- The document appears to be a practice test containing multiple choice questions in Thai. It includes 4 parts with a total of 100 questions.
- Part 1 has 20 questions on expression with choices for completing blanks in 4 short conversations. Part 2 has 25 questions testing structure with choices for completing blanks in sentences.
- Parts 3 and 4 continue testing additional grammar and vocabulary points through multiple choice questions with conversations and passages to read. The document provides the questions and answer choices but not the answers.
- The document appears to be a practice test containing multiple choice questions in Thai. It includes 4 parts with a total of 100 questions.
- Part 1 has 20 questions on expression with choices for completing blanks in 4 short conversations. Part 2 has 25 questions testing structure with choices for completing blanks in sentences.
- Parts 3 and 4 continue testing additional grammar and vocabulary points through multiple choice questions with conversations and passages to read. The document provides the questions and answer choices but not the answers.
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
Creative operations teams expect increased AI use in 2024. Currently, over half of tasks are not AI-enabled, but this is expected to decrease in the coming year. ChatGPT is the most popular AI tool currently. Business leaders are more actively exploring AI benefits than individual contributors. Most respondents do not believe AI will impact workforce size in 2024. However, some inhibitions still exist around AI accuracy and lack of understanding. Creatives primarily want to use AI to save time on mundane tasks and boost productivity.
Organizational culture includes values, norms, systems, symbols, language, assumptions, beliefs, and habits that influence employee behaviors and how people interpret those behaviors. It is important because culture can help or hinder a company's success. Some key aspects of Netflix's culture that help it achieve results include hiring smartly so every position has stars, focusing on attitude over just aptitude, and having a strict policy against peacocks, whiners, and jerks.
PEPSICO Presentation to CAGNY Conference Feb 2024Neil Kimberley
PepsiCo provided a safe harbor statement noting that any forward-looking statements are based on currently available information and are subject to risks and uncertainties. It also provided information on non-GAAP measures and directing readers to its website for disclosure and reconciliation. The document then discussed PepsiCo's business overview, including that it is a global beverage and convenient food company with iconic brands, $91 billion in net revenue in 2023, and nearly $14 billion in core operating profit. It operates through a divisional structure with a focus on local consumers.
Content Methodology: A Best Practices Report (Webinar)contently
This document provides an overview of content methodology best practices. It defines content methodology as establishing objectives, KPIs, and a culture of continuous learning and iteration. An effective methodology focuses on connecting with audiences, creating optimal content, and optimizing processes. It also discusses why a methodology is needed due to the competitive landscape, proliferation of channels, and opportunities for improvement. Components of an effective methodology include defining objectives and KPIs, audience analysis, identifying opportunities, and evaluating resources. The document concludes with recommendations around creating a content plan, testing and optimizing content over 90 days.
How to Prepare For a Successful Job Search for 2024Albert Qian
The document provides guidance on preparing a job search for 2024. It discusses the state of the job market, focusing on growth in AI and healthcare but also continued layoffs. It recommends figuring out what you want to do by researching interests and skills, then conducting informational interviews. The job search should involve building a personal brand on LinkedIn, actively applying to jobs, tailoring resumes and interviews, maintaining job hunting as a habit, and continuing self-improvement. Once hired, the document advises setting new goals and keeping skills and networking active in case of future opportunities.
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
The document provides career advice for getting into the tech field, including:
- Doing projects and internships in college to build a portfolio.
- Learning about different roles and technologies through industry research.
- Contributing to open source projects to build experience and network.
- Developing a personal brand through a website and social media presence.
- Networking through events, communities, and finding a mentor.
- Practicing interviews through mock interviews and whiteboarding coding questions.
Google's Just Not That Into You: Understanding Core Updates & Search IntentLily Ray
1. Core updates from Google periodically change how its algorithms assess and rank websites and pages. This can impact rankings through shifts in user intent, site quality issues being caught up to, world events influencing queries, and overhauls to search like the E-A-T framework.
2. There are many possible user intents beyond just transactional, navigational and informational. Identifying intent shifts is important during core updates. Sites may need to optimize for new intents through different content types and sections.
3. Responding effectively to core updates requires analyzing "before and after" data to understand changes, identifying new intents or page types, and ensuring content matches appropriate intents across video, images, knowledge graphs and more.
A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
2024 State of Marketing Report – by HubspotMarius Sescu
https://www.hubspot.com/state-of-marketing
· Scaling relationships and proving ROI
· Social media is the place for search, sales, and service
· Authentic influencer partnerships fuel brand growth
· The strongest connections happen via call, click, chat, and camera.
· Time saved with AI leads to more creative work
· Seeking: A single source of truth
· TLDR; Get on social, try AI, and align your systems.
· More human marketing, powered by robots
ChatGPT is a revolutionary addition to the world since its introduction in 2022. A big shift in the sector of information gathering and processing happened because of this chatbot. What is the story of ChatGPT? How is the bot responding to prompts and generating contents? Swipe through these slides prepared by Expeed Software, a web development company regarding the development and technical intricacies of ChatGPT!
Product Design Trends in 2024 | Teenage EngineeringsPixeldarts
The realm of product design is a constantly changing environment where technology and style intersect. Every year introduces fresh challenges and exciting trends that mold the future of this captivating art form. In this piece, we delve into the significant trends set to influence the look and functionality of product design in the year 2024.
How Race, Age and Gender Shape Attitudes Towards Mental HealthThinkNow
Mental health has been in the news quite a bit lately. Dozens of U.S. states are currently suing Meta for contributing to the youth mental health crisis by inserting addictive features into their products, while the U.S. Surgeon General is touring the nation to bring awareness to the growing epidemic of loneliness and isolation. The country has endured periods of low national morale, such as in the 1970s when high inflation and the energy crisis worsened public sentiment following the Vietnam War. The current mood, however, feels different. Gallup recently reported that national mental health is at an all-time low, with few bright spots to lift spirits.
To better understand how Americans are feeling and their attitudes towards mental health in general, ThinkNow conducted a nationally representative quantitative survey of 1,500 respondents and found some interesting differences among ethnic, age and gender groups.
Technology
For example, 52% agree that technology and social media have a negative impact on mental health, but when broken out by race, 61% of Whites felt technology had a negative effect, and only 48% of Hispanics thought it did.
While technology has helped us keep in touch with friends and family in faraway places, it appears to have degraded our ability to connect in person. Staying connected online is a double-edged sword since the same news feed that brings us pictures of the grandkids and fluffy kittens also feeds us news about the wars in Israel and Ukraine, the dysfunction in Washington, the latest mass shooting and the climate crisis.
Hispanics may have a built-in defense against the isolation technology breeds, owing to their large, multigenerational households, strong social support systems, and tendency to use social media to stay connected with relatives abroad.
Age and Gender
When asked how individuals rate their mental health, men rate it higher than women by 11 percentage points, and Baby Boomers rank it highest at 83%, saying it’s good or excellent vs. 57% of Gen Z saying the same.
Gen Z spends the most amount of time on social media, so the notion that social media negatively affects mental health appears to be correlated. Unfortunately, Gen Z is also the generation that’s least comfortable discussing mental health concerns with healthcare professionals. Only 40% of them state they’re comfortable discussing their issues with a professional compared to 60% of Millennials and 65% of Boomers.
Race Affects Attitudes
As seen in previous research conducted by ThinkNow, Asian Americans lag other groups when it comes to awareness of mental health issues. Twenty-four percent of Asian Americans believe that having a mental health issue is a sign of weakness compared to the 16% average for all groups. Asians are also considerably less likely to be aware of mental health services in their communities (42% vs. 55%) and most likely to seek out information on social media (51% vs. 35%).
AI Trends in Creative Operations 2024 by Artwork Flow.pdfmarketingartwork
Creative operations teams expect increased AI use in 2024. Currently, over half of tasks are not AI-enabled, but this is expected to decrease in the coming year. ChatGPT is the most popular AI tool currently. Business leaders are more actively exploring AI benefits than individual contributors. Most respondents do not believe AI will impact workforce size in 2024. However, some inhibitions still exist around AI accuracy and lack of understanding. Creatives primarily want to use AI to save time on mundane tasks and boost productivity.
Organizational culture includes values, norms, systems, symbols, language, assumptions, beliefs, and habits that influence employee behaviors and how people interpret those behaviors. It is important because culture can help or hinder a company's success. Some key aspects of Netflix's culture that help it achieve results include hiring smartly so every position has stars, focusing on attitude over just aptitude, and having a strict policy against peacocks, whiners, and jerks.
PEPSICO Presentation to CAGNY Conference Feb 2024Neil Kimberley
PepsiCo provided a safe harbor statement noting that any forward-looking statements are based on currently available information and are subject to risks and uncertainties. It also provided information on non-GAAP measures and directing readers to its website for disclosure and reconciliation. The document then discussed PepsiCo's business overview, including that it is a global beverage and convenient food company with iconic brands, $91 billion in net revenue in 2023, and nearly $14 billion in core operating profit. It operates through a divisional structure with a focus on local consumers.
Content Methodology: A Best Practices Report (Webinar)contently
This document provides an overview of content methodology best practices. It defines content methodology as establishing objectives, KPIs, and a culture of continuous learning and iteration. An effective methodology focuses on connecting with audiences, creating optimal content, and optimizing processes. It also discusses why a methodology is needed due to the competitive landscape, proliferation of channels, and opportunities for improvement. Components of an effective methodology include defining objectives and KPIs, audience analysis, identifying opportunities, and evaluating resources. The document concludes with recommendations around creating a content plan, testing and optimizing content over 90 days.
How to Prepare For a Successful Job Search for 2024Albert Qian
The document provides guidance on preparing a job search for 2024. It discusses the state of the job market, focusing on growth in AI and healthcare but also continued layoffs. It recommends figuring out what you want to do by researching interests and skills, then conducting informational interviews. The job search should involve building a personal brand on LinkedIn, actively applying to jobs, tailoring resumes and interviews, maintaining job hunting as a habit, and continuing self-improvement. Once hired, the document advises setting new goals and keeping skills and networking active in case of future opportunities.
A report by thenetworkone and Kurio.
The contributing experts and agencies are (in an alphabetical order): Sylwia Rytel, Social Media Supervisor, 180heartbeats + JUNG v MATT (PL), Sharlene Jenner, Vice President - Director of Engagement Strategy, Abelson Taylor (USA), Alex Casanovas, Digital Director, Atrevia (ES), Dora Beilin, Senior Social Strategist, Barrett Hoffher (USA), Min Seo, Campaign Director, Brand New Agency (KR), Deshé M. Gully, Associate Strategist, Day One Agency (USA), Francesca Trevisan, Strategist, Different (IT), Trevor Crossman, CX and Digital Transformation Director; Olivia Hussey, Strategic Planner; Simi Srinarula, Social Media Manager, The Hallway (AUS), James Hebbert, Managing Director, Hylink (CN / UK), Mundy Álvarez, Planning Director; Pedro Rojas, Social Media Manager; Pancho González, CCO, Inbrax (CH), Oana Oprea, Head of Digital Planning, Jam Session Agency (RO), Amy Bottrill, Social Account Director, Launch (UK), Gaby Arriaga, Founder, Leonardo1452 (MX), Shantesh S Row, Creative Director, Liwa (UAE), Rajesh Mehta, Chief Strategy Officer; Dhruv Gaur, Digital Planning Lead; Leonie Mergulhao, Account Supervisor - Social Media & PR, Medulla (IN), Aurelija Plioplytė, Head of Digital & Social, Not Perfect (LI), Daiana Khaidargaliyeva, Account Manager, Osaka Labs (UK / USA), Stefanie Söhnchen, Vice President Digital, PIABO Communications (DE), Elisabeth Winiartati, Managing Consultant, Head of Global Integrated Communications; Lydia Aprina, Account Manager, Integrated Marketing and Communications; Nita Prabowo, Account Manager, Integrated Marketing and Communications; Okhi, Web Developer, PNTR Group (ID), Kei Obusan, Insights Director; Daffi Ranandi, Insights Manager, Radarr (SG), Gautam Reghunath, Co-founder & CEO, Talented (IN), Donagh Humphreys, Head of Social and Digital Innovation, THINKHOUSE (IRE), Sarah Yim, Strategy Director, Zulu Alpha Kilo (CA).
Trends In Paid Search: Navigating The Digital Landscape In 2024Search Engine Journal
The search marketing landscape is evolving rapidly with new technologies, and professionals, like you, rely on innovative paid search strategies to meet changing demands.
It’s important that you’re ready to implement new strategies in 2024.
Check this out and learn the top trends in paid search advertising that are expected to gain traction, so you can drive higher ROI more efficiently in 2024.
You’ll learn:
- The latest trends in AI and automation, and what this means for an evolving paid search ecosystem.
- New developments in privacy and data regulation.
- Emerging ad formats that are expected to make an impact next year.
Watch Sreekant Lanka from iQuanti and Irina Klein from OneMain Financial as they dive into the future of paid search and explore the trends, strategies, and technologies that will shape the search marketing landscape.
If you’re looking to assess your paid search strategy and design an industry-aligned plan for 2024, then this webinar is for you.
5 Public speaking tips from TED - Visualized summarySpeakerHub
From their humble beginnings in 1984, TED has grown into the world’s most powerful amplifier for speakers and thought-leaders to share their ideas. They have over 2,400 filmed talks (not including the 30,000+ TEDx videos) freely available online, and have hosted over 17,500 events around the world.
With over one billion views in a year, it’s no wonder that so many speakers are looking to TED for ideas on how to share their message more effectively.
The article “5 Public-Speaking Tips TED Gives Its Speakers”, by Carmine Gallo for Forbes, gives speakers five practical ways to connect with their audience, and effectively share their ideas on stage.
Whether you are gearing up to get on a TED stage yourself, or just want to master the skills that so many of their speakers possess, these tips and quotes from Chris Anderson, the TED Talks Curator, will encourage you to make the most impactful impression on your audience.
See the full article and more summaries like this on SpeakerHub here: https://speakerhub.com/blog/5-presentation-tips-ted-gives-its-speakers
See the original article on Forbes here:
http://www.forbes.com/forbes/welcome/?toURL=http://www.forbes.com/sites/carminegallo/2016/05/06/5-public-speaking-tips-ted-gives-its-speakers/&refURL=&referrer=#5c07a8221d9b
ChatGPT and the Future of Work - Clark Boyd Clark Boyd
Everyone is in agreement that ChatGPT (and other generative AI tools) will shape the future of work. Yet there is little consensus on exactly how, when, and to what extent this technology will change our world.
Businesses that extract maximum value from ChatGPT will use it as a collaborative tool for everything from brainstorming to technical maintenance.
For individuals, now is the time to pinpoint the skills the future professional will need to thrive in the AI age.
Check out this presentation to understand what ChatGPT is, how it will shape the future of work, and how you can prepare to take advantage.
The document provides career advice for getting into the tech field, including:
- Doing projects and internships in college to build a portfolio.
- Learning about different roles and technologies through industry research.
- Contributing to open source projects to build experience and network.
- Developing a personal brand through a website and social media presence.
- Networking through events, communities, and finding a mentor.
- Practicing interviews through mock interviews and whiteboarding coding questions.
Google's Just Not That Into You: Understanding Core Updates & Search IntentLily Ray
1. Core updates from Google periodically change how its algorithms assess and rank websites and pages. This can impact rankings through shifts in user intent, site quality issues being caught up to, world events influencing queries, and overhauls to search like the E-A-T framework.
2. There are many possible user intents beyond just transactional, navigational and informational. Identifying intent shifts is important during core updates. Sites may need to optimize for new intents through different content types and sections.
3. Responding effectively to core updates requires analyzing "before and after" data to understand changes, identifying new intents or page types, and ensuring content matches appropriate intents across video, images, knowledge graphs and more.
A brief introduction to DataScience with explaining of the concepts, algorithms, machine learning, supervised and unsupervised learning, clustering, statistics, data preprocessing, real-world applications etc.
It's part of a Data Science Corner Campaign where I will be discussing the fundamentals of DataScience, AIML, Statistics etc.
Time Management & Productivity - Best PracticesVit Horky
Here's my presentation on by proven best practices how to manage your work time effectively and how to improve your productivity. It includes practical tips and how to use tools such as Slack, Google Apps, Hubspot, Google Calendar, Gmail and others.
The six step guide to practical project managementMindGenius
The six step guide to practical project management
If you think managing projects is too difficult, think again.
We’ve stripped back project management processes to the
basics – to make it quicker and easier, without sacrificing
the vital ingredients for success.
“If you’re looking for some real-world guidance, then The Six Step Guide to Practical Project Management will help.”
Dr Andrew Makar, Tactical Project Management
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ft ufi oil:nnror.fi t fidrn?1ruo3.,:riJuoir
utnsdlnuer (t) : { -!-
-
[o rfi o:J:vvrorf t fidro?'rru03.: uflurfio
rYr f(p) .f(q) = 0 Ltns f(r) + f(p) = 2 rrd'r
o.tn'tritto.: f(p -) r) + f(q
-) s) * f(r)
h rfiox(o
I
4. rirHuotri'f(x) :1" rfioo<x(1 unyg(x) =*2+1
l^2 rfiax)1
L
ri'"r n: .f o g ud'r o.ln't h(3)
2, td' A - {0, 1, 2,... ..., 99}
B - {too, 101 , 102 .., tss}
rirHuqtd' A.B - {"ola € A rny o
=
a}
o.:urdlu?unrutfinr 0.,: rssr A. B
3. td' p(x)
- x5 + gx4 * 2x3 * ox2 - 2x- 6
LLns x + 3 rilusiril;ynoufid.:oot p(x)
oi.,rriurirqr oufi riludruruo?{?J a{ niln1r p(x) = 0 fr frtru?t*
o. d'r zk: dk +bki tilu:rnfd 6 to.t G4u#r o.rn'r
EFnl
la ufr g eu a a ut#intuer m ru i
s. x. , = []
t.l
u* s2 +ge-1 - ["" "'f udr oru.reilr'{ a12
[o -t] l.r, ^zz )
3. a'/ A dA aJ
?%o1r1nun 21 6%?1stEJ y,l .G1. 2551
214
05 nrfisrs[1cila{ 1
tyj
H%',I?l 2
T. a{H'tni't c fdri'.rtnl' tim [.*+l -ux+0[ ./*+4-2)
B. e.r14'rtfluiduSn ilfd urr{llr+ril qiotrtfiqt
9. u3:inruviuad.:ru6ql6'vao.:tfiq6o A uns e Iqudr{finld'grfiq n,iruru x sTr unsnrfiqrld's
tfiq e 'iruru y or-r ri'rtri'c riluoi'u4unr:rufio unsfiria,irriqelieialild
C=4x*'2y
zx*y222
x*Y) 21
x*zy)39
x)o
v)o
o ltr'r oi'uyr unr:ar 6 n fi #o ufi acr
I
10. nr:tfionoto.:slt8nnnr{rrnu:r:*4Tta{o-.n4?-gradrd.:finrurfin'lsi' 3 nu fin::ernr:rfiovi.n*?u9ld
9Ya
vt'.:fiu 4 vl;Tn ci.:{an-n:iurdanqr'.:ll::nne 3 nu o.:nliruruifidfi'lqi'iunr:rdanotrororjcI ql - -qt
tv&
al{1lTTnnilfl{fiilo
-x
'[n lfr s s,r 6{ o t,t'[#in'[r,la ?1 sJ i
4. e/ A da e.,
?%o"lYt nun 21 fi%?1nil n .F1.2551
215
05 nrfisrr{'16[n{ 1 rarirfi s
aa:v'fr2
1ii zo ila ilane 3 nerr,tr,t)
1. drnun A = {x e nl ,2 - 7x * 10 < o} olfior:rurriaormrusio'l:Jd
n. tir a - {r.l I x il1r 25 uns 5l udrfirqurrdorrirfi'u} u#r n .rr=
Q
fl. rYr c-{-=Ilsr-'rrr:drilrnnra{ xunco6oz} rrd'r aac=Q
eq ct
lJ0 tOHJIAOT.I
1. n.en unr r. nn 2. n.Qn unc r. fio g. n. fio une r. 0n 4.
B-[;]
fidr z 6 orioter
?40J.
7
4.
lz a+1 a+1
I
lo a a+3
I
I
L1 1 2
ud'r rruuflun'rr
2.
AA
n. zuo $ny lJ. 29t
2. ri'rut,tqt A -
ri'r detA - T
1. 5
[*l
"_lul
L;l
AX-B frFi
38
7
[Lnv
j
'l9tOuTl
3. ri'rut*otd'A-fr,2,3,.. ,1oI B-{+,s,0}
I r ct o,r da.' A , A
F - {r, n + nlr lilurd.lrifurail.: qi silfrr
rud'r n(F) rvir n-urioto
1. 10! 2. 3! 7t 3.
1. sx2 * gy2 : 4s
3. gx2 * 2sy2 : 22s
un3
rLnv (b) - b
7l
?ln b€Bl
-4 LLnr (*-u)'*y2 -e
3!
unrYilruil 30oq
4.
4. tri' r- riJur#uar.rfi rJrt,t1eroTqr0.r?{nnil
^2
+ y2q
#ur#usr:r x = 5 fliln1Tto.rr#uq:{ L fiafoto
1 y-+x-+r/s r/s
3. y:.ft" - 2^l; 4. y--'.6"-2",[;
5. r.:3r.:radtfiooTrln-aoqjfi (*c,o) oouooarjfi 1r1c*r1,01 rfio c rilu:su;yrr.::;u'jr.:
o er u o q rrn so oh^l rYst a.: nt:rlu nr *2 + t zy = o fl il nlTt o.lr.rfu :J dd oriolet
2 y-+x*+
r/s r/s
2. 7x2 * 16y2
- 112
4. 13x2 * 36y2 : 46g
ln u8 g e,r a a ut#inlun m ar i
5. a.r A da L/
?%a1Yl nttn 21 fi?t?'lGtil yl .6.2551
216
os nrfinc['16{n{ 1 rarirf{ +
o. tri' t- ril ur#uq:.r fi fr nm ilfuryir n-u m un r r.ir uo o surin nrrr a rnlarn aflu nrq9
(*-2)2 -(v -1)2
- r ud'rrir r i4*rtri r- lrid'olarna{Iunr:rJddariote
4'
1.m=0.52.m=1.03.m=1.54.m=2.5
(z )
< B[t--J d odoter
(- m, 21 3. (2,
7 . rtarirsrouro.to6[iln17
1. (- oc, 2)
) - tn(x + 1) - ln9 6oriotcr
X
{r} 3. {2,3}
8. L{gtri'rqrouro.t6[run1T
1 t)
3.1. 1
7
i-j+2k
A 9,/ 6l
Ftofl 0 Lo
8
"l
r
2*'
(*-g)
2.
ln(x2 - 1
2.
@) m)4, fz,
G
7
4.
4. fz,3)
-9
2
9. eirr o.:
10.
o
n'lilltgl u - 2i- j+ k
ri'r 6+(u.v)-alu"vl
8
1.
11
[,.,;),,{,,,ccos ft)
2.:
A e,/ 6l
9tolj 0 [9t
z"l-2
7
LLNg V _
C,/ r
tLn?nl a
2. 4.3.
11 . drr o.: x tdriltrl'
^+x2
+x3 +.. .....*xn
2
1.
13
Ae)61
9t01J 0 L9t
3.
fotofio
'[n rfr s il aa?bl#inlluelrT eri
T
6
+
2.
aa
= 0.18
4.-4
12. rirrauo 6rrJnr:u#uTri'.: y -
,2
., d-y - 25
| :-r'
,2 3
OX
4(1 - 5*)2
2.
3.
4.
Ft?'rrud'uto.:r#uki'..rfr1o (0 , 1) 6o +2
frrri'fu y: {EA rflufr.:rid'udorfio.rfr x-0
6nJnlrro.tr#u#rurisTri'.:fdnr (0 , 1) 6o 2y *5x * 2:0
6. iuarfi n$fr z'l f;'r,nrail il .Gl.2ss1
217
05 nrfisrorasr{ 1
tvi
14%111 5
13. drnuo f(x)- x4 -4x3 + qx2 +r riotoon,u
1. eirinqnra.:t6o t uR;2 2. trilufirri'fudTrfiruuuri?{(1 ,2)
3. tfirirqrqofifinf,'fi x:r 4. uurir{ilq[0,1] tfirirg.:qo#ru!:nlfi
'-oqlqq.U
14. #rts::lrRusTruvi.:nd.: d'ofionrrilfluurnilnnrYrfifirordr"rur'rufiouh qirunr:trinnrY'r
9rutu
cirunfiunn uon,iruru 3 nn ornneio.:turadrdrurraflnu0flnuroryirn-ufifn:*rucrilfioun1uq lll { q.u
,iruru 10 nR tu'irurudfinnuonf,rm'iruru s nR unvnnuonfruor''iril?u 5 nn Torritauo'ir,u(u.ullru
9 a llv a e Vleu r a
- d'rn Eu'[si'n nu o nRuo.: n nriros'lqi'fu et:J o.l unurT uao ru neir t 00 uryr
tor.tot.u.-t,^t
- d'rnEu'[d'n nr o nRrm n n riro s'[d'fu n:J o.: rrmuriuno ru n rir 50 ur n
nrrrurirosrituduna'rou"dodfiurrrf,rr'ruf$,u1, .rrt*0unnuanel-rncimunsleinilot$q.ug
um u ti uao r n rir :r er n-u'l ai rio s n'ir 2oo u'r yr rvir riuriater.u
.5_5^7 11
1. 2.
6121212
1 5. nl:fl o u n-o tfi o n u n er n tririu:rrnr: tui m nm ruin rr ru ar ur:n vir'[:l n s uuur6 r 1 00 n s uuil
nu'irnsuuuaauto.:firrirnoufinr:uonuo.::JnG firirrqfrurngflrf,qryirfiu 50 nsrtuu unsfict
airutfiu.:tuutllarolr{lvirn-u '12 nru]tu urrfiGnuf$nsu'r{fl't?o:Erf,ut rilufirrirnautun*.:dq9t
unsaou'loi 74 rtng*o2 nruul.r srtruiiror-u qi'.:riuiosJnrro.:firdrnaufiaould'nr"rruurioln'ir
ur.: sm a :*rfl ut ui a rur n n'ir ur u fi ?n uf rvir riu rioterq
rir ra uot# duiitol'r *t*LYr :l n 6 sYr qr :r r
z 0.00 - 1.00 0.00 - 1.50 0.00 - 2.00 0.00 - 2.50
ftr,r{dt sTr #uTrTo rJ n 6 0.3413 0.4332 0.4772 0.4938
1 . 1 3.59 2. 79.15 3. 84.13 4. 86.41
ln rfr s il 6r a %:L#in'[r,ra x1 il f
7. iuo'rfi n$fr zt fir,lmaal ilr .Fr. zss1
218
os orfisrrlran{ 1
tyj
14%1?1 6
1 o. en:'r.J uo R ua { n ?'r rr d ri rll n usq.: r{ n r{fi q rad u ei oti lrar.ir u : fi In niru ;
,i
or n un si r fi il n n vir il :y ryr g,ir ur u so o-.: n l-err o.l :J :g ryt fi '[n EJ
L A i A ue,/
lJO.ln?tilnO.lnzunA LO
I
AVATI
9{ArunAn?[mao'0lilaEJ
r ?r
ma [5
!
rl
a?'liln
120 - 139
140 - 159
160 - 179
180 - 199
200 - 219
6
10
18
14
2
v v af, & A , !- -,q e y y - Aa ^ & a A r u,
n1T0u1nil [Frr.]n1TTU'tu1^rl{mn1:tlr''rvilnRn?riln0{ 6nnru0.:nrofilil.rnrudnnrtndottafruqio'[iru
q.:n'jr {rilr-qdu 1 :Jxrurr*iounv 75 toro-rfifqfifidufd:Jnnilu?ra 50 o-.:nfo erifu6'tfir-qfiqr / ----ri'
!tee, t u t v d a L a j , u, ,l^s u
0 r [9t rlj't:? rl tFtT{ nl:q { n nl ? 0 r qt 0.] rj ru n ru ri n n I rnd o.: ta6 u qi 0
-tiat
nir fl fl [n nfit
1. 184.5 2. 182.0 3. 159.5 4. 146.0
tz. rioqrlrrulonn9t
1. nr:foreirnnr.:to.:t"orynoi":ugrufiururorriarynqoter l rirgrufiuruossio.rfiriro$:rn.jrtei.rqt d { q . e ---"' cl
v Ay j
- t u j j q q y
6r{ tR 9t yt lt 0 u n fl o n u n1 fl .l [n o m il'l n m fl q [1t1, 0 3,J fl Tgt 1.{1.[ t fl il 0
2. rirfoilnqotqfidrfiq:JnG nairr6ofieirq'rrfiu'l:Jratooirrfiul:J ovfirunn:smuqiofiuoru usiqrql|l'@
l4 ra
[tJ u il n nrsytu qr aoluiiu ru
3. t{nr?iluo{runsir{:sn'irruqinveirro.:riarunir-urirradurnrnfinrotrioai*mtit* fisirryirn-uq| d _,,,_.
d
fll,lutflila,u
4. nir rur m:orur o.:rio il nrqlo I oseior fi rir lr nn.ir sufraru aa qt q ) qi--- ---
ln rfr s il 6r a ll'l#intun ?'r il ;
8. iuarfi n.ffr zt fiueralu n .d.2ss1
219
05 nrfisrrrran{ 1
s,/ j
14}t1?1 7
te. riorynoiolrJduaqrrirtd'sirutunr:Ts.iunnRudr lrar.iru : uauurm) rotuS:iyruvicadt turirril
u.st.2545 - 2549
tl Tr.Ff. oir'l#Eir er
2545
2546
2547
2548
2549
1
2
4
5
7
f,rnmru#rur{uf':sra'ir'reirt:fi'sirutunr:TruururRu6'rn-udrrrrnrro.:riorunfr fin:llrilur#uq:r
rf,rnre'irrirlfdrutunr:Izur*rur?uri'rtufl fl.sr.2553 osrfiruduornfl n.s.zsst rvirriurioto
(Hr.iru : LL6[uu'lYr)
1. 1.5 2. 3.0 3. 9.8 4, 12.8
v a u a y t f a & A t dv a u &X
19. n1:fl0unqtn0nunliuu[{lT?ri[n:{n1:i5'rnr:er:ttailr lruirilun[5EJurfrsouiliRu tZO ou
6l
-.:..-.--.3.*t-.-y' a u a a f A v a at
t1.t01t{?tnt[1]ilun trullr'r u 70 nu t,tn rruul4cu{ 50 nil [q ufi o r uuuaour orun iSuutr u fr eir
i{rutdurtuutJlarg'n{?a{nruuuflourvirrir 12 nsuuu unsfroir#rurl:sRnfnr:ru:J:r.r-uryi'rri':-r
0.24 airun;uul.lflau?JOrrinGrurnfi.rftri'rradrrvirriu oz osuilu o-.:rfunsuuuradurarfinGuu
Ao&taeqv
7l tlj',r fl 0u?1itfi tJo t?11nulj I t9l
1. 55 2. 60 3. 63 4. 66
zo. lri A uns e rilurn nnr:rrflo 1 dld rnodaru fr'ulu:Jin fi sl-r o Eirr
fir p(A)
= s.3 unr p(B)
- o.+ u#r eirro.: e1R'n e'; rvirn-uriotor
1. 0.3 2. 0.4 3. 0.5 4. 0.6
nf
{
#jk
'[n rfi s N 6t o lt'l#intr,ra x1 EJ {
9. 22I eiT rinirrnr:'lnufisil
rads ntf,neirasr{ t
rans imsrrfisrf,'rcleli r
no$fi t
1) 3
7)2
naltfi z
1.) 2
7)1
13).3
1e) 1
2) 6,126
p' g)8
2)4
8)2
14) 4
20) 1
4) 100
10) 108
4)3
10) 3
16) 1
3)3
e) 48
5)e
5)2
11) 1
17) 3
6)8
6)4
12) 4
18) 2
3)3
e)2
15) 4
1 n rfi s ru a a r,t1#5n'[r'ln er ru f
10. rans arfiqorasr{ 1 222 atT rlnirT nr:larfisil
A CIY
?ra:1s14ua6{0u imnrfisrrt16ta{ r
grar,tfi 1
lv
?ro 1 aou 3
1 ufio
'.
fid'rn?lruq3.,ruiluo3r
A
L}[0.lQln f (r)
LLflY f (p)
T do
alnlovruri'rnuotd'f (p) .f (q) = 0 lLnsLT'llTru'jt f (p) =
a.t U
el.l}[ltf(q)=0
&AArAdrd
1,[U9t 0 q 3J gt',l gt?'l 3.JaT.,] nJl,tLma
p-)r p->s
?
dA
o tuo r ruoi'tot?'1ru03.:uiluufio
d A r A
1 lfio p fiei'rn?1il03{riluoSr
o rfio p frdrfl?'lru03.:rflurfio
={
={
T6-o6lc,'
01n IOYIU nlilUq LH f (r) + f (p) = I
a,t &
9l.lltl.tf (r)=1IIflUf (p) =1
;)A&ArcrA
1*1[nA n.l r LLflY p u9l'l9l?'lilLUltQT.l
( 1 rfi o q fi drfl?'lruo3.: rfluoS.:jl
t1.[0.]01n f (q) =
I
Lo rfio q fidrn?'rru03.:rflurfro
r)= 1
s)= 1
.'. f (p -+
.'. f (q -+
1+1+1 = 3
e.t &
gt.rul,l p -+
unr q -+
.'. f (p -+
a{TACtA
r il Fl'l Ft?'l il a T.,l t:.J l.to T.l
AtACra
r tl Fl'l 9l?'l il 0 T.l tU }[A T.1
r)+f(Q-)s)+f(r)=
'[ n ufr s a,r a a ut#intr,ln m ar i
11. raas nrfinnran{ 1 223 atr#nirrnr:'ta rfrs,il
ila z oou orzo flfTrtruR:ilnoilfierooflarnna-nf1
Aau,av
tflo.:orna b e R6orrfifiaunr:6'uci:sn'irr a uns o uqiosfirunfi'rrftor aofidrrTu
.'. fir',iru'runrnfirfga.: au = [n(A)xn(B)] - f ,iruruusincHnnufro.r ab ddln-u - tI
= [rooxroo] - 1'ilru'luttoinsrunfft'tfiio.: ao f4"i'rrYu - rl
runffnf,io.: ao i4d'rrTu
rriu0 X 100 =0, 0 X 101 = 0, ..., 0 X 199= 0
.'. druruHna'lrfdfirirrvirn-u o 6a too'iruru
rriuz x 150 = 300, uns 3 x 1oo = 300
.'. 'ilruruHnfir#ficirrvirn-u eoo 6o 2'iru':u
il il'r u ril sr ru n #r r f,r o.: au d"i'r ri'ufi il nr u,irur u rir'lril#rr nrtunr:6 our ururn
#o g erou 3
A
rflotorn x + 3 rilusr-til:;nouto.: e(x)
u>.trlu x = -3 rijurhnautoitfltlR't: P(x) = O Eiru
nr rir qr oudu 6JT o{ fl il n1: P(x) = o'loilo u nt:uu n qt-l :J:;n oilT o.i 1 t U u1 il P(x)
-2 -6
.1..,
2
2x6
-3
-6
-2
=0
=0
-0
=0
O1nfliln'lT P(x) = 0
x5 + 3xa + 2x3 +6x2
(x+s) ("t +2x2 -2)
LL u n qir :J :s n o uhjld'oi'o .,rtd'g or :
tfii atri'rri'rto ir u rir H uqtd' a
x4 +2x2 -2
a2 + 2a-2
x2
-2+
2(1)
ln rfi s il 6r a ltl#intua?1 er i
22 - 4(1)(-2)
12. 7
ranlJ arfisrrrlan{ 1 224 eirrinisrnr:la rfisil
rrqi a = ^2>09t/
a./ aJ f
9t.l,1,b1,[ a = -1 + r/g
*2 = -1 +,16
,
x - + {-r*"6
rirsrau?Jo{fliln1T P(x) = 0
9'/
ra4
9v
?la 5
OU
'l
9t
H
=
=
da-3,ffiLLnv-ffi
100
h (3)
fos (3)
r (g(3))
f (10)
102 =
aou 9
oln 82
LLflY B-1
82 + 3B-1 _
82 + 3B-1 -
oln g (3) = 32 +1
"'
g (3) = 10
L: :,1 [: :,]
1 [-t -s.l
oetalo 3l
[: ;]
+{
t[;'
[: :]
.[;
:]
rro e
]
L' -z)
["', 1 a,r]
l^r, 'rr)
I
ornloyrri
rs.]
lo1
1 [-t_t
-3*oLo
tl l
?tz =
ln rfi er ru aout#in'lr,lsrrT rui
13. r6rasJ nrf,ngrasr{ 1 22s eirrinisrnr:'[arfrsru
aou I
oQtv
n1nugt 114 Z
Yrul al
s$aartYi I
k-2
k=3
k=4
=64
1r/ ,i
-.1
I a &
eto.lrunuu z tu:rj ufrflr$
nu'ir r = l=l
frae
[rn3 e
a.t &
O',11t1{ Z
.'. Z
=0
: r(cosO * isin0)
= 64(cos0 + isin0)
tl r !
*r .l
?lrdna$n 2 gTa.,:n1Tnaor1nfr
6tsl:ts zk
k=1
6 ta.,: Z
V;(
"or2kr*o
+ isinSl"-fo)
n
"-)
1r2r"" n
W(cos
2(1)n+o
+ isin
2(1)ru+o)
6
+lsln
6 )
z(
"o"L
+isinr) = ,( I.{,.]
3 3) [2 2 )
z1
/
W(cos
2(2)n+o
+ isinz(z)n+o)
66)
z(
"o"?n
+ isin'"]
t 3 3)
/ .6.)
2l -! + = -1+ ,.6i
t-2 2)
W(cos
2(3)n+o
+ isin K"+o)
6
+lsrn
6 )
z(cosn + isinru)
-2
?l*(cos
2@)T*o
+ i sin
z(+)l + o)
66)
z(
"o"!n
+ i sin
o"')
3 3)
/
"6.) . t:2l -! - -1-"6i
t2 2)
z2=
zg=
zg=
z4=
:
zt = r*16
z2
la rfr s rr a a ul#intun er ru i
14. ranEJ Frrflsrrfran{ 1 226 ei'r ri'n i rr n r :'[ a rfi s e,r
W(cos
2(5)zu+o
+ isin K)n+o)
6
+rsln
6 )
,(
"o"-sn
+ i sin
u")
. 3 3)
,( r-s,l : r-",8
[2 2)
w(cos
2(6)rc + o + i sin
z(6)ru + o)
66)
z(coszn + isin2ru)
2
+ l-rl + l-,1 + l,l + lrl
+1+1+2 = I
z5
.'. Z6 :
:
:
lorl : l,l + l-,1
= 1+1+2
k:5
k:6
6
14'l Ik-1
Tra 7 nou 2
tx-l01n lim rc* ,- |
x-)0[ r/x +4 -2)
limc+ lim
-
r+0 x-)0r/x +4 -2
ffi+2lim
-
x
*50
^l
**+ -2 ffi +2
c+
c
a
oa
c+
lim
x-)0
-6X
+4 = 6
c=2
x+ 4-4
ln rfi s sr a a ut#intr,rn m ru i
15. rans ertflsrgfran{ 1
227 eir fini gr n'l :'t a tfi et eJ
etou I
x iA j
1^l UYI U T t? TUYI LLT.I t.] 1
2 (2
- 7r*2d* + I - J-
-2d^
I
o l.d )
: [+F]
+[L+F])
: T.[ L:])
16 B 24I-
T
333
r?a s
r?o g
=8
9tou 48
9
o
(x,y)
(x,y)
(3 , 18)
(12 , 9)
@
@
a"t
0 9t9t9rq
AJ
aoaoq
o
n1il}b91 27+
21+
30 -+
LLny @
LLflU @
rYirrTu +a
3x+y
x+y :
x+2y :
ttti:vuuflalnr: O
uuti':ruu6[un1T @
eir c ri'tidqer
I
T{U't1
qoqru (x,y) c
(0 ,27)
(3 , 18)
(12 , 9)
(30 , 0)
54
48
66
120
ln ufi s il a a ?t'[#in'[nner al f,
16. r6rnE a$srrrran{ 1 228 ei'r rin?gr nr :'ta 16 s ar
ly
?lo 10 aou 108
g d- A A
fl%ao}svr 1 rfionilTTgtn1Trila: 3 yr::n o1n 4 y,t:Tgt
.,iruruifi = C+,g
rYt rrt fi z o1n y{rrn g nttofd'lui'lurlrur*urn r6onfinl-n:v{r:nnr 1 nr{
'iruruifr = Ce,r XCs,r XGs,r
^aAilrv- a &
.'. 'irurui3m{1oi'iurdaner-roraqjoirryl::nfiu = cc,e X cs,r X cs,r X ce,r
= toe if
sraufiz
ila 1 oou ila z n. Bn rrn& s. fio
o1n A-{"eRl/x2 Tx+10
x2 7x + 10
(x-2) (x-5)
H
A = (2,5)
ria n gn o1n g = {x€t / x nr:2b uns st fire:*ru6orvirfiu}
-&er.lilu AnB = {x€tlz<x(5 unrnl:2sunrs1 firer:*rn6ormfru)=Q
A
tilo.:ornx€luflr 2(x(5
x*3 rlt:1r 3141:2s rnfiorerr* 1 unr 3 n1T s1 n{qr-r
x* 4 ry{:1s 4 141: Z5 rndorerr* 1 ttns 4 il1T St rilfiorqs g
fa s fio o1n g = {xct / qr-rnr:iailil1nra{ x rns o 6o z}
-&rt
otuu Anc = {x€ t I z <x (S uoyqr-lnr:jrrururnloit x rtnr 6 6o z]
= {+) +A
A
tflo.:otnx€luns2(x(5
x*3 [y{:'13 t4.T.rJ. Ta{ 3 un; O 6o g
x = 4 [?{T'li 14.T.il. ljoil 4 Unv O 6O Z
ln ufr sr N 6r o ilt#intr,ra ?1 il i
17. r6rner nrf,nerran{ 1
229 rtrrinirrnr:-[n rfrgn
l)'/
%a2
9L/
sa3
lv
%a4aou
2
detA A =
Q1n det A
.'. 5a-3
a
6
a+1 2 a+1
&
- gcu1jl.[
+ 4a* 3l -b'z
n.1
a2
3
'2
tu
+
fl
lo^
5a
7
7
2
.11J
11
+ a +2a* 6l
&
niln{ - nculuq, qr
Z= =
40 - (-2)
7
Z =6
aou #a g 7l
rirHt,ter t(4)= (4) LLnvf =(5) =5LLnrf -(6)=6
!- - -" ri'fuo'rn A+A lijufi.rri'd'urad.:qi oHdr0'11*?u1 l.tnTl,[Qln A+A LUl+l l.]nTuulti
= 7 x q x q x L x I x I x I x E
A-+o@@@@@@@
X Z X T
@@
7!
ilat aou #as y=
"6*-2"[39"/ &
H't o q a q fl a { ? { n n il n .t 6[8.: Tq u n'] T Llti;y u u 6ril nl Tq
^2+y2 - 4-O
(*-5)'+y2 = e-@
(*-s)'+^2 - 5
- 10x +25 - 5
5
@-o
'[ a rfi g er a a r+t#in'[r,r or er ar i
18. rcrner nrfisroT asr{ 1 230 eirrinirrnr:'tnrfrsru
ttYlil x
4+y'
v
L p.iru qooi'ollo.t?.tnnurionol6o e, 0) =q
Ft?'le.Juu (m) 10.1 L
= -2 tuO
=4
=0
(xr,Yr )
X=5
6[iln17 Y -Yt
y-0
v
= tan60o
=rG
m(x-xr)
"6t* -2)
"[g* -2-rli
ly
?lA5 aau ila Z 7x' + lily' = 112
6[iln']Tnr;rTun1 *2 + 12y = o
^2
_ -12y
.'. 4C = -12
C - -3
ArJ rruu dil nr: ?'tr: rlunr
do *2 = 4cy
C:3
?=4
u fi o .t a'l nIo vr riri r H uotri' c r fl u:y u y yr 1 .: :s u'i 1 .r
n
o u o q u n y o qlill n-fl
gY..:riu c)0 .'. c = 3
si'.,:riuoeTillrinto.,:r.:3 (t .,0) : (t s,o)
unsarurerro{r.ri (* G + r)o) - (r 4,0)
a2 - b2+c
16
b2
la ufi s ru a a ul#intuerer au i
a
aa
a
aa
= b2+9
7
01n
19. rerns errfiodran{ 1 231 iirrinirrnr:'tarfrsil
froe
-A
6tr,In1:?07
*2 u2
J-t : 0
16 7
7x2 +16y2 - 112
gtou ilal m = 2.5
nilnlrlarr{oflunr (x - z)2 -(y -1)2 = 1
4
olncrilnlTri'rrfu 6o y = + 2(x- 2) +1
^J
tl.to.,lotn L lilqlortaul r ofTu nl unsn?'r rufur#uri'rri'u uvirrYu
e.. &
ol.,rriu m>2 Hto m<-2
ln rfr e, il a a %'[#in'Lr,rn er eu i
A
9t0 2 LLny -2
20. r6las ntf,nerrasr{ 1 232 eiT #nirrnr:'[nrfisau
lv
nau so 1
Ton ri
vvel
9l',11{1,[
(-@, 2l
l)/
ra7
+3x -2
-2
z+
ttflnri'rrj:ynouro(l *3 - 3x2
{:)
','[9-lL*-J
'[:)
'[:)
IX
0
0
-3
2
3
-2
014il'lutfiaq
t3)r7o a nau ila z
Ton ri rn("' - r)- rn(x + 1)
,n[*' -
'IL x+1J
,n(x-1Xx+t )
x+1
ln(x - 1)
.'. x-1
^2-x-o
(x-3Xx +2)
x=3 , -2
x = -2 rfio.,ro'ln x 2 1
.'. x=3
Uns x+1 q
'[ n rfi s er a a u'[#in'[uor tr er i(u
21. rcrds afisrorasr{ 1 233 etr rin irr nr ;-[n rfi g a,r
Ntv
IN2
=l-1,t,1;;1,.1;_ll,l-r zl
= (-z-r-rl) T -d-r) J* (-z-r-rl) [
= -l-sJ-[
ornTonri 6+(u.v) = "lu'vl
fro e aou ilaz I
7
rirHuo A = arccos
cosA =
ila io nou fra g 'Jn
a1n u = 2l-j*[LLnv V = i-j-zk
U'V = 2+1+2-5
2
Jt
2
Jt
q,& Tt t 2lo.,tul* sin- sinf2arccos
T )
.77
sin- x sin2A
3
= sinl x 2sinA cosA
3
t- t-
r/g A r/g 2
^, G-/-,t:. j
2
"lt "lt
=97
6+5 = t
11 = .Jna
.'.a=L t-
4tt
= .Jn
uXV =
ijRl
2 -1 ,|l
1-1 2l
ln ufr sJ ar a a ul#in'[r,rn rr e.r i
22. r6ras arfisrnrasr{ 'l 234 itrrin?r'rnr:-tn rfrHil
9v
?to 11
tv
aou ?to
fd
a1n Lam u
A
9t0 nlTn'l
1-x
99x
117x
X
- o i8
a,/douA
O,}|nTil01*1,[A?l0.1n1quLTlJ'lFltUgl f -X , a1 =X
a,
AlnfTAT S -
|
', 1-r
x = 18
99
1B - 18x
18
2
13
ila tz aou ila + 6{iln1:?ro0r#u#arfraT6.rlr*nr 1o , t; 6o zy + sx+ 2= 0
o nn !T'lT'ly(u
dy
d-
d
dx
_h
"(1-5x)
2
: * --Z(1-5x)-1r :;(1-5x) -t
25
d-
rllouunt,l x=o tu
tr
1) = -',2
2+(1 -s*)
d25
d_
(1 - 5x) _ -;(1 - 5x)
X
j
d;
7d
(,- s*)t:;(,' -s*)-
d'y
;F
I
4(1- 5x) 2
nn LilT'ly(u
ar 9,/ f q.z
H't9t?'liltut6[1,[[9t.] rt[ 19t
(0,
.'. Ft?'lrufur#uki'.: il qgl (0,
Bn LvrTlr
f qiotfit.:fi x:o lfio.taln
O H1(o)_1
@ (o) =
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2
@
@
dy
dx
@
la 16 s ar a a r,rt#intnn m er i
1-5x
23. rilau nrfisrcrran{ 1 23s airrinisrnr:'tn16sru
@ figr t?lTry
nr:nfr.t6[iln1T T0.,]l#u#lrin il nq (0, 1)
O oqhiru (xr,yr) = 1o#'u#n (0, 1)
@ n?1rud'ur#u#ruein (m) = qo#rurin (0, 1)q'
@ freJnlT y-yt-m(x-xr)
tr
y 1 _ -t(* 0)
2
2y+5x-2 - 0
9" - 4 t e./ v eA
?ro3 f e,ra16[oqo6[rJT{niiri x:1
,1,2
fio Lilrlry
r rfilufr.,rri-d'ueirufiru rfro tt(*)
4x3 -12x2 + Bx
*(*-zX*-1)
m
o0@'o2@r rilufi.rri'd'uni'rrfiiluurir.,r (0 , 1) v(2, *)
tv
?ro 13 aou
o t{o Ll^lT'ly
a'ln f(x) : x4 - 4x3 + 4x2 + 1
rt(*) -4x3 -12x2 +gx
rareir?nqorTou ufi'arun1: tt(") - o
4x3 -12x2 + 8x - o
"(+*' - 12x* 8) _ o
*("'-3x*2) _ o
x(*-zX"-1) - o
X-0
@
ln rfr s e,r a o r,r1#in'[r,ln rr er i
24. rans afisretrasr{ t 236 iiT rlnigr nr :'tn 16 s e,r
@ en Lwr'lv
f"(*) _
*4x3-12x2+8x
- 12x2 - 24x+ 8
rir?nqorturio O unu'lu f"(*)
lru,ir f" (1) - - 4
.'. rftoir6[.tflgr#run-yrffi x - 1(Uq
@ fior LilT'tv
sirinqorturio O unutuftt(*) nu'jr rtt(o) - 8
,,r
.'. rfioirqofi'ruU;nlfi x-0turir.rilq t0,1]qqJ
ila t+ aou ila+ 11
12
n(s)=Cro,g=#=Po
ririluq'hi E rnu uaqnT:nffi4nri"rld'n:Jorriunqilncir:?iln-uillnn'jrntorvirriu zoo
ad - ve , :
t- qr ru
n:rflfi t toi'orrJo.rtiunq:rilrYu 200 ulyr 1rafiu'loinnuonfiuo.r 1 nn uncerrr 2 nn)
.rj _ T:tTut^=
cs,zxcs,z = 5ifr
n:rfifi z "lsierrJottiuaq :rilriu 250 u'ryr 1ra0u'[oi'nnuonfiuq{ z nn ttn;f;sl? 1 nn)
'iruruii = Cs,zXCs,r =5ii
aA ue a ^ u.d e
n:rfifi a tein:Jorriunq:riln-u 3oo uryr 1rafiu1ffiuro.:vr'.: 3 4n1ql'
'iruruif = cs,3 = 1o ifr
n(E) = 50+50+10=110
Fri.lfiu p(E) =
n(E)
=
110
=
11
n(S) 120 12
1 a rfr sr il 6r a %:[#intr,rrr ?1 Er ;
25. raa EJ Grrfisrrlran{ 1 237 siriintrT nrr'lnrfrsil
.yu
sa 15 glou ra 4 86.41
fd-
0'ln[Anu x=50t1fl3S:12
nE': Z -
*-r
ts
a d utv 74-50
finufnou"ld'z+ :.2^ "-'-
"u-2
frnur 12
o:*rfi:grnould az .'. z ^ : 62-50
= 1
q ot*rut*..I 12
n:rilrrso.:'irururirrireoudaould'nyttuurioun'irourfl:*rniorurnn'irurufiiluf,.uq
cr vX
tu1,[o.11{
9,/ I
AA
1 l1,[71ttTt.l'l Y,l.Yl e<1) +Y{.Yt e>2)
(o.u+o.341 3) +(o.s- o.4rr2)
0.8641
i[s,/9/rAA.Adtet
vl fl 0 u L9t 9t v ttul{lAo u n ?'l o 19tut91 14 t 0 ul n n?1 u't u fln uf uytr n u 86.4 1
c)/ 9,/ 9,/
T0 U nf lJ0.l zu L1J'l flO
il
U
91,/ 9Y
?to 16 aou ?to 1 184.5
ALAi,vt
h fl zunan? Liln 0.1 tan un 0 LT
j
9t?1iln
6
10
18
14
2
ln rfr u E r 6{ o %61#in'[r,la ?1 il {
A
gt?'l iln 6[96[u
6
16
34
48 * Prro Ei
frr,lor:R'ln#nfi
50
120 - 139
140 - 159
160 - 179
180 - 199
200 - 219
oJaArurts-A
r{nilfiqnxrfi6olradueialdg.:n'jr o-.:nr"q6u I rJxrurruiauni zs 6a pru
druur.it Pzc : tn
=
75x50
:37.5
100 100
('"-s
) 100 LfL
-l
r |
-L.r|-
f
- 1re.5 + ,o(
st 's - "/
. 14-)
:184.5
6[A: Pcr 75
26. raall nrf,gtgrasrf 1 238 et'r ri'n irr nr :'[ a rfi s sr
lY t/
ila tt oou rTa g fla:rru?roiretnsi'lo:rra'irousiasrirsoofroslariucirrodE rnsnlfiorsaoU
9/ & ar ! s d
?l o il atro}[l.[ 3.t Ft1 [?11 n u G{$El t6tet o
O figr til:rs orufiuruaroovfinirtvirn-ueir#.rrnqfifoudqo ntoo'roorrvirriurir#{rnsrI
il
ilil1nflfl9r
@ fio tn:'tg ri'rriapnrotqfi€irfioilnG os'lrifirunn:rvrusion-r'us'nr unrolufiuil usios
. ,.1
t,
a c, iu ,
4
yt't lil n1 tiln il tnlj n ilq tu iln1 n n1 { 71 [u [14 tJ't r fl tJ
N/-
@ en !r{r1t I F' - *)= o rntJo
i=1
@ fio rn:r; eirilre:oru 1z; ro.:riorunfiritioun'jr niorvi'rriugurl'loi'
9'/ 9r'/
?lo 18 aou %a 2 3.0
ilarJn rfjualrnral r?n1qq
Tl T{.F1. X cir'l#Eirs (y) xy
2
x
2545 -2 1 -2 4
2546 -1 ,2 -2 1
2547 0 4 0 0
2s48 1 5 5 1
2549 2 7 14 4
ailnr:tffuq:.: y = ax+b
NNn
arunr::Jn6 It, = "I"i +Nb-O ilil.lrrp4st I*, =0
i=1 ' F1 i4'
19 = 5b
.:.b = 19 : .
5
.I",u, = "I*,' * o$*, -@i-,1 ' '
l-l l:l I:l
15 = 10a
3
,.4 =
2
o1 riu sru nr::J :y rur rudrtdd'r utunr :IsJ :*rur fi usir 6 o
319y--x+-
25
ln rfr s ilr 6r a r,t:[#intun ?rar i
27. rons arfisretrasr{ 1 239 eir rin ?rr nr :'[ a rfr s a,r
r tl vr al I u
n1t501Utun1:lnl]9rU',tflUFt't 1r{.fl.2553 tlytlr x = 6
.'. Yl =it l.f -e
r aN vr q f a e
nlttro'ru[1.[n1T[eNJ:*il'tflun1 v{.f1.2551 rryru x = 4
,. Yz=ltol.T -@
ri rtfd r utunr :I"ru unn duoirlufl n .?t .2ssg ufi ru duo r nfl il.q .2ss1 r vi r riu
Y'r -Y z= ]rut -|et
_.)_)
tt/ I
sa 19 nou ?to 1 55
or n #ru :J :s?yrf,nr : u:J : niur a.: rin 6 r um r ryir riu o. 2+
.. :ro = 0.24
x5'lU
12
-
= 0.24
XT'I U
NnXn +Nqfq
Nn Nq
x.. =
(zo t so)+ (so t oz)
-
3500 + 3100
= 5s nrrr.rilv 70+50 120
ila zo aou r7o r 0.3
orn A ras B rilurilqnr:nilr t fil*rfioderufiu
"'P(AAB)
= 0
plRtne'; = p(AUB)'
= l- P(AJB)
= t_ tp(A) + p(B) _ p(AnB)l
= l- [0.3 + 0.4 - 0]
= 0.3
ln rfi u il 6r a r,lt#intua ?1 il i
.'. xT'lu = 50
ets rLuuLilfi ur o.trin 6ur*fd rrir 610 urf;o" uor fr) :