everyday life. It provides examples of using math for making budgets, exercising, shopping, cooking, sports, problem-solving, and time management. For each example, it describes the specific math concepts used, such as addition, subtraction, percentages, ratios, and logical reasoning. The document argues that while some see math as complicated formulas, it is actually all around us in daily activities and is the "universal language" that is applied in many aspects of life.
Additional Mathematics Project (form 5) 2016Teh Ming Yang
This document is a math project submitted by Teh Ming Yang for class 5C. It examines volume and surface area calculations for different shapes like cylinders and cones. Through experiments using cylinders made of paper, it demonstrates that cylinders with larger radii hold more popcorn even if they are shorter in height. This is because radius has a greater impact on volume than height due to how it is calculated in the volume formula. The project also explores maximizing volume for a given surface area, comparing cones and cubes. The objectives are to apply math concepts to solve problems and appreciate the importance and beauty of mathematics.
Additional Mathematics Project Work Form 5 2014Oliver Louise
There are tons of grammar mistakes I had found in this project work, so please don't mind about the mistakes and use the layout of this assignment only as your reference for Add Math project work and good luck!
This document contains information about using scale drawings and scale factors to solve geometry problems involving real-world objects and distances. It includes examples of using scale drawings of maps to find actual distances between locations by setting up proportions from the scale. It also demonstrates how to find the actual size of an object drawn on a scale drawing or model by again using proportions and scale factors. The document emphasizes that geometry helps describe real-world objects by allowing accurate representations using scale drawings and conversions between actual sizes and scaled sizes.
MEASURES OF CENTRAL TENDENCY AND VARIABILITYMariele Brutas
The document introduces focus questions about norms, standards, and how data is analyzed using descriptive statistics. It then provides an overview of different measures used to analyze ungrouped and grouped data, including measures of central tendency (mean, median, mode) and measures of variability (range, standard deviation). Finally, it includes sample pre-assessment questions about these concepts.
Six students presented on the importance of mathematics in daily life. They discussed how mathematics originated from words meaning "what is learnt" and how it has been defined as the science of quantity and figures. They provided examples of how mathematics is used in areas like commerce, banking, foreign exchange, and more. Famous mathematicians from India and other parts of the world were discussed along with their contributions. In conclusion, the presentation emphasized that mathematics is essential for both educated and uneducated people in their daily lives and activities.
This lesson discusses the normal distribution and its key properties. A normal distribution is symmetrical and bell-shaped, with the mean, median, and mode occurring at the center. It extends indefinitely in both directions but never touches the x-axis. The standard deviation determines the width of the curve. The total area under the curve is 1, representing the total probability. The z-table can be used to find the exact probability or area associated with a given z-score.
This document summarizes key concepts about proportional reasoning. It defines proportional reasoning as a mathematical relationship between two quantities that involves a constant multiplicative relationship. It discusses proportional reasoning as developing between concrete and formal operations. It also provides examples of using proportional relationships to solve problems and discusses research on how to best teach proportional reasoning concepts to students.
This document discusses how math is used in everyday life. It provides examples of using math for making budgets, exercising, shopping, cooking, sports, problem-solving, and time management. For each example, it describes the specific math concepts used, such as addition, subtraction, percentages, ratios, and logical reasoning. The document argues that while some see math as complicated formulas, it is actually all around us in daily activities and is the "universal language" that is applied in many aspects of life.
This document summarizes a student's Additional Mathematics project on household expenditure. The project includes:
1) Analysis of the student's family monthly income allocation using graphs, mean, and standard deviation.
2) Comparison of monthly income allocation for 5 friends using data tables, graphs, and analysis.
3) Examination of education and recreation spending for 6 families using line graphs, bar charts, and statistical measures.
4) Exploration of literacy rates in the 20 richest and 20 poorest countries, finding rich countries achieve higher literacy.
The student concludes Additional Mathematics requires perseverance but helps develop high-level thinking skills.
- The survey collected data from 50 people aged 18-23 who go to the gym. It found that most gym-goers were male, between the ages of 21-23.
- For those aged 18-20, the average weight was around 68kg for males and 50kg for females. Most males fell into the 61-70kg category while most females were in the 41-50kg range.
- Those aged 21-23 averaged around 78kg, with most males falling into the 71-80kg category.
This document provides sample questions and answers related to various mathematics topics, including functions, quadratic equations/functions, simultaneous equations, indices and logarithms, and coordinate geometry.
The questions are multiple choice or short answer questions assessing skills like solving equations, graphing functions, finding inverse functions, and working with logarithmic and exponential expressions.
The answers section provides fully worked out solutions to each question in a clear format. This document appears to be a reference for teachers or students to use for exam preparation or review, with the goal of assessing conceptual understanding of core algebra and geometry topics.
The maximum value of y occurs when x = 4.
Plugging x = 4 into the equation for y gives:
y = -4sin60° + 80(4)sin60°
y = -4√3 + 320√3
y = 316√3
So the maximum area is 316√3 square units.
The document discusses the application of mathematics in popcorn packaging. It begins with an introduction to popcorn and its history. It then presents the objectives and sections of the project. Section A involves an experiment comparing the volume of cylinders made from paper. Calculations show that a cylinder with a larger radius holds more popcorn. Section B discusses finding the container shape from given materials that can hold the most popcorn volume. A cuboid is determined to have the greatest volume. In conclusion, different container shapes are compared and a cuboid is found to hold the most popcorn.
The document is a career folio for Nurul Syazwani Izzati Bt Khairi, a student at MRSM Taiping pursuing a career in accounting. It includes her personal details, educational background, skills, languages, and an introduction explaining her interest in choosing a career in accounting. The folio also defines accounting, explains why she chose this course, and describes the process for becoming a chartered accountant through various professional qualifications.
This document contains an additional mathematics project by Nabila Syuhada binti Mohd Kamal Azmy. It includes an introduction to the history of calculus development. Part 1 discusses British mathematician Brook Taylor's contributions, including discovering Taylor's expansion and founding the calculus of finite differences. Part 2 contains work on kinematics graphs and integrals. Part 3 works through area problems under curves using Riemann sums. Further exploration looks at applying concepts to gold prices. A reflection discusses the importance of calculus in daily life and appreciation for those who help unseen.
Additional Mathematics Project 2014 Selangor Sample AnswersDania
This document summarizes key ideas from Gottfried Leibniz's contributions to calculus and provides examples of how to solve calculus problems involving velocity, acceleration, integration, and area under a curve. It also explores calculating volumes of revolution and costs associated with gold rings. The summary explores Leibniz's notation of dx and dy, how he viewed variables as sequences, and how his approach generalized calculus to multiple variables. Examples are provided to demonstrate calculating distances, speeds, and areas using graphs and integration.
This document provides information about coordinate geometry, including finding the distance between two points, the midpoint and division of a line segment, area of polygons, and equations of straight lines. It gives formulas and examples for calculating the distance between points using the Pythagorean theorem, finding the midpoint and points dividing a line segment in a given ratio, and computing the area of triangles and quadrilaterals. It also explains how to determine the gradient, x-intercept, and y-intercept of a straight line and write the equation of a straight line in general and gradient forms. Exercises are provided to apply these concepts.
This document provides an overview of functions from chapter 1 of an additional mathematics module. It defines key terms like domain, codomain, range, and discusses different types of relations including one-to-one, many-to-one, and many-to-many. It also covers function notation, evaluating functions, composite functions, and provides examples of calculating images and objects of functions. The chapter aims to introduce students to the fundamental concepts of functions through definitions, diagrams, and practice exercises.
This document provides notes on additional mathematics for Form 4 students. It includes definitions and examples of functions, inverse functions, quadratic equations, and logarithms. Some key points summarized:
1. A function f maps objects to images. To find the inverse function f-1, change f(x) to y and solve for x in terms of y.
2. To find the roots of a quadratic equation, one can use factorisation, the quadratic formula, or complete the square. The nature of the roots depends on the sign of b2 - 4ac.
3. To solve a system of equations involving one linear and one non-linear equation, one can substitute one equation into the other and solve
- The document is a thank you letter from a student thanking various people who helped with their project work, including their parents, teacher, and friends.
- The student thanks their parents for providing financial support and advice throughout the project. They thank their teacher for teaching the subject and guiding them. They also thank their friends for sharing ideas, helping each other, and helping complete the project without problems.
Unit i introduction to engineering economics.Chandra Kumar S
This document provides an introduction to economics. It defines economics as the study of how limited resources are used to satisfy unlimited human wants. The objectives of economics are outlined as achieving a high level of employment, price stability, an equitable distribution of income, and economic growth. The basic flow of goods, services, resources and money payments between households and business firms in a simple economy is described. Key economic concepts like demand, supply, and the laws of supply and demand are introduced. Factors influencing demand and supply are also discussed. Engineering economics and its scope and procedures are defined. Cost elements, pricing of products, and other cost and revenue concepts are covered. Break even analysis and charts are explained. Material selection and process planning for manufacturing
Get the best quality preparations for your class 11 exams with studymate. Our economics sample paper class 11 covers all the topics and helps the students in clearing their concepts and perform well in their exams. Visit https://bit.ly/2mlSjJf
This document provides an introduction to economics. It defines economics as the study of how limited resources are used to satisfy unlimited human wants. The objectives of economics are outlined as a high level of employment, price stability, efficiency, and an equitable distribution of income and growth. It then discusses the flow of goods, services, resources and money payments in a simple economy between households and business firms. Key economic concepts are introduced such as the law of supply and demand, factors influencing demand and supply, and break even analysis. Engineering economics is defined and its scope and tools such as cost analysis, contribution ratio, and break even charts are explained.
This document provides an introduction to economics. It defines economics as the study of how limited resources are used to satisfy unlimited human wants. The objectives of economics are outlined as a high level of employment, price stability, efficiency, an equitable distribution of income, and growth. The flow of goods, services, resources and money payments in a simple economy is described involving households, business firms, and the payments between them. The law of supply and demand and the factors influencing supply and demand are explained. Engineering economics is introduced as analyzing alternatives within a project to compare monetary returns. The concepts of cost, revenue, profit, break even analysis, and margin of safety are defined in the context of economics.
Chapter 14 developing pricing strategies and programs zhou妍希 周
1. The document provides a summary of key concepts in developing pricing strategies and programs from a chapter. It includes 10 multiple choice questions about pricing steps, objectives, methods, and tactics. Examples include how Sony priced its early HDTVs using market skimming and how supermarkets use loss leaders. The questions cover estimating costs, competitor analysis, auctions, cost types, differentiated pricing, and promotional pricing.
This document contains a lesson plan on market demand and the law of demand. It includes objectives, a review, motivation, activities, definitions of key terms like demand, quantity demanded, demand schedule, demand curve, and price elasticity. It provides examples of computing elasticity. Learners are asked to analyze a demand schedule for onions, including computing elasticity, plotting the graph, and describing the curve. An evaluation and assignment are also included.
An index number measures changes in a variable over time by comparing values in one period to another. There are different types of index numbers including price, quantity, and value indexes. Price indexes compare price levels over time, quantity indexes measure changes in quantity, and value indexes combine price and quantity changes to measure total monetary worth. Index numbers are used for various purposes such as measuring inflation, forecasting economic trends, and analyzing trade balances. They are constructed by selecting representative commodities, collecting price data, choosing a base period for comparison, and determining appropriate weights and averages.
Macroeconomic that will help you understand more and help the country by understanding the topic well. Other than that, it also emphasizes in the stability of the country's economical state. Food security as well no poverty plays a huge part in the balance of the economic state of the country.
This document summarizes a student's Additional Mathematics project on household expenditure. The project includes:
1) Analysis of the student's family monthly income allocation using graphs, mean, and standard deviation.
2) Comparison of monthly income allocation for 5 friends using data tables, graphs, and analysis.
3) Examination of education and recreation spending for 6 families using line graphs, bar charts, and statistical measures.
4) Exploration of literacy rates in the 20 richest and 20 poorest countries, finding rich countries achieve higher literacy.
The student concludes Additional Mathematics requires perseverance but helps develop high-level thinking skills.
- The survey collected data from 50 people aged 18-23 who go to the gym. It found that most gym-goers were male, between the ages of 21-23.
- For those aged 18-20, the average weight was around 68kg for males and 50kg for females. Most males fell into the 61-70kg category while most females were in the 41-50kg range.
- Those aged 21-23 averaged around 78kg, with most males falling into the 71-80kg category.
This document provides sample questions and answers related to various mathematics topics, including functions, quadratic equations/functions, simultaneous equations, indices and logarithms, and coordinate geometry.
The questions are multiple choice or short answer questions assessing skills like solving equations, graphing functions, finding inverse functions, and working with logarithmic and exponential expressions.
The answers section provides fully worked out solutions to each question in a clear format. This document appears to be a reference for teachers or students to use for exam preparation or review, with the goal of assessing conceptual understanding of core algebra and geometry topics.
The maximum value of y occurs when x = 4.
Plugging x = 4 into the equation for y gives:
y = -4sin60° + 80(4)sin60°
y = -4√3 + 320√3
y = 316√3
So the maximum area is 316√3 square units.
The document discusses the application of mathematics in popcorn packaging. It begins with an introduction to popcorn and its history. It then presents the objectives and sections of the project. Section A involves an experiment comparing the volume of cylinders made from paper. Calculations show that a cylinder with a larger radius holds more popcorn. Section B discusses finding the container shape from given materials that can hold the most popcorn volume. A cuboid is determined to have the greatest volume. In conclusion, different container shapes are compared and a cuboid is found to hold the most popcorn.
The document is a career folio for Nurul Syazwani Izzati Bt Khairi, a student at MRSM Taiping pursuing a career in accounting. It includes her personal details, educational background, skills, languages, and an introduction explaining her interest in choosing a career in accounting. The folio also defines accounting, explains why she chose this course, and describes the process for becoming a chartered accountant through various professional qualifications.
This document contains an additional mathematics project by Nabila Syuhada binti Mohd Kamal Azmy. It includes an introduction to the history of calculus development. Part 1 discusses British mathematician Brook Taylor's contributions, including discovering Taylor's expansion and founding the calculus of finite differences. Part 2 contains work on kinematics graphs and integrals. Part 3 works through area problems under curves using Riemann sums. Further exploration looks at applying concepts to gold prices. A reflection discusses the importance of calculus in daily life and appreciation for those who help unseen.
Additional Mathematics Project 2014 Selangor Sample AnswersDania
This document summarizes key ideas from Gottfried Leibniz's contributions to calculus and provides examples of how to solve calculus problems involving velocity, acceleration, integration, and area under a curve. It also explores calculating volumes of revolution and costs associated with gold rings. The summary explores Leibniz's notation of dx and dy, how he viewed variables as sequences, and how his approach generalized calculus to multiple variables. Examples are provided to demonstrate calculating distances, speeds, and areas using graphs and integration.
This document provides information about coordinate geometry, including finding the distance between two points, the midpoint and division of a line segment, area of polygons, and equations of straight lines. It gives formulas and examples for calculating the distance between points using the Pythagorean theorem, finding the midpoint and points dividing a line segment in a given ratio, and computing the area of triangles and quadrilaterals. It also explains how to determine the gradient, x-intercept, and y-intercept of a straight line and write the equation of a straight line in general and gradient forms. Exercises are provided to apply these concepts.
This document provides an overview of functions from chapter 1 of an additional mathematics module. It defines key terms like domain, codomain, range, and discusses different types of relations including one-to-one, many-to-one, and many-to-many. It also covers function notation, evaluating functions, composite functions, and provides examples of calculating images and objects of functions. The chapter aims to introduce students to the fundamental concepts of functions through definitions, diagrams, and practice exercises.
This document provides notes on additional mathematics for Form 4 students. It includes definitions and examples of functions, inverse functions, quadratic equations, and logarithms. Some key points summarized:
1. A function f maps objects to images. To find the inverse function f-1, change f(x) to y and solve for x in terms of y.
2. To find the roots of a quadratic equation, one can use factorisation, the quadratic formula, or complete the square. The nature of the roots depends on the sign of b2 - 4ac.
3. To solve a system of equations involving one linear and one non-linear equation, one can substitute one equation into the other and solve
- The document is a thank you letter from a student thanking various people who helped with their project work, including their parents, teacher, and friends.
- The student thanks their parents for providing financial support and advice throughout the project. They thank their teacher for teaching the subject and guiding them. They also thank their friends for sharing ideas, helping each other, and helping complete the project without problems.
Unit i introduction to engineering economics.Chandra Kumar S
This document provides an introduction to economics. It defines economics as the study of how limited resources are used to satisfy unlimited human wants. The objectives of economics are outlined as achieving a high level of employment, price stability, an equitable distribution of income, and economic growth. The basic flow of goods, services, resources and money payments between households and business firms in a simple economy is described. Key economic concepts like demand, supply, and the laws of supply and demand are introduced. Factors influencing demand and supply are also discussed. Engineering economics and its scope and procedures are defined. Cost elements, pricing of products, and other cost and revenue concepts are covered. Break even analysis and charts are explained. Material selection and process planning for manufacturing
Get the best quality preparations for your class 11 exams with studymate. Our economics sample paper class 11 covers all the topics and helps the students in clearing their concepts and perform well in their exams. Visit https://bit.ly/2mlSjJf
This document provides an introduction to economics. It defines economics as the study of how limited resources are used to satisfy unlimited human wants. The objectives of economics are outlined as a high level of employment, price stability, efficiency, and an equitable distribution of income and growth. It then discusses the flow of goods, services, resources and money payments in a simple economy between households and business firms. Key economic concepts are introduced such as the law of supply and demand, factors influencing demand and supply, and break even analysis. Engineering economics is defined and its scope and tools such as cost analysis, contribution ratio, and break even charts are explained.
This document provides an introduction to economics. It defines economics as the study of how limited resources are used to satisfy unlimited human wants. The objectives of economics are outlined as a high level of employment, price stability, efficiency, an equitable distribution of income, and growth. The flow of goods, services, resources and money payments in a simple economy is described involving households, business firms, and the payments between them. The law of supply and demand and the factors influencing supply and demand are explained. Engineering economics is introduced as analyzing alternatives within a project to compare monetary returns. The concepts of cost, revenue, profit, break even analysis, and margin of safety are defined in the context of economics.
Chapter 14 developing pricing strategies and programs zhou妍希 周
1. The document provides a summary of key concepts in developing pricing strategies and programs from a chapter. It includes 10 multiple choice questions about pricing steps, objectives, methods, and tactics. Examples include how Sony priced its early HDTVs using market skimming and how supermarkets use loss leaders. The questions cover estimating costs, competitor analysis, auctions, cost types, differentiated pricing, and promotional pricing.
This document contains a lesson plan on market demand and the law of demand. It includes objectives, a review, motivation, activities, definitions of key terms like demand, quantity demanded, demand schedule, demand curve, and price elasticity. It provides examples of computing elasticity. Learners are asked to analyze a demand schedule for onions, including computing elasticity, plotting the graph, and describing the curve. An evaluation and assignment are also included.
An index number measures changes in a variable over time by comparing values in one period to another. There are different types of index numbers including price, quantity, and value indexes. Price indexes compare price levels over time, quantity indexes measure changes in quantity, and value indexes combine price and quantity changes to measure total monetary worth. Index numbers are used for various purposes such as measuring inflation, forecasting economic trends, and analyzing trade balances. They are constructed by selecting representative commodities, collecting price data, choosing a base period for comparison, and determining appropriate weights and averages.
Macroeconomic that will help you understand more and help the country by understanding the topic well. Other than that, it also emphasizes in the stability of the country's economical state. Food security as well no poverty plays a huge part in the balance of the economic state of the country.
1. Engineering economics involves analyzing alternatives and making decisions to obtain the best monetary return. It considers factors like costs, benefits, risks, and time value of money.
2. Cost components include fixed costs, variable costs, marginal costs, and opportunity costs. Break-even analysis determines the sales volume needed to recover total costs.
3. Material, design, and process selection are important economic decisions in manufacturing. The most cost-effective options are chosen while meeting requirements.
This document provides an overview of marketing mix and branding. It begins by outlining the objectives of recognizing the importance of marketing mix in developing marketing strategy. It then describes the 7Ps of marketing mix: product, place, price, promotion, people, packaging, and positioning. It discusses the marketing mix framework including the 4Ps and how it evolved into the 7Ps. It covers various elements of each P such as the product life cycle, factors that influence pricing, different promotional methods, and the roles of people and packaging. The document also discusses branding, including defining needs and wants, developing brand names and logos, branding strategies, and key considerations for effective branding.
This document contains 6 questions and summaries of the answers from an online study resource for a Managerial Economics course. The questions cover topics like production functions, survey methods for estimating demand, cost curves, inflation, price and income elasticity of demand, and the relationship between total revenue, average revenue and marginal revenue. For full answers, students are directed to the website www.smuHelp.com.
Economics 2106 (Fall 2012) — Prof. Greg Trandel — Homework Assignment # 4 (first part)
Answers due: Beginning of class, Friday, November 9th.
Instructions/Information: Depending on how much material is covered in class by Wednesday,
November 7th, it’s possible that students won’t have to answer the last question on this assignment.
A definite announcement will be made in class.
1. Suppose that a firm is currently charging $45 for its product. The firm knows that its marginal
cost of producing the product is $25, and it believes that the elasticity of demand for the
product (at least at its current price) equals 3. Given this belief, does it appear that setting its
price at $45 is a profit-maximizing decision? If not, and if the firm’s goal is indeed to maximize
its current profit, should the firm raise or lower its price?
2. Suppose that a monopoly firm produces a good at a constant marginal cost of $30 per unit
(to keep things simple, assume that the firm has no fixed cost, so that its average total cost
of production also always equals $30). The firm sells its product to consumers in two di!erent
markets. [Market A and Market B are two completely separate markets; the firm can charge a
di!erent price is each.] Market A has the following characteristic: if the firm wants to increase
its sales in that market by one unit, it can do so only by lowering its price in that market by
$1. In order to sell one additional unit in Market B, in contrast, the firm must lower its price
there by only $.50.
(a) Use the information given above
and the formula (from class) for
marginal revenue to complete
the accompanying table.
Market A Market B
Marginal Marginal
Unit Price Revenue Unit Price Revenue
8 46 39 8 41 37.5
9 45 37 9 40.5 36.5
10 44 35 10 40 35.5
11 43 11 39.5
12 12
13 13
14 14
15 15
16 16
(b) Considering Market A alone,
what quantity should the firm
sell in that market in order to
maximize its profit there?
What price should it charge in
that market? What profit does
the firm make on its sales in
Market A?
(c) Considering Market B alone,
what quantity should the firm
sell in that market in order to
maximize its profit there? What price should it charge in that market? What profit does
the firm make on its sales in Market B?
(d) Assume that the firm can charge di!erent prices in each market, and that a consumer
located in one market can only buy at the price set in that market (i.e., a consumer in the
market in which the firm sets the higher price can’t switch to the other market in order
to buy at the lower price). In other words, assume that the firm can practice direct price
di!erentiation; that it can simply maximize its profit by charging the prices (and earning
the profits) found in parts (b) and (c). Adding together those profit values, what total
profit does a price-di!erentiating firm make on its sales?
(e) In contrast, suppose that the firm has to charge the same price to all its customers (i.e.,
it can’t practice price discrim ...
This document provides an overview of index numbers and related statistical concepts. It defines index numbers as statistical devices that measure relative changes over time in variables like prices, production, or sales. It discusses the construction of price, quantity, and value indexes and covers topics like purposes of indexes, selecting items and weights, choosing formulas, and fixed base versus chain base methods. The key uses of price indexes are also summarized, such as measuring inflation and purchasing power.
This document provides an overview of statistics index numbers. It discusses:
1. The introduction and definition of index numbers, which measure changes over time in variables like prices, production, sales, imports/exports, and cost of living.
2. The uses of index numbers including deflating data, identifying economic trends, and informing policymaking.
3. Problems in constructing index numbers such as selecting commodities, choosing a base period, and determining appropriate weights.
4. The concept of price, quantity, and value index numbers, which compare prices, quantities, or values of items respectively over time.
1) The document discusses concepts related to supply analysis including the concept and law of supply, factors affecting supply, accounting and economic costs, and short and long run cost analysis.
2) It defines supply as the quantity of goods producers are able and willing to offer for sale at a given price and time, outlines the key determinants of supply, and explains the law of supply.
3) The document also distinguishes between accounting and economic costs, describes fixed, variable, and total costs, and explains average and marginal costs in both the short and long run.
The document discusses various types of economies of scale that firms can achieve through large scale production, including technical, managerial, marketing/commerce, finance, labor, transport/storage, and overhead economies. It also defines total fixed cost, total variable cost, total cost, average fixed cost, average variable cost, and average total cost, and provides formulas for calculating each. Graphs are included to illustrate the shapes of the total cost, average cost, and marginal cost curves.
বাংলাদেশের অর্থনৈতিক সমীক্ষা ২০২৪ [Bangladesh Economic Review 2024 Bangla.pdf] কম্পিউটার , ট্যাব ও স্মার্ট ফোন ভার্সন সহ সম্পূর্ণ বাংলা ই-বুক বা pdf বই " সুচিপত্র ...বুকমার্ক মেনু 🔖 ও হাইপার লিংক মেনু 📝👆 যুক্ত ..
আমাদের সবার জন্য খুব খুব গুরুত্বপূর্ণ একটি বই ..বিসিএস, ব্যাংক, ইউনিভার্সিটি ভর্তি ও যে কোন প্রতিযোগিতা মূলক পরীক্ষার জন্য এর খুব ইম্পরট্যান্ট একটি বিষয় ...তাছাড়া বাংলাদেশের সাম্প্রতিক যে কোন ডাটা বা তথ্য এই বইতে পাবেন ...
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BÀI TẬP BỔ TRỢ TIẾNG ANH 8 CẢ NĂM - GLOBAL SUCCESS - NĂM HỌC 2023-2024 (CÓ FI...
Additional mathematics
1. Name : AmirulIkram bin Aslian
I/C No : 960804-10-5667
Class : 5 Anggerik
Teacher : EncikRavinderan
School : SekolahMenegahKebangsaanBandar
UtamaDamansara (4)
Title : Price Index
2. CONTENTS:
Title Page
Acknowledgement
Objectives
Introduction
Part 1 (a)
(i) Index Number
(ii) Weightage
(iii) Composite Index
(b) Weightage Representation
Part 2
(a) Family’s Monthly
Expenditure for year 2013
(b) (i)(ii) Calculating Price
Indexes
(c) (i)(ii) Composite Index for
Average Monthly
Expenditure for year 2013
Based on year 2012
(d) Conclusion
Part 3
(a) Survey on prices of
Televisions
(b) Television That I Want to
Buy
(c) Fair Price Shop Award
Part 4
(a) Modified Monthly
Expenditure to Buy New
Television
(b) My Own Monthly
Expenditure Planning
Conclusion
Further Explaination
Reflection
3. ACKNOWLEDGEMENT:
First of all, I wish to express gratitude to Allah s.w.t for his guidance and also giving me the
strength to do this project work. Finally, the additional mathematics project work was
successfully completed with the inspiration, the gift and the instruction were given by Him.
Not forgotten my parents for providing everything, such as money, to buy anything
that are related to this project work and their advice, support which are the most needed for
this project. Internet, books, computers and all that. They also supported me and encouraged
me to complete this task so that I will not procrastinate in doing it.
Then I would like to thank my teacher, Mr Ravi for guiding me and my friends
throughout this project. We had some difficulties in doing this task, but he taught us patiently
until we knew what to do. He tried and tried to teach us until we understand what we
supposed to do with the project work.
Last but not least, my friends who were doing this project with me and sharing our
ideas. They were helpful that when we combined and discussed together, we had this task
done.
4. OBJECTIVES:
The aims of carrying out this project work are:
to apply and adapt a variety of problem-solving strategies to solve problems.
to improve thinking skills.
to promote effective mathematical communication.
to develop mathematical knowledge through problem solving in a way that increases
students’ interest and confidence.
to use the language of mathematics to express mathematical ideas precisely.
to provide learning environment that stimulates and enhances effective learning.
to develop positive attitude towards mathematics
5. Introduction:
A price indexis a normalized average (typicallyaweighted average) of prices for a given class
ofgoods or services in a given region, during a given interval of time. It is a statistic designed
to help to compare how these prices, taken as a whole, differ between time periods or
geographical locations.Price indices have several potential uses. For particularly broad
indices, the index can be said to measure the economy's price level or a cost of living. More
narrow price indices can help producers with business plans and pricing. Sometimes, they can
be useful in helping to guide investment
Some notable price indices include:
Consumer price index
Producer price index
GDP(Gross Domestic Product) Deflator
History of early price index:
No clear consensus has emerged on who created the first price index. The earliest
reportedresearch in this area came from Welshman Rice Vaughan who examined price level
change in his 1675 book ‘A Discourse of Coin and Coinage’. Vaughan wanted to separate the
inflationaryimpact of the influx of precious metals brought by Spain from the New World
from the effectdue to currency debasement. Vaughan compared labor statutes from his own
time to similar statutes dating back to Edward III. These statutes set wages for certain tasks
and provided a goodrecord of the change in wage levels. Vaughan reasoned that the market
for basic labor did notfluctuate much with time and that a basic laborers salary would
probably buy the same amount of goods in different time periods, so that a laborer's salary
acted as a basket of goods. Vaughan's analysis indicated that price levels in England had
raised six to eightfold over the precedingcentury
While Vaughan can be considered a forerunner of price index research, his analysis did not
actually involve calculating an index. In 1707 Englishman William Fleetwood created
perhaps the first true price index. An Oxford student asked Fleetwood to help show how
prices had changed. The student stood to lose his fellowship since a fifteenth century
stipulation barred students with annual incomes over five pounds from receiving a
fellowship. Fleetwood, who already had an interest in price change, had collected a large
amount of price data going back hundreds of years. Fleetwood proposed an index consisting
of averaged price relatives and usedhis methods to show that the value of five pounds had
changed greatly over the course of 260years. He argued on behalf of the Oxford students and
published his findings anonymously in a volume entitled ‘ChroniconPreciosum’
6. PART 1 :
a)(i) Price Index :
• An index number expressing the level of a group of commodity prices relative to the
level of the prices of the same commodities during an arbitrarily chosen base period
and used to indicate changes in the level of prices from one period to another
(ii) Weightage :
• The assignment of a quota (as of members of a legislature) to a particular segment of
the population as a special favor or concession in a proportion abovethat allowable on
a strictly numerical basis
(iii) Composite Index :
• A grouping of equities, indexes or other factors combined in a standardized way,
providing a useful statistical measure of overall market or sector performance over
time.
b) Ways To Represent Weightage
Weightage in a set of data can be represented in certain ways.
1)Bar Chart:
8. Part 2:
a)My Family Expenditure
Items
Average Monthly
Expenditure for the year
2013
(to the nearest RM)
Percentage of monthly
expenses
(to the nearest %)
Food 1250 25
Accommodation
(Rental/Loan)
600 12
Transportation
(Petrol/Loan/Bus fare etc)
250 5
Clothing 250 5
Education 600 12
Recreation 650 13
Utilities
(Water/Electricity/Telephone)
600 12
Medication 500 10
Miscellaneous 300 6
TOTAL 5000 100
Table 1
b)(i)Base year 2012
(ii)Complete Table 2
Items
Average monthly expenses
for the year 2012 as the base
year
(RM)
Average monthly expenses
for the year 2013
(RM)
Food 1000 1250
Accommodation
(Rental/Loan)
500 600
Transportation
(Petrol/Loan/Bus fare etc)
250 250
Clothing 200 250
Education 400 600
Recreation 550 650
Utilities
(Water/Electricity/Telephone)
450 600
Medication 400 500
Miscellaneous 250 300
TOTAL 4000 5000
9. c)(i)
Items Price Indices for the year
2013
Based on the Year 2012
Weightage
Food 125 11
Accommodation
(Rental/Loan)
120 11
Transportation
(Petrol/Loan/Bus fare etc)
100 9
Clothing 125 11
Education 150 13
Recreation 118 11
Utilities
(Water/Electricity/Telephone)
133 12
Medication 125 11
Miscellaneous 120 11
TOTAL 1116 100
Table 3
Formula to calculate price index:
I= × 100
I = Index Number
Q₁= Quantity of specific time
Q₀ = Quantity at base time
(ii)The composite index for my family average monthly expenditure in the year 2013 based
on the year 2012 can be calculated by using this formula below:
Composite index=
W = Weightage
I = Index Number
=
=
=125.09
10. d)Conclusion
The composite index for the average monthly expenditure in year 2013 based on year 2011
increases. This shows that almost all the items in the table have increased. Nevertheless, this
shows that my family needs a higher income as. As we can observe, the case of inflation
occurs as price of goods increases but the value of money spent remains the same.It can also
be concluded that my family’s expenditure has increased as time passes by based on my
findings.
12. The mean and standard deviation of the data can be calculated using formula
13. b) Based on my findings from part (a) above, I have decided to buy the television Sony,
32 inches from Infinito Graphic by using the cash payment method. From the data above, we
can see that the price of the television that I have chosen which is RM788 is below the mean
price. This shows that the price ischeaper than the average price for that kind of television.
This gives me advantage and chance to save some money. Apart from that, the price is
affordable accordance to my family average household expenditure. Other than that, the
standard deviation for that television brand, Sony 32 inches is RM81.65 which means the
average data value is not extreme. A high standard deviation value means that the average
data value is extreme which will result in insensibility for the consumers to buy. The
television Sony 32 inches has reasonable price as the standard deviation is not too high.
c) Fair Price Shop Award
The Ministry of Domestic Trade and Consumer Affairs wishes to present the Fair Price Shop
Award for the shops above. I am one of the panels for this award. Based on my findings, the
shop that deserves this award is Infinito Graphic. By considering the value of the mean and
the value of standard deviation, here are my justifications.Offers prices of television for both
brands which are below the mean price which the Infinito Graphic average market price. This
shows that Infinito Graphic is able to offer lower prices for the consumers compared to other
shops. Hence, this will benefit the consumers especially for those who come from a low
income family.The data of standard deviation for prices of television offered from Infinito
Graphic is acceptable and sensible as the standard deviation values are not too high. This
shows that the data does not have extreme values by both means of payment. This means that
the shop has put reasonable prices of the televisions.
14. PART 4:
a) My family has a fixed monthly income. In order to buy the television, my family
needs to make some adjustment on the various types of expenditure. Here is the
revised monthly expenditure.
Items Average Monthly Expenditure for the
Year 2013 (to the nearest RM)
Food 1250
Accomodation
(Rental/Loan)
600
Transportation
(Petrol/Loan/Bus Fare etc)
200
Clothing 200
Education 600
Recreation 400
Utilities (Water/Electricity/Telephone) 600
Medications 500
Miscellaneous 150
Savings 500
TOTAL 5000
Revised Monthly Family Expenditure
From the table above, my family is able to save RM500 per month. By the using cash
payment to buy a television from Infinito Graphic, 40inches which is priced at
RM1599 from Sony. My family will be able to buy the television price after saving
the money for four months, which the amounts of savings will reach RM2000
15. b) Assuming that I have just started working with a monthly salary of RM2500, I intend
to save 10% of my salary every month. Besides, I also plan to contribute some money
to my parents monthly.
Items Average Monthly
Expenditure for the Year
2013 (to the nearest RM)
Percentage of Monthly
Expenses (to the nearest
%)
Food 400 16
Accomodation(Rental/Loan) 300 12
Transportation
(Petrol/Loan/Bus Fare etc)
300 12
Clothing 200 8
Education 0 0
Recreation 300 12
Utilities
(Water/Electricity/Telephone)
250 10
Medication 50 2
Miscellaneous 150 6
Savings 300 12
Contributions to my Parents 250 10
TOTAL 2500 100
My monthly Expenditure Budget
Here is my own monthly expenditure budget after getting a job with monthly salary of
RM2500.
16. CONCLUSION:
After doing research, answering questions and some solving problem, I notice that we usually
use index number in our daily life. We can solve our financial problems with ease using price
index and composite index
FURTHER EXPLORATION:
For further investigation, I have chosen to investigate the prices of two superbikes from a
well-known brand, Yamaha and Honda
Brands Model Price (RM)
Honda CBR600RR 74000
CBR1000RR 98000
Yamaha YZF-R6 75000
YZF-R1 97000
*The Honda CBR600RR is compared to the Yamaha YZF-R6 as a supersport motorcycle.
The Honda CBR1000RR is compared to the Yamaha YZF-R1 as a litre motorcycle.
17. REFLECTION:
While I was conducting this project, a lot of information that I had found. I have
learnt how index number appears in our daily life. Apart from that, this project encourages
the student to work together and share their knowledge. It is also encourage student to gather
information from the internet, improve thinking skills and promote effective mathematical
communication. Not only that, I had learned some moral values that I practice. This project
had taught me to responsible on the works that are given to me to be completed. This project
also had made me felt more confidence to do works and not to give easily when we could not
find the solution for the question. I also learned to be more discipline on time, which I was
given about three weeks to complete this project and pass up to my teacher just in time. I also
enjoy doing this project I spend my time with friends to complete this project and it had
tighten our friendship. Last but not least, I proposed this project should be continue because it
brings a lot of moral value to the student and also test the students understanding in
Additional Mathematics.