1. The histogram shows the distribution of heights of seedlings in a sample. It has frequencies on the y-axis and height ranges from -30 to 60 cm on the x-axis.
2. Most of the seedlings have heights between 10-30 cm as this has the highest frequencies.
3. There are no seedlings with heights below 0 cm or above 50 cm as those parts of the x-axis have a frequency of 0.
This document provides information about a mathematics exam taken by students in the Caribbean Examinations Council Secondary Education Certificate Examination in January 2010. The exam consisted of two sections, with Section I containing 7 compulsory questions and Section II containing 2 questions to choose from. The document provides the exam questions and instructions to candidates. It details the format, timing, materials permitted and copyright information regarding the exam.
The exam assessed students' mathematical skills and knowledge in areas such as algebra, geometry, trigonometry, statistics and calculus. Students had to show working for questions involving calculations, constructions and proofs. They were required to use mathematical tools like calculators, compasses and rulers accurately. The questions progressed from straightforward calculations and manip
This document provides examples of employee performance reviews and feedback. It analyzes some reviews that lack important details or have inconsistencies. A good review is highlighted that identifies both strengths and weaknesses, provides advice but doesn't dictate the plan of action, and ensures the employee is involved in developing their own improvement plan based on the feedback. The document also includes a link to additional resources on performance reviews.
This document provides information on CXC Sets including the syllabus language and objectives as well as examples of past CXC exam questions from 2009 to 2013 related to those objectives.
The document provides details about a business plan for a restaurant called "Shauntel de' Restaurante". It includes sections on acknowledging contributions, describing the business and its location, justifying the location choice, selecting appropriate labor, sources of capital, the role of the entrepreneur, types of production, quality control measures, use of technology, linkages, potential for growth, government regulations, and ethical issues. The business will be a sole proprietorship restaurant located in New Kingston providing meals, pastries, and beverages while also offering delivery and catering services.
The document is an exam for the Caribbean Examinations Council's Secondary Education Certificate in Mathematics. It contains 8 questions testing various math skills like algebra, geometry, trigonometry, and statistics. The exam is 2 hours and 40 minutes long and students must answer all questions in Section I and any two questions in Section II. Working must be shown clearly and formulas are provided.
Dans ce numéro, nous vous donnerons les clés pour comprendre ce qui se joue vraiment pendant les 100 premiers jours d’un collaborateur : cette période cruciale qui donne le la de la relation professionnelle à venir. Quels sont les enjeux véritables de l’intégration pour l’entreprise et le collaborateur ? Comment bien accueillir un nouveau collaborateur ? Se poser les bonnes questions, lancer des pistes de réflexion, inviter au débat : c’est à tout cela que nous vous convions dans ce nouveau numéro d’Apec RH, pour apprendre, progresser et performer dans vos démarches de recrutement.
This document appears to be an exam paper for mathematics from the Caribbean Examinations Council. It consists of two sections, with Section I containing 8 questions and Section II containing 3 questions. Students are instructed to answer all questions in Section I and any two questions from Section II. The paper provides a list of formulas, instructions for required materials, and sample questions on topics including algebra, geometry, trigonometry, and data analysis.
This document contains an 11-question mathematics exam for the Caribbean Examinations Council Secondary Education Certificate. The exam has two sections, with Section I containing 8 questions and Section II containing 3 questions. Candidates must answer all questions in Section I and any two questions from Section II. The exam covers topics such as algebra, geometry, trigonometry, and data analysis.
This document provides information about a mathematics exam taken by students in the Caribbean Examinations Council Secondary Education Certificate Examination in January 2010. The exam consisted of two sections, with Section I containing 7 compulsory questions and Section II containing 2 questions to choose from. The document provides the exam questions and instructions to candidates. It details the format, timing, materials permitted and copyright information regarding the exam.
The exam assessed students' mathematical skills and knowledge in areas such as algebra, geometry, trigonometry, statistics and calculus. Students had to show working for questions involving calculations, constructions and proofs. They were required to use mathematical tools like calculators, compasses and rulers accurately. The questions progressed from straightforward calculations and manip
This document provides examples of employee performance reviews and feedback. It analyzes some reviews that lack important details or have inconsistencies. A good review is highlighted that identifies both strengths and weaknesses, provides advice but doesn't dictate the plan of action, and ensures the employee is involved in developing their own improvement plan based on the feedback. The document also includes a link to additional resources on performance reviews.
This document provides information on CXC Sets including the syllabus language and objectives as well as examples of past CXC exam questions from 2009 to 2013 related to those objectives.
The document provides details about a business plan for a restaurant called "Shauntel de' Restaurante". It includes sections on acknowledging contributions, describing the business and its location, justifying the location choice, selecting appropriate labor, sources of capital, the role of the entrepreneur, types of production, quality control measures, use of technology, linkages, potential for growth, government regulations, and ethical issues. The business will be a sole proprietorship restaurant located in New Kingston providing meals, pastries, and beverages while also offering delivery and catering services.
The document is an exam for the Caribbean Examinations Council's Secondary Education Certificate in Mathematics. It contains 8 questions testing various math skills like algebra, geometry, trigonometry, and statistics. The exam is 2 hours and 40 minutes long and students must answer all questions in Section I and any two questions in Section II. Working must be shown clearly and formulas are provided.
Dans ce numéro, nous vous donnerons les clés pour comprendre ce qui se joue vraiment pendant les 100 premiers jours d’un collaborateur : cette période cruciale qui donne le la de la relation professionnelle à venir. Quels sont les enjeux véritables de l’intégration pour l’entreprise et le collaborateur ? Comment bien accueillir un nouveau collaborateur ? Se poser les bonnes questions, lancer des pistes de réflexion, inviter au débat : c’est à tout cela que nous vous convions dans ce nouveau numéro d’Apec RH, pour apprendre, progresser et performer dans vos démarches de recrutement.
This document appears to be an exam paper for mathematics from the Caribbean Examinations Council. It consists of two sections, with Section I containing 8 questions and Section II containing 3 questions. Students are instructed to answer all questions in Section I and any two questions from Section II. The paper provides a list of formulas, instructions for required materials, and sample questions on topics including algebra, geometry, trigonometry, and data analysis.
This document contains an 11-question mathematics exam for the Caribbean Examinations Council Secondary Education Certificate. The exam has two sections, with Section I containing 8 questions and Section II containing 3 questions. Candidates must answer all questions in Section I and any two questions from Section II. The exam covers topics such as algebra, geometry, trigonometry, and data analysis.
CSEC Business Cognate SBA (Principles of Business & Accounts) SAMPLENyahJohnson
Nyah Johnson conducted research on JMJ Car Rental Ltd. to investigate whether its marketing strategies contributed to profitability. JMJ Car Rental uses social media marketing on Facebook and prices vehicles based on competitors. While gross profit was high, net profit was low, indicating marketing revenue did not fully cover costs. The student recommends JMJ Car Rental expand advertising methods and reduce expenses to improve profitability.
This document discusses the importance of record keeping for small businesses. It identifies key records that should be kept, such as those related to business operations, tracking details, planning, legal requirements, contracts, licenses, permits, payroll, personnel, and taxes. The document also reviews different record keeping tools that can be used, including paper filing systems, computer software, cloud computing, accounting software, and file hosting services. It stresses that small businesses should establish a record keeping system tailored to their needs and should start basic record keeping practices now even as their business grows.
Divine Jewels is a sole proprietorship jewelry production business owned by Sue-Tannia Hibbert located in Ocho Rios, Jamaica. The business will employ 10 skilled workers such as jewelers, gemologists, and a production manager to produce and sell jewelry made from gems. The entrepreneur obtained a loan for fixed capital and will use personal savings for working capital. Quality control measures and use of technology like CAD/CAM will help ensure high quality products. The business has potential for growth through expanding production and entering new markets. Government regulations around registration and copyright will impact operations.
So. Yes. I am aware that this is done not up to my current standards but this was for a business subject I did back in high school. I can't believe almost five years have passed now...I can see growth :)
This document summarizes an employee's performance review. It rates the employee in several criteria like quality of work, communication skills, safety practices, and attendance on a scale of outstanding, exceeds expectations, meets expectations, needs improvement, and unsatisfactory. Based on the ratings in each criteria and comments from the employee and supervisor, an overall performance rating is given. Areas for improvement are identified and goals are set to enhance the employee's performance over the coming review period.
The document provides details of a student's school-based assessment project on office orientation and procurement and inventory management. It includes sections on the aims of the assessment, functions of the department studied, methodology used including questionnaires and interviews, findings from the research, and the impact of office equipment. The key findings were that the business studied operates primarily in an open-plan office layout and employees reported having a generally good relationship with their coworkers. The research showed the importance of the office orientation and procurement department in improving the business's growth, services, and efficiency.
This document provides guidelines for administering examinations and completing School-Based Assessments (SBAs) in 2023 given disruptions from COVID-19. It discusses:
1. No reduction in syllabus coverage will occur to maintain certification standards across years.
2. SBAs are important for comprehensive assessment but adjustments may be needed. Subjects requiring research papers/projects will see no changes, while some practical/lab assignments may be reduced or rules relaxed. Alternate approaches to fieldwork/performance SBAs are encouraged.
3. Examinations will proceed in 2023 with COVID-19 precautions. Some dates/locations may change but the format/structure of exams will be unchanged to ensure compar
Guidelines for office administration sbaLisa Forbes
This document provides guidelines for completing a School Based Assessment (SBA) project on office administration for the Caribbean Secondary Education Certificate (CSEC). It outlines the required sections and content for the SBA, including:
1. Preparation with a title page, aim, and correspondence letter.
2. Gathering data through a methodology outlining data collection and analysis, questions asked during research, and an activities schedule.
3. Addressing regulations by stating relevant legislation, how it was learned, health and safety practices observed, and staff rules complied with.
4. Presenting findings in a report on results and recommendations, and explaining the use and suitability of office equipment for tasks.
This document contains materials for evaluating the job performance of an HR operations manager, including:
1) A 4-page performance evaluation form with ratings for various performance factors like administration, communication, decision-making, and customer service.
2) Links to additional resources on performance appraisal best practices and materials like review phrases and sample KPIs.
3) 3 pages of sample performance review phrases for evaluating different aspects of job performance like attitude, creativity, and decision-making.
The evaluation form and review phrases are intended to help managers objectively assess an HR operations manager's performance and identify areas for improvement.
- The writer is inviting a friend to accompany them on a summer vacation trip to Disney World in Florida from August 12-18, 2014.
- They plan to purchase 5-day park passes for $289 each, totaling $1538.95 with taxes.
- The luxury resort they will stay at is located on 20 private acres with an outdoor pool, and is just a 10 minute drive from the Disney theme parks. It features deluxe suites with kitchens, washers/dryers, and whirlpools.
Dennis Stewart is proposing to establish a business called Country-side Jerk Centre that will prepare authentic Jamaican jerked meats. The business will be a sole proprietorship located in Port Antonio, Portland for its access to ingredients and customers. It will employ 10 people including chefs, cashiers, and delivery staff. Funding will come from loans and personal savings to purchase equipment and supplies. The entrepreneur's roles will include planning, organizing, and evaluating the business. Country-side Jerk Centre will engage in secondary production and domestic sales by preparing meats to customer orders. Quality control, technology, linkages, and ethical practices are discussed to ensure proper operation and growth of the business.
Cxc past questions and answers – principles of businessleroy walker
The document provides discussion and guidelines for answering past CXC Principles of Business exam questions. It includes sample questions on topics like economic systems, types of business organizations, contracts, leadership styles, entrepreneurship, and migration. For each question, it lists the required parts and number of marks, then provides a discussion of how to approach answering each part. This includes defining key terms, listing examples for different parts of questions, and describing different concepts in detail. The goal is to help students understand how to structure their responses to earn full marks for past paper questions.
This document summarizes a student's research project on the records and information management, sales, and customer service functions of PC Clinic Company. The student conducted interviews and distributed questionnaires to employees in the marketing, sales, and customer service departments. The main findings were that the marketing department's core functions are promotional activities, budgeting, and advertising. The customer service department focuses on addressing customer complaints and ensuring satisfaction. The sales department maintains sales records and monitors stock. Some challenges encountered were employees fearing victimization and some information being withheld due to confidentiality.
This document provides information about starting a proposed business called Austin's Car Wash and Guest House. It includes sections on acknowledging assistance received, introducing the business, justifying its location, selecting appropriate labor, identifying sources of capital, defining the entrepreneur's role, describing production methods and levels, discussing use of technology, outlining linkages, addressing potential for growth, noting government regulations, and ethical considerations. The business will provide car washing and guest house services, using various manual and semi-skilled labor. It will be located for accessibility and to provide local employment.
This document provides information and resources for conducting a performance appraisal for a senior civil engineer. It includes:
1. A sample performance appraisal form with sections for reviewing job performance based on key criteria, identifying strengths and areas for improvement, setting goals, and obtaining signatures.
2. Examples of performance review phrases focused on attributes like attitude, creativity, decision-making, interpersonal skills, and problem-solving.
3. An overview of the top 12 methods for conducting performance appraisals, such as management by objectives, critical incident method, behaviorally anchored rating scales, and 360-degree feedback.
This document provides a report on the performance of candidates who sat exams for the Caribbean Examinations Council's Advanced Proficiency Examination in Chemistry in May/June 2010. It summarizes the exam structure, number of candidates, and provides analysis of candidate performance on each exam paper and module. Overall, candidate performance was adequate, though some weaknesses were observed, particularly in calculations, writing equations, and practical skills. The report makes recommendations to teachers on strategies to help students improve.
The document provides details of a student's school-based assessment project on workplace attitudes and relationships. It includes an introduction outlining the research topic, acknowledgements, a table of contents listing the criteria covered, and sections addressing the project title and aims, methodology used, findings and limitations. The student investigated how skills, attitudes and attributes of employees impact workplace relationships at the National Land Agency. They distributed questionnaires, conducted interviews and observed interactions. The findings suggested staff could improve politeness towards customers, even when faced with inappropriate attitudes. The student recommended maintaining discipline and courtesy in all workplace interactions.
1) The document is an exam for mathematics taken in May/June 2007. It contains instructions for students and lists common formulas.
2) Section 1 contains 3 questions testing skills in calculations, ratios, fractions, and writing equations. Section 2 has 4 sub-questions evaluating algebraic manipulation, simplification of expressions, writing equations from word problems, and geometry constructions.
3) The exam tests a wide range of mathematics concepts and skills through multi-step word problems and diagrams requiring calculations, algebraic manipulations, geometric constructions, and use of formulas.
This document contains a mathematics exam for the Caribbean Examinations Council Secondary Education Certificate. The exam has two sections and contains 8 questions. Section I contains 5 compulsory questions testing algebra, geometry, and data analysis skills. Section II contains 2 optional questions on algebra and relations/functions, geometry and trigonometry, or statistics. The exam tests a range of mathematical concepts and requires both calculations and explanations. It aims to comprehensively assess students' general mathematics proficiency.
CSEC Business Cognate SBA (Principles of Business & Accounts) SAMPLENyahJohnson
Nyah Johnson conducted research on JMJ Car Rental Ltd. to investigate whether its marketing strategies contributed to profitability. JMJ Car Rental uses social media marketing on Facebook and prices vehicles based on competitors. While gross profit was high, net profit was low, indicating marketing revenue did not fully cover costs. The student recommends JMJ Car Rental expand advertising methods and reduce expenses to improve profitability.
This document discusses the importance of record keeping for small businesses. It identifies key records that should be kept, such as those related to business operations, tracking details, planning, legal requirements, contracts, licenses, permits, payroll, personnel, and taxes. The document also reviews different record keeping tools that can be used, including paper filing systems, computer software, cloud computing, accounting software, and file hosting services. It stresses that small businesses should establish a record keeping system tailored to their needs and should start basic record keeping practices now even as their business grows.
Divine Jewels is a sole proprietorship jewelry production business owned by Sue-Tannia Hibbert located in Ocho Rios, Jamaica. The business will employ 10 skilled workers such as jewelers, gemologists, and a production manager to produce and sell jewelry made from gems. The entrepreneur obtained a loan for fixed capital and will use personal savings for working capital. Quality control measures and use of technology like CAD/CAM will help ensure high quality products. The business has potential for growth through expanding production and entering new markets. Government regulations around registration and copyright will impact operations.
So. Yes. I am aware that this is done not up to my current standards but this was for a business subject I did back in high school. I can't believe almost five years have passed now...I can see growth :)
This document summarizes an employee's performance review. It rates the employee in several criteria like quality of work, communication skills, safety practices, and attendance on a scale of outstanding, exceeds expectations, meets expectations, needs improvement, and unsatisfactory. Based on the ratings in each criteria and comments from the employee and supervisor, an overall performance rating is given. Areas for improvement are identified and goals are set to enhance the employee's performance over the coming review period.
The document provides details of a student's school-based assessment project on office orientation and procurement and inventory management. It includes sections on the aims of the assessment, functions of the department studied, methodology used including questionnaires and interviews, findings from the research, and the impact of office equipment. The key findings were that the business studied operates primarily in an open-plan office layout and employees reported having a generally good relationship with their coworkers. The research showed the importance of the office orientation and procurement department in improving the business's growth, services, and efficiency.
This document provides guidelines for administering examinations and completing School-Based Assessments (SBAs) in 2023 given disruptions from COVID-19. It discusses:
1. No reduction in syllabus coverage will occur to maintain certification standards across years.
2. SBAs are important for comprehensive assessment but adjustments may be needed. Subjects requiring research papers/projects will see no changes, while some practical/lab assignments may be reduced or rules relaxed. Alternate approaches to fieldwork/performance SBAs are encouraged.
3. Examinations will proceed in 2023 with COVID-19 precautions. Some dates/locations may change but the format/structure of exams will be unchanged to ensure compar
Guidelines for office administration sbaLisa Forbes
This document provides guidelines for completing a School Based Assessment (SBA) project on office administration for the Caribbean Secondary Education Certificate (CSEC). It outlines the required sections and content for the SBA, including:
1. Preparation with a title page, aim, and correspondence letter.
2. Gathering data through a methodology outlining data collection and analysis, questions asked during research, and an activities schedule.
3. Addressing regulations by stating relevant legislation, how it was learned, health and safety practices observed, and staff rules complied with.
4. Presenting findings in a report on results and recommendations, and explaining the use and suitability of office equipment for tasks.
This document contains materials for evaluating the job performance of an HR operations manager, including:
1) A 4-page performance evaluation form with ratings for various performance factors like administration, communication, decision-making, and customer service.
2) Links to additional resources on performance appraisal best practices and materials like review phrases and sample KPIs.
3) 3 pages of sample performance review phrases for evaluating different aspects of job performance like attitude, creativity, and decision-making.
The evaluation form and review phrases are intended to help managers objectively assess an HR operations manager's performance and identify areas for improvement.
- The writer is inviting a friend to accompany them on a summer vacation trip to Disney World in Florida from August 12-18, 2014.
- They plan to purchase 5-day park passes for $289 each, totaling $1538.95 with taxes.
- The luxury resort they will stay at is located on 20 private acres with an outdoor pool, and is just a 10 minute drive from the Disney theme parks. It features deluxe suites with kitchens, washers/dryers, and whirlpools.
Dennis Stewart is proposing to establish a business called Country-side Jerk Centre that will prepare authentic Jamaican jerked meats. The business will be a sole proprietorship located in Port Antonio, Portland for its access to ingredients and customers. It will employ 10 people including chefs, cashiers, and delivery staff. Funding will come from loans and personal savings to purchase equipment and supplies. The entrepreneur's roles will include planning, organizing, and evaluating the business. Country-side Jerk Centre will engage in secondary production and domestic sales by preparing meats to customer orders. Quality control, technology, linkages, and ethical practices are discussed to ensure proper operation and growth of the business.
Cxc past questions and answers – principles of businessleroy walker
The document provides discussion and guidelines for answering past CXC Principles of Business exam questions. It includes sample questions on topics like economic systems, types of business organizations, contracts, leadership styles, entrepreneurship, and migration. For each question, it lists the required parts and number of marks, then provides a discussion of how to approach answering each part. This includes defining key terms, listing examples for different parts of questions, and describing different concepts in detail. The goal is to help students understand how to structure their responses to earn full marks for past paper questions.
This document summarizes a student's research project on the records and information management, sales, and customer service functions of PC Clinic Company. The student conducted interviews and distributed questionnaires to employees in the marketing, sales, and customer service departments. The main findings were that the marketing department's core functions are promotional activities, budgeting, and advertising. The customer service department focuses on addressing customer complaints and ensuring satisfaction. The sales department maintains sales records and monitors stock. Some challenges encountered were employees fearing victimization and some information being withheld due to confidentiality.
This document provides information about starting a proposed business called Austin's Car Wash and Guest House. It includes sections on acknowledging assistance received, introducing the business, justifying its location, selecting appropriate labor, identifying sources of capital, defining the entrepreneur's role, describing production methods and levels, discussing use of technology, outlining linkages, addressing potential for growth, noting government regulations, and ethical considerations. The business will provide car washing and guest house services, using various manual and semi-skilled labor. It will be located for accessibility and to provide local employment.
This document provides information and resources for conducting a performance appraisal for a senior civil engineer. It includes:
1. A sample performance appraisal form with sections for reviewing job performance based on key criteria, identifying strengths and areas for improvement, setting goals, and obtaining signatures.
2. Examples of performance review phrases focused on attributes like attitude, creativity, decision-making, interpersonal skills, and problem-solving.
3. An overview of the top 12 methods for conducting performance appraisals, such as management by objectives, critical incident method, behaviorally anchored rating scales, and 360-degree feedback.
This document provides a report on the performance of candidates who sat exams for the Caribbean Examinations Council's Advanced Proficiency Examination in Chemistry in May/June 2010. It summarizes the exam structure, number of candidates, and provides analysis of candidate performance on each exam paper and module. Overall, candidate performance was adequate, though some weaknesses were observed, particularly in calculations, writing equations, and practical skills. The report makes recommendations to teachers on strategies to help students improve.
The document provides details of a student's school-based assessment project on workplace attitudes and relationships. It includes an introduction outlining the research topic, acknowledgements, a table of contents listing the criteria covered, and sections addressing the project title and aims, methodology used, findings and limitations. The student investigated how skills, attitudes and attributes of employees impact workplace relationships at the National Land Agency. They distributed questionnaires, conducted interviews and observed interactions. The findings suggested staff could improve politeness towards customers, even when faced with inappropriate attitudes. The student recommended maintaining discipline and courtesy in all workplace interactions.
1) The document is an exam for mathematics taken in May/June 2007. It contains instructions for students and lists common formulas.
2) Section 1 contains 3 questions testing skills in calculations, ratios, fractions, and writing equations. Section 2 has 4 sub-questions evaluating algebraic manipulation, simplification of expressions, writing equations from word problems, and geometry constructions.
3) The exam tests a wide range of mathematics concepts and skills through multi-step word problems and diagrams requiring calculations, algebraic manipulations, geometric constructions, and use of formulas.
This document contains a mathematics exam for the Caribbean Examinations Council Secondary Education Certificate. The exam has two sections and contains 8 questions. Section I contains 5 compulsory questions testing algebra, geometry, and data analysis skills. Section II contains 2 optional questions on algebra and relations/functions, geometry and trigonometry, or statistics. The exam tests a range of mathematical concepts and requires both calculations and explanations. It aims to comprehensively assess students' general mathematics proficiency.
This document appears to be an exam paper for mathematics from the Caribbean Examinations Council. It consists of two sections, with Section I containing 8 questions and Section II containing 3 questions. Students are instructed to answer all questions in Section I and any two questions from Section II. The paper provides a list of formulas, instructions for required materials, and sample questions on topics including algebra, geometry, trigonometry, and data analysis.
This document provides instructions and information for a mathematics exam, including:
1) The exam consists of two sections, with Section I containing multiple choice questions and Section II containing extended response questions. Students must answer all questions in Section I and two questions in Section II.
2) A list of formulas is provided to use for reference.
3) The exam materials allowed are a non-programmable calculator, geometry set, mathematical tables, and graph paper.
4) The exam code, date, time limit and copyright information are provided.
This document contains instructions and questions for a mathematics preliminary examination. It consists of 7 questions testing skills in algebra, trigonometry, geometry, statistics, and problem solving. Students are instructed to show their working, use formulas provided, and give answers to a specified degree of accuracy. A total of 100 marks are available across the exam.
The document is an unsolved physics paper from 2008 for IITJEE (Indian Institute of Technology Joint Entrance Examination). It contains multiple choice and reasoning questions about physics concepts. The questions cover topics like mechanics, electromagnetism, thermodynamics, and waves. There are four sections with different question types including objective, reasoning, comprehension, and matrix-match questions. The document provides figures and diagrams to accompany some of the physics problems.
The passage discusses Deborah Mayo's philosophy of science, which focuses on rigorously validating claims made through experimentation. According to Mayo, a claim can only be considered supported by an experiment if the experiment investigates and eliminates all possible ways the claim could be false. For an experiment to serve as a severe test of a claim, the claim would have to be unlikely to pass the experiment if it were false. The passage provides examples to illustrate this point, such as how imprecise measurements of Snell's law of refraction would allow alternative historical laws to also seem consistent with the experimental results, demonstrating the experiment was not a true severe test of Snell's law.
This document contains a past paper for the IITJEE physics exam from 2009. It includes 3 sections - multiple choice questions with single answers, multiple choice questions with multiple answers, and questions requiring integer answers. The document provides the questions and options/choices for each question but does not include the solutions. It addresses topics in physics including photoelectric effect, simple harmonic motion, centripetal force, gas laws, electromagnetic induction, sound waves, and fluid mechanics.
This document is a mathematics exam for Secondary 4 students consisting of 10 questions testing various math concepts. It provides instructions for students on how to answer the questions, lists relevant mathematical formulas, and presents the questions which cover topics like matrices, trigonometry, financial math, algebra, geometry, and statistics. The exam is 100 marks total and students are given 150 minutes to complete it.
This document contains notes and formulae on solid geometry, circle theorems, polygons, factorisation, expansion of algebraic expressions, algebraic formulae, linear inequalities, statistics, significant figures and standard form, quadratic expressions and equations, sets, mathematical reasoning, straight lines, and trigonometry. The key concepts covered include formulas for calculating the volume and surface area of various 3D shapes, properties of angles in circles and polygons, factorising and expanding algebraic expressions, solving linear and quadratic equations, set notation and Venn diagrams, types of logical arguments, equations of straight lines, and defining the basic trigonometric ratios.
This document discusses the uses of a theodolite in mine surveying. It describes how a theodolite can be used to measure horizontal and vertical angles, determine magnetic bearings, prolong survey lines, and conduct traverses. Key uses include measuring angles between points, determining elevations, setting horizontal lines, and establishing grades. A theodolite is a precise surveying instrument useful for laying out surveys, locating points, and establishing curves in mine sites.
This document contains an unsolved physics paper from 2007 for the IIT JEE entrance exam. It includes multiple choice, assertion-reason, and matrix-match style questions testing concepts in physics. The questions cover topics such as circuits, electrostatics, nuclear physics, optics, mechanics, and thermodynamics. The document provides context, diagrams, and multiple potential answers for 22 questions testing understanding of fundamental physics principles.
This document contains a past paper for the GATE electrical engineering exam from 2009. It consists of 30 multiple choice questions testing concepts in areas like circuits, electronics, power systems, control systems, and digital electronics. The questions cover topics such as dynamometer wattmeters, error analysis in measurement systems, circuit analysis, characteristics of generators and motors, properties of semiconductors, logic gates, transformers, stability analysis, and more.
The document provides information about:
1) The syllabus and marking scheme for a mathematics exam, dividing the test into various units and topics and allocating marks.
2) Details about a problem solving assessment that will contribute to students' final marks.
3) Samples of different types of questions that may appear on the exam, including multiple choice, short answer, and long answer questions.
4) A value-based question asking students to make a pie chart based on a budget plan and answer questions about mathematical concepts, spending allocation, and values depicted.
(1) The document is an examination paper for Secondary 4/5 students in mathematics. It consists of 13 printed pages containing 11 questions testing various math concepts.
(2) Instructions are provided for candidates, including writing their name, working clearly, using calculators where appropriate, and expressing some answers to a given degree of accuracy or in terms of pi.
(3) The exam covers topics like algebra, trigonometry, geometry, calculus, statistics, and financial mathematics. Questions involve factorizing expressions, solving equations, using circle properties, graphing functions, and probability.
At Apex Institute, we endeavour to amalgamate the ancient values of uttermost dedication and responsibility that gave teaching a very pious and sacred status, with latest teaching methodologies so as to make the act of learning, a delectable experience. The arduous task is accomplished by a team of diligent academicians and entrepreneurs, who with the years of experience have mastered the techniques to transform even the most abstruse topics easy to comprehend.
Great emphasis is laid on the concepts and fundamentals with a smooth and systematic transition to the advanced levels of teaching. The interaction between students and teachers is always encouraged so as to provide a very healthy environment for growth and learning. During the process of training the students for IIT-JEE/Engg./Medical entrance examinations, great emphasis is laid on the fundamentals so as to excel in the CBSE examination also.
Illustrious faculty and excellent teaching techniques provide you will an infallible approach to success only at Apex Institute.
Our Mission
Generating excellence both in academic and competitive aspects thereby training the youth for most gruelling entrance level exams viz. IIT-JEE/Engg.& Medical entrance.
Our Vision
Generating excellence in academic, exploring creative areas of the dormant self, nurturing talent & aptitude & including perseverance among the students to keep themselves abreast of the latest developments in the field of competitive examinations.
Our Objectives
1. Striving for the best possible education to ambitious students aspiring to join corporate world as medical professionals.
2. Creating a comprehensive understanding of the subjects & help developing strategies to meet arduous competitions among the students to match, excel & ameliorate the competition oriented education.
This document contains an unsolved physics practice paper from 2007 for the IITJEE entrance exam. It has four sections: 1) Multiple choice questions about physics concepts, 2) Assertion/reason questions, 3) Linked comprehension questions about light refraction and the Doppler effect, and 4) Matching questions about physics situations and characteristics. The document provides context for 9 multiple choice questions, 4 assertion/reason questions, 6 linked comprehension questions, and 3 matching questions/tables to complete.
This document contains instructions and questions for a mathematics exam. It provides information about the exam such as the date, time allowed, materials permitted, and instructions for completing and submitting the exam. The exam contains 7 multi-part questions testing a variety of mathematics concepts including algebra, geometry, trigonometry, statistics, and matrix operations.
This document contains 15 multiple choice questions from an IME 2019 exam covering topics in trigonometry, functions, geometry, complex numbers, and algebra. The questions involve concepts like progressions, function definitions, probability, areas of shapes, coordinate transformations, inequalities, and solving equations. The answers to each question are provided in a key at the end.
Valdes Pierre conducted a social studies project on gambling in Chateaubelair, St. Vincent and the Grenadines. Chateaubelair has high illiteracy and unemployment, so some residents resort to gambling. Valdes distributed printed questionnaires at four locations over four hours to collect data on gambling prevalence. Twenty respondents of varying ages, genders, education levels and employment statuses anonymously answered 16 questions about their gambling behaviors, preferences, expenditures and opinions. The questionnaires aimed to determine how common gambling is and suggest alternatives to address its growth.
The document discusses a student's social studies research project on alcohol abuse among 5th form students at their school. It outlines the research tasks which include: 1) determining the levels of alcohol abuse, 2) explaining why this topic was selected after reading a newspaper article about secondary student alcohol use, and 3) using a questionnaire method to collect data from students because it allows for easy yet confidential collection of information. It then provides the questionnaire to be administered which includes questions about student demographics, alcohol use behaviors, influences, and potential solutions.
1. Small organisms rely on diffusion for transport as their large surface area to volume ratio allows gases and nutrients to reach cells via diffusion. Larger multicellular organisms have developed transport systems like circulatory systems using blood and vessels due to their smaller surface area to volume ratio making diffusion insufficient.
2. Plants have vascular bundles containing xylem and phloem for transport. Xylem transports water and minerals upwards from roots while phloem transports carbohydrates made in leaves to other plant parts.
3. The human circulatory system uses blood, heart, arteries, veins and capillaries to transport substances between lungs, tissues and organs. Blood contains red blood cells, white blood cells, platelets
1. Respiration is the process by which energy is released from food molecules through oxidation. It occurs through aerobic and anaerobic respiration. Aerobic respiration fully breaks down glucose and releases more energy, while anaerobic respiration occurs without oxygen and releases less energy.
2. The respiratory system includes the nose, throat, windpipe, lungs, and alveoli. Gas exchange occurs in the alveoli through diffusion. Breathing is the process of inhaling and exhaling that supplies the alveoli with oxygen and removes carbon dioxide.
3. Smoking has negative health effects and increases the risk of diseases like cancer, bronchitis, emphysema and heart disease due to chemicals like nicotine
Carbohydrates provide energy and are made up of sugars like glucose, fructose, starch and cellulose. They lack energy leads to lack of energy. Proteins are needed for growth, repair of tissues, enzymes and antibodies. They are made up of amino acids. Lipids provide long-term energy storage and insulation and are made up of fatty acids and glycerol. Vitamins and minerals are required in small amounts daily for bodily processes but cannot be stored if unused. A balanced diet with sufficient amounts of each food group is needed to prevent malnutrition as each group provides nutrients for specific tasks.
This document provides information on excretion in humans and other organisms. It discusses the key organs and processes involved in excretion in the human body, including the lungs, skin, and kidneys. In the kidneys, glomerular filtration occurs, along with reabsorption of useful substances and production of urine. The liver is described as having many functions including detoxification and producing urea from excess proteins. Excretion in plants, fish, and amoebas is also summarized, noting their various adaptations for osmoregulation.
The document is a cover letter and questionnaire for a geography student's field study on factors affecting banana production in Richmond, St. Vincent. The student, Leroy Walker, is conducting the study for a high school geography SBA (School-Based Assessment) in order to gain marks for their CXC/CSEC exam. The cover letter introduces the student and their study topic, and asks recipients to support their research by filling out the attached 16 question questionnaire about banana farming. The questionnaire asks farmers about demographics, crop details, diseases affecting production, storage issues, financial support, and suggestions for improving banana cultivation.
The document summarizes a geography student's research project on factors affecting banana production in Richmond, St. Vincent. The student conducted a questionnaire with 20 banana farmers to investigate factors like diseases, finances, and government assistance. Key findings include: most farmers were over 27 years old with primary education; the most cited disease was Black Sigatoka but some farmers lacked knowledge of disease dangers; many farmers lacked sufficient finances but felt government assistance for disease control was limited; suggested solutions included more effective disease control, extension officers, transportation assistance, and credit/attention for farmers.
This document provides information on banana production in St. Vincent and the Grenadines. It discusses the history of banana exports from the region and outlines the key steps in banana farming: planting, tending, harvesting, as well as common problems and solutions. The problems discussed include diseases like moko and leaf spot, nematodes, and slugs/snails. Solutions involve practices like sanitation, use of chemicals, and applying baits/pesticides. The overall goal is to produce high quality export fruit through effective farm management.
(1) Solve the equations: 5.2q(q-1) = 12.2q^2 and 1.68/1.52-1.45 = 0.8/2.1
(2) Calculate: A trains runs at 60 km/h and B runs at 50 km/h. How long will it take them to travel 660 km together?
(3) Calculate: There are 3 lines with 10 passengers each. The fare is $10 per person. Calculate the total fare.
1. TEST CODE OI234O2O
FORM TP 2012017 %. JANUARY 2012
CARIBBEAN EXAMINATIONS COUNCIL
SECONDARY EDUCATION CERTIFICATE
EXAMINATION
MATHEMATICS
Paper 02 - General Proficiency
2 hours 40 minutes
04 JANUARY 2012 (a.m.)
READ THE FOLLOWING INSTRUCTIONS CAREFULLY.
1. This paper consists of TWO sections.
2. There are EIGHT questions in Section I and THREE questions in Section II.
3. Answer ALL questions in Section I, and any TWO questions from Section II.
4. Write your answers in the booklet provided.
5. All working must be clearly shown.
6. A list of formulae is provided on page 2 of this booklet.
Reouired Examination Materials
Electronic calculator
Geometry set
Graph paper (provided)
-
T DO NOT TURN THIS PAGE UNTILYOU ARE TOLD TO DO SO.
-
: Copyight O 2009 Caribbean Examinations Council
:
: All rights reserved.
ot234ozotJANUARY/r'2012
:=
=
2. v
Page 2
LIST OF F'ORMULAE
Volume of a prism V :
Ah where I is the area of a cross-section and h is the perpendicular
length.
Volume of cylinder Y: nf h where r is the radius of the base and & is the perpendicular height.
Volume of a right pyramid V : !m where A is the area of the base and h is theperpendicular height.
3
Circumference C:2nr where r is the radius of the circle.
Arc length S: * x2nr where 0 is the angle subtended by the arc, measured in
degrees.
Area of a circle A: nf where r is the radius of the circle.
e
Area of a sector A: 360
x nl where 0 is the angle of the sector, measured in degrees.
Area of trapezium A :
+ @ b) ft where a and b are the lengths of the parallel sides and ft is
+
the perpendicular distance between the parallel sides.
Roots of quadratic equations If ax2 +bx+c:0,
V
then x -b+"16'i;
2a
opposite side
Trigonometric ratios sin 0 : aypotenuse
Opposite
cos ^ adjacent side
u : -l-------;-
nypotenuse
Adjacent
tan ^ oDDosite
0 : -++-.:: side
adlacent srde
Area of triangle Area of A : U, where b is the length of the base and ft is
I
the perpendicular height.
Area of L,ABC : ;I ab sin C
Areaof MBC : s(s-a)(s-b)(s-c)
wnere
, a+b+c
2
*b
Sine rule
abc
sinA sinB sin C
Cosine rule a2 : b2 * c2 - 2bccosA
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0 1 234020/JANUARYiF 20 I 2
3. Page 3
SECTION I
AnswerALL the questions in this section.
All working must be clearly shown.
1. (a) Using a calculator, or otherwise, calculate the EXACT value of
/ t2
(i) ^l
-- 31
' expressing vour answer as a fraction ( 3 marks)
[t;,,)
(ii) Jaos29 + 0.216, expressing your answer in standard form.
( 3 marks)
(b) A typist is paid a basic wage of $22.50 per hour for a 4O-hour week.
(i) Calculate the typist's basic weekly wage. ( l mark)
Overtime is paid at one and a half times the basic hourly rate.
(iD Calculate the overtime wage for ONE hour of overtime work. ( l mark)
To earn some extra money, the typist decided to work overtime.
Calculate
(iiD the wage she would earn for overtime if she worked for a TOTAL of 52 hours
during agivenweek. ( 2marks)
(i") the number of overtime hours she must work during a given week to eam a
TOTALwage of $1440. ( 2marks)
Total 12 marks
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0 123 4020/ IANUARY/p 20 I 2
4. ./
Page 4
(a) Solve the pair of simultaneous equations
3x + 2Y: 13
x - 2Y: -1. ( 3 marks)
(b) Factorise completely
(i) x2 - 16 (1mark)
(ii) 2x2 - 3x + 8x - 12. ( 2 marks)
(c) Tickets for a football match are sold at $30 for EACH adult and $15 for EACH child.
A company bought 28 tickets.
(i) Ifx of these tickets were for adults, write in terms ofx,
a) the number of tickets for children ( lmark )
b) the amount spent on tickets for adults ( lmark )
c) the amount spent on tickets for children. ( lmark )
(iD Show that the TOTAL amount spent on the 28 tickets is $(15x + 420).
( lmark )
(iiD Given that the cost of the 28 tickets was $660, calculate the number of adult
tickets bought by the company. ( 2 marks)
Total12 marks
3. (a) A universal set, U, is defined as:
U : { 51, 52, 53, 54, 55, 56, 57,58, 59 }
A andB are subsets of U, such that:
I: { odd numbers }
.B: { prime numbers }
(i) List the members of the setl. (lmark)
(ii) List the members of the set B. ( lmark )
(iiD Draw a Venn diagram to represent the sets A, B and U. ( 3 marks)
(b) (i) Using a pair of compasses, a ruler and a pencil
a) construct a triangle CDE in which DE : 10 cm, DC : 8 cm and
Z CDE:45". ( 4 marks)
b) construct a line, CF, perpendicular to DE such that F lies on DE.
( 2 marks)
(ii) Using a protractor, measure and state the size of I DCE. ( 1 mark )
Total 12 marks
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0 1 234020/JANU ARY E 2012
5. Page 5
4. (a) The following is an extract from a bus schedule. The bus begins its journey at Belleview,
travels to Chagville and ends its journey at St. Andrews.
Town Arrive Depart
Belleview 6:40 a.m.
Chagville 7:35 a.m. 7:45 a.m.
St. Andrews 8:00 a.m.
(i) How long did the bus spend at Chagville? ( 1 mark )
(ii) How long did the bus take to travel from Belleview to Chagville?
( lmark )
(iiD The bus travelled at an average speed of 54 km/hour from Belleview to Chagville.
Calculate, in kilometres, the distance from Belleview to Chagville.
( 2 marks)
(b) Water is poured into a cylindrical bucket with a base area of 300 cm2. If 4.8 litres of
water was poured into the bucket, what is the height of the water in the bucket?
( 3 marks)
(c) The diagram below, not drawn to scale, shows a cuboid with length 13 cm, width 4 cm
and height ft cm.
I
thcm
I
t_
ryl.
(i) State, in terms of ft, the area of the shaded face of the cuboid. ( 1 mark )
(ii) Write an expression, in terms of h, for the volume of the cuboid. ( 1 mark )
(iiD If the volume of the cuboid is 286 cm3 calculate the height, h, of the cuboid.
( 2 marks)
Total ll marks
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O1 23 4O2O I JANUARY/F 20 I 2
6. v
Page 6
5. (a) The diagram below, not drawn to scale, shows TWO triangles, JKL and, MLP,with
JK parallel to ML. LM: MP, KLP is a straight line, angle JLM: 22" and angle
LMP:36.
Calculate, giving reasons for your answers, the measure of EACH of the following:
(i) z MLP
(iD t rJK
(iiD z JKL
(iv) z KLJ ( 4 marks)
(b) The diagrambelow shows atriangle, PQR,andits image, P'e,R,.
v
(D State the coordinates of P and, Q. ( 2 marks)
(ii) Desciibe fully the transformation that maps triangle PQRonto triangle P,Q,R,.
( 2 marks)
(iiD Write down the coordinates of the images of P and Qunder the translation
I ',l. ( 2 marks)
[-6] Total 10 marks
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0l 234020/JANUARY/r' 20 1 2
7. Page 7
6. Thetablebelowshowscorrespondingvaluesofxandyforthefunctiony:f-2x-3,for
integer values ofx from -2to 4.
.| a
x -1 0 I 2 J 4
v 5 -J -4 0 5
(a) Copy and complete the table. ( 2marks)
(b) Using a scale of 2 cm to represent I unit on thex-axis, and 1 cm to represent L unit
on they-axis, plot the points whose x andy values are recorded in your table, and draw
a smooth curve through your points. ( 4 marks)
(c) Using your graph, estimate the value ofy when x:3.5. Show on your graph how the
value was obtained. ( 2 marks)
(d) Without further calculations,
(D write the equation of the axis of symmetry of the graph ( 1 mark )
(iD estimate the minimum value of the functiony ( I mark )
(iiD state the values of the solutions of the equation: x2 - 2x - 3 : 0. ( I mark )
Total ll marks
(
(
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0 1 234020IJANUARY/F 20 1 2
8. l,
Page 8
The histogram below shows the distribution of heights of seedlings
in a sample.
7.
ia:r
ir:l
+-.i i i i:i:
"i"i-i- i
j...i...i...i.1.. i-l l."l iir:
- i i-.i" i !iii 'n".i" i..-i"
{requ enclT !i i...i...i.. ..1...j....i....1
"j-t- i"i i:iii i;!i -i-: -i"i- ...i,..i...i.,,i..
''l-...: -i ii:i .,i,...i...i--i.'
.i...i..i.i'1. .i i r-i _!..-t_f.-1_ .i..i.-i-i
-30r -i"t- i" l
+-l-.i -i
.i. - f- f..t.' l- -j -l "t-:
.i.--:.-.i..-i..
iiii i--l- i.-i-
...i....!...r...1... .1...i....1....i..
i 1...!...:.
'f-t- f- r.' -.i-.i-i-.i i:ii -l -i-1 -l -
ii:l
-i'i-i--i
-i-;-.i-.i- -i-.i-i-.i
i-i-i-i il- +-.n-.i,
li -r-t i
: : ._i_...:...i...;..
-.i-i-.i-.1"
tlii i
..!...t...:....1... li
]i.': i-i iil-i..1 --.j....;--..i-..;
-i-j" : - i-
rzui. i ._:_...i...:-.
llii -t.,-!..-i-.,,i..
:iii
-i-i-i-'i i '.t-: :_ i"t".l-i' ri:i
;...i....i...j. r".f..+- !
"i-l -i-l- t-.1.-t-1" .4-.i-.t-.1. i-i-:-1
-+'.i-.i'.i"
.i...i--.;-...i-.. '1" t- t_1"
-1- f" t_-l
"f- t" f-t
ii: _i.. i" i..:'
i_i- i_i li...i..'i...i.. .i...:...i...:...
!iii
- .....,...+.
lU.!. .+...i-i-.i. i" t- i"1 i-i !1
!.. ii:i
!....i...:...i iii:
...!-+ l'. i
ii
i-i-i-i' tti: i....1.-i.-i
:ii: i.':''''i'''i i i-.l i- t".t-t-.i
iiii i-i .i-i-i i i....i...i...i i-i-r'i 'l : t-l'
i:::
..:...!.,.i....i..
-i_ i- i- i ii::
.i...1...i-...:.,.
i-.i"i" i-
::i: -f- t" f-l ..i--i....i- i
.! 1-t-t- i....i...i-.i.. .i...:...i-...i. iiii
Iii::
i....:....i
r r-j--r l-: i l-l'-r'-i i i iil i ii 'i... i. .i. | .;... i -i- .
"i-i -l-l' l -r--i--r- i
10...i i r i-20-i-i
i
ro..i .i ..i i-r- 40-i-i
i
:- ii50 i1i
;...i , ., 1 1..i...i.i
..i...1...i..-1.- .1...r....i....i...r .i..1......, I, i...i
f j-;-r-i
..,....i....
1
,...:. .1...:.
'
-n".n-.n";- -i-i-.n-.i Heigh rn cn
..i-:-t'
li:: ..1....i...!...1. -l
iii:
!iti "i-.i--t".i' t:ii
-i" i -i-i
"i-i-l -l .1...1....1...i.
-r-i i-i "i-i"i i ...i...i-.i.-.i.-.
"|_ i- f"i'
"f-l "t-l' - t_1- f- l
..i.,,i...i..,i.
(a) copy and complete the frequency table for the data in the sample.
Height in cm Mid-point tr'requency
1-10 5.5 18
11 - 20 15.5 25
2t-30
31-40
41-50
( 3 marks)
(b) Determine
(i) the modal class interval
( lmark )
(ii) the number of seedlings in the sample
( 2 marks)
(iiD the mean height of the seedlings
( 4 marks)
that is GREATER
(iv) the probability that a seedling chosen at random has a height
-
than3o"-'' (2marks)
Total 12 marks
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o r23 4020 I JANUARY/F 20 I 2
9. !/
Page 9
8. An answer sheet is proyided for this question.
Sarah is making a pattern of squares using straws. She uses four straws for the sides and two
longer straws for the diagonals. The first three figures in her sequence of shapes are shown
below:
Figure 1 Figure 2 Figure 3
(a) On your answer sheet, draw Figure 4,the FOURTH shape in the pattern.
( 2 marks)
(b) On your answer sheet, complete the TWO rows in the table for
(D Figure 4
(ii) Figure 10.
Total Number of Straws
tr'igure Formula Number
1(6) - 0 6
2 2(6) - r 1l
J 3(6) - 2 16
(i) 4
tll
ttt
F------+ +---
ttt
ltt
I
(ii)
( 4 marks)
(c) Which figure in the sequence uses 106 straws? ( 2 marks)
(d) Obtain an expressi on in n, for the total number of straws used in the nth pattern.
( 2marks)
Total l0 marks
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0 t23 4020 I JANUARY/p 20 I 2
10. t
Page 10
SECTION II
Answer TWO questions in this section.
ALGEBRAAND RELATIONS, FUNCTIONS AND GRAPHS
9. (a) (D Make I the subject of the formula
2x +3
' ( 2 marks)
-r-4
(ii) 2x+3
Hence,determinetheinverseof f(x = x*4.
x-4' "
where
( 2 marks)
(iii) Find the value ofx for which/(:r) : 0. ( 2 marks)
(b) The diagram below shows the graphs of three lines and a shaded region defined by three
inequalities associated with these lines.
The inequality associated with the line 3y: * is 3y > _r.
lY'
iii
N x- ) ".'i-:'-i'
+i30
$
$
.i-.j-
:!5i
[H +;i ii!
J--;-rn
..i...;.... "iiFl
+,"-i-l
*..i_.i_.1
H,i:l
Fffi
w --i I
i+10 *E !n-FEEi.
F..i
N
-i-i-l
_
1"1" f-
i
:
t
i::i...i:
i;-*
ffi ffifi
fr Ilni-';'
>rfr
'.1...i .:.i.''.i, N
N40 -x
10 20 30
(D State the other TWO inequalities which define the shaded region.
( 2 marks)
The function p : 4x + 3y satisfies the solution set represented by the closed triangular
regron.
(ii) Identi$' the three pairs of (x, y) values for whichp has a maximum or a minimum
value. ( 3 marks)
(iii) Which pair of (x, y) values makesp a maximum? Justify your answer.
( 4 marks)
Total 15 marks
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0 123 4020 I JANUARY/p 20 1 2
11. t
Page 1l
MEASUREMENT, GEOMETRY AND TRIGONOMETRY
10. (a) The diagram below, not drawn to scale, shows a regular hexagon with centre, O, and
AO: 5 cm.
(i) Determine the size of angle AOB. ( 2 marks)
(iD Calculate, to the nearest whole number, the area of the hexagon.
( 3 marks)
(b) The diagram below, not drawn to scale, shows a vertical pole, PL, standing on
a hoizontal plane, KLM. The angle of elevation of P from K is 28", KL: 15 M,
LM:19mand ZKLM:115".
P
M
(D Copy the diagram. Show the angle of elevation ,28" and ONE right angle.
( 2 marks)
(iD Calculate, giving your answer to 2 significant figures, the measure of
a) PL ( 2 marks)
b) KM ( 3 marks)
c) the angle of elevation of P from M. ( 3 marks)
Total 15 marks
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O 123 4O2O / JANUARYIF 20 1 2
12. v
Page 12
11. (a) The diagram below shows two position vectors & una dg.
'i-i-i ir |y ij.
'i-' f' I i_
.'....i...+...i..
4
-i.--f-t--?-'
...t_..i....:.__!_.
-i-i A' ...!...i....:.,,i,. 'i-
F*1.
; ii ..i....i...i
:ii
;ll
i'
z
r
-!-:'i.'
i.,l-ir
ilii 'i-i-i- i..:...!...i..
! tt:
''': ; r
ri-i-i iij
'''i''." i:i
i-i O i...!....i t ....i .
3 .::| i".i 4 :.i ii6 ;:..1: x
f iii il
i
1...i....i...: i:.itii
t....i...1...:...i...
i i..:; il i
?--i- i-1
i" a---t-1
(i) Write as a column vector, ln tn" for- [t] .
Y)
a) dt ( lmark )
b) ota ( l mark )
c) 3A ( 2 marks) !
(iD Given that G is the mid-point of the line AB, write as a column vector in the
/x
forml l:
v)
a) ic (lmark)
b) ic (lmark)
(b) L and M are two matrices where
(t 2 (-t 3)
4) anaM:[o 2)
':['
Evaluate
(i) L+2M (2marks) I
(iD LM (2marks)
(+ 2)
(c) The matrix, Q, is such that O: t)
[l
(i) FindQ-1. (2marks)
(iD Using a matrix method, find the values of x andy in the equation
(+ 2 /x /s
( 3 marks)
[' ')l;: [,J
Total 15 marks
END OF'TEST
IF YOU FINISH BEFORE TIME IS CALLED, CHECK YOUR WORK ON THIS TEST.