Self Esteem in Athletes Compared to Non-Athletes Essays

Self Esteem in Athletes Compared to Non-Athletes The correlation of playing competitive sports at college level and self esteem are measured. Subjects were given the Barksdale self esteem questionnaire to fill out and levels of self esteem are measured by scores out of one hundred. The subjects are then separated into categories determined by gender and whether they played sports at the college level. The results indicated that the elite athletes have a higher self esteem than non athletes. The survey also revealed that women have a slightly higher self esteem than men. These findings agree with our hypothesis that athletes will have a higher level of self esteem than non athletes will. Self esteem is defined†¦show more content†¦As well as looking at that research we also referred to the Encyclopaedia of human intelligence and an interesting article about exercise and cognitive functioning. The purpose of this research then is to find out of levels of self esteem differ in athletes and non athletes. The hypothesis drawn was that athletes would prove to have a higher overall average of self esteem when compared to non athletes. The null hypothesis is that their will be no difference between the two groups. Goals of this research are to satisfy some curiosity in the area and maybe dispel of some long reaching stereo types. Method It was decided that the goal would best be reached through a questionnaire given to people to fill out that would evaluate their self esteem. After going through many the Baarksdale self esteem evaluation no.69 , it was decided on as being the most thorough and the one most pertaining to he research. Some questions at the end were added asking for age, sex, and whether or not they play competitive sports. These questions were added so we could separate them onto the respective categories: athlete/non athlete. Our control group would be the group that does not play on a sports team. The athletes would be compared to them. The questionaries were handed out randomly.Show MoreRelatedEating Disorders Has Affected The Lives Of Many Athletes Around The World1546 Words   |  7 PagesEating disorders have affected the lives of many athletes around the world. Being scared of being overweight but rather caused by an addiction to food can result in the development of an eating disorder. There are several reasons as to why someone may have an eating disorder such as the sports they play or even the worldly view of how an ideal body is supposed to be. They have an effect on the person’s health and also on their social interactions with others. Many sports where the player’s weightRead MoreAre Athletes Trea ted Differently From The Rest Of The Student Body?1457 Words   |  6 Pages1) Are athletes treated differently from the rest of the student body? If so, how? 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Id also like to find some studies that may compare student athletes to the general student body to see if there is a correlation of usage betweenRead MoreThe Social Benefits Of Sports1248 Words   |  5 Pagesthe court or field. Aside from the physical aspect, sports benefit the athlete both during and far beyond their athletic careers. Socially, emotionally, and academically sports benefit the athlete and prepare him/her for upcoming phases in life such as career, family, and relationships. Home and school education are crucial for personal growth, but sports play a key role developing the social aspect of a person. Whether the athlete is the star of the team or the second st ring, the sport can teach skillsRead MoreThe Effects of Athletics on Student Performance Essay1302 Words   |  6 Pagesin athletic activities often have higher physical, mental and emotional abilities than their non-participating peers. Stereotypically student athletes are portrayed as popular but unintelligent and unmotivated to excel in academics, seeking only the glory that comes from excelling on the football, baseball or other sports field. This portrayal has led to the term â€Å"dumb jock,† which is how student athletes are often portrayed in Hollywood and by media. For example, Danny Zuko in the movie â€Å"Grease†Read MorePositive Influences Of Sport Participation770 Words   |  4 PagesBradley, Keane and Crawford proved the positive influences of sport participation in 402 Irish secondary school students on the Leaving Certificate. The no sport group, forming the control group, compared to the soccer and rugby team had slightly lower test scores in the Leaving Certificate, whereas the only individual sport, rowing, was significantly higher then the other two groups (Bradley, et al., 2013). In this study, rowing, as the only individual sport tested, proved higher test results, whichRead Mo reSports And Male Domination : The Female Athlete As Contested Ideological Terrain998 Words   |  4 Pagesand Male Domination: The Female Athlete as Contested Ideological Terrain† written by Michael A. Messner in 1988 sheds light on the idea that traditional images of femininity have come to solidify male privilege through the construction and naturalization of gendered characteristics regarding women such as weakness, fragility and dependency . By turning women away from playing certain sports, we are influenced to believe that they are not as qualified to play, compared to men. (Creedon, 1994). IronicallyRead MoreSports and Academic Achievement1494 Words   |  6 Pagespositive impact athletics has on a student’s academic abilities. Introduction Participating in athletics offers students the opportunity to learn valuable lessons they can use for the rest of their lives. Some lessons include teamwork, self-esteem, perseverance, discipline, time management, and healthy living. However, these lessons are not the only lessons a student learns. Students also learn lessons that carry over into the classroom and have a positive impact on academic achievementRead MoreThe Effects Of Extracurricular Activities On Sports Participation795 Words   |  4 Pagesstudents and not to the majority of the American population. In research, a small correlation between intensity of the extracurricular activity and negative adjustment has been proven in boys, but overall the achievement pressure made by parents, the athletes themselves, the society, the century we live in and their surroundings has shown to be much more influential on the psychological adjustment than does the intensity of extracurricular participation (Fredericks, 2012). Additionally, greater academicRead MoreBenefits in Youth Football1608 Words   |  7 Pagesof sport participation is that sports can boost the self esteem of the people participating. The self-esteem of children is boosted when parents, coaches, and other teammates give the child positive feedback and show a sense of pride in what the child has accomplished (Bilich, 2006). Numerous studies have shown that girls who participate in physical activity such as sports are more likely to have more positive feelings of self-worth/self-esteem and a more positive body image than girls who are not

Essay †Bride and Prejudice Free Essays

People interact with and also with their surroundings. This impacts on their sense of belonging or their sense of isolation. We see this is William Shakespeare’s play ‘As You Like It’ and the Anglo-Indian genre movie, ‘Bride and Prejudice’ by Gurinder Chadha. We will write a custom essay sample on Essay – Bride and Prejudice or any similar topic only for you Order Now The relationship between people and the interaction with place heavily impacts on the sense of belonging among the characters in the prescribed text. Rosalind and Celia are cousins who share a common understanding and identical values. Being from the same parental stock their social perception of life is similar. Their fathers being brothers, they share the same social economic circle. Their closeness is stressed when Celia paradoxically emphasises, â€Å"you know my father hath no child but I, nor none is like to have†. This shows Celia is prepared to forfeit the dutchy for her cousin Rosalind, which cements their friendship and helps them to improve their sense of bonding with each other. The ducal court and the lust for power sees Celia’s father usurp the dukedom from his elder brother, Duke Senior, Rosalind’s father. This chaotic deed breaks the bond of unity and segregates Duke Senior, Rosalind, Celia, Orlando, Jacques and Adam. The two fathers are located in a contrasting environment. The court of Duke Fredrick is seen as a contrast to the forest od Arden. Duke Fredrick’s court seems to foster values of flattery, falsity and autocracy. These values create friction on the bond of belonging and unity. Where as the forest of Arden is an allusion of the garden of Eden. The interaction with this rustic setting acts as a whet stone to refine the disturbed banished crew of exiles. Duke Senior’s syntactical expression, â€Å"running brooks’† and â€Å"sermon in stones† shows the peace and serenity of the forest of Arden. This natural environment of forest of Arden also fosters friendship. Hardship also accompanies the calm serenity of this so-called paradise because the harsh, â€Å"churlish chidings† and â€Å"bites and bolows† of the weather fosters a sense of independence on each of the exiled members in the forest. Rosalind’s impersonating as Ganymede protects not only her virginity but also her cousin Celia’s maidenhood. These good times and bad times and the will to succeed are essential qualities that assist the sense of belonging in the prescribed text. Love is another pervading factor in emotional belonging. The sisterly affection between Rosalind and Celia acts as a wedge that not only glues them together but also binds Orlando with Rosalind; Duke senior with his younger brother Duke Fredrick; Celia with Oliver and Phoebe with Silvius. Thus we see how Shakespeare portrays how belonging can be nurtured with love, understanding and a firm purpose of commitment for a common good. Shakespeare justifies the power of love and in the concept of belonging by making Rosalind metaphorically refer to love as madness, â€Å"love is merely a madness†¦that he whispers are in love too†. By this quibble Rosalind tries to humorously convince Orlando that just as he is in love with her, she is also madly in love with him. This reciprocal interaction with each other helps to foster unity among all the characters in the play. Similarly Gurinder Chadha’s romantic musical film, Bride and prejudice portrays the concept of belonging that is nurtured on account of interaction with people and places. The Bakshi Family has a strong sense of togetherness within the home and also the microscopic environment of their rural setting in Amritsar. The film in the opening scene uses mise en scene with the protagonist Lalita Bakshi serene in her environ. In the scene that follows we see The Bakshi Family, in their Indian accent, discuss marriage. The love and closeness of the sisters, Jaya, Maya and Lakhi establish their security, warmth and comfort within their home. This closeness and sacrifice is also displayed in the prescribed text where Rosalind and Celia make sacrifices for each other. Interaction with a place is presented where Lalita, the heroine, has to build an affinity not only with Amritsar in India but also with Will Darcy’s wealthy American family hotel in America. Her education al competence helps her easily integrate with the American way of life. In like manner even though Darcy felt out of place on his first visit to Amritsar in India, his love for Lalita made him adjust with the Indian culture and also with the Indian locale. The contrast of Darcy’s occidental attire in the early scenes is different in the concluding part of the film. The oriental drum beat played by Darcy himself and his Indian outfit piloted, by an elephant, shows how in belonging sacrifices need to be made. These sacrifices create a bond between the members who yearn for a common goal. In the case of Bride and Prejudice the love between Will Darcy and Lalita Bakshi cement a relationship between the Bakshi family and the Darcy family; so also in As You Like It the love between Celia and Oliver and Rosalind and Orlando foster a sense of belonging between the members of the ducal court and the members in The Forest of Arden. Thus establishing the fact that interaction between people and places heavily impacts on the sense of belonging. On analysing both texts we see, William Shakespeare and Gurinder Chadha uncover how a sense of belonging or isolation is created by the people we interact with, the environment in which we are and the love , understanding and concern we express for each other. How to cite Essay – Bride and Prejudice, Essay examples

Project Management Methodology Improvement Plan Helps

Question: Discuss about the case study Project Management Methodology for Improvement Plan Helps. Answer: Reflection The outcome of this course in week 10 is associated with the project management methodologies which explains the practices of continuous improvement plan helps to achieve the objectives effectively. The outcome of this course facilitated me to gain the depth understanding of the role of change management in order to define requirements of the work and also enables me to make continuous improvement in the project. Cheshire cat quotes that if you dont know where you are going, any road will get you there. This quotes gain my knowledge that firstly we have to need to develop understanding about the reason behind the improvement in the project after that needs to understand the position of the project and then need to understand the continuous performance that has carried out within the project. These things have considered by me in the professional life as it enables me to accomplish the goal successfully. Besides this, the course of week 10 also offers me an effective learning as I taken the practical experience to develop the project management maturity model on the real life practices. It also supported me to learn about how to develop the optimized process in the project. Apart from this, I have also gained experience about the different level of project management maturity model in order to accomplish the project on time. In this way, I have gained knowledge that first level is related to awareness of the process, the second level identifies the repeatable process, the third level defined the process, the fourth level manage the process, and the fifth level optimized the process. These different levels are beneficial to me to develop great understanding in terms of recognizing the responsibilities of a senior manager from an initial level to the last level of the project management maturity model. Further, I was enabled to optimize a different process that is essential due to changes in business need. This course also develops my understanding about the different thinks that is to be considered in the continuous improvement plan. These things are the current state of the project, strategies to bridge the gap, monitoring and capturing the process of the project. I have considered these things in the project in order to get the continuous improvement in the project. This course outcome also facilitated me a great knowledge about the lean six sigma roadmap. This roadmap defines the five steps that are effective to improve the quality of the project. These steps involved define the quality, measure the quality, analyze it, improve it, and then control the quality. It is effective to me in order to quality improvement in the project. Further, I have gained experiences about the ways that help to determine the current state and future state of the project and also helped me to develop the structure associated with the planned improvement actions. At the same time, from this course, I have developed the knowledge about the effectiveness of project management methodology in order to continuous improvement in the project. Due to this, I enabled to execute the effective methodology to get success. It will also facilitate for me to enhance growth related to my professional career in terms of building the project with respect to the benefit of the company. Weekly Portfolio Learning Table Date Issues Identified Related policies/ procedures Planned Action Planned completion date 6.10.2016 Article about project management methodology indicated that continuous improvement assessment tool does not incorporate the ease and comprehensible steps. It creates difficulty to me in order to execute the continuous improvement plan in the project. Project management methodologies such as continuous improvement plan, lean six sigma roadmap, and different ways to determine the current state and future state of the project. There should be a continuous improvement to bridge the gap. 7 October 2016 (Completed) Supporting Documentation including your Prior Learning Kerzner, Chapter 20.0-20.8, and 21.0-21.4 https://books.google.co.in/books?id=QgQQC5qRtzgCprintsec=frontcoverdq=kerzner+project+managementhl=ensa=Xved=0ahUKEwjiysP9j8bPAhVEMo8KHZpQDW8Q6AEIKjAB#v=onepageq=kerzner%20project%20managementf=false PMI Managing Change Chapter 6 https://marketplace.pmi.org/Pages/ProductDetail.aspx?GMProduct=00101469401

Maslahah Mursalah free essay sample

Historically, the notion of maslahah mursalah originated in the practice of the Companions. This is, of course, not to say that the Prophet did not rule in favour of maslahah, but merely to point out that as a principle of jurisprudence, maslahah mursalah does not apply to the rulings of the Sunnah. The main support for istislah as a proof and basis of legislation (tashri) comes from Imam Malik, who has given the following reasons in its favour: The Companions have validated it and have formulated the rules of Shariah on its basis. When the maslahah is compatible with the objectives of the Lawgiver (maqasid al-shari`) or falls within the genus or category of what the Lawgiver has expressly validated, it must be upheld. For neglecting it under such circumstances is tantamount to neglecting the objectives of the Lawgiver, which is to be avoided. Hence maslahah as such is a norm of the Shariah in its own right; it is by no means extraneous to the Shari`ah but an integral pair of it. We will write a custom essay sample on Maslahah Mursalah or any similar topic specifically for you Do Not WasteYour Time HIRE WRITER Only 13.90 / page When maslahah is of the genus of the approved masalih and is not upheld, the likely result would be to inflict hardship on the people, which must be prevented. Shatibi, I`tisam, II, 282-287; Abu Zahrah, Usul, p. 223. ] Conditions (Shurut) of Maslahah MursalahThe following conditions must be fulfilled in order to validate reliance on maslahah mursalah. The maslahah must be genuine (haqiqiyyah), as opposed to a specious maslahah (maslahah wahmiyyah), which is not a proper ground for legislation. The second condition is that the maslahah must be general (kulliyyah) in that it secures benefit, or prevents harm, to the people as a whole and not to a particular person or group of persons. The maslahah must not be in conflict with a principle or value which is upheld by the nass or ijma`.

Sample Ap World History Compare Contrast Essay - The Spanish Culture

Sample Ap World History Compare Contrast Essay - The Spanish CultureWith a Sample Ap World History Compare Contrast Essay, you are able to learn more about the Spanish culture, while also getting a good idea of how native Spanish speakers compare with other native Spanish speakers. There are several sources of information about a culture like the Spanish language; however, many of them can seem overwhelming.This Sample Ap World History Compare Contrast Essay by the Name of 'Contrast Comparison Aids' helps to make the process of learning Spanish much easier for you. For more information on the 'Contrast Comparison Aids', simply visit our website at the link below.In order to learn Spanish and then move on to Spanish literature and grammar in a more advanced way, it is often the case that you need to purchase a course that is able to do this. The reason for this is that courses like this are extremely expensive, even if you are able to find one that is low priced.Now, the different sch ools of thought on this topic tend to be: Should English Literature be included in the course; Should English Literature be optional; Should English Literature be included in all subjects; Should English Literature be included in all subjects and should it be in high school? All of these topics are subject to debate, especially as Spanish courses become more sophisticated.Another point that is being debated is the idea of including Spanish Literature in English Literature courses. Some feel that there is no real difference between English Literature and Spanish Literature, but we strongly disagree and feel that there is a big difference and a great deal of difference.Whether or not you decide to include Spanish Literature in English Literature courses will depend on your preferences, your kids, your family, your teaching philosophy, your school's mission statement, your funding structure, etc. Regardless, of which option you decide upon, the main thing is that you are giving your st udents a better understanding of Spanish Literature and you are giving them a better understanding of their own society.As long as you are doing things the right way and you are teaching in an effective manner, there is no reason why you cannot use Spanish Literature as a means of connecting to Spanish culture. Simply visit our website to learn more about 'Contrast Comparison Aids' and why you need to get one now!

Causes of the American Revolutionary War essays

Causes of the American Revolutionary War essays The American colonists were justified in waging war and breaking away from Britain because of unjust laws and a tyrannical king. All of these things outraged the colonists in different ways, leading them to unite together and rebel against Britain, hence leading to the Revolutionary War. First off, Parliament imposed many unjust laws. According to Document 2, the colonists believed that Britain had the right to impose laws to regulate trade, however, on the contrast, the introduction of the Stamp Act was pure to gain revenue. The Stamp Act particularly affected lawyers, merchants, and editors, as well as the general public. Document 5 reads "Parliament can 'of right make laws to bind us in all cases whatsoever.'" This can lead someone to argue that Parliament felt it had complete control over the colonies and that it could pass numerous laws to keep that control. For instance, once the Sons of Liberty used mob violence to force all stamp agents to resign and the Stamp Act was repealed, Parliament asserted its rights with the Declaratory Act. Document 5 also infers that the unfair laws and taxes imposed on the colonists were enforced by the "tyranny of irritated [British officials]." The colonists argued that they were unfairly being taxed without representation, th is being the first time that the colonies began to unite and rebel against the British government. Secondly, a cruel and intolerable king oppressed the colonists. Document 6 blames the King of England for the Battles of Lexington and Concord on April 19, 1775, and refers to him as "the hardened, sullen-tempered [King of England]." This document excerpted from Thomas Paine's pamphlet "Common Sense," convinced many Americans that independence was the only resolve to the conflicts between America and England. Accusations in Document 7 also suggest that the king had "a history of repeated injuries and usurpation," and that his overall character could describe a "tyrant"...

The Basic Guide to Integers on ACT Math

The Basic Guide to Integers on ACT Math SAT / ACT Prep Online Guides and Tips "Let x and y be integers such that...", "If y is a positive integer, what is...?" If you've taken a practice test or a real ACT before, these types of questions may look familiar to you. You've likely come across several questions on the ACT that mention the word "integer." And if you don't know what that word means, they will be difficult problems for you to solve. Questions involving integers are common, so it's important to have a solid grasp of what integers are as you continue in your ACT math study. But what are "integers" and how do they fit into the larger ACT math picture? This article will be your guide to basic integers for the ACT, what they are, how they change, and how you'll see them used on the test. For the more advanced integer conceptsincluding absolute values, exponents, roots, and morelook to our advanced guide to ACT integers. What is an Integer? An integer is a whole number. This means an integer is any number that is NOT expressed with a decimal or a fraction. Integers include all negative whole numbers, all positive whole numbers, and zero. Examples of Integers: -32, -2, 0, 17, 2,035 NOT integers: Ï€, $2/3$, 0.478 Think of an integer as an object that cannot be divided into pieces. For example, you can't have half an egg in a basket. Positive and Negative Integers A number line is used to demonstrate how numbers relate to each other and to zero. All numbers to the right of zero are positive numbers. All numbers to the left of zero are negative numbers. Positive numbers get larger the farther they are from zero. 154 is larger than 12 because 154 is farther along the number line in a positive direction (to the right). Negative numbers get smaller the farther away they are from zero. -154 is SMALLER than -12 because -154 is a farther along the number line in a negative direction (to the left). And a positive number is always larger than any negative number. 1 is larger than -10,109 Because we don't have a reference for 0, we cannot say for sure whether A is positive or negative, which eliminates answers F, G, and K. We do know that any number to the left of another number will be less, so the answer must be H, A is less than B. The very opposite of a number line. Typical Integer Questions on the ACT Most ACT math integer questions are a combination of word problem and equation problem. The question will usually present you with an equation and tell you that you must use "integers" in place of a variable. You must know that an integer means a whole number (and that integers also include negative numbers and zero) to solve these problems. When x≠ 0, there are two possible integer values for x such that y=x(1+x). What is a possible value for y? (A) −30(B) −1(C) 0(D) 15(E) 20 (We'll walk through how to solve this problem in the next section.) Sometimes you’ll have to answer more abstract questions about how integers relate to one another when you add, subtract, multiply and divide them. You don't need to find a numerical answer for these types of questions, but you must instead identify whether certain equations will be even or odd, positive or negative. For these types of questions, you can either guess and check how integers change in relation to one another by plugging in your own numbers and solving, or you can memorize the rules for how integers interact. How you do it is completely up to you and depends on how you learn and/or like to solve math problems. For example, in the charts below, you'll see that: aâ€Å' positiveâ€Å' number * aâ€Å' positiveâ€Å' number = aâ€Å' positiveâ€Å' number, each and every time. If you forget this rule (or simply don't want to learn it in the first place), you can always try it by saying 2 * 3 = 6. Because you can always find these results by plugging in your own numbers, these rules are categorized as â€Å"good to know,† but not â€Å"necessary to know.† negative * negative = positive -2 * -3 = 6 positive * positive = positive 2 * 3 = 6 negative * positive = negative -2 * 3 = -6 Another way to think of this is, â€Å"When multiplying numbers, the result is always positive unless you’re multiplying a positive number and a negative number.† odd * odd = odd 3 * 5 = 15 even * even = even 2 * 4 = 8 odd * even = even 3 * 4 = 12 Another way to think of this is, â€Å"When multiplying numbers, the result is always even until multiplying an odd number and an odd number.† odd +/- odd = even 5 + 7 = 12 even +/- even = even 10 - 6 = 4 odd +/- even = odd 5 + 6 = 11 Another way to think of this is, â€Å"When adding or subtracting numbers, the result is always even unless adding or subtracting an odd number and an even number.† With these understandings in mind, let us look again at the above ACT math problem. Choice A is incorrect, because b is an even integer. And we know that an even number * an odd number = an even number. Choice B is incorrect because a is an odd integer. And we know that an odd number + an odd number = an even number. Choice C is incorrect because a is an odd integer and b is an even integer. An even number + an odd number = an odd number. And an odd number * an even number (in this case 2) = an even number. Choice D is correct. Twice b will be even, because an even number * an even number = an even number. And the final result will be odd because an odd number (a) + an even number (2b) = an odd number. Choice E is incorrect. Twice an odd number (a) will be an even number, because an even number * an odd number = an even number. And an even number + an even number = an even number. So your final answer is D, a + 2b. You can see how you could also solve this by double-checking these rules by using your own numbers. If you assign an odd number to a and an even number to b, you can test out each option in about the same amount of time it would take you to go through your rules like this. So for this question, you could have said a was 5 and b was 6. Then option D would have looked like this: 5 + 2(6) = 17 Again, because you can figure out these kinds of questions using real numbers, these rules are classified as "good to know," not "necessary to know." If you follow the right steps, solving an integer problem is often much easier than it appears. Steps to Solving an ACT Math Integer Problem #1: Identify if the problem is, in fact, an integer problem. If you must use integers to solve a problem, the ACT will explicitly use the word "integer" in the question so that you don't waste your time and effort looking for decimal or fraction solutions. For example, questions may begin with: "x is a positive integer such that...", "For all negative integers...", or "How many integers give the solution to...?" For any problem that doesn’t specify that the variables (or the solution) are â€Å"integers," your answer or the variables can be in decimals or fractions. So let's look again at the problem from earlier: When x ≠  0, there are two possible integer values for x such that y = x(1+x). What is a possible value for y? (A) −30(B) −1(C) 0(D) 15(E) 20 We are told that x ≠  0, so we know that our y cannot be 0. Why not? Because the only integer values that can give you y = 0 are x = 0 and x = −1 because 0(1+0) = 0 and (−1)(1+(−1)) = 0. BUT we were told that x ≠  0. So y can not equal 0 either, as the question told us that there were TWO integer values for x, neither of which is 0. This means we can cross off C from the answer choices. We can also cross off A and B. Why? Because there is no possible way to have x(1+x) equal a negative. Even when x is negative, we would distribute the problem to look like: y = (1x) + (x * x) We know that a negative * a positive = a negative, so 1x would be negative if x were negative. BUT a positive * a positive = a positive. And a negative * a negative = a positive. So x * x would be positive, whether x was positive or negative. And adding the original negative value for x will not be a large enough number to take away from the positive square and make the final answer a negative. For example, we already saw that: x =−1 makes our y zero. x =−2 gives us −2(1+−2) = y = 2. x =−3 gives us −3(1+−3) = y = 6, etc. So we are left with answer choices D and E. Now how could we get 15 with x(1+x)? We know x must not be very large to get y = 15, so let's test a few small numbers for x. If x = 2, then x(1+x) = 2(1+2) = 6. This means x = 2 is too small. If x = 3, then x(1+x) = 3(1+3) = 12. So x = 3 is too small. If x = 4, then x(1+x) = 4(1+4) = 20. This means there is no positive integer value that could give us 15. But we did manage to get y = 20, so answer choice E is looking pretty good! Now we can tell that if we kept going higher with x, the y value would keep getting larger (x = 5 would give us y = 30, etc.). This means we probably need a negative integer to give us our second value for x. So let's try to get y = 20 with a negative value for x this time. We already saw above that x = −2 gave us y = 2, and x = −3 gave us y = 6. So let's try some more negative values for x. If x = −4, then x(1+x) = −4(1+−4) = 12 If x = −5, then x(1+x) = −5(1+−5) = 20 We were able to get y = 20 with both x = 4 and x = −5 So our final answer is E, y = 20 #2: If the problem asks you to identify equations that are always true, test out multiple different kinds of integers. If the question asks you to identify whether certain equations or inequalities are true for ALL integers, the equation must work equally with 10 as with 0 and -5. A good rule of thumb is to try -1, 0, and 1 with variable questions like these. These numbers often have special properties that make or break conditions. I'll explain what that means with a practice example. If x is an integer, which of the following equations MUST be true? I. $x^3 ≠¥ (-x)^3$ II. ${x^3}/x ≠¥ {x^2}/x$ III. $x(x + 1) ≠¤ -x + x^3$ (A) I only(B) II only(C) III only(D) I and III only(E) I, II, and III For questions like these, we should test out our sample numbers, as it can get confusing to use our rules of integer behaviors with complex problems such as these. So for option I, let use our test numbers of -1, 0, and 1. $−1^3= (−1)(−1)(−1) = −1$ $(−−1)^3 = $1^3 = (1)(1)(1) = 1$ -1 is NOT greater than +1. This automatically eliminates option I. And by eliminating option I, we can eliminate answer choices A, D, and E right away. Now let's look at choice II with our same test numbers. ${(-1)^3}/{-1} = {(-1)(-1)(-1)}/{-1} = {-1}/{-1} = 1$ ${(-1)^2}/{-1} = {(-1)(-1)}/{-1} = 1/{-1} = -1$ 1 -1 This means that option II works so far when we use a negative number. So let's try it with our positive number, 1. ${1^3}/1 = {(1)(1)(1)}/1 = 1/1 = 1$ ${1^2}/1 = {(1)(1)}/1 = 1/1 = 1$ 1 = 1. So option II still works. Lastly, we should test if the equation still works with 0. ${0^3}/0 = 0$ $0^2/0 = 0$ Option II works for all answer choices, so our final answer is B, II only. Because we know that option I doesn't work, we have eliminated all other answer choices. But if you want to make absolutely sure you didn't make a mistake somewhere, you can test out option III as well. −1(−1+1) = 0 $−(−1)+(−1)^3 = 1+(−1)(−1)(−1) = 1+−1 = 0$ 0 = 0 The two are equal, which means that option III works so far. Now let's try it with 1. 1(1+1) = 2 $−1+1^3 = −1+(1)(1)(1) = −1+1 = 0$ 2 0 When we used a positive number, the equation was incorrect. This means that answer choice C is eliminated and our choice of B has been confirmed to be the only correct answer. #3: If the problem asks you to find the answer to long calculations, use your rules that you learned above or test it out with smaller numbers. a, b, c, d, e, f are odd integers such that a b c d e f. Which statement(s) must be true? I. abcdef is odd II. a + b + c + d + e + f is odd III. a(b + c + d + e + f) is odd (A) I only(B) II only(C) III only(D) I and III only(E) I, II, and III Now you can approach this problem in one of two ways: by using your number rules or by using your own numbers. First, let's use our number rules to test option I. We know that each letter represents an odd integer and that the product of an odd number and another odd number is an odd number. Because an odd * an odd will always be odd, we know that option I is true. This means we can also eliminate answer choices B and C. Now let's look at option II. We know that an odd number + an odd number = an even number. We also know that an even number + an even number = an even number. So if we split a + b + c + d + e + f into pairs of numbers, we'll have: (a + b) + (c + d) + (e + f) We know that each pair of numbers will have an even sum, so we're left with: an even number + an even number + an even number, which will give us an even final result. So option II is incorrect. This means we can eliminate answer choice E. Finally, let's look at option III. As we saw before, when we have six odd numbers (in other words, an even number of odd numbers), the sum will be even. Now, our parenthesis holds five (an odd number) of odd numbers, and an even number + an odd number = an odd number. So we know the number in the parenthesis will be odd. We also know that an odd number (a) * an odd number (the sum of b, c, d, e, f) = an odd number. So option III is correct. This means that our final answer is D, I and III only. The other way you could solve this problem would be to test out these rules with small numbers and extrapolate to find the larger answer. In other words, use small numbers in place of the variables. So for option I, if you didn't know an odd * an odd = an odd, you could replace a and b with the numbers 5 and 3. 5*3=15, so you know that an odd * an odd = an odd number, no matter how many times you multiply it. So option I is correct. For option II, again test it out with smaller numbers. 7+5=12, and 7+5+3=15. So you know that adding odd numbers an even number of times gets you an even answer and adding an odd number of times gets you an odd answer. There are six odd numbers, so the final answer must be even. Option II is incorrect. Taking what you learned by testing option II, you know that adding odd numbers an even number of times gets you an odd answer. And, taking what you learned from testing option I, you know that an odd number * an odd number = an odd number. This means your final answer must be odd, so option III is correct. This means the final answer is D, I and III only. Whoo! There are many ways to solve integer problems and whichever way works for you is perfect. The Take-Aways In order to solve both the basic and advanced ACT integer questions, you must first understand what an integer is. Only then can you build up your integer knowledge to the more advanced concepts. But simply knowing that an integer is a whole number (and that 0 and negative numbers are also integers), will allow you to solve some of the more basic questions about how to plug integers into equations and how integers relate to one another. For the more advanced integer concepts, including absolute values, exponents, etc., be sure to check out our advanced guide to ACT integers. What's Next? Now that you’ve learned about what integers are, you may want to check out the advanced guide to ACT integers where we will go through absolute values, prime numbers, and exponents (among other concepts). Make sure that you also have a solid understanding of all the ACT math concepts on the test as well as all the ACT formulas you'll need to know. Running out of time on ACT math? Check out our article on how to buy yourself those extra precious seconds and minutes and complete your ACT math problems before time’s up. Feeling overwhelmed? Start by figuring out your ideal score. Already have pretty good scores and looking to get a perfect 36? Check out our article on how to get a perfect score written by a 36 ACT-scorer. Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. 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