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In addition, students use 3D design software to design and document solutions for major course projects. Students communicate and present solutions to their peers and member of a professional community of engineers and architects. This course provides opportunity for students in the hands-on practical use and performance of activities directed toward a general understanding and skill in a variety of printing occupations. Students gain skill in both technical and operational fundamentals, which include an overview of the offset printing industry, desktop publishing, electronic pre-press, platemaking, offset press operations, and bindery and finishing procedures in a modern computerized laboratory.
This course provides an opportunity for students to learn communication principles and concepts, technical information, and operational experiences necessary for desktop publishing and electronic pre-press to support the offset printing process. Prerequisite s : Printing and Graphic Communication I.
This course will give students the opportunity to perform advanced technical procedures and applied science as they relate to graphic communications. Students will have the opportunity to gain knowledge and skill in advanced desktop publishing, electronic pre-press, press operation, job estimating, paper selection, fundamentals of shop management, and employment preparation.
This capstone course will allow students to work in teams to design and develop an original solution to a valid open-ended technical problem by applying the engineering design process. Students perform research to choose, validate, and justify a technical problem. After carefully defining the problem, teams design, build, and test their solutions while working closely with industry professionals who provide mentoring opportunities. At the end of the course, student teams present and defend their original solution to an outside panel.
CT Licensed Cosmetology I. This course provides opportunity for students to acquire knowledge and skills in the care and beautification of the hair, complexion, and hands. Students acquire skill in shampoos, rinses, and scalp treatments; hair styling, setting, cutting, coloring, tinting, and lightening; permanent waving; giving facials; and manicuring.
This course provides opportunity for students to gain knowledge in bacteriology, anatomy, hygiene, sanitation, and customer relations, as well as advanced skills in hair design, cutting, and coloring. Students gain experience in basic shop operations, appointment setting, and processes and practices. They also have the opportunity to practice cosmetology on adult day care clients at no charge.
Prerequisite s : Licensed Cosmetology I. This course emphasizes preparation for the state board of cosmetology examination and completion of clock hours of instruction in theory and practical skills. Students gain skill in the operation of the school's cosmetology clinic and practice professional cosmetology on customers. They also can participate in the Career Research and Development Program. Successful completion of this course earns three credits.
Prerequisite s : Licensed Cosmetology II. This specialized course provides opportunities for students to develop the related knowledge and skills that are needed to provide care for clients in a variety of clinical settings. This includes, but is not limited to, infection control, safety, body mechanics, communication, and understanding human behavior. This course has two components. There is their first clinical experience at John Archer, working with students who have special needs. They are able to apply their concepts of human growth and development.
The students learn and demonstrate skills in a classroom lab which simulates the clinical setting. The nursing assistant students will perform skills in a patient care lab preparing them for their long term care clinical hours and their hospital internships. This course provides students with an opportunity to learn and use basic techniques and equipment to prepare food for commercial restaurant and retail distribution. Students gain experience and skill in following safety and sanitation procedures, using tools and equipment, measuring ingredients, following recipes, utilizing kitchen staples, preparing stocks and sauces, and demonstrating professionalism.
This course provides students with an opportunity to learn and practice commercial food preparation skills. Students utilize principles of nutrition, menu planning, cooking, and baking to prepare a variety of foods for customers of the "Thomas Run Inn. Prerequisite s : Food Preparation and Management I. They also have the opportunity to earn ServSafe Sanitation Management certification. Successful completion of this course earns four credits. This course provides opportunities for students to apply academic and practical knowledge in a variety of allied health settings based on their interests and career goals.
CT Health Occupations I. This introductory course provides a foundation for students interested in pursuing careers in a wide variety of allied health fields. Basic skills such as temperature, pulse, respiration, blood pressure and height and weight are learned.
Students are exposed to a variety of career opportunities in the health care field via speakers, classroom activities, and field trips. At the end of this course, students will choose to pursue the Nursing Assistant or Sports Technician tract. This one-year program provides a state certification in the area of fire, rescue, and emergency medical skills and techniques, and b a Career and Technology Education program completer status for registered students.
Individuals electing this program must register in the Career Research and Development Program and receive one credit for the first course. Upon completion of the program, students will receive four credits, and will be Career and Technology Education CTE program completers and receive articulated credits through the University of Maryland at College Park.
The program will encompass one full year of half days. This course will introduce students to Homeland Security and Emergency Preparedness guidelines, concepts, and action plans.
Emphasis will be placed on unique aspects of public safety and public health. The course will explore the various methodologies for intelligence gathering and dissemination and will introduce students to various local, state, and federal assets.
Students will prepare an action plan that includes initial notification, emergency response on and off scene , and recovery. Student work involves the study of human medicine, research processes and an introduction to bio-informatics. Students investigate the human body systems and various health conditions including heart disease, diabetes, sickle-cell disease, hypercholesterolemia, and infectious diseases.
A theme through the course is to determine the factors that led to the death of a fictional person. After determining the factors responsible for the death, the students investigate lifestyle choices and medical treatments that might have prolonged the person's life. Key biological concepts including: homeostasis, metabolism, inheritance of traits, feedback systems, and defense against disease are embedded in the curriculum.
Engineering principles including: the design process, feedback loops, fluid dynamics, and the relationship of structure to function are incorporated in the curriculum where appropriate. The course is designed to provide an overview of all the courses in the Biomedical Sciences program and to lay the scientific foundation necessary for student success in the subsequent courses.
This course will engage students in the study of basic human physiology, especially in relationship to human health. The human body is a complex system requiring care and maintenance. Students will use a variety of monitors to examine body systems respiratory, circulatory, and nervous at rest and under stress, and observe the interactions between the various body systems. Prerequisite s : Principles of Biomedical Science. This course includes interventions to support humans in treating disease and maintaining health.
Student projects will investigate various medical interventions that extend and improve quality of life, including gene therapy, pharmacology, surgery, prosthetics, rehabilitation, and supportive care. Students will study the design and development of various medical interventions including vascular stents, cochlear implants, and prosthetic limbs. They will review the history of organ transplants and gene therapy, and read current scientific literature to be aware of cutting edge developments.
Using 3-D imaging software and current scientific research, students will design and build a model of a therapeutic protein. Prerequisite s : Human Body Systems. This capstone course gives student teams the opportunity to work with a mentor, identify a science research topic, conduct research, write a scientific paper, and defend team conclusions and recommendations to a panel of outside reviewers.
Prerequisite s : Medical Interventions. This course will introduce students to Homeland Security and Emergency Preparedness threats to public safety and health, decontamination, protection, detection and identification, and planning concepts. Emphasis will be placed on the utilization of science to protect the public against chemical and biological threats.
The course will explore the various methodologies, capabilities and limitations for individual and collective protection, handheld and fixed detection, and field sampling and laboratory identification. Students will prepare a chemical and biological incident response plan as an end of course assessment. This course will focus on developing the student's scientific research, problem solving and writing skills. Emphasis will be placed on research and analysis, technical writing, team dynamics, and laboratory analysis and skills.
The course will actively engage the student in market survey techniques, technical publication layout and design, team building skills and role play, and proper implementation of laboratory instrumentation and equipment. Prerequisite s : Homeland Security Science. This class will introduce students to multiple aspects of criminal justice and law enforcement.
Students will explore the criminal process, various forces that impact law enforcement, and the rights of citizens. Students will understand the difference between juvenile and adult justice, and classifications of different crimes. This class will give students a general knowledge needed for students to enter various law enforcement careers at the federal, state, and local levels. Note: Students earning an "A" or "B" are eligible to receive credit through Harford Community College under the articulation agreement.
See your teacher for further information. This class will continue the student's knowledge of criminal justice and law enforcement. In this course students will be introduced to evidence collection, analysis, and forensic examination.
The role of law enforcement officials as a first responder will also be discussed as well as the duties of police officers. Students will also identify various careers in law enforcement. Prerequisite s : Administration of Justice l. Teachers and students will use a locally customized Geographic Information System GIS to learn about their local community.
They will use the same data, imagery and software that NASA uses to study their state, county and school campus. Students and teachers will follow a course of hands-on instruction to learn skills ranging from introductory digital mapping to image analysis. Follow-up applied practice application will direct the student to apply acquired skills to cases in the local community using the supplied data.
This repetition will set the stage for further student driven projects. In Course III, students will learn to apply those skills. Students will learn and apply Spatial Analyst and 3D Analyst. The ArcGIS Spatial Analyst extension allows students to examine the spatial relationships within a specific area as well as study site suitability. The ArGIS 3D Analyst extension allows students to gain a different perspective on their environment by modeling surfaces three dimensionally.
Students will also learn methods of integrating external hardware in order to incorporate real time data from GPS units in order to accurately survey their community.
In the beginning of this course, students will use the Project Management Model to discuss and build a campus-wide base map. Once finished with the base map, each student selects one of the campus-based projects to complete. Each of the "final" projects are designed to let the students put their Geospatial skills to use. Prerequisite s : S. Course I and ll. Students will have the option of completing an industry-mentored project, internship, or enrolling in a post-secondary course.
They will play an integral part in determining which type of experience will be most beneficial and supportive of their individual goals. At the end of the course, students will compile a working portfolio which documents their academic and technical skill attainment and present it for critique. Subject to administrative approval, students will enroll in approved post-secondary courses in lieu of completing a project or internship. Links between secondary and post-secondary institutions will be established to allow students to dual enroll in criminal justice or environmental technology-related courses, receiving both high school and college credit.
This course will begin researching careers and will take a variety of career and interest assessments. Students will begin to develop a portfolio demonstrating workplace and academic readiness.
Students will learn how to effectively plan for their future incorporating both employment, education and training goals, begin developing financial literacy skills, and integrate the Maryland's Skills for Success as they begin to manage their career choices and educational choices. This course involves students applying the knowledge gained in the first course to the practical experience of their work-based learning placement.
Students will continue building a career portfolio that demonstrates proficiencies in workplace readiness, personal financial management, personal growth and development, and employment experiences. Students will learn to plan effectively for their future incorporating employment, education and training goals, building financial literacy skills, and integrating the Maryland's Skills for Success as they begin to manage their career and educational choices.
Prerequisite s : Course I: Career Research and Development and concurrent enrollment in work-based learning experience. The Work-Based Learning Coordinator will coach and assist students as they secure employment based on the results from career research, interest inventories, and aptitude assessments taken in the Career Research and Development course and the Career Development, Preparation, and Transition.
This workplace component is mentored, on-the-job training enables students to receive the knowledge, skills, and appropriate attitudes needed to be successful in today's workplace. CT96W: Clinical Internship. The students have a clinical rotation in long-term care experience and obtain the required clinical hours qualifying them to obtain their Certified Nursing Assistant CNA and Geriatric Nursing Assistant GNA certification.
This course also includes a classroom component which continues the required theory for certification. In the classroom, students are further able to reinforce the concepts they have learned during their clinical experience.
Note: Students earning an "A" or "B" in this program are eligible to receive credit through Harford Community College under the articulation agreement. See your teacher or counselor for further information. This course is designed to help students acquire skills to prepare to take the ACT, SAT, or any college or career readiness assessment.
Students will have the opportunity to review basic English and mathematics skills through participating in content-specific lessons tailored to their instructional needs. Additionally, students will have the opportunity engage in real-time experiences that mirror the various college or career readiness assessments through a variety of learning platforms to practice acquired skills.
Upon successful completion, students will possess the tools and strategies necessary to complete any college or career readiness assessment to the best of their ability. Successful completion of this course earns one-half elective credit. Prerequisite s : Algebra I, Geometry, and English 10 are recommended. EL Mentors. EL Avid I. Advancement Via Individual Determination AVID is an academic elective course that prepares students for college readiness and success, and it is scheduled during the regular school day as a year-long course.
Each week, students receive instruction utilizing a rigorous college preparatory curriculum provided by AVID Center, tutor-facilitated study groups, strengthen metacognitive development, analytical reading and writing, communication skills, and academic success skills.
In AVID, students participate in activities that incorporate strategies focused on writing, inquiry, collaboration, organization and reading to support their academic growth. Students will increase awareness of their personal contributions to their learning, as well as their involvement in their school and community. Students will prepare for and participate in college entrance and placement exams, while refining study skills and test-taking, note-taking, and research techniques.
EL Avid II. This second sequence of Advancement Via Individual Determination AVID is an academic elective course that prepares students for college readiness and success, and it is scheduled during the regular school day as a year-long course.
In the tenth grade year, students will continue to refine their academic learning plans and goals, increasing awareness of their actions and behaviors, as well as develop an increased ability to self-monitor, self-regulate, and manage time. Students will expand their writing portfolio to include: analyzing prompts, supporting arguments and claims, character analysis and detailed reflections.
Lastly, students will narrow down their college and careers of interest, based on personal interests and goals. The course emphasizes rhetorical reading, analytical writing, collaborative discussion strategies, tutorial inquiry study groups, preparation for college entrance and placement exams, college study skills and test-taking strategies, note-taking and research. In addition to the academic focus of the AVID seminar, there are college-bound activities, methodologies and tasks that should be undertaken during the junior year to support students as they apply to four-year universities and confirm their postsecondary plans.
EL Avid IV. This fourth sequence of Advancement Via Individual Determination AVID is an academic elective course that prepares students for college readiness and success, and it is scheduled during the regular school day as a year-long course.
Students will expand their writing portfolio to include: an argumentative research paper on a social issue and detailed reflections. Lastly, students will prepare for college through the use of inquiry based collaborative study groups utilizing higher order thinking questioning techniques. EL Newspaper and Yearbook Editor. This course provides students with training in newspaper and yearbook publications through actual on-the-job production.
Topics covered include business management, public relations, photojournalism, and thematic copy. Students will have opportunities to learn and use advanced computer technology for the production of the yearbook.
EL Yearbook. This course provides students with training in yearbook publications through actual on-the-job production. Students will have the opportunity to learn and use advanced computer technology for the production of the yearbook.
Successful completion of this course earns one elective credit. The Bridge Plan for Academic Validation course will provide students with the strategies and support needed to complete the Bridge Plan for Academic Validation for English Students who have passed the English 10 course, and have not met the graduation assessment requirement as measured by PARCC English 10 may enroll in the course. Prerequisite s : Passed English 10 Course.
Prerequisite s : Passed Algebra I Course. This course follows the same structure as English I with some variation in course content to allow for an accelerated pace and an advanced study of appropriately complex text. Honors English I incorporates additional writing opportunities for students to refine and strengthen their writing skills to an advanced level. Students are expected to manage independent work, collaborate with others, and fully participate in student generated discussions and research.
Successful completion of this course earns one required English credit. EN English I blended. The ninth grade English curriculum is the beginning of a four-year sequential program. Ninth grade students will read a variety of texts arranged thematically and write in a variety of forms including argument, informational, and narrative. Language and speaking and listening skills are integrated in both reading and writing.
EN English I. This course is the beginning of a four-year sequential program. This course follows the same structure as English II with some variation in course content to allow for an accelerated pace and an advanced study of appropriately complex text. Students will engage in an in-depth analysis of texts. Focus is given to writing that aligns to future English Advanced Placement courses. Prerequisite s : English I.
EN English II. This course will further assist students in developing a global awareness. Tenth grade students will build upon the integration of reading, writing, speaking and listening while strengthening language usage.
Prerequisite s : English l. EN English II blended. Building on the fundamental concepts taught in ninth grade, the tenth grade English curriculum will further assist students in developing a global awareness. This course will continue to develop techniques of discussion and written expression through critical reading of American writers with emphasis on an analysis of the interrelationships of culture and literature.
Students will write with sophistication in a variety of forms. Students will demonstrate their college and career readiness by independently showing increased proficiency in reading, writing, listening, and speaking. Prerequisite s : English II. Eleventh grade students will continue to develop techniques of discussion and written expression through critical reading of American writers with emphasis on an analysis of the interrelationships of culture and literature.
This course is the culmination of the students' study of language, literature, and writing in high school. The thematic curriculum uses works of British literature to refine skills in critical reading, literary analysis, and written expression. Students will participate in civil, democratic discussions around topics related to their reading and writing.
Prerequisite s : English III. The twelfth grade English curriculum is the culmination of the students' study of language, literature, and writing in high school. This college level course is designed for juniors.
Rigorous training in college-level composition skills and literary analysis is provided. The literature will also be used as the foundation for instruction and practice in various types of exposition and systematic instruction in college-level grammar and usage. This college level course focuses Mathematics 10th Class Ncert Book Question on selected classic and modern novels, poetry, and general non-fiction. It is designed for seniors who have ability in and motivation toward the study of literature. This course provides rigorous training in literary analysis.
Students will discuss and assess literary qualities and ideas, trends, and techniques. Types of exposition will be reviewed and practiced.
EN Journalism I. This course provides the student with an opportunity to learn and apply the principles of writing for publications. In addition to news writing, students study production techniques and management, public relations, typography, lay-out formats, and photographic concepts.
Students will be introduced to the technology of publication. EN Journalism II. This course expands the knowledge of journalistic principles and techniques developed in Journalism I. Students in this course assist in publishing the school newspaper each month and in preparing weekly press releases to local media.
Students will continue in their development of technological skills in publication. This course enables students to assist in the publishing of the school newspaper. They will also learn to interview both adults and students, to contact the public to meet deadlines, and to work cooperatively. Students will make use of and develop expertise in the technology of publication through the use of advanced computer technology for the production of the newspaper.
EN Speech Communications. This course helps give students the skills 10th Class Mathematics All Formulas Mac needed to be successful communicators in the many different personal, social, and professional situations they may experience in life.
The first half of the course concentrates on oral communication, physical communication, and listening skills in intrapersonal, interpersonal, and group discussions. The second half of the course concentrates on public speaking. Instruction emphasizes research and organization of information, awareness of audience, personal poise, language style, and critique.
EN Creative Writing I. This course offers practice and guidance in creative writing and evaluation of the student's work. Students practice a wide variety of written forms. Journals of thoughts and observations are kept throughout the year. As expertise increases, students plan, produce, and revise their own writing projects.
Students may be involved in the production and layout of the school literary magazine. This course offers an opportunity for further development of the student's work. Students experiment with an advanced variety of forms, styles, and techniques. Students will develop individualized methods of generating, recording, and assessing writing ideas and resources.
Students will be responsible for maintaining a writers' community and pursuing professional development endeavors. Students will work independently to plan, produce, revise, and publish their own writing projects and pursue professional publication. Prerequisite s : Creative Writing I. This course expands the knowledge of writing skills and techniques developed in Creative Writing II.
Prerequisite s : Creative Writing II. EN Humanities. This course encompasses art, music, theatre, literature, and philosophy. Each area receives emphasis as a separate discipline, but interrelationships between disciplines are explored throughout the course.
A creative project by each student is among the requirements for this course. EN Women In Perspective. This course focuses on women in literature. Through the study of literature, students will examine and discuss such topics as the origin of sexual stereotypes, changing roles of women in society, and different cultural expectations of women. This course will provide an in-depth study of literature and will require application, analysis, synthesis and evaluation by the student. EN Strategic Reading I.
This course is recommended for students who have not reached proficiency on school, county, and state assessments. Strategic Reading aims to give students reading two to four years below grade level an opportunity to accelerate their reading in an age-appropriate, motivational, and innovative program. Prerequisite s : Criteria-based Recommendation. This course is a continuation of Strategic Reading I and is recommended for students reading two to four years below grade level.
This course is designed to prepare students for the introductory year of college English and for the writing demands of the workplace. Writing, reading, critical thinking, and discussion are the key components of the class that focuses on rhetorical analysis. Contemporary fiction and non-fiction selections will provide the springboard for discussions and originals essays in a variety of rhetorical modes.
EN Film Criticism. This course is a writing-intensive, English elective that examines American films in a manner similar to the way literature is examined in traditional English classes. The analytical techniques used to study novels, plays, poetry and other literature are applied in this class when viewing, discussing and writing about films utilizing the same principles found in traditional, literature-based classes.
This course will expose students to the genres, motifs, techniques and influential leaders in the American filmmaking experience. Students will be expected to screen films and apply learned theories to them through several full-process writings and productions.
EN Read This course is an intensive reading intervention program designed to meet the needs of students whose reading achievement is below the proficient level. SE Corrective Reading I.
This course is the first year of a two-year research-based reading intervention course designed to accelerate reading proficiency with explicit, sequential, and systematic instruction through the use of direct instruction. The course is intended to support students reading four or more years below grade level. This course is the second year of a two-year research-based reading intervention course designed to accelerate reading proficiency with explicit, sequential, and systematic instruction through the use of direct instruction.
Prerequisite s : Corrective Reading I. AR Art Appreciation. AR Fine Art Preparation. This course is a basic foundation course that allows for exploration of historical and cultural art trends, as well as skill development in drawing, painting, three-dimensional design, and visual communications. The art elements and principles of design are applied to compositions and processes involving a variety of media.
Upon completion of this course, the student should demonstrate competency in handling drawing, painting, and sculptural media and be prepared for further study in upper level art courses. Home assignments and a sketchbook are required. Successful completion of this course earns one required Fine Arts credit. AR Crafts. This course focuses on the study of the applied arts, artistic objects with functional Algebra Math 10th Class C purposes. This includes, but is not limited to, ceramics, stained glass, mosaics, jewelry, fiber arts, batik, bookmaking, and metal works.
The evolution of crafts is explored historically and culturally. Prerequisite s : Fine Art Preparation. AR Drawing And Painting. This course focuses on the practices and applications of basic drawing and painting principles and techniques. Various media and composition applications will be explored in studio assignments. Upon completion of this course, the student should demonstrate proficiency with different media and in the utilization of the principles of design in compositions.
Successful completion of this course earns one Fine Arts credit. AR Advanced Drawing. This course provides an in-depth concentration and application of drawing processes and composition problems. Exploring creative problem solving and developing personal imagery are approached through mastery of drawing media, techniques, and assignments.
Home assignments, a sketchbook, and some additional materials may be required. Prerequisite s : Drawing and Painting. AR Advanced Painting. This course provides an in-depth concentration and application of painting processes and composition problems. Exploring creative problem solving, color theory, and developing personal imagery are approached through mastery of painting media, techniques, and assignments.
AR Photography. This course provides instruction in the utilization of photography as a means of communication and expression. The historical and cultural context of photography is also explored. Camera use, darkroom procedures and technology, picture selection, and composition are emphasized. If this course is offered in a dark room setting, students should have use of a 35 mm camera and will be required to pay for film and developing expenses.
If offered as a digital course, students should have access to a digital camera and will be required to pay for printing expenses. Note: Students who successfully complete this course in a traditional darkroom experience may earn articulated credit at HCC. Not all schools offer the traditional darkroom experience. See your Art teacher for further information.
AR Advanced Studio Drawing. This course is designed for the advanced art student who is capable of an intense individualized program of instruction. Students will be using problem solving processes in response to various conceptual and creative challenges.
Development of a portfolio based on the evaluation of personal work and career exploration will be included in the program of instruction.
Media may include, but not be limited to, graphite, charcoal, ink, conte, pastel, marker, and dry point. Prerequisite s : Advanced Drawing. AR Advanced Studio Painting.
Media may include, but not be limited to, tempera, acrylic, watercolor, pastel, ink, oil paint, and gouache. Prerequisite s : Advanced Painting. This course provides an in-depth concentration and application of sculpture processes and composition problems.
Exploring creative problem solving and developing personal imagery are approached through mastery of sculpture media, techniques, and assignments. Prerequisite s : Advanced Three-Dimensional Design. Students will be using the problem solving processes in response to various conceptual and creative challenges. Media may include, but not limited to, graphite, charcoal, ink, conte, pastel, marker, watercolor, acrylic, oil paints, computer editing, paint or digital manipulation software.
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Perez, and Nicanor M. San Gabriel Jr. Introduction This material is written in support of the K to 12 Basic Education Program to ensure attainment of standards expected of students. In the design of this Grade 10 materials, it underwent different processes - development by writers composed of classroom teachers, school heads, supervisors, specialists from the Department and other institutions; validation by experts, academicians, and practitioners; revision; content review and language editing by members of Quality Circle Reviewers; and finalization with the guidance of the consultants.
There are eight 8 modules in this material. Module 1 � Sequences Module 2 � Polynomials and Polynomial Equations Module 3 � Polynomial Functions Module 4 � Circles Module 5 � Plane Coordinate Geometry Module 6 � Permutations and Combinations Module 7 � Probability of Compound Events Module 8 � Measures of Position With the different activities provided in every module, may you find this material engaging and challenging as it develops your critical-thinking and problem-solving skills.
Table of Contents Unit 1 Module 1: Sequences Module 2: Polynomials and Polynomial Equations After 10 minutes, there were already 15 who had signed up. After 10 more minutes, there were 20, then 25, 30, and so on. The above scenario illustrates a sequence. In this learning module, you will know more about sequences, and how the concept of a sequence is utilized in our daily lives. Choose the letter of the best answer. Take note of the items that you were not able to answer correctly and find the right answer as you go through this module.
Find the common difference in the arithmetic sequence 13 7 15 3, , , , Which set of numbers is an example of a harmonic sequence? What is the sum of all the odd integers between 8 and 26? If three arithmetic means are inserted between 11 and 39, find the second arithmetic mean. If three geometric means are inserted between 1 and , find the third geometric mean. What is the next term in the harmonic sequence 1 1 1 1 , , , ,? What is the 6th term of the geometric sequence 2 2 , , 2, 10,?
The first term of an arithmetic sequence is 2 while the 18th term is Find the common difference of the sequence. What is the next term in the Fibonacci sequence 1, 1, 2, 3, 5, 8,?
Find the sum of the geometric sequence where the first term is 3, the last term is 46 , and the common ratio is 5. Find the eighth term of a geometric sequence where the third term is 27 and the common ratio is 3. Which of the following is the sum of all the multiples of 3 from 15 to 48?
What is the 7th term of the sequence whose nth term is 2 2 1? What is the nth term of the arithmetic sequence 7, 9, 11, 13, 15, 17,. What is the nth term of the harmonic sequence 1 1 1 1 , , , ,? Find p so that the numbers 7 2, 5 12, 2 1, What is the sum of the infinite geometric series 3 9 27 ?
Glenn bought a car for Php, What is its value after 4 years? Php, B. Php, C. Php, D. Php, During a free-fall, a skydiver jumps 16 feet, 48 feet, and 80 feet on the first, second, and third fall, respectively. If he continues to jump at this rate, how many feet will he have jumped during the tenth fall? On the first day, he sent one red rose, on the second day, two red roses, and so on.
How many roses did Nicole receive during the tenth day? A new square is formed by joining the midpoints of the consecutive sides of a square 8 inches on a side.
If the process is continued until there are already six squares, find the sum of the areas of all squares in square inches. One stormy day, the principal announces the suspension of classes to two teachers, each of whom sends this message to two other teachers, and so on. Hold on to HOPE Because of the super typhoon Yolanda, there was a big need for blood donors, medicines, doctors, nurses, medical aides, or any form of medical assistance. The Red Cross planned to involve different agencies, organizations, and offices, public and private, local and international, in their project to have massive medical services.
The Red Cross contacted first three of the biggest networks, and each of these networks contacted three other networks, and agencies, organizations, and offices, and so on, until enough of these were contacted.
It took one hour for an organization to contact three other organizations and all the contacts made were completed within 4 hours.
Assume that no group was contacted twice. Suppose you are one of the people in the Red Cross who visualized this project.
How many organizations do you think were contacted in the last round? How many organizations were contacted within 4 hours? Make a table to represent the number of organizations, agencies, and offices who could have been contacted in each round. Write an equation to represent the situation.
Let the independent variable be the number of rounds and the dependent variable be the number of organizations, agencies, and offices that were contacted in that round. If another hour was used to contact more organizations, how many additional organizations, agencies, and offices could be contacted?
Use the given information in the above situation to formulate problems involving these concepts. Write the necessary equations that describe the situations or problems that you formulated. Solve the problems that you formulated. Recognizing and extending patterns are important skills needed for learning concepts related to an arithmetic sequence. Each item below shows a pattern. Answer the given questions. What is the next shape?
What is the next number? What is the 10th number? What is the 8th number? What is the 12th number? What is the 7th number? Were you able to find patterns and get the next number in the sequence? Let us now give the formal definition of a sequence. What is a sequence? We may use the notation 1 2 3, , , In Grade 10, we often encounter sequences that form a pattern such as that found in the sequence below. Example: 1 2 3 A general term or nth term will be given to you and you will be asked to give the next few terms.
You will also be asked to give the nth term or the rule for a particular sequence. You may now start with Activity 2. Find the first 5 terms of the sequence given the nth term.
Did you find it easy to give the first 5 terms of each sequence? In Activity 3, you will be given the terms of a sequence and you will be asked to find its nth term. You may now do Activity 3. What is the nth term for each sequence below? Knowing all these will enable you to easily understand a particular sequence. This sequence will be discussed after doing the following activity.
Activity 3: Activity 2: Form a group of 3 students. Below are squares formed by matchsticks. Count the number of matchsticks in each figure and record the results in a table. Is there a pattern in the number of matchsticks?
If there is, describe it. How is each term number of matchsticks found? What is the difference between any two consecutive terms? How was the activity? What new thing did you learn from the activity? The above activity illustrates a sequence where the difference between any two consecutive terms is a constant. This constant is called the common difference and the said sequence is called an arithmetic sequence.
An arithmetic sequence is a sequence where every term after the first is obtained by adding a constant called the common difference. The sequences 1, 4, 7, 10, Is the meaning of arithmetic sequence clear to you? Are you ready to learn more about arithmetic sequences?
If so, then you have to perform the next activity. Activity 4: With your groupmates, take a look at the completed table below. We see that the number of matchsticks forms an arithmetic sequence. Suppose we want to find the 20th, 50th, and th terms of the sequence. How do we get them? Do you think a formula would help? If so, we could find a formula for the nth term of the sequence. In this case, it will not be difficult since we know the common difference of the sequence.
Let us take the first four terms. Consider the table below and complete it. Observe how each term is rewritten. How else can we write the terms? Study the next table and complete it. What is 5? What is the formula for determining the number of matchsticks needed to form n squares? The rule for finding the nth term of an arithmetic sequence is very useful in solving problems involving arithmetic sequence.
Find the missing terms in each arithmetic sequence. Find three terms between 2 and 34 of an arithmetic sequence. Were you able to get the missing terms in each sequence in Part A? Were you able to get the 3 terms in Part B? Let us discuss a systematic way of finding missing terms of an arithmetic sequence.
Finding a certain number of terms between two given terms of an arithmetic sequence is a common task in studying arithmetic sequences.
The terms between any two nonconsecutive terms of an arithmetic sequence are known as arithmetic means. Activity 6: Solution: Since we are required to insert 4 terms, then there will be 6 terms in all.
Substituting the given values for 6a and 1a , we obtain 25 5 5. At this point, you know already some essential things about arithmetic sequence. Now, we will learn how to find the sum of the first n terms of an arithmetic sequence.
Do Activity 7. What is the sum of the terms of each finite sequence below? A famous story tells that this was the problem given by an elementary school teacher to a famous mathematician to keep him busy. Do you know that he was able to get the sum within seconds only? Can you beat that? His name was Karl Friedrich Gauss The day of the test arrived and a few questions that I did not recognize were on the exam.
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