Taiwan Facts Essays - Republic Of China, Republics, Taiwan

Taiwan Facts title = Taiwan Facts Taiwan, formally Republic of China, island (in 1994 est. populace was 21,299,000), 13,885 sq mi, in the Pacific Ocean, isolated from the territory of S China by the 100-mi-wide (161-km) Taiwan Strait. The capital is TAIPEI. Other significant urban communities incorporate KAOHSIUNG, Tainan, Taichong, and Chilung. Around one fourth of Taiwan's territory region is developed; rice, wheat, sugarcane, and yams are the most significant harvests. During the 1970s business supplanted horticulture as the significant fare worker. Light industry is the significant assembling area, with hardware a long ways ahead. Different makes incorporate electrical hardware, synthetic concoctions, engine vehicles, and apparatus, and administration businesses are starting to be increasingly significant. The principle regular assets are woods and other timberland items. Religions incorporate Confucianism, Taoism, Buddhism, and Christianity. Taiwan was first settled by the Chinese in the seventh century, the island was reached by the Portuguese in 1590. It was held by the Dutch during the 1640s, and by China's Ch'ing line from 1683. Involved by Japan after the First Sino-Japanese War , Taiwan stayed in Japanese hands until 1945. When CHIANG KAI-SHEK and the Nationalists, or Kuomintang, were kicked from terrain CHINA by the Communists, they moved the seat of their legislature to Taiwan. The U.S. since quite a while ago bolstered and supported the Nationalists, however during the 1970s Taiwan's universal political position had dissolved. In 1971 it lost China's seat in the UN to the People's Republic of China, and in 1979 the U.S. broke discretionary relations with the Nationalists to build up relations with the People's Republic of China, in spite of the fact that keeping great monetary and social ties. Military law, basically since 1949, was lifted in 1987, and many imprisoned political protesters were liberated. Pres. C hiang Ching-kuo passed on in 1988 and was prevailing by LEE TENG-HUI, a Taiwan local. In 1991 Lee finished crisis rule, which had allowed the control of the National Assembly by maturing terrain delegates chose in 1947. In decisions in 1992 the Kuomintang held control of the gathering, yet the significant resistance won 33% of the seats.

Learning Styles Essay

* Did your character range profile shock you? Why or why not? I was and was not amazed on what the consequences of my character range were, I have consistently known that I’m a coordinator. What shock me is that coordinator is my most grounded character; I would have felt that explorer would have been my most grounded. Be that as it may, in the wake of perusing the depiction of the coordinator is, everything bodes well and I see why it is my most grounded character. In spite of the fact that globe-trotter is my second most grounded character, I get an alleviation to realize that explorer was not very away from being my most grounded character. * How would you be able to adjust your examination procedures to exploit your specific capacities and abilities as controlled by the character range? Since I comprehend what my most grounded character is, I plan on keeping it that way and remaining composed. I accept that remaining composed would help me through my excursion in school and in my future vocation, particularly in the profession field I decided to be in, association is significant. Likewise by remaining composed I will maintain a strategic distance from all the pressure and migraines that I will presumably experience in school and in my future vocation. By keeping to the aftereffects of my character range, I trust I will be exploiting my capacities. * How can knowing your aptitudes and capacities show on the character range assist you with adjusting your investigation propensities? Realizing that my aptitudes and capacities demonstrate that I’m a coordinator, I will have the option to utilize that ability and better set myself up to adjust to my investigation propensities. By remaining sorted out and getting ready ahead of time, I will have the option to deal with my school calendar and individual timetable all the more proficiently and in wording I will maintain a strategic distance from all undesirable pressure. * How might you approach collective work later on given what you presently comprehend about your expertise and capacities from the character range? The manner in which I would move toward community work later on will be, by encouraging our gathering to execute a work routine. By having actualized a work routine I accept that it will permit us to remain sorted out. By being readied and viably utilizing my hierarchical capacities and abilities will permit us to achieve our expected objective of getting our work finished on schedule.

Coping With Treatment-Resistant OCD

Coping With Treatment-Resistant OCD OCD Treatment Print Coping with Treatment-Resistant OCD By Owen Kelly, PhD Updated on June 18, 2018 Ned Frisk/Getty Images More in OCD Treatment Causes Symptoms and Diagnosis Types Living With OCD Related Conditions Although there are many effective treatments for obsessive-compulsive disorder, up to a third of people with OCD have what is called treatment-resistant OCD, which means they do not respond to standard treatments like medication and psychotherapy. If you or a loved one are dealing with treatment-resistant OCD, here are some options to consider, along with links to more information. Explore Reasons Your Medication May Not Be Working Although there are many FDA-approved medications available for the treatment of OCD, medications dont seem to be effective for one-third of people’s OCD symptoms. This can happen because of genetics, body chemistry, other medications youre on, skipping doses, as well as whether or not you use alcohol and/or drugs. Sometimes, it can take a lot of time and experimenting with dosage and medication types to find the right one for you. Consider Augmentation Treatment Strategies Augmentation therapy treats OCD symptoms with more than one medication. This strategy improves the odds of relieving symptoms by using combinations of drugs, rather than a single drug. Augmentation antidepressant treatment may be helpful for people who do not achieve remission with just one medication. Adding antipsychotic drugs to an antidepressant is one way of augmenting treatment that has been shown to be effective. Explore Reasons Psychotherapy May Not Be Helping Although psychological treatments have come to the forefront in the treatment of OCD, they are not always effective. There are multiple reasons why psychotherapy for OCD may not be working for you, including not being ready for therapy, receiving the wrong type of therapy for OCD, an insufficient relationship with your therapist, lacking social support, financial difficulties and not having the social or family support you need. Investigate Intensive Treatment Programs While there are many effective medical and psychological treatments available for OCD, not all treatments work for everybody. Unfortunately, for some people, nothing seems to be effective. This has led to the development of a number of intensive residential OCD treatment programs. Consider Taking Part in a Clinical Trial Clinical trials often offer free, cutting-edge treatments that are not yet widely available to the public that can be helpful for treatment-resistant OCD. A clinical trial can also help you understand your disorder better while serving to help others with OCD receive more effective treatments in the future. Explore Psychosurgery and Deep Brain Stimulation A very small minority of individuals with OCD have symptoms severe enough to consider brain surgery. Surgical procedures for OCD involve inactivating certain brain regions that are responsible for the symptoms associated with OCD. In most cases, approximately 50% to 70% of people who have these procedures see a significant improvement in symptoms. One of these neurosurgical procedures is deep brain stimulation, which appears promising, although it is still in the experimental stage and often considered a last resort.

Persuasive Speech On Organ Donation - 973 Words

Magdalena Marquez Barbara Hastings Composition 1 22 October 2017 Donate today! I’m waiting in line at the grocery store finally it’s my turn to check out. Next to the register tucked in the corner stands a little plastic jar with a handwritten note â€Å"Donate Today!!!†. Inside the jar there is a good amount of change, a few dollar bills, a button, and a rubber band. By throwing our spare change in we are helping the cause which might make us feel more noble even just for a short instant. However, are we actually helping? How can we truly make a difference? I had an opportunity to make a major, life changing difference by deciding to become a live organ donor and donating a kidney to my husband Keisy. Nowadays the number of people in†¦show more content†¦Many hospital visits and multiple tests later it was time to simply wait for the results. With anticipation I waited what it seemed like an eternity for the most important phone call of my life. I would jump every time my phone rung. One very peaceful morning I was s tanding in the kitchen, the aroma of freshly brewed coffee filled the room, suddenly the silence was broken by phone ringing, I startled. Looking down on the screen it was the hospital, I answered it quickly. I could feel my heart rising to my throat. It was my living donor coordinator calling with the results: I was a MATCH!!! Pure joy rushed through my body like a lightning sending a chill down my spine raising up every hair on my body. Immediately after I called my husband to share the incredible news. At first, he couldn’t believe it but deep down in our hearts we knew I will be the right candidate. When he got home from work we looked into each other eyes and just started to cry from joy, fear and love all together. Without any further delays we selected a date for the operation August 1st which has a special double meaning for us our first wedding anniversary and the transplant. On August 1st, 2015 we went through a successful kidney transplant surgery with the help of an amazing team of doctors and nurses at Brigham and Women’s Hospital in Boston. I woke up inShow MoreRelatedPersuasive Speech : Organ Donation1076 Words   |  5 PagesTopic: Persuasive Speech Assignment #2: Organ Donation Specific Purpose: To persuade my audience to become registered organ donors. Thesis: Today I want to persuade my audience to become registered organ donors. Introduction I. To start, by a show of hands, only if you feel comfortable, how many of you are registered organ donors? II. According to organdonor.gov, â€Å"an average of 22 people die each day waiting for transplants that can t take place because of the shortage of donated organs.† Read MoreOrgan Donation : Persuasive Speech909 Words   |  4 PagesOrgan Donation Rhetorical Analysis Organ donation has been a major controversy for many years now. There are those people who favor it and the ones who do not. According to the United States Organ and Tissue Transplantation Association, organ donation is defined as tissue or organ removal from a deceased or living donor, for transplantation purposes. Tissues and organs are moved in a surgical procedure. Afterwards, they are transplanted to a recipient to ensure their recovery (Francis 2015). OrganRead MorePersuasive Speech On Organ Donation1150 Words   |  5 Pagesshortage of donated organs.† (Brazier) Due to the shortage of organs, this causes many people to go to extreme measures to save a loved one. Maybe even to the point of doing something illegal. The more we help promote and contribute to organ donation, the more lives we can save. There is a new name added to the list every 10 minutes while around 20 people die a day waiting for an organ. Organ donation is the process of surgically removing an organ or tissue from one person (the organ donor) and placingRead MoreA Persuasive Speech On Organ Donation947 Words   |  4 Pagesname is, Lizette Vazquez, and I am here to talk to you about becoming an organ donor. Many people wait for years for organs to become available, the need for organ donors is growing. Donate and save a life. If you had a chance to save a life and or change their life, would you do it? If you answered no, to this question would your feelings change, towards organ donation if someone in your family or close to you need an organ transplant? Can you imagine, what it would feel like to get handed a deathRead MorePersuasive Speech : Organ Donation1335 Words   |  6 Pagesto make. C. My name is Morgan Silva and I am here to talk to you about organ donation, how you can become one, and the ways your family and donor recipients benefit from the donation you made. II. Body A. People often ask themselves what organ donation is and what it involves. 1. According to Medline Plus, organ donation takes healthy organs and tissues from one person for transplantation into another. a. All kinds of organs can be donated to save a life: the kidneys, the heart, the liver, the pancreasRead MorePersuasive Speech On Organ Donation1048 Words   |  5 Pageshigh enough. These people need organs, and it is on us to help. It takes just one of us to save as many as eight people on the list. People need to be educated on organ donation and the opportunities it creates rather than a hasty decision that is made when you apply for your driver’s license. Organ donation is an amazingly powerful and underestimated practice. I believe everyone should become more open to the idea of helping others through the donation of their organs, which would otherwise be entirelyRead MoreOrgan Donation Persuasive Speech Essay1115 Words   |  5 Pagescouldn’t live without? Imagine you are lying in a hospital bed and you have no choice but to impatiently wait for that one organ you and your body are depending on to survive. Many people face this struggle every day. These people are waiting on a list for their perfect match†¦ the perfect person to be their organ donor. An organ donor is a person who has an organ, or several organs, removed in ordered to be transplanted into another person. Imagine that one of your loved ones are in the hospital†¦Read MorePersuasive Speech About Organ Donation1369 Words   |  6 Pagesan organ transplant (â€Å"Data†). These people wait patiently as death knocks on their door. In America, we can do so much to ensure that people will live on with the donations of organs. Unfortunately, many are unaware of the amount of people who are dying that are waiting for an organ. Organ donation is a great way to save someones life, and continue the life of a loved one. Although it is a great way to give someone a new life many people are uninformed about donation and how valuable organs areRead MorePersuasive Outline-Organ Donation886 Words   |  4 PagesPERSUASIVE SPEECH OUTLINE – ORGAN DONATION Topic:  Organ donation Thesis Statement:  Becoming an organ donor after death is not only an important decision for yourself, but it is also an important decision for the life that you may have the power to save. Purpose:  To persuade my audience to consider becoming organ donors after death    Introduction: 1. Organ donation is a selfless way to give back to others, and to be able to make a huge difference by giving another person a second chanceRead MorePersuasive Speech Outline Essay examples942 Words   |  4 PagesPersuasive Speech Outline Topic: Organ Donation General Purpose: To persuade Specific Purpose: After listening to my speech my audience will consider donating their organs and tissues after death and to act upon their decision to donate. Central Idea: The need is constantly growing for organ donors and it is very simple to be an organ donor when you no longer need your organs. Introduction: How do you feel when you’re waiting for something you really really want? Or what if it’s not even

Silent Screams Cases of Domestic Violence in The United...

Silent Screams This is the tenth time that Lisa has been admitted to the hospital within the past two years. At least this time there aren’t any broken bones or concussions to worry about. Lisa only has two black eyes, a patch of her beautiful long hair forcibly yanked from her head, a nasty black and blue bruise on her neck and a few nails ripped directly from the newly manicured nail beds. Lisa swore to God and her best friend Brandy that this was the final straw. Actually, she made that exact same pledge under oath just three months ago, yet she is coincidently in the same position she vowed never to return to. This time was different though. She was making plans to move her things out of the small apartment that she shared with her†¦show more content†¦There are cases where a victim of abuse feel that if they leave, the abuser will manipulate the children in taking their side. Men who abuse their wives tend to persuade them into believing that there is nothing or nobody else out side the relationship. There has been several cases where the abuser will actually convince the children that it is the victim’s fault why they did bad things to them in hopes to mislead the child to turn their back on the abused parent. Although it is very important that a person consider the sake of the kids when deciding if they want to go through with a divorce, the jeopardy of one’s life should always take precedence. Low self-esteem can be a contributing factor when women decide to stay in abusive relationships. In many relationships where physical abuse is an issue, the victim is usually verbally abused also. The abuser uses manipulative tactics to make the victim feel worthless, useless, and too afraid to leave them. Many women have confessed that they believe it is their own fault why there are initially abused. After being brainwashed into thinking that they are ugly, disgusting, and lazy or other derogatory characteristics, verbally abused women are being almost forced to believe that if they leave the relationship that there is nobody else that would want to be with them. This unfortunate mindset leaves battered women in an extremely unhealthy and catastrophicShow MoreRelatedPersonal Rights Vs. Religious Beliefs1627 Words   |  7 Pages ABORTION PERSONAL RIGHTS VS. RELIGIOUS BELIEFS AECHMIA COTE LAW 103 BAY PATH UNIVERSITY One of the many controversial topics in the United States is ABORTION. It is defined as a Removal of an embryo or fetus from the uterus in order to end a pregnancy as described on dictionary.com. I must say that, days of research it seems to be a debatable issue especially when it comes to religion and one’s personal choice in life to choose to do it, and remains to beRead MoreA Streetcar Named Desire By Tennessee Williams1263 Words   |  6 Pagesof the twentieth century beheld changes in almost every aspect of the day-to-day lives of women, from the domestic domain to the public. By the midpoint of the twentieth century, women s activities and concerns had been recognized by the society in previously male-dominating world. The end of the nineteenth century saw tremendous growth in the suffrage movement in England and the United States, with women struggling to attain political equality. However, this was not to last however, and by the fiftiesRead MoreThe Effects Of Domestic Violence On Children1813 Words   |  8 PagesEffect Of Domestic Violence On Children Everyday women are being beaten , terrorized and murdered at the hands of their husbands, boyfriends and ex-husbands. At least one woman is battered every 15 seconds. As society we tend to close our eyes to this big problem that affects everybody. we use excuses like that’s none of our business and that we don’t want to get involved, that until someone is murdered and then we are shocked and terrified. united states reports that domestic violence is the greatestRead MoreWhen Leaving Is Not An Option2498 Words   |  10 Pagestemporary and soon comes to an end. The love story they have ones longed for turns into a horrible nightmare. The emotional words they were once spoiled with turn into howling screams and name-calling. The flattering gifts turn into physical abuse. This relationship is referred to as domestic violence or intimate partner violence. This happens when a partner or significant other declares power, authority and control over the other partner. To maintain this authority and control, the abusive partner usesRead MoreDomestic Violence And Sexual Abuse2537 Words   |  11 Pagestemporary and soon comes to an end. The love story they have ones longed for turns into a horrible nightmare. The emotional words, they were once spoiled with turn into howling screams and name-calling. The flattering gifts turn into physical abuse. This relationship is referred to as domesti c violence or intimate partner violence. This happens when a partner or significant other declares power, authority and control over the other partner. To maintain this authority and control, the abusive partner usesRead MoreThe Fetal Position: A Pro-Life Argument Essay2142 Words   |  9 PagesPregnancy). Everyone has a right to life; this right is exercised in many parts of the American life, namely the Declaration of Independence (The Abortion Controversy 113-116). Therefore, the United States’ federal government should go to greater lengths to prohibit these so called ‘abortions’ in every case, regardless of the situation. It matters not what the women who get these abortions think, and it matters to many that this is looked upon to be immoral (Guttmacher, The Abortion Controversy 21-46Read MoreDomestic Violence in Immigrant Families Essay5608 Words   |  23 PagesPolicy  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Assignment Three: Canadian Human Rights Report Topic – Violence against immigrant women in South Asian, African and Korean communities Instructor: Jane Birbeck March 21st, 2011 Annotated Bibliography: Violence against Immigrant Women in South Asian, African and Korean Communities An annotated bibliography Annotated Bibliography Introduction This paper analyzes the phenomenon of violence against immigrant women, specifically within South Asian, African and KoreanRead MoreMovie Review : High Anxiety2356 Words   |  10 Pagesdisorders mimics the master of psychological thrillers. Mel Brooks does a masterful job in his tongue-in-cheek performance of a psychiatrist, Dr. Richard Thorndyke, who takes a job at the Psycho-Neurotic Institute for the Very, Very Nervous and develops a case of â€Å"high anxiety†. This film has what many would consider over the top scenes of Dr. Thorndyke dealing with his anxiety but reality is much closer to the comedic scenes than most people who do not have anxiety disorders would understand. WhileRead MoreEpekto Ng Polusyon19213 Words   |  77 PagesDomestic violence: Moving On A Qualitative Investigation Exploring How women Move On From Violent Relationships Researcher: Carole Le Darcy Supervisor: Dr Sue Becker Acknowledgements I would like to express my sincerest thanks and gratitude to all of the exceptionally strong women that participated in this research that have freely given not only some of their precious and valuable time but have also revealed that which is sadly all too often concealed; the remarkable, courageous and oftenRead MoreExaming the Cultural Practice of Ukuthwala and Its Impact on the Rights of the Child13071 Words   |  53 Pagesdifferentiation and expectations in society relegate women to an inferior position from birth throughout their lives. Harmful traditional and cultural practices maintain the subordination of women in society and legitimize and perpetuate gender based violence. This paper attempts to closely examine the practice of ukuthwala in the Eastern Cape which is proving to be a harmful traditional practice. In an effort to achieve that, this paper will put in proper perspective the practice of ukuthwala; it will

Silent Screams Cases of Domestic Violence in The United...

Silent Screams This is the tenth time that Lisa has been admitted to the hospital within the past two years. At least this time there aren’t any broken bones or concussions to worry about. Lisa only has two black eyes, a patch of her beautiful long hair forcibly yanked from her head, a nasty black and blue bruise on her neck and a few nails ripped directly from the newly manicured nail beds. Lisa swore to God and her best friend Brandy that this was the final straw. Actually, she made that exact same pledge under oath just three months ago, yet she is coincidently in the same position she vowed never to return to. This time was different though. She was making plans to move her things out of the small apartment that she shared with her†¦show more content†¦There are cases where a victim of abuse feel that if they leave, the abuser will manipulate the children in taking their side. Men who abuse their wives tend to persuade them into believing that there is nothing or nobody else out side the relationship. There has been several cases where the abuser will actually convince the children that it is the victim’s fault why they did bad things to them in hopes to mislead the child to turn their back on the abused parent. Although it is very important that a person consider the sake of the kids when deciding if they want to go through with a divorce, the jeopardy of one’s life should always take precedence. Low self-esteem can be a contributing factor when women decide to stay in abusive relationships. In many relationships where physical abuse is an issue, the victim is usually verbally abused also. The abuser uses manipulative tactics to make the victim feel worthless, useless, and too afraid to leave them. Many women have confessed that they believe it is their own fault why there are initially abused. After being brainwashed into thinking that they are ugly, disgusting, and lazy or other derogatory characteristics, verbally abused women are being almost forced to believe that if they leave the relationship that there is nobody else that would want to be with them. This unfortunate mindset leaves battered women in an extremely unhealthy and catastrophicShow MoreRelatedPersonal Rights Vs. Religious Beliefs1627 Words   |  7 Pages ABORTION PERSONAL RIGHTS VS. RELIGIOUS BELIEFS AECHMIA COTE LAW 103 BAY PATH UNIVERSITY One of the many controversial topics in the United States is ABORTION. It is defined as a Removal of an embryo or fetus from the uterus in order to end a pregnancy as described on dictionary.com. I must say that, days of research it seems to be a debatable issue especially when it comes to religion and one’s personal choice in life to choose to do it, and remains to beRead MoreA Streetcar Named Desire By Tennessee Williams1263 Words   |  6 Pagesof the twentieth century beheld changes in almost every aspect of the day-to-day lives of women, from the domestic domain to the public. By the midpoint of the twentieth century, women s activities and concerns had been recognized by the society in previously male-dominating world. The end of the nineteenth century saw tremendous growth in the suffrage movement in England and the United States, with women struggling to attain political equality. However, this was not to last however, and by the fiftiesRead MoreThe Effects Of Domestic Violence On Children1813 Words   |  8 PagesEffect Of Domestic Violence On Children Everyday women are being beaten , terrorized and murdered at the hands of their husbands, boyfriends and ex-husbands. At least one woman is battered every 15 seconds. As society we tend to close our eyes to this big problem that affects everybody. we use excuses like that’s none of our business and that we don’t want to get involved, that until someone is murdered and then we are shocked and terrified. united states reports that domestic violence is the greatestRead MoreWhen Leaving Is Not An Option2498 Words   |  10 Pagestemporary and soon comes to an end. The love story they have ones longed for turns into a horrible nightmare. The emotional words they were once spoiled with turn into howling screams and name-calling. The flattering gifts turn into physical abuse. This relationship is referred to as domestic violence or intimate partner violence. This happens when a partner or significant other declares power, authority and control over the other partner. To maintain this authority and control, the abusive partner usesRead MoreDomestic Violence And Sexual Abuse2537 Words   |  11 Pagestemporary and soon comes to an end. The love story they have ones longed for turns into a horrible nightmare. The emotional words, they were once spoiled with turn into howling screams and name-calling. The flattering gifts turn into physical abuse. This relationship is referred to as domesti c violence or intimate partner violence. This happens when a partner or significant other declares power, authority and control over the other partner. To maintain this authority and control, the abusive partner usesRead MoreThe Fetal Position: A Pro-Life Argument Essay2142 Words   |  9 PagesPregnancy). Everyone has a right to life; this right is exercised in many parts of the American life, namely the Declaration of Independence (The Abortion Controversy 113-116). Therefore, the United States’ federal government should go to greater lengths to prohibit these so called ‘abortions’ in every case, regardless of the situation. It matters not what the women who get these abortions think, and it matters to many that this is looked upon to be immoral (Guttmacher, The Abortion Controversy 21-46Read MoreDomestic Violence in Immigrant Families Essay5608 Words   |  23 PagesPolicy  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚  Ã‚   Assignment Three: Canadian Human Rights Report Topic – Violence against immigrant women in South Asian, African and Korean communities Instructor: Jane Birbeck March 21st, 2011 Annotated Bibliography: Violence against Immigrant Women in South Asian, African and Korean Communities An annotated bibliography Annotated Bibliography Introduction This paper analyzes the phenomenon of violence against immigrant women, specifically within South Asian, African and KoreanRead MoreMovie Review : High Anxiety2356 Words   |  10 Pagesdisorders mimics the master of psychological thrillers. Mel Brooks does a masterful job in his tongue-in-cheek performance of a psychiatrist, Dr. Richard Thorndyke, who takes a job at the Psycho-Neurotic Institute for the Very, Very Nervous and develops a case of â€Å"high anxiety†. This film has what many would consider over the top scenes of Dr. Thorndyke dealing with his anxiety but reality is much closer to the comedic scenes than most people who do not have anxiety disorders would understand. WhileRead MoreEpekto Ng Polusyon19213 Words   |  77 PagesDomestic violence: Moving On A Qualitative Investigation Exploring How women Move On From Violent Relationships Researcher: Carole Le Darcy Supervisor: Dr Sue Becker Acknowledgements I would like to express my sincerest thanks and gratitude to all of the exceptionally strong women that participated in this research that have freely given not only some of their precious and valuable time but have also revealed that which is sadly all too often concealed; the remarkable, courageous and oftenRead MoreExaming the Cultural Practice of Ukuthwala and Its Impact on the Rights of the Child13071 Words   |  53 Pagesdifferentiation and expectations in society relegate women to an inferior position from birth throughout their lives. Harmful traditional and cultural practices maintain the subordination of women in society and legitimize and perpetuate gender based violence. This paper attempts to closely examine the practice of ukuthwala in the Eastern Cape which is proving to be a harmful traditional practice. In an effort to achieve that, this paper will put in proper perspective the practice of ukuthwala; it will

Silent Screams Cases of Domestic Violence in The United...

Silent Screams This is the tenth time that Lisa has been admitted to the hospital within the past two years. At least this time there aren’t any broken bones or concussions to worry about. Lisa only has two black eyes, a patch of her beautiful long hair forcibly yanked from her head, a nasty black and blue bruise on her neck and a few nails ripped directly from the newly manicured nail beds. Lisa swore to God and her best friend Brandy that this was the final straw. Actually, she made that exact same pledge under oath just three months ago, yet she is coincidently in the same position she vowed never to return to. This time was different though. She was making plans to move her things out of the small apartment that she shared with her†¦show more content†¦There are cases where a victim of abuse feel that if they leave, the abuser will manipulate the children in taking their side. Men who abuse their wives tend to persuade them into believing that there is nothing or nobody else out side the relationship. There has been several cases where the abuser will actually convince the children that it is the victim’s fault why they did bad things to them in hopes to mislead the child to turn their back on the abused parent. Although it is very important that a person consider the sake of the kids when deciding if they want to go through with a divorce, the jeopardy of one’s life should always take precedence. Low self-esteem can be a contributing factor when women decide to stay in abusive relationships. In many relationships where physical abuse is an issue, the victim is usually verbally abused also. The abuser uses manipulative tactics to make the victim feel worthless, useless, and too afraid to leave them. Many women have confessed that they believe it is their own fault why there are initially abused. After being brainwashed into thinking that they are ugly, disgusting, and lazy or other derogatory characteristics, verbally abused women are being almost forced to believe that if they leave the relationship that there is nobody else that would want to be with them. This unfortunate mindset leaves battered women in an extremely unhealthy and catastrophicShow MoreRelatedPersonal Rights Vs. Religious Beliefs1627 Words   |  7 Pages ABORTION PERSONAL RIGHTS VS. RELIGIOUS BELIEFS AECHMIA COTE LAW 103 BAY PATH UNIVERSITY One of the many controversial topics in the United States is ABORTION. It is defined as a Removal of an embryo or fetus from the uterus in order to end a pregnancy as described on dictionary.com. I must say that, days of research it seems to be a debatable issue especially when it comes to religion and one’s personal choice in life to choose to do it, and remains to beRead MoreA Streetcar Named Desire By Tennessee Williams1263 Words   |  6 Pagesof the twentieth century beheld changes in almost every aspect of the day-to-day lives of women, from the domestic domain to the public. By the midpoint of the twentieth century, women s activities and concerns had been recognized by the society in previously male-dominating world. The end of the nineteenth century saw tremendous growth in the suffrage movement in England and the United States, with women struggling to attain political equality. However, this was not to last however, and by the fiftiesRead MoreThe Effects Of Domestic Violence On Children1813 Words   |  8 PagesEffect Of Domestic Violence On Children Everyday women are being beaten , terrorized and murdered at the hands of their husbands, boyfriends and ex-husbands. At least one woman is battered every 15 seconds. As society we tend to close our eyes to this big problem that affects everybody. we use excuses like that’s none of our business and that we don’t want to get involved, that until someone is murdered and then we are shocked and terrified. united states reports that domestic violence is the greatestRead MoreWhen Leaving Is Not An Option2498 Words   |  10 Pagestemporary and soon comes to an end. The love story they have ones longed for turns into a horrible nightmare. The emotional words they were once spoiled with turn into howling screams and name-calling. The flattering gifts turn into physical abuse. This relationship is referred to as domestic violence or intimate partner violence. This happens when a partner or significant other declares power, authority and control over the other partner. To maintain this authority and control, the abusive partner usesRead MoreDomestic Violence And Sexual Abuse2537 Words   |  11 Pagestemporary and soon comes to an end. The love story they have ones longed for turns into a horrible nightmare. The emotional words, they were once spoiled with turn into howling screams and name-calling. The flattering gifts turn into physical abuse. This relationship is referred to as domesti c violence or intimate partner violence. This happens when a partner or significant other declares power, authority and control over the other partner. To maintain this authority and control, the abusive partner usesRead MoreThe Fetal Position: A Pro-Life Argument Essay2142 Words   |  9 PagesPregnancy). Everyone has a right to life; this right is exercised in many parts of the American life, namely the Declaration of Independence (The Abortion Controversy 113-116). Therefore, the United States’ federal government should go to greater lengths to prohibit these so called ‘abortions’ in every case, regardless of the situation. 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Henry Howard Holmes, One of Americas first Serial Killers Free Essays

string(33) " actually had and who they were\." I researched who is to be believed as the one of america’s First Serial Killers, Herman Webster Mudgett aka Dr. Henry Howard Holmes. He had confessed to 27 murders, but only 9 could actually be proven. We will write a custom essay sample on Henry Howard Holmes, One of Americas first Serial Killers or any similar topic only for you Order Now He had several victims during his time and choose what he felt was the perfect place for these murders. Herman was born on May 16th, 1861 in Gilmanton, New Hampshire to Levi Horton Mudgett and Theodate Page Price, both of whom were descended from the first settlers in the area. His father was a very violent alcoholic and his mother was a Methodist who would often read the bible to her son. Holmes had a privileged childhood. It has been said that he appeared to be unusually intelligent at an early age. Still there were haunting signs of what was to come. He expressed an interest in medicine, which reportedly led him to practice surgery on animals. Some accounts indicate that he may have been responsible for the death of a friend. As a child Herman was scared of the local doctor and when this got out bullies at his school forced him to view and touch a human skeleton. It turns out that this fascinated Herman so much that he actually scared the bullies who forced him into very badly. During much of his life he was considered a loner and very shady. Herman would later graduate from the University of Michigan Medical School in 1884, but while he was enrolled there he began to explore a new area or hobby. He would steal bodies from the lab disfigured the bodies, and claimed that the people were killed accidentally in order to collect insurance money from policies he took out on each deceased person he had stolen. After Graduation he began to dabble in more shady work such as pharmaceuticals, real estate and promotional deals under his created alias H.  H. Holmes. On July 4th 1878, Holmes married Clara Lovering in Alton, New Hampshire; their son, Robert Lovering Mudgett, was born on February 3rd 1880 in Loudon, New Hampshire (in adult life Robert was to become a Certified Public Accountant, and served as City Manager of Orlando, Florida). On January 28th 1887, while he was still married to Clara, Holmes married Myrta Belknap in Minneapolis, Minnesota; their daughter, Lucy Theodate Holmes, was born on July 4th 1889 in Englewood, Illinois. (in adult life Lucy was to become a public schoolteacher). Holmes lived with Myrta and Lucy in Wilmette, Illinois, and spent most of his time in Chicago tending to business. He filed for divorce from Clara after marrying Myrta, but the divorce was never finalized. He married Georgiana Yoke on January 9th 1894 in Denver, Colorado while still married to Clara and Myrta. He also had a relationship with Julia Smythe, the wife of one of his former employees; Julia later became one of Holmes’s victims. While in Chicago, Holmes had started to grow even more shady and criminal. Holmes took a job in a drugstore which he would buy and promise to let the current store owner live even after her husband died. When her husband died however she simply disappeared and as people began to question where she was Holmes lied and told them she went to California and liked it there so much that she decided she would stay there. These people would actually turn out to be his first victims in his long murder spree and it is unknown how and when he murdered them. Holmes purchased a lot across from the drugstore and built what would be later known as his Murder Castle (which is where it is believed that he hid the bodies of Dr.  E. S. Holton and his wife). Holmes would open it up as a hotel for the World’s Columbian Exposition in 1893, with part of the structure used as commercial space. The ground floor of the Castle contained Holmes’s own relocated drugstore and various shops, while the upper two floors contained his personal office and a maze of over one hundred windowless rooms with doorways opening to brick walls, oddly angled hallways, stairways to nowhere, doors opened only from the outside, and a host of other strange and labyrinthine constructions. Holmes repeatedly changed builders during the construction of the Castle, so only he fully understood the design of the house, thus decreasing the chance of being reported to the police. Holmes selected mostly female victims from among his employees (many of which were required as a condition of employment to take out life insurance policies for which Holmes would pay the premiums but also be the beneficiary), as well as his lovers and hotel guests. He tortured and killed them in some of the worst possible ways you could imagine. Some were locked in soundproof bedrooms fitted with gas lines that let him asphyxiate them at any time and some were locked in a huge soundproof bank vault near his office where they were left to suffocate. He would then take the victims’ bodies and drop by secret chute to the basement where some were meticulously dissected, stripped of flesh, crafted into skeleton models, and then sold to medical schools. Holmes also cremated some of the bodies or placed them in lime pits for destruction. Holmes had two giant furnaces as well as pits of acid, bottles of various poisons, and even a stretching rack which he would use to help dispose of the bodies and any evidence. Through the connections he had gained in medical school, he sold skeletons and organs with little difficulty and therefore was able to get rid of even more evidence. He had some of the best methods for disposing of all of his victims and the evidence that anything had ever even happened which is why it is so difficult to determine just how many victims he actually had and who they were. You read "Henry Howard Holmes, One of Americas first Serial Killers" in category "Essay examples" There were also trapdoors and chutes so that he could move the bodies down to the basement where he could burn his victims’ remains in a kiln there or dispose of them in other ways. All the while, Holmes continued to work insurance scams and it was one of these scams that led to his undoing. He joined forces with Benjamin Pitezel to collect $10,000 from a life insurance company. Holmes would leave Chicago due to the economy and move down to Fort Worth, Texas, to a property that he inherited from two sisters he promised to marry and later murdered. He had planned to build another castle, but would abandon that idea and move about the US as well as Canada and he was believed to have killed several more victims on his travels, but no evidence of this could be found. Holmes’s murder spree finally ended when he was arrested in Boston on November 17, 1894, after being tracked there from Philadelphia by the Pinkertons(a national detective agency). He was held on an outstanding warrant for horse theft in Texas, as the police had little more than suspicions at this point and Holmes appeared ready to leave the country, with his unsuspecting third wife. After the custodian for the Castle informed police that he was never allowed to clean the upper floors, police began a thorough investigation over the course of the next month, uncovering Holmes’s efficient methods of committing murders and then disposing of the corpses. While Holmes sat in prison in Philadelphia, not only did the Chicago police investigate his operations in that city, but the Philadelphia police began to try to unravel the Pitezel situation, the fate of the three missing children. Philadelphia detective Frank Geyer was given the task of finding out and his quest for the children, like the search of Holmes’s Castle, received wide publicity. He would eventually discover their remains essentially sealed Holmes’s fate, at least in the public mind. Holmes was put on trial for the murder of Pitezel and confessed, following his conviction, to 27 murders in Chicago, Indianapolis and Toronto, and six attempted murders. Holmes was paid $7,500 ($197,340 in today’s dollars) by the Hearst Newspapers in exchange for this confession. He gave various contradictory accounts of his life, claiming initially innocence and later that he was possessed by Satan. His faculty for lying has made it difficult for researchers to ascertain any truth on the basis of his statements. On May 7, 1896, H. H. Holmes went to the hangman’s noose. His last meal was boiled eggs, dry toast, and coffee. Even at the noose, he changed his story. He claimed to have killed only two people, and tried to say more but at 10:13 the trapdoor opened and he was hanged, it took him fully 15 minutes to strangle to death on the gallows. Afraid of body-snatchers who might capitalize on his corpse, Holmes had made a request: He wanted no autopsy and he instructed his attorneys to see that he was buried in a coffin filled with cement. This was taken to Holy Cross Cemetery south of Philadelphia and two Pinkerton guards stood over the grave during the night before the body was finally interred in a double grave also filled with cement. No stone was erected to mark it, Larson states, although its presence is recorded on a cemetery registry. Holmes attorneys had turned down an offer of $5,000 for his body, and even refused his brain to Philadelphias Wistar Institute, which hoped to have its experts analyze the organ for better understanding of the criminal mind. Larson recounts a series of strange events afterward that gave credence to the rumors that Holmes was satanic, including several weird deaths and a fire at the D. A. s office that destroyed everything there save a photograph of Holmes. During this case, another American phenomenon arose from society’s fascination with sensational crime. Thousands of people lined up to see the Chicago murder site, so a former police officer remodeled the infamous building as â€Å"Holmes’s Horror Castle,† an attraction that offered guided tours to the suffocation chambers and torture rooms. But before it opened it mysteriously burned to the ground. So many people who’d rented rooms from Holmes during the fair had actually gone missing that sensational estimates of his victims reached around 200, and some people perpetuated this unsubstantiated toll even today. Its likely that Holmes own figure from his recanted confession is low, but there is no way to know just how many he actually killed. In the end he was so worried that someone would want to do to him what he had done to so many others that he felt the only way he could rest in peace was to be encased in concrete. He was one of the first ever serial killers and one of the worst. It was horrible what he did and all of the lives lost because of this man. In my opinion his request for a protected grave was one of the things that show you how crazy this man really was and how smart he was all at the same time. In my opinion the starting point in H. H. Holmes spiral to murder would be that as a child, schoolmates forced him to view and touch a human skeleton after discovering his fear of the local doctor. The bullies initially brought him there to scare him, but instead he was utterly fascinated, and he soon became obsessed with death. He started by stealing bodies from the morgue, would disfigure them and then claim they were accidentally killed so he could collect on an insurance policy he would take out on each person. Some of his fellow students became scared of him while trying to bully him, he was a bigamist, some felt he was charming, he was manipulative, and many of those around him viewed him as suspicious and shady. H. H. Holmes seemed to have the perfect idea on how to get rich and how to get away with murder and in fact he did for a long time. He was a very smart man and that is the reason that I believe he was able to go so long without getting caught. On New Year’s Eve, 1910, Marion Hedgepeth, who had been pardoned for informing on Holmes, was shot and killed by a police officer during a holdup at a Chicago saloon. Then, on March 7, 1914, the Chicago Tribune reported that, with the death of the former caretaker of the Murder Castle, Pat Quinlan, â€Å"the mysteries of Holmes’ Castle† would remain unexplained. Quinlan had committed suicide by taking strychnine. Quinlan’s surviving relatives claimed Quinlan had been â€Å"haunted† for several months before his death and could not sleep. How to cite Henry Howard Holmes, One of Americas first Serial Killers, Essay examples

Marriage in the Bible

Table of Contents Introduction Importance of Marriage Is it compulsory? Role of Husband and Wife in Marriage Divorce and Remarriage-marriage Conclusion References Introduction The Bible regards marriage as a union between a man and woman. In the Garden of Eden, God created man and woman and then established the marriage institution. During creation, God realized that man would be alone and lonely without company, hence the need to come up with a helper.Advertising We will write a custom essay sample on Marriage in the Bible specifically for you for only $16.05 $11/page Learn More The book of genesis 2:24 (King James Version), says â€Å"therefore shall a man leave his father and his mother, and shall cleave unto his wife: and they will be one flesh.† From the creation story, it is evident that God instituted marriage as a union between man and woman. Although God instituted marriage as the foundation of family and society, His apostle declared that Christians could opt to remain single so long as they could control their urges and avoid indulging in immoral sexual behaviors. Some patriarchs and prophets such as Jeremiah, Elijah, Paul, and even Jesus never married. Hence, marriage in the Bible is an issue that has divided Christians based on the Biblical interpretation because some root for marriage while others support celibacy. Importance of Marriage After creating man, God realized that man could not live happily without companionship and thus created a helper for him. Since the Garden of Eden was very expansive and Adam was not able to dress it on his own, God reasoned that he needed a companion and helper. When Adam woke up from deep sleep, he recognized Eve as part of his bones and flesh. Adam expressed satisfaction in having Eve as his companion and helper. Adams (1986) asserts, â€Å"God designed marriage as the foundational element of all human society† (p.4). During creation, Adam and eve formed the basic unit of society and thus set the precedent of marriage as a union of a man and a woman. Hence, God instituted marriage as a source of companionship for man and woman as they tended the Garden of Eden (Hanegraaff, 2012).Advertising Looking for essay on religion theology? Let's see if we can help you! Get your first paper with 15% OFF Learn More Marriage is also important to humans because it provides them with the ability to procreate and build strong societies that respect human dignity. God created only Adam and Eve and through procreation, they have multiplied and filled the earth with billions of people. According to the book of genesis 1:28, after creating a man and a woman, God bestowed them with blessings and told them to â€Å"†¦be fruitful, and multiply, and replenish the earth, and subdue it: and have dominion over the fish of the sea, and over the fowl of the air, and over every living thing that moveth upon the earth.† Adam and Eve used their p ower to procreate and multiply populations, thus replenishing the earth so that they could rule the world. Hence, the procreation capacity of marriage has helped humanity to multiply and replenish the earth as per the blessings that God gave to Adam and Eve during creation. Is it compulsory? In the Bible, marriage is not compulsory, but it depends on the interests of a person. However, catholic has made it compulsory for nuns and monks to stay away from marriage. Catholics believe that celibacy is a better option because it relieves a person from marriage and family responsibilities and increases commitment to spiritual issues. In his concession, Paul asserts, â€Å"†¦it is not good for a man to touch a woman† (1 Corinthians 7:1). Some Christians have taken the concession that Paul made in Corinthians and practiced celibacy as a means of dedicating their lives to spiritual matters. Christians who practice celibacy have accepted that marriage is not good because it interf eres with spiritual matters that God has ordained for them to perform. For example, when Jesus was selecting his disciples, he told them â€Å"follow me†, but one gave an excuse that he wanted to go home and bury the dead while another said he wanted to return home and bid farewell to his family (Luke 9:59). In marriage, people experience many challenges that can distract them from pursing their missions as ordained by God. Hence, Paul’s sentiments explain why nuns and monks do not marry. However, most Christians accept marriage as a holy institution that should form the basis of family and society. Without marriage, it would be very hard for Christians to instill Christian values and principles on families and the general society. Thus, marriage is a basic unit of family and society, which has a noble role of defining morality in the society.Advertising We will write a custom essay sample on Marriage in the Bible specifically for you for only $16.05 $11 /page Learn More Sexual immorality has been a setback, which has been downgrading the essence of marriage in modern society. Campbell (2003) argues, â€Å"Extramarital acts of sexual love are, no less than unloving begetting, attempts to put asunder on what God joined together†¦Ã¢â‚¬  (p. 266). Owing to immorality, Paul admonishes Christians, â€Å"to avoid fornication, let every man have his own wife, and let every woman have her own husband† (1 Corinthians 7:2). Therefore, most Christian factions advise their members to marry to avoid the temptations of immorality, which is exceedingly rampant in the modern society. Role of Husband and Wife in Marriage During creation, God defined the responsibility of a woman as a helper. After God created Adam, He noted that he had a great responsibility of tending the Garden of Eden, and thus decided to create a helper for him. The creation story says that God made Adam sleep before removing one of his ribs out of w hich he molded Eve. When Adam woke up, he recognized eve as part of his bones and flesh. As a helper, a wife plays a significant role in assisting her husband to perform certain duties. According to Adams (1986), God created Eve to help man in procreation purposes and in tending the Garden of Eden. Therefore, wives and husbands have common duties on this earth. The Bible states that a husband should be the head of the family. Husband has a great responsibility of providing to the family and ensuring that family members have protection from external forces. The book of Ephesians advises women to submit to their husbands â€Å"for the husband is the head of the wife, even as Christ is the head of the church: and he is the savior of the body† (5:23). Moreover, the Bible apprises husbands to show their wives unconditional love for Christ did the same when He went on the cross. In this view, Campbell (2003) advises that husbands should not treat their wives and children as slaves, but rather they should â€Å"treat their wives as equals, assuming their God-given responsibility of caring, protecting, and providing for them† (p. 60). Hence, husband and wife have complementary roles in the family, which are essential in caring, providing, and protecting their family members.Advertising Looking for essay on religion theology? Let's see if we can help you! Get your first paper with 15% OFF Learn More Divorce and Remarriage-marriage Problems in marriages have compelled many couples to divorce and remarry. Cases of divorce are rampant is the modern society because social, economic, and cultural problems have increased in the past decades. The Bible views marriage as an eternal union between man and woman as it states that when people get married, they become one flesh and thus, â€Å"what therefore God hath joined together, let not man put asunder† (Mathew 19:6). Although Moses instructed Israelites to divorce their wives by giving them a divorce certificate, Jesus said that God permitted divorce because people have hardened their hearts; however, but God does not sanction divorce. Hence, when Jesus came, he tightened the issue of divorce among Christians by saying, â€Å"Whosoeuer putteth away his wife, marrieth another, committeth adultery: and whosoeuer marrieth her that is put away from her husband, committeth adultery† (Luke 16:18). In this statement, Jesus pre vents married couples from divorcing and remarrying as they please for it is against marriage principles as instituted by God in the Garden of Eden. Conclusion Fundamentally, marriage is a holy institution that God started in the Garden of Eden. It consists of union between a man and woman who have agreed to stay together in a marriage. Although Paul gave his opinion that celibacy is good, some religions have made it compulsory for religious servants to uphold chastity in a bid to ensure total commitment to spiritual matters. However, the Bible teaches that to marry or not to remain single is a personal issue that no one should impose on another. Therefore, people should respect marriage by making an informed decision on whether to marry or not, and when they marry, they should understand that the Bible does not permit divorce. References Adams, J. (1986). Marriage, Divorce, and Remarriage in the Bible: A fresh look at what  Scripture teaches. New York, NY: Zondervan. Campbell, K. (2003). Marriage and Family in the Biblical World. New York, NY: InterVarsity Press. .Hanegraaff, H. (2012). The Creation Answer Book. Colorado, CO: Thomas Nelson. This essay on Marriage in the Bible was written and submitted by user Samara C. to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

Social Comparison Theory

Social Comparison Theory With regards to questions about identity, the average person responds by comparing himself to others. However, it is important to point out that the person compares himself to people that are in his immediate vicinity. Comparisons are made based on unique attributes, such as, age, gender, eye color, and height.Advertising We will write a custom research paper sample on Social Comparison Theory specifically for you for only $16.05 $11/page Learn More Thus, the average person relies on distinguishing features in self-description (Kassin, Fein, Markus, 2014). Interestingly, the answer to the question does not remain constant. If the interviewer has the power to change the person’s social surroundings, then, he must also expect a different set of answers based on the same questions. Therefore, the self is a â€Å"relative† social construct (Kassin, Fein, Markus, 2014). The significance of social comparison theory is in the idea that an individual has the capability to change his behavior, and how he perceives himself. Defining Social Comparison Theory The core concept of social comparison theory is the brainchild of Leon Festinger. He pointed out that a person belongs to a particular social group. Festinger added that the said social group influences a person’s opinion and abilities. Social comparison theory asserts that a person’s self-description is dependent on information gleaned from observing family members, friends, acquaintances, and other important person in the lives of the interviewee. Festinger asserted that, â€Å"individuals adopted a group’s standards by comparing their own opinions, and abilities with the consensus in the group, and modifying their views so that they were in accordance with the group’s norms† (Krizan Gibbons, 2014, p.39). Festinger emphasized the idea that â€Å"individuals compare themselves to others in order to seek information about the world and thei r place in it† (Krizan Gibbons, 2014, p.39).  It is important to point out, that to some extent self-description is even influenced by the â€Å"fleeting, everyday exposure to strangers† (Kassin, Fein, Markus, 2014, p.64). Nevertheless, the average person compares himself to those who are similar to him in relevant ways. For example, a college student will determine his reading ability based on how he sees himself in comparison to other college students. He will not compare himself to high school students.Advertising Looking for research paper on social sciences? Let's see if we can help you! Get your first paper with 15% OFF Learn More Significance of Social Comparison Theory Social comparison theory’s biggest contribution is the discovery that â€Å"the more uncertain people are, the more they will rely on those comparison for definition and validation† (Gerber, 1999, p.173). As a consequence, â€Å"individuals resolve their uncertainties by reference to groups, and that group definition often comes from comparison with other groups (Gerber, 1999, p.173). One of the problematic stages in personal development occurs during the teenage years when an individual is least uncertain and more vulnerable. Teenagers are prone to make choices that will negatively affect their future. It is therefore interesting to apply social comparison theory in crafting strategies that will help solve social problems involving teenagers. There are a variety of ways that social scientists can apply insights gleaned from the study of social comparison theory. Two of the most exciting areas are in the study of gang-related violence, and the creation of more effective intervention strategies in cases involving alcoholism or drug addiction. In this regard it is important to point out that the family is the â€Å"primary and most influential group for comparison, and for establishment of lifestyle† (Gerber, 1999, p.173). The focus must be on the family. It is imperative to support parents. It is imperative to focus resources to families in order to help parents build a strong family structure. Community resources must be redirected to the family. When it comes to gang-related problems, it is imperative to consider the impact of the group when it comes to validation, and the establishment of the person’s lifestyle. It is therefore foolish to attempt reforming behavior without creating a mechanism that can help the individual receive positive validation and develop a different kind of lifestyle. This is perhaps the reason why Alcoholics Anonymous is successful in helping people change their behavior towards the consumption of liquor. Alcoholics Anonymous created a new group or an environment filled with new social interconnections that help the individual create new social norms. Conclusion Social comparison theory has many applications. This theory offers insights when it comes to personal develop ment and human behavior. However, one of the key aspects of social comparison theory is the way it explains how an individual’s self-description is influenced by social factors that surround him.Advertising We will write a custom research paper sample on Social Comparison Theory specifically for you for only $16.05 $11/page Learn More According to this theory, â€Å"self† is a relative construct. This is an interesting insight into human behavior and personal development. This theory can be utilized to solve social issues, such as, gang-related violence and drug addiction. It means that a person is dependent on social factors when it comes to altering behavior. It is therefore important to strengthen family structures. In the struggle against gang-related violence and drug addiction, half the battle is already won if a child belongs to a family that can help him establish a positive lifestyle. With regards to individuals that needed a way out of their troubled past, counselors and intervention specialists must develop a mechanism that will enable patients to generate positive validation. They need a mechanism that will help them establish a new kind of lifestyle. It can be argued that Alcoholics Anonymous is successful in helping people overcome destructive behavior, because they create a new environment that helps patients alter their â€Å"self† construct in a positive way. References Gerber, S. (1999). Enhancing counselor intervention strategies: An integrational  viewpoint. PA: Taylor Francis Group. Kassin, S., Fein, S., Markus, H. (2014). Social psychology. CA: Cengage Learning. Krizan, Z. Gibbons, F. (2014). Communal functions of social comparison.  New York: Cambridge University Press.Advertising Looking for research paper on social sciences? Let's see if we can help you! Get your first paper with 15% OFF Learn More

Complete Guide to Integers on SAT Math (Advanced)

Complete Guide to Integers on SAT Math (Advanced) SAT / ACT Prep Online Guides and Tips Integer questions are some of the most common on the SAT, so understanding what integers are and how they operate will be crucial for solving many SAT math questions. Knowing your integers can make the difference between a score you’re proud of and one that needs improvement. In our basic guide to integers on the SAT (which you should review before you continue with this one), we covered what integers are and how they are manipulated to get even or odd, positive or negative results. In this guide, we will cover the more advanced integer concepts you’ll need to know for the SAT. This will be your complete guide to advanced SAT integers, including consecutive numbers, primes, absolute values, remainders, exponents, and roots- what they mean, as well as how to handle the more difficult integer questions the SAT can throw at you. Typical Integer Questions on the SAT Because integer questions cover so many different kinds of topics, there is no â€Å"typical† integer question. We have, however, provided you with several real SAT math examples to show you some of the many different kinds of integer questions the SAT may throw at you. Over all, you will be able to tell that a question requires knowledge and understanding of integers when: #1: The question specifically mentions integers (or consecutive integers). Now this may be a word problem or even a geometry problem, but you will know that your answer must be in whole numbers (integers) when the question asks for one or more integers. If $j$, $k$, and $n$ are consecutive integers such that $0jkn$ and the units (ones) digit of the product $jn$ is 9, what is the units digit of $k$? A. 0B. 1C. 2D. 3E. 4 (We will go through the process of solving this question later in the guide) #2: The question deals with prime numbers. A prime number is a specific kind of integer, which we will discuss in a minute. For now, know that any mention of prime numbers means it is an integer question. What is the product of the smallest prime number that is greater than 50 and the greatest prime number that is less than 50? (We will go through the process of solving this question later in the guide) #3: The question involves an absolute value equation (with integers) Anything that is an absolute value will be bracketed with absolute value signs which look like this:| | For example: $|-210|$ or $|x + 2|$ $|10 - k| = 3$ $|k - 5| = 8$ What is a value for k that fulfills both equations above? (We will go through how to solve this problem in the section on absolute values below) Note: there are several different kinds of absolute value problems. About half of the absolute value questions you come across will involve the use of inequalities (represented by $$ or $$). If you are unfamiliar with inequalities, check out our guide to inequalities. The other types of absolute value problems on the SAT will either involve a number line or a written equation. The absolute value questions involving number lines almost always use fraction or decimal values. For information on fractions and decimals, look to our guide to SAT fractions. We will be covering only written absolute value equations (with integers) in this guide. #4: The question uses perfect squares or asks you to reduce a root value A root question will always involve the root sign: $√$ $√81$, $^3√8$ You may be asked to reduce a root, or to find the square root of a perfect square (a number that is the square of an integer). You may also need to multiply two or more roots together. We will go through these definitions as well as how all of these processes are done in the section on roots. (Note: A root question with perfect squares may involve fractions. For more information on this concept, look to our guide on fractions and ratios.) #5: The question involves multiplying or dividing bases and exponents Exponents will always be a number that is positioned higher than the main (base) number: $2^7$, $(x^2)^4$ You may be asked to find the values of exponents or find the new expression once you have multiplied or divided terms with exponents. We will go through all of these questions and topics throughout this guide in the order of greatest prevalence on the SAT. We promise that integers are a whole lot less mysterious than...whatever these things are. Exponents Exponent questions will appear on every single SAT, and you will likely see an exponent question at least twice per test. An exponent indicates how many times a number (called a â€Å"base†) must be multiplied by itself. So $4^2$ is the same thing as saying $4 * 4$. And $4^5$ is the same thing as saying $4 * 4 * 4 * 4 * 4$. Here, 4 is the base and 2 and 5 are the exponents. A number (base) to a negative exponent is the same thing as saying 1 divided by the base to the positive exponent. For example, $2^{-3}$ becomes $1/2^3$ = $1/8$ If $x^{-1}h=1$, what does $h$ equal in terms of $x$? A. $-x$B. $1/x$C. $1/{x^2}$D. $x$E. $x^2$ Because $x^{-1}$ is a base taken to a negative exponent, we know we must re-write this as 1 divided by the base to the positive exponent. $x^{-1}$ = $1/{x^1}$ Now we have: $1/{x^1} * h$ Which is the same thing as saying: ${1h}/x^1$ = $h/x$ And we know that this equation is set equal to 1. So: $h/x = 1$ If you are familiar with fractions, then you will know that any number over itself equals 1. Therefore, $h$ and $x$ must be equal. So our final answer is D, $h = x$ But negative exponents are just the first step to understanding the many different types of SAT exponents. You will also need to know several other ways in which exponents behave with one another. Below are the main exponent rules that will be helpful for you to know for the SAT. Exponent Formulas: Multiplying Numbers with Exponents: $x^a * x^b = x^[a + b]$ (Note: the bases must be the same for this rule to apply) Why is this true? Think about it using real numbers. If you have $2^4 * 2^6$, you have: $(2 * 2 * 2 * 2) * (2 * 2 * 2 * 2 * 2 * 2)$ If you count them, this give you 2 multiplied by itself 10 times, or $2^10$. So $2^4 * 2^6$ = $2^[4 + 6]$ = $2^10$. If $7^n*7^3=7^12$, what is the value of $n$? A. 2B. 4C. 9D. 15E. 36 We know that multiplying numbers with the same base and exponents means that we must add those exponents. So our equation would look like: $7^n * 7^3 = 7^12$ $n + 3 = 12$ $n = 9$ So our final answer is C, 9. $x^a * y^a = (xy)^a$ (Note: the exponents must be the same for this rule to apply) Why is this true? Think about it using real numbers. If you have $2^4 * 3^4$, you have: $(2 * 2 * 2 * 2) * (3 * 3 * 3 * 3)$ = $(2 * 3) * (2 * 3) * (2 * 3) * (2 * 3)$ So you have $(2 * 3)^4$, or $6^4$ Dividing Exponents: ${x^a}/{x^b} = x^[a-b]$ (Note: the bases must be the same for this rule to apply) Why is this true? Think about it using real numbers. ${2^6}/{2^2}$ can also be written as: ${(2 * 2 * 2 * 2 * 2 * 2)}/{(2 * 2)}$ If you cancel out your bottom 2s, you’re left with $(2 * 2 * 2 * 2)$, or $2^4$ So ${2^6}/{2^2}$ = $2^[6-2]$ = $2^4$ If $x$ and $y$ are positive integers, which of the following is equivalent to $(2x)^{3y}-(2x)^y$? A. $(2x)^{2y}$B. $2^y(x^3-x^y)$C. $(2x)^y[(2x)^{2y}-1]$D. $(2x)^y(4x^y-1)$E. $(2x)^y[(2x)^3-1]$ In this problem, you must distribute out a common element- the $(2x)^y$- by dividing it from both pieces of the expression. This means that you must divide both $(2x)^{3y}$ and $(2x)^y$ by $(2x)^y$. Let's start with the first: ${(2x)^{3y}}/{(2x)^y}$ Because this is a division problem that involves exponents with the same base, we say: ${(2x)^{3y}}/{(2x)^y} = (2x)^[3y - y]$ So we are left with: $(2x)^{2y}$ Now, for the second part of our equation, we have: ${(2x)^y}/{(2x)^y}$ Again, we are dividing exponents that have the same base. So by the same process, we would say: ${(2x)^y}/{(2x)^y} = (2x)^[y - y] = (2x)^0 = 1$ (Why 1? Because, as you'll see below, anything raised to the power of 0 = 1) So our final answer looks like: ${(2x)^y}{((2x)^{2y} - 1)}$ Which means our final answer is C. Taking Exponents to Exponents: $(x^a)^b = x^[a * b]$ Why is this true? Think about it using real numbers. $(2^3)^4$ can also be written as: $(2 * 2 * 2) * (2 * 2 * 2) * (2 * 2 * 2) * (2 * 2 * 2)$ If you count them, 2 is being multiplied by itself 12 times. So $(2^3)^4 = 2^[3 * 4] = 2^12$ $(x^y)^6 = x^12$, what is the value of $y$? A. 2B. 4C. 6D. 10E. 12 Because exponents taken to exponents are multiplied together, our problem would look like: $y * 6 = 12$ $y = 2$ So our final answer is A, 2. Distributing Exponents: $(x/y)^a = {x^a}/{y^a}$ Why is this true? Think about it using real numbers. $(2/4)^3$ can be written as: $(2/4) * (2/4) * (2/4)$ $8/64 = 1/8$ You could also say $2^3/4^3$ = $8/64$ = $1/8$ $(xy)^z = x^z * y^z$ If you are taking a modified base to the power of an exponent, you must distribute that exponent across both the modifier and the base. $(3x)^3$ = $3^3 * x^3$ (Note on distributing exponents: you may only distribute exponents with multiplication or division- exponents do not distribute over addition or subtraction. $(x + y)^a$ is NOT $x^a + y^a$, for example) Special Exponents: For the SAT you should know what happens when you have an exponent of 0: $x^0=1$ where $x$ is any number except 0 (Why any number but 0? Well 0 to any power other than 0 is 0, because $0x = 0$. And any other number to the power of 0 is 1. This makes $0^0$ undefined, as it could be both 0 and 1 according to these guidelines.) Solving an Exponent Question: Always remember that you can test out exponent rules with real numbers in the same way that we did above. If you are presented with $(x^2)^3$ and don’t know whether you are supposed to add or multiply your exponents, replace your x with a real number! $(2^2)^3 = (4)^3 = 64$ Now check if you are supposed to add or multiply your exponents. $2^[2+3] = 2^5 = 32$ $2^[2 * 3] = 2^6 = 64$ So you know you’re supposed to multiply when exponents are taken to another exponent. This also works if you are given something enormous, like $(x^23)^4$. You don’t have to test it out with $2^23$! Just use smaller numbers like we did above to figure out the rules of exponents. Then, apply your newfound knowledge to the larger problem. And the philosophical debate continues. Roots Root questions are common on the SAT, and you should expect to see at least one during your test. Roots are technically fractional exponents. You are likely most familiar with square roots, however, so you may have never heard a root expressed in terms of exponents before. A square root asks the question: "What number needs to be multiplied by itself one time in order to equal the number under the root sign?" So $√36 = 6$ because 6 must be multiplied by itself one time to equal 36. In other words, $6^2 = 36$ Another way to write $√36$ is to say $^2√36$. The 2 at the top of the root sign indicates how many numbers (2 numbers, both the same) are being multiplied together to become 36. (Note: you do not expressly need the 2 at the top of the root sign- a root without an indicator is automatically a square root.) So $^3√27 = 3$ because three numbers, all of which are the same ($3 * 3 * 3$), multiplied together equals 27. Or $3^3 = 27$. Fractional Exponents If you have a number to a fractional exponent, it is just another way of asking you for a root. So $16^{1/2} = ^2√16$ To turn a fractional exponent into a root, the denominator becomes the value to which you take the root. But what if you have a number other than 1 in the numerator? $16^{2/3} = ^3√16^2$ The denominator becomes the value to which you take the root, and the numerator becomes the exponent to which you take the number under the root sign. Distributing Roots $√xy = √x * √y$ Just like with exponents, roots can be separated out. So $√20$ = $√2 * √10$ or $√4 * √5$ $√x * √y = √xy$ Because they can be separated, roots can also come together. So $√2 * √10$ = $√20$ Reducing Roots It is common to encounter a problem with a mixed root, where you have an integer multiplied by a root (like $3√2$). Here, $3√2$ is reduced to its simplest form, but let's say you had something like this instead: $2√12$ Now $2√12$ is NOT as reduced as it can be. In order to reduce it, we must find out if there are any perfect squares that factor into 12. If there are, then we can take them out from under the root sign. (Note: if there is more than one perfect square that can factor into your number under the root sign, use the largest one.) 12 has several factor pairs. These are: $1 * 12$ $2 * 6$ $3 * 4$ Well 4 is a perfect square because $2 * 2 = 4$. That means that $√4 = 2$. This means that we can take 4 out from under the root sign. Why? Because we know that $√xy = √x * √y$. So $√12 = √4 * √3$. And $√4 = 2$. So 4 can come out from under the root sign and be replaced by 2 instead. $√3$ is as reduced as we can make it, since it is a prime number. We are left with $2√3$ as the most reduced form of $√12$ (Note: you can test to see if this is true on most calculators. $√12 = 3.4641$ and $2 *√3 = 2 * 1.732 = 3.4641$. The two expressions are identical.) Now to finish the problem, we must multiply our reduced form of $√12$ by 2. Why? Because our original expression was $2√12$. $2 * 2√3 = 4√3$ So $2√12$ in its most reduced form is $4√3$ Remainders Questions involving remainders generally show up at least once or twice on any given SAT. A remainder is the amount left over when two numbers do not divide evenly. If you divide 12 by 4, you will not have any remainder (your remainder will be zero). But if you divide 13 by 4, you will have a remainder of 1, because there is 1 left over. You can think of the division as $13/4 = 3{1/4}$. That extra 1 is left over. Most of you probably haven’t worked with integer remainders since elementary school, as most higher level math classes and questions use decimals to express the remaining amount after a division (for the above example, $13/4 = 3 \remainder 1$ or $3.25$). But for some situations, decimals simply do not apply. Joanne’s hens laid a total of 33 eggs. She puts them into cartons that fit 6 eggs each. How many eggs will she have left that do NOT make a full carton of eggs? $33/6 = 5 \remainder 3$. So Joanne can make 5 full baskets with 3 eggs left over. Some remainder questions may seem incredibly obscure, but they are all quite basic once you understand what is being asked of you. Which of the following answers could be the remainders, in order, when five positive consecutive integers are divided by 4? A. 0, 1, 2, 3, 4B. 2, 3, 0, 1, 2C. 0, 1, 2, 0, 1D. 2, 3, 0, 3, 2E. 2, 3, 4, 3, 2 This question may seem complicated at first, so let’s break it down into pieces. The question is asking us to find the list of remainders when positive consecutive integers are divided by 4. This means we are NOT looking for the answer plus remainders- we are just trying to find the remainders by themselves. We will discuss consecutive integers below in the guide, but for now understand that "positive consecutive integers" means positive integers in a row along a number line. So positive consecutive integers increase by 1 continuously. , 12, 13, 14, 15, etc. are an example of positive consecutive integers. We also know that any number divided by 4 can have a maximum remainder of 3. Why? Because if any number could be divided by 4 with a remainder of 4 left over, it means it could be divided by 4 one more time! For example, $16/4 = 4 \remainder 0$ because 4 goes into 16 exactly 4 times. (It is NOT $3 \remainder 4$.) So that automatically lets us get rid of answer choices A and E, as those options both include a 4 for a remainder. Now we also know that, when positive consecutive integers are divided by any number, the remainders increase by 1 until they hit their highest remainder possible. When that happens, the next integer remainder resets to 0. This is because our smaller number has gone into the larger number an even number of times (which means there is no remainder). For example, $10/4 = 2 \remainder 2$, $/4 = 2 \remainder 3$, $12/4 = 3 \remainder 0$, and $13/4 = 3 \remainder 1$ Once the highest remainder value is achieved (n - 1, which in this case is 3), the next remainder resets to 0 and then the pattern repeats again from 1. So we’re looking for a pattern where the remainders go up by 1, reset to 0 after the remainder = 3, and then repeat again from 1. This means the answer is B, 2, 3, 0, 1, 2 Luckily, Joanne's remaining eggs did not go unloved for long. Prime numbers The SAT loves to test students on prime numbers, so you should expect to see one question per test on prime numbers. Be sure to understand what they are and how to find them. A prime number is a number that is only divisible by two numbers- itself and 1. For example, is a prime number because $1 * $ is its only factor. ( is not evenly divisible by 2, 3, 4, 5, 6, 7, 8, 9, or 10). 12 is NOT a prime number, because its factors are 1, 2, 3, 4, 6, and 12. It has more factors than just itself and 1. 1 is NOT a prime number, because its only factor is 1. The only even prime number is 2. Questions about primes come up fairly often on the SAT and understanding that 2 (and only 2!) is a prime number will be invaluable for solving many of these. A prime number $x$ is squared and then added to a different prime number, $y$. Which of the following could be the final result? An even number An odd number A positive number A. I onlyB. II onlyC. III onlyD. I and III onlyE. I, II, and III Now this question relies on your knowledge of both number relationships and primes. You know that any number squared (the number times itself) will be an even number if the original number was even, and an odd number if the original number was odd. Why? Because an even * an even = an even, and an odd * an odd = an odd ($6 * 6 = 36$ $7 * 7 = 49$). Next, we are adding that square to another prime number. You’ll also remember that an even number + an odd number is odd, an odd number + an odd number is even, and an even number + an even number is even. Knowing that 2 is a prime number, let’s replace x with 2. $2^2 = 4$. Now if y is a different prime number (as stipulated in the question), it must be odd, because the only even prime number is 2. So let’s say $y = 3$. $4 + 3 = 7$. So the end result is odd. This means II is correct. But what if both x and y were odd prime numbers? So let’s say that $x = 3$ and $y = 5$. So $3^2 = 9$. $9 + 5 = 14$. So the end result is even. This means I is correct. Now, for option number III, our results show that it is possible to get a positive number result, since both our results were positive. This means the final answer is E, I, II, and III If you forgot that 2 was a prime number, you would have picked D, I and III only, because there would have been no possible way to get an odd number. Remembering that 2 is a prime number is the key to solving this question. Another typical prime number question on the SAT will ask you to identify how many prime numbers fall in a certain range of numbers. How many prime numbers are between 30 and 50, inclusive? A. TwoB. ThreeC. FourD. FiveE. Six This might seem intimidating or time-consuming, but I promise you do NOT need to memorize a list of prime numbers. First, eliminate all even numbers from the list, as you know the only even prime number is 2. Next, eliminate all numbers that end in 5. Any number that ends is 5 or 0 is divisible by 5. Now your list looks like this: 31, 33, 37, 39, 41, 43, 47, 49 This is much easier to work with, but we need to narrow it down further. (You could start using your calculator here, or you can do this by hand.) A way to see if a number is divisible by 3 is to add the digits together. If that number is 3 or divisible by 3, then the final result is divisible by 3. For example, the number 31 is NOT divisible by 3 because $3 + 1 = 4$, which is not divisible by 3. However 33 is divisible by 3 because $3 + 3 = 6$, which is divisible by 3. So we can now eliminate 33 ($3 + 3 = 6$) and 39 ($3 + 9 = 12$) from the list. We are left with 31, 37, 41, 43, 47, 49. Now, to make sure you try every necessary potential factor, take the square root of the number you are trying to determine is prime. Any integer equal to or less than the square root will be a potential factor, but you do not have to try any numbers higher. Why? Well let’s take 36 as an example. Its factors are: 1, 2, 3, 4, 6, 9, 12, 18, and 36. But now look at the factor pairings. 1 36 2 18 3 12 4 9 6 6 (9 4) (12 3) (18 2) (36 1) After you get past 6, the numbers repeat. If you test out 4, you will know that 9 goes evenly into your larger number- no need to actually test 9 just to get 4 again! So all numbers less than or equal to a potential prime’s square root are the only potential factors you need to test. Going back to our list, we have 31, 37, 41, 43, 47, 49. Well the closest square root to 31 and 37 is 6. We already know that neither 2 nor 3 nor 5 factor evenly into 31 and 37. Neither do 4, or 6. You’re done. Both 31 and 37 must be prime. As for 41, 43, 47, and 49, the closest square root of these is 7. We already know that neither 2 nor 3 nor 5 factor evenly into 41, 43, 47, or 49. 7 is the exact square root of 49, so we know 49 is NOT a prime. As for 41, 43, and 47, neither 4 nor 6 nor 7 go into them evenly, so they are all prime. You are left with 31, 37, 41, 43, and 47. So your answer is D, there are five prime numbers (31, 37, 41, 43, and 47) between 30 and 50. Prime numbers, Prime Directive, either way I'm sure we'll live long and prosper. Absolute Values Absolute values are a concept that the SAT loves to use, as it is all too easy for students to make mistakes with absolute values. Expect to see one question on absolute values per test (though very rarely more than one). An absolute value is a representation of distance along a number line, forward or backwards. This means that an absolute value equation will always have two solutions. It also means that whatever is in the absolute value sign will be positive, as it represents distance along a number line and there is no such thing as a negative distance. An equation $|x + 3| = 14$, has two solutions: $x = $ $x = -17$ Why -17? Well $-17 + 3 = -14$ and, because it is an absolute value (and therefore a distance), the final answer becomes positive. So $|-14| = 14$ When you are presented with an absolute value, instead of doing the math in your head to find the negative and positive solution, rewrite the equation into two different equations. When presented with the above equation $|x + 3| = 14$, take away the absolute value sign and transform it into two equations- one with a positive solution and one with a negative solution. So $|x + 3| = 14$ becomes: $x + 3 = 14$ AND $x + 3 = -14$ Solve for $x$ $x = $ and $x = -17$ $|10 - k| = 3$ $|k - 5| = 8$. What is a value for $k$ that fulfills both equations above? We know that any given absolute value expression will have two solutions, so we must find the solution that each of these equations shares in common. For our first absolute value equation, we are trying to find the numbers for $k$ that, when subtracted from 10 will give us 3 and -3. That means our $k$ values will be 7 and 13. Why? Because $10 - 7 = 3$ and $10 - 13 = -3$ Now let's look at our second equation. We know that the two numbers for $k$ for $k - 5$ must give us both 8 and -8. This means our $k$ values will be 13 and -3. Why? Because $13 - 5 = 8$ and $-3 - 5 = -8$. 13 shows up as a solution for both problems, which means it is our answer. So our final answer is 13, this is the number for $k$ that can solve both equations. Consecutive Numbers Questions about consecutive numbers may or may not show up on your SAT. If they appear, it will be for a maximum of one question. Regardless, they are still an important concept for you to understand. Consecutive numbers are numbers that go continuously along the number line with a set distance between each number. So an example of positive, consecutive numbers would be: 4, 5, 6, 7, 8 An example of negative, consecutive numbers would be: -8, -7, -6, -5, -4 (Notice how the negative integers go from greatest to least- if you remember the basic guide to integers, this is because of how they lie on the number line in relation to 0) You can write unknown consecutive numbers out algebraically by assigning the first in the series a variable, $x$, and then continuing the sequence of adding 1 to each additional number. The sum of four positive, consecutive integers is 54. What is the first of these integers? If x is our first, unknown, integer in the sequence, so you can write all four numbers as: $x + (x + 1) + (x + 2) + (x + 3) = 54$ $4x + 6 = 54$ $4x = 48$ $x = 12$ So, because x is our first number in the sequence and $x= 12$, the first number in our sequence is 12. You may also be asked to find consecutive even or consecutive odd integers. This is the same as consecutive integers, only they are going up every other number instead of every number. This means there is a difference of two units between each number in the sequence instead of 1. An example of positive, consecutive even integers: 8, 10, 12, 14, 16 An example of positive, consecutive odd integers: 15, 17, 19, 21, 23 Both consecutive even or consecutive odd integers can be written out in sequence as: $x, x + 2, x + 4, x + 6$, etc. No matter if the beginning number is even or odd, the numbers in the sequence will always be two units apart. What is the median number in the sequence of five positive, consecutive odd integers whose sum is 185? $x + (x + 2) + (x + 4) + (x + 6) + (x + 8) = 185$ $5x + 20 = 185$ $5x = 165$ $x = 33$ So the first number in the sequence is 33. This means the full sequence is: 33, 35, 37, 39, 41 The median number in the sequence is 37. Bonus history lesson- Grover Cleveland is the only US president to have ever served two non-consecutive terms. Steps to Solving an SAT Integer Question Because SAT integer questions are so numerous and varied, there is no set way to approach them that is entirely separate from approaching other kinds of SAT math questions. But there are a few techniques that will help you approach your SAT integer questions (and by extension, most questions on SAT math). #1: Make sure the question requires an integer. If the question does NOT specify that you are looking for an integer, then any number- including decimals and fractions- are fair game. Always read the question carefully to make sure you are on the right track. #2: Use real numbers if you forget your integer rules. Forget whether positive, even consecutive integers should be written as $x + (x + 1)$ or $x + (x + 2)$? Test it out with real numbers! 14, 16, 18 are consecutive even integers. If $x = 14$, $16 = x + 2$, and $18 = x + 4$. This works for most all of your integer rules. Forget your exponent rules? Plug in real numbers! Forget whether an even * an even makes an even or an odd? Plug in real numbers! #3: Keep your work organized. Like with most SAT math questions, integer questions can seem more complex than they are, or will be presented to you in strange ways. Keep your work well organized and keep track of your values to make sure your answer is exactly what the question is asking for. Santa is magic and has to double-check his list. So make sure you double-check your work too! Test Your Knowledge 1. If $a^x * a^6 = a^24$ and $(a^3)^y = a^15$, what is the value of $x + y$? A. 9B. 12C. 23D. 30E. 36 2. If $48√48 = a√b$ where $a$ and $b$ are positive integers and $a b$, which of the following could be a value of $ab$? A. 48B. 96C. 192D. 576E. 768 3. What is the product of the smallest prime number that is greater than 50 and the greatest prime number that is less than 50? 4.If $j, k$, and $n$ are consecutive integers such that $0jkn$ and the units (ones) digit of the product $jn$ is 9, what is the units digit of $k$? A. 0B. 1C. 2D. 3E. 4 Answers: C, D, 2491, A Answer Explanations: 1. In this question, we are being asked both to multiply bases with exponents as well as take a base with an exponent to another exponent. Essentially, the question is testing us on whether or not we know our exponent rules. If we remember our exponent rules, then we know that we must add exponents when we are multiplying two of the same base together. So $a^x * a^6 = a^24$ = $a^{x + 6} = a^24$ $x + 6 = 24$ $x = 18$ We have our value for $x$. Now we must find our $y$. We also know that, when taking a base and exponent to another exponent, we must multiply the exponents. So $(a^3)^y = a^15$ = $a^{3 * y} = a^15$ $3 * y = 15$ $y = 5$ In the final step, we must add our $x$ and $y$ values together: $18 + 5 = 23$ So our final answer is C, 23. 2. We are starting with $48√48$ and we know we must reduce it. Why? Because we are told that our first $48 = a$ and our second $48 = b$ AND that $a b$. Right now our $a$ and $b$ are equal, but, by reducing the expression, we will be able to find an $a$ value that is greater than our $b$ So let's find all the factors of 48 to see if there are any perfect squares. 48 $1 * 48$ $2 * 24$ $3 * 16$ $4 * 12$ $6 * 8$ Two of these pairings have perfect squares. 16 is our largest perfect square, which means that it will be the number we must use to reduce $48√48$ down to its most reduced form. Though we are not explicitly asked to find the most reduced form of $48√48$, we can start there for now. So $48√48 = 48 * √16 * √3$ $48 * 4 *√3$ $192√3$ This means that our $a = 192$ and our $b = 3$, then: $ab = 192 * 3 = 576$ So our final answer is D, 576. (Special note: you'll notice how we are told to find one possible value for $ab$, not necessarily $ab$ when $48√48$ is at its most reduced. So if our above answer hadn't matched one of our answer options, we would have had to reduce $48√48$ only part way. $48√48 = 48 * √4 * √12$ $48 * 2 * √12$ $96√12$ This would make our $a = 96$ and our $b = 12$, meaning that our final answer for $ab$ would be $96 * 12 = 52$.) 3. This question requires us to be able to figure out which numbers are prime. Let us use the same methods we used during the above section on prime numbers. All prime numbers other than 2 will be odd and there is no prime number that ends in 5. So let's list the odd numbers (excluding ones that end in 5's) above and below 50. 41, 43, 47, 49, 51, 53, 57, 59 We are trying to find the ones closest to 50 on either side, so let's first test the highest number in the 40's. 49 is the perfect square of 7, which means it is divisible by more than just itself and 1. We can cross 49 off the list. 47 is not divisible by 3 because $7 + 4 = $ and is not divisible by 3. It is also not divisible by any even number (because an even * an even = an even), by 5, or by 7. This means it must be prime. (Why did we stop here? Remember that we only have to test potential factors up until the closest square root of the potential prime. $√47$ is between $6^2 = 36$ and $7^2 = 49$, so we tested 7 just to be safe. Once we saw that 7 could not go into 47, we proved that 47 is a prime.) 47 is our largest prime less than 50. Now let's test the smallest number greater than 50. 51 is odd, but $5 + 1 = 6$, which is divisible by 3. That means that 51 is also divisible by 3 and thus cannot be prime. 53 is not divisible by 3 because $5 + 3 = 8$, which is not divisible by 3. It is also not divisible by 5 or 7. Therefore it is prime. (Again, we stopped here because the closest square root to 53 is between 7 and 8. And 8 cannot be a prime factor because all of its multiples are even). This means our smallest prime less than 50 is 47 and our largest is 53. Now we just need to find the product of those two numbers. $47 * 53 = 2491$ Our final answer is 2491. 4. We are told that $j$, $k$, and $n$ are consecutive integers. We also know they are positive (because they are greater than 0) and that they go in ascending order, $j$ to $k$ to $n$. We are also told that $jn$ equals a number with a units digit of 9. So let's find all the ways to get a product of 9 with two numbers. $1 * 9$ $3 * 3$ The only way to get any number that ends in 9 (units digit 9) from the product of two numbers is in one of two ways: #1: Both the original numbers have a units digit of 3 #2: The two original numbers have units digits of 1 and 9, respectively. Now let's visualize positive consecutive integers. Positive consecutive integers must go up in order with a difference of 1 between each variable. So $j, k, n$ could look like any collection of three numbers along a consistent number line. 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, , 12, 13, 14, 15, 16, etc. There is no possible way that the units digits of the first and last of three consecutive numbers could both be 3. Why? Because if one had a units digit of 3, the other would have to end in either 1 or 5. Take 13 as an example. If $j$ were 13, then $n$ would have to be 15. And if $n$ were 13, then $j$ would have to be . So we know that neither $j$ nor $n$ has a units digit of 3. Now let's see if there is a way that we can give $j$ and $n$ units digits of 1 and 9 (or 9 and 1). If $j$ were given a units digit of 1, $n$ would have a units digit of 3. Why? Picture $j$ as . $n$ would have to be 13, and $ * 13 = 143$, which means the units digit of their product is not 9. But what if $n$ was a number with a units digit of 1? $j$ would have a units digit of 9. Why? Picture $n$ as now. $j$ would be 9. $9 * = 99$. The units digit is 9. And if the last digit of $j$ is 9 and the numbers $j, k, \and n$ are consecutive, then $k$ has to end in 0. So our final answer is A, 0. The Take-Aways Integers and integer questions can be tricky for some students, as they often involve concepts not tested in high school level math classes (when’s the last time you dealt with integer remainders, for example?). But most integer questions are much simpler than they appear. If you know your definitions- integers, consecutive integers, absolute values, etc.- and you know how to pay attention to what the question is asking you to find, you’ll be able to solve most any integer question that comes your way. What’s Next? Whew! You’ve done your paces on integers, both basic and advanced. Now that you’ve tackled these foundational topics of the SAT math, make sure you’ve got a solid grasp of all the math topics covered by the SAT math section, so that you can take on the SAT with confidence. Find yourself running out of time on SAT math? Check out our article on how to buy yourself time and complete your SAT math problems before time’s up. Feeling overwhelmed? Start by figuring out your ideal score and check out how to improve a low SAT math score. Already have pretty good scores and looking to get a perfect 800 on SAT Math? Check out our article on how to get a perfect score written by a full SAT scorer. Want to improve your SAT score by 160 points? 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