Wednesday, October 30, 2019
Software Design Defects Detection and Classification Literature review
Software Design Defects Detection and Classification - Literature review Example This essentially refers to â€Å"fitness for use†. On a detailed elucidation of quality, software design defects come into the picture. Quality software not only meets the full user requirements, but is also usable for the purpose it was designed( Du Bois, Verelst and Demeyer 2004). Given the software process as earlier mentioned morphs the information from one form to another, errors are likely to occur in any of the forms (user needs, design, code etc.) of the product. This paper focuses on the design of software and the relation to the overall product. Generally, it ties software quality management to the success of the software process. In a more specific perspective, realised by careful examination of the models and frameworks of the software process, the paper reviews the software design defects are detected. The models reviewed are an indispensable part of software development and as such, it is important to examine how they help â€Å"clean up†the software proc ess(Leszak, Perry and Stoll 2002). In addition, the paper classifies the software design defects â€Å"shortcomings†that stem from poor design of software. In software development, the writing of a defect free code is one of the major concerns. This concern is cuts across the e software development and object oriented programming community. ... The shortcoming of this approach was that the same defects would still be realised in another software process(Moha and Gueheneuc 2005). It is important to consider the uniqueness, of each piece of software. They are designed as artefacts and meant to serve the user needs adequately. However, the process – individuals, tools, methodology- followed are is the same. This aspect of software development shows that the defects in the process are likely to be repeated. Applying quality management â€Å"control†on the software process is being adopted as a guarantee to achieve software quality. Total quality management of the software design aims at continuously improving the quality of the end product( Kessentini, Sahraoui and Boukadoum 2011 ). Managing the software design by controlling the end product at the design stage is a technique to curve out the causes of defects. This technique adopts a set of practices throughout the software process and is aimed at consistently m eeting the end user needs. While focussing on the software design defects, it is important to note that poor customer requirements elicitation could contribute to poor design of the software (Moha 2007). The focus here is the practices of software management adopted to counter software defects and detect the defects. Most importantly, the main idea is using established processes to catch the software design defects. From this perspective, we are able to examine how total quality management – continuous management of the process – is effected using the design The development of code for software development is a practice that requires skill and experience, producing a design defect free code that does
Monday, October 28, 2019
Relationships In A Time That This Novel Is Set Essay Example for Free
Relationships In A Time That This Novel Is Set Essay How does Steinbeck present ideas of relationships in a time that this novel is set? Steinbeck portrays a world dominated by authoritative white males. It is the attitude of this social structure that permeate ranch society and those who come from outside these expectations are inferior. Of Mice and Men describes the plight of which women, disabled people, black people and people with mental difficulties endure and suffer simply because they do not fit into the ideal category which we see whilst they interact with each other. Lennie’s brief interaction with Crooks reveals the complexity of racial prejudice during the ranch life. Like many of the men on the characters in the story, Crooks admits to being very lonely. â€Å"This here’s my room. Nobody got any right in here but me.†When Lennie visits him in his room, Crooks turns him away, in hope that he will prove a point that if a black man cannot enter a white man’s room then it is unacceptable for the reverse to occur. However, his desire for company ultimately wins out and he invites Lennie to sit with him. In addition, he seems very suspicious of any kindness he receives. The fact that he doubts Lennie being kind to him refers to the strong racism on the ranch. Crooks is not sure how to react to Lennie and his instant reaction is for Lennie to leave. This outsider status causes him to lament his loneliness, but we can see the corrosive effects it has on him as he seems delighted in seeing loneliness in others. For example, he suggests that George is gone for good and it is not until Lennie threatens Crooks with physical violence does he relent. We cannot blame Crooks. On the other hand, this evokes sympathy as the origins of his cruel behaviour are made evident. We can infer that he is jealous and lonely that he wants to see someone else hurt just like he is. Curley and his wife have an unstable marriage, lacking in respect, compassion and communication. Curley believes that his wife is his posse ssion and shows her off to the other men. Throughout the novel we see Curley asking the other men where his wife is and likewise we see Curley’s wife looking for him. This could be a metaphor that although they are together they are still lonely. Their relationship is unhealthy as he manipulates and intimidates his wife. However, Curley seems very selfish and he did not seem to care for his wife. He used her for sex. Furthermore, the fact that she is referred to as â€Å"Curley’s wife†suggests that women did not have an identity. Curley is too protective over his wife as he knew she flirted with the other men and Curley felt threatened, especially as she was the only woman on the ranch. There is not trust between them which is very unhealthy and not good. I think she enjoyed flirting because she felt isolated and lonely. Most of the ranch hands looked down upon her and thought she was a â€Å"slut.†This was the typical attitude towards women during this time period. They were seen as possessions of their husband. At the end of the novel, Steinbeck said that when she died, she was released and â€Å"discontent and the ache for attentions were all gone from her face. She was very pretty and simple, and her face was sweet.†When she was alive, she was wearing a mask and no one knew her true identify, as there was no one there to understand or get to know the real her but now she is dead, and the mask is off she looks better: â€Å"Her reddened lips made her seem alive.†Finally, in death, she could find the peace and calm that evaded her when she was alive in the harsh society. Ironically, her corpise is praised more in death than she was life. We begin to question Steinbeck’s intentions in giving us an unsympathetic view of this women and in women in general. Whenever she expresses her loneliness they are followed by acts of manipulation or violence. He seems to characterise women as trouble and they are â€Å"the downfall of man.†She is the catalyst of the drama which links to that point also. I don’t necessarily think that Steinbeck was sexist and is instead making a point about society’s sexism. She is the only character without a name, and even Crooks- who at that time was a member of a even more hated social group and if she talks to anyone â€Å"he gets mad.â€
Saturday, October 26, 2019
Harassment Essay -- essays research papers
OUTLINE THESIS STATEMENT: In today’s society 40 percent of the nation’s 55 million working women have experienced sexual harassment in the workplace. I.     Introduction II.     Types of sexual harassment      A.     Requirements of sexual harassment           1.     Concept of unwelcome conduct           2.     Sexual nature of conduct      B.     Claims of harassment           1.     Quid quo pro           2.     Hostile environment III.     Types of Recourse      A.     Face-to-face      B.     Employer intervention      C.     Legal action IV.     Prevention of sexual harassment      A.     Written document      B.     Proper and supervising      C.     Rumors and Innuendo V.     Conclusion      SEXUAL HARASSMENT IN THE WORKPLACE OF WOMEN Bernesha Benson SEXUAL HARASSMENT IN THE WORKPLACE OF WOMEN      What is sexual harassment? It is the conduct to unwelcome and affect the terms and conditions of employment. There are several different ways an individual can be sexual harassed . ∙     Derogatory or vulgar comments about someone’s gender, physical anatomy or characteristics. ∙     Sexually suggestive or vulgar language. ∙     Threats or physical harm. ∙     Sexually oriented or suggestive pictures, posters, magazines, or other materials. ∙     Touching someone in a sexually suggestive way, or in a way calculated ... ...bsp;   Anyone who supervisw needs to have some basic education in a number of employee relations areas, including sexual harassment . They also need to have an interpersonal of behavior awarness component in their training. All supervisors and managers should have a fundmental knowledge of equal opportunity and affirmiative action issues, the provisionsof TitleVII and its impact on the workplace. Basic information of human resources policies will also help managers. Supervsiors and managersshould understand what sexual harassment is and what it is not from both legal and practical point of view.      Human resources professionals and line managers are frequently in a position to hearthe latest corporate gossip. While we all know the exaggeration and elaboration are the gossipers stock in trade we also know that there is usually a kernel of truth inside the mass of rumor and innuendo when whispers have to do with possible sexual harassment, particularly when same players are featured again and again, the employer ignores these rumors at its peril. Discreet inquires may well uncover a situation that requires fast and professional intervention.
Thursday, October 24, 2019
Humans and Nature: The Sad Truth about the Relationship between Humans
Since the shift into the Holocene era with the rise of sedentism throughout various millenniums across six continents to present day human ingenuity, respect and attention towards the site gradually declined as technologies advanced human capability and chances of survival. Digging deep in time back to the ancestral hunter-gathering tribes of southwestern France in the Caves of Lascaux, where the site was the structure itself, shifting towards the Anasazi of Mesa Verde who created a structure utilizing the site, finally ending with modern day commercial chain buildings stamped onto landscape with neither respect nor consideration of natural landform and the grim outlook for the city of New Orleans, these sites offer insight to the nulling of human reverence to Earth as technology replaces the necessity for natural provisions. Evolution among ideas and communities both on a communal and global scale show the rising ignorance of Earth throughout history. Although co ntemporary sites break from this shift towards a product over placement, the overall generalization of architecture must recognize this change to shed light for a future of reinvesting in the earth’s protection and prolonging of humanity. Rewind the historical clock 19,000 years ago when anatomically correct, coherent humans first set out to alter the natural world’s many caverns and crevices such as in the Caves of Lascaux. In Paleolithic times when the formation of complex languages and cognitive skills replaced instinctive traits of nourishment, shelter, and procreation, so too did the formation of non-domestic ancestral sites. Archeologically, structures in prehistoric sites are either debunked as domestic or non-domestic, usually associating... ...history. Hurricane Katrina acts as a message to humanity across the globe, architecture must recognize this numbness and utilize the features of the Earth to rekindle light for a future within Earth’s protection and prolonging of humanity. Works Cited Ingersoll, Kostof. . World Architecture, A Cross-Cultural History. New York: Oxford University Press, USA, 2013. print. Varien, M. . Sedentism and Mobility in a Social Landscape: Mesa Verde & Beyond. Arizona: The University of Arizona Press, USA, 1999. print. Venturi et al. . LEARNING FROM LAS VEGAS: THE FORGO'rI'EN SYMBOUSM OF ARCHITECTURAL FORM. Massachusetts: The MIT Press, USA, 2013. print. Williams, R. . Keywords, a vocabulary of culture and society. New York: Oxford University Press, USA, 1976. print. 1 The Citation referring to Brush and Turner comes from a cited source in Varien, M’s book.
Wednesday, October 23, 2019
Police Abuse Essay
Police brutality is the excessive, unreasonable use of force against citizens, suspects, and offenders. A study showed that most citizens complained against police officers because of the use of profanity and abusive language towards them, the use of commands to move on or get home, stopping and questioning people on the street or searching them and their cars without probable cause, the use of threats to use force if not obeyed, prodding with a nightstick or approaching with a pistol, and actual use of physical force or violence itself for no reason at all. Police brutality causes a lack of communication between minority groups and the police department and a lack of trust because of previous run-ins with brutality. In some cases police brutality runs over into an officer’s personal life as well. There have been several cases where an officer is arrested due to domestic violence and leads to an investigation of their work life. Most of the time there are cover ups, when domestic disputes occur so that the department does not get negative coverage if the incident was to get out, (2002, November). Ethics are considered a structure for most departments in the United States. There are several bad apples that get greedy and are cocky at times and think that they cannot be touched if they do wrong. Police departments around the U.S. have several issues with corruption, misconduct, and brutality. Most of the time these issues are covered up so that, these officers do not give the departments bad names and people do not trust them and they, are having more crime on their hands instead of defeating the crime. In recent years, police actions, particularly police abuse has come into view of a wide, public and critical eye. While citizens worry about protecting themselves from criminals, it has now been shown that they must also keep a watchful eye on those who are supposed to protect and serve. This paper will discuss the types of police abuse prevalent today, including the use of firearms and recovery of private information. I will also discuss what and how citizens’ rights are taken advantage of by the police. Some measures necessary to protect ourselves from police taking advantage of their positions as law enforcement officers with greater permissive rights than private citizens. All citizens must take affirmative actions from physical brutality, rights violations, and information abuse. Members of the police force are government officials who enforce the law and maintain order. They are engaged in dangerous and stressful occupation that can involve violent situations that must be controlled. In many of these confrontations with the public it may become necessary for the police to administer force in order to take control of the situation. As unfortunate as it may seem however, police officers are injuring and even killing people through the use of excessive force and brutal treatment. In regard to police abuse, there will be many officers who feel that their job of fighting escalating street crime, gangs, narcotics violations, and other violent crimes is difficult already, to such an extent that worrying about excessive policy for abuse behavior will only further decrease their ability to fight crime effectively, efficiently, and safely. This abuse must be monitored so that police do not forget who they are serving; not themselves, but the public. This means that even the criminals, who are a part of the public, have certain rights, accurately identified as civil rights. One of the main police abuse problems is physical brutality. I think that there should be some kind of written policy that would restrict physical force to the narrowest possible range of specific situations. For example, there should be limitations on the use of hand to hand combat, batons, mace, stun guns and firearms. However, limiting policies actions will bring much debate, especially from police officers and administrators themselves. Many feel that their firepower is already too weak to battle the weapons that criminals have out on the streets, thus limiting their legality of gun use will not only endanger them, but the innocent bystanders who must endure the hierarchy gun power creates in the benefit of criminals. In simple terms, corruption in policing is usually viewed as the misuse of authority by a police officer acting to fulfill personal needs or wants. For a corrupt act to occur, three distinct elements of police corruption must be present simultaneously: Misuse of authority, Misuse of official capacity, Misuse of personal attainment, (Kornblum 1976: p 71). It has been said that power inevitably leads to corruption, and it is yet to be recognized that , while there is no reason to suppose that policemen as individuals are any less fallible than other members of society, people are often shocked and outraged when policemen are exposed to violating the law. Not only should officers use brutality in very limited situations, I think that it would help requiring officers to file a written report after any use of physical force, regardless of how seemingly insignificant. Although, if every incidence of police abuse was requested to be reported, how many actually would be? Maybe only those serious enough, as depicted in new guidelines, would make it, leaving some space for officers to exert pressure without crossing serious and abusive policy. Another good tactic to control police brutality is to establish a system to identify officers who have been involved in an inordinate number of incidents that include the inappropriate use of physical fo rce. The incidents should then be investigated. For those offices who are frequently involved in unnecessary police brutality, they should be charged, disciplined, re-trained, and offered counseling. If such treatment proves ineffective, officers who violate abuse standards should be brought up on review before an administrative board made up of citizens and police officials. Officers will most likely ask, â€Å"Is identifying abusive officers a form of prejudice? The police officer is there to serve and protect the public who pays his or her salary. The officer should then be subject to any investigations into his or her abusive actions on the job. Yet even if internal policy and external government supervision is successful, it is difficult to say how the ethics of police officers will affect abuse policy as they are based on personal background and upbringing that have little to do with the issue at hand. While there are specific solutions to brutality and rights abuse, there are also some general solutions that could be implemented before the problems even arise. For example, there should be changes in police officer training. Some communities have demanded their officers receive higher education. However, there is no proof that well-educated officers rely less on abuse and more on departmentally sound investigation techniques. The length of training of police personnel should be increased, as has been the recent trend throughout the years. â€Å"The average length of police academy programs has more than doubled, from about 300, to over 600 hours; in some cities, 900 up to even 1200 hours has become the new rule.†(Silverman 1999: p 124) As the time devoted to training has increased, the institutions should also stress the importance of the growing trends in criminal activity so that they are prepared to deal with them. These include such areas as race relations, domestic violence, handling the mentally ill, and so on. This will, in turn, enable operations run more smoothly, hopefully avoiding police abuse problems in the future. Methods must be implemented which effectively deal with police who tend to cross the line, from simple situations to serious firearm use or prejudice. Some of the solutions, particularly the policy changes, will be met with controversy and will be difficult to implement. Keeping track of police actions is the next step in self-protection. There have been thousands of reported incidents of police misconduct in the countless cities throughout the nation, and probably thousands more that transpire without any mention. Law enforcement officers in the United States have been granted powerful authority to assist them in serving and protecting the people of this country. Many of them use their authority to uphold their duties with honor and integrity. However, the abuses of these powers are taking place with more and more frequency. The police scandals that have surfaced within the past decade have been multiplying. If drastic measures are not taken to restore the integrity of the United States Law Enforcement, chaos will permeate throughout the nation. As citizens begin to lose their trust for law enforcement, they will gradually lose their trust in the â€Å"system†. While the threat of a world war has diminished, the violence on the streets across America has increased at a dramatic rate. Police are forced to face this violence and are sometimes caught up in the same violent and abusive cycle whole trying to fight it. Citizens realize that there are limits as to what a police officer can do. To make society a safe place for both citizens and officers, it is imperative that they work together for a comprehensive checks and balances system. The United States Constitution guarantees certain rights for everyone, and is the very backbone of this country. If these rights are to be ignored, either through permissive laws enacted by law enforcement against private citizens, or through a lack of maintenance of existing protective legislation, private citizens; which means the entire country, will become paralyzed. Because of this, the opportunity and freedom which this country is built on must be enforced, and those charged with doing so must not abuse their power. References (2002, December) Police Corruption, http://www.iejs.com/policing word-slash-word police_corruption.htm (2002, November) Addressing police misconduct, http://www.usdoj.gov (2002, November) Police brutality: the cop crimes homepage for law enforcement and government corruption, http://www.copcrimes.comword-slashwordhomepage.htm Alpert, Geoffrey P., Dunham Roger G. Police Use of Deadly Force. Washington D.C.: Police Executive Research Forum, 1995. Chevigny, Paul. Police Power. Toronto: Random House, 1994. Cohen, Henry. Brutal Justice. New York: John Jay Press, 1980. Kornblum, Alan N. The Moral Hazards. New York: D.C. Heath, 1976. Silverman, Eli B. NYPD Battles Crime. Boston: Northeastern Univ. Press, 1999.
Tuesday, October 22, 2019
Conductivity and Conductive Elements
Conductivity and Conductive Elements Conductivity refers to the ability of a material to transmit energy. There are different types of conductivity, including electrical, thermal, and acoustical conductivity. The most electrically conductive element is silver, followed by copper and gold. Silver also has the highest thermal conductivity of any element and the highest light reflectance. Although it is the best conductor, copper and gold are used more often in electrical applications because copper is less expensive and gold has a much higher corrosion resistance. Because silver tarnishes, it is less desirable for high frequencies because the exterior surface becomes less conductive. As to why silver is the best conductor, the answer is that its electrons are freer to move than those of the other elements. This has to do with its valence and crystal structure. Most metals conduct electricity. Other elements with high electrical conductivity, are aluminum, zinc, nickel, iron, and platinum. Brass and bronze are electrically conductive alloys, rather than elements. Table of the Conductive Order of Metals This list of electric conductivity includes alloys as well as pure elements. Because the size and shape of a substance affect its conductivity, the list assumes all samples are the same size. In order of most conductive to least conductive: SilverCopperGoldAluminumZincNickelBrassBronzeIronPlatinumCarbon SteelLeadStainless Steel Factors That Affect Electrical Conductivity Certain factors can affect how well a material conducts electricity. Temperature: Changing temperature of silver or any other conductor alters its conductivity. In general, increasing the temperature causes thermal excitation of the atoms and decreases conductivity while increasing resistivity. The relationship is linear, but it breaks down at low temperatures.Impurities: Adding an impurity to a conductor decreases its conductivity. For example, sterling silver is not as good of a conductor as pure silver. Oxidized silver is not as good a conductor as untarnished silver. Impurities hinder electron flow.Crystal structure and phases: If there are different phases of a material, conductivity will slow slightly at the interface and may be different from one structure than another. The way a material has been processed can affect how well it conducts electricity.Electromagnetic fields: Conductors generate their own electromagnetic fields when electricity runs through them, with the magnetic field perpendicular to the electric field. External electromagneti c fields can produce magnetoresistance, which can slow the flow of current. Frequency: The number of oscillation cycles an alternating electrical current completes per second is its frequency in Hertz. Above a certain level, a high frequency can cause current to flow around a conductor rather than through it (skin effect). Since there is no oscillation and hence no frequency, the skin effect does not occur with direct current.
Monday, October 21, 2019
How to Actually Use Your SAT Math Formulas
How to Actually Use Your SAT Math Formulas SAT / ACT Prep Online Guides and Tips On average, you’ll need to use an SAT math formula once every four to five questions. This accounts for approximately 20-25% of the combined math sections, which means it is crucial that you understand how and when to employ your formulas on the SAT. We’ve put together the list of your need-to-know SAT formulas (prioritized in the order from greatest to least that you’ll see them on the SAT) as well as how to best use them for test-day. What Formulas Will You Need on the SAT? You will always be given nine geometry formulas and two geometry laws on the test, but NO algebra or coordinate geometry formulas. We’ve put together a list of the 21 SAT math formulas you should know for test dayand prioritized them according to â€Å"need to know†and â€Å"good to know.†If you feel rusty on any formula or math topic on the list, check out one of our individual math topic guidesto see how the formula works (and even why it works), as well as how to recognize when to use it. We’ll also show you the alternatives to using formulas for many questions. For instance, you can solve your distance questionsby either using the distance formula or by drawing a picture and using the Pythagorean Theorem. Both of these methods require formulas, but you are given the Pythagorean Theorem in the formula box, and so we have classified the distance formula as â€Å"good to know†but ultimately not â€Å"necessary.†SAT math questions are designed to be solved in a multitude of ways, so don't worry about having to find the one "right" path. How to Use Your Formulas Effectively So how do you best utilize your formulas, both given and not given? Let’s take a look. 1) MEMORIZE your formulas The best thing you can do for yourself (and your SAT math score) is to memorize your formulasyes, even the ones you’re given. Though it is nice to have the formula box as a fallback option to double-check your work, it is both a distraction and a time suck to continuously flip back and forth from problem to formula box, problem to formula box. Dividing your focus like this can lead to careless errors and is not something that we recommend. Unless you, for any reason, cannot memorize your formulas, then absolutely do so. Memorization (and practice, to drill them into your head) is going to be one of the strongest tools in your belt when taking the SAT math section. If you're a visual learner, make yourself a set of formula flash cards. If you're a kinesthetic (movement) learner, practice drawing and/or writing them out on a separate piece of paper. And if you're an auditory learner, get a parent or a friend to help you drill them aloud. Once you feel you've got your formulas down, practice using them on actual SAT questions to help you both remember them and learn how to use a particular formula for a particular problem. (We'll give you the opportunity to practice using your formulas in the next section.) 2) Prioritize learning your most crucial formulas Some formulas come up over and over (and over!), while others show up sparingly at best. If you are pressed for time, nervous about memorizing so many formulas, or simply trying to map out your plan of attack, memorize your formulas in the order that they appear most often on the test. Of your â€Å"necessary†formulas, they appear on the test from greatest prevalence to least in roughly this order: Law: the sum of the interior degrees of a triangle is 180 Area of a triangle Law: the sum of the degrees of a straight line is 180 Area of a rectangle (or other quadrilateral) Pythagorean Theorem Finding slope of a given line (rise/run) Finding slope of line connecting two points Finding percentages Law: the number of degrees of arc in a circle is 360 Area of a circle Circumference of a circle Finding averages Area of a circle’s arc Circumference of a circle’s arc Finding probabilities Finding combinations Finding the midpoint of a line Volume of rectangular solid Volume of cylinder Of the â€Å"good to know†or â€Å"shortcut†formulas, you will need them roughly in this order: Special right triangle properties, 30-60-90 Special right triangle properties, 45-45-90 Arithmetic sequences Geometric sequences Distance formula 3) Decide NOW which (if any) of your â€Å"good to know†formulas you want to memorize The reason they are called â€Å"good to know†formulas is exactly how it soundsyou can find all the answers to your SAT math problems without knowing these formulas or shortcuts at all. On the other hand, knowing them can save you time and effort, so it’s entirely your decision whether or not to memorize them. Just keep in mind that it is worse to remember a formula incorrectly than it is to have not attempted memorizing it at all. So if you do decide to memorize, say, the distance formula, make sure you’ve got it locked down tight. Otherwise, just decide here and now to only pay attention to your necessary formulas and leave the â€Å"good to know†formulas in the dust. 4) Practice SAT math questions at home without looking up your formulas It’s one thing to memorize your formulas with flash cards, but it’s a whole other ball game to remember them when you come face to face with real SAT math problems. You’ll have to figure out which formulas to use and how to execute them, in addition to remembering just what they are. And the only way you’re going to be able to do this is by practicing. After you’ve made the effort to memorize your formulas, practice your SAT questions without the safety net. Try to solve them as if you were really taking the testso memorize your formulas if possible, but feel free to use the given formulas as a fallback in case you get stuck or need to double-check your answers. 5) Don’t panic if you forget a formula Most of all don’t panic! We’ve said it before, and we’ll say it againthere are always multiple ways for you to solve your SAT math questions. So if you forget a formula, don’t worry about it! Is it a problem that can’t be solved without a formula? You will always have your given formulas in your formula box to rely on in a pinch. Is it a problem that requires an algebraic (aka, NOT given) formula? Then you will likely be able to solve it in a way that does not require a formula. On most occasions, you will be able to use the strategies of plugging in answers,plugging in numbers,or even just making a logical guess, to help you solve questions that you otherwise cannot. If necessary, you can usually eliminate one or two answer choices that are obvious outliers, even if you don’t know the formulas or strategies for how to solve the problem. For example, let's check out how we narrow down our answer options for an SAT math problem without using any formulas at all. If, for any reason, you forgot your formulas and even forgot that you had a formula box at your disposal, you can still eliminate several answer choices for this problem. If we remember that all SAT figures are drawn to scale unless otherwise noted, we can see at a glance that angles $a$ and $c$ are clearly smaller than angles $b$, $d$, and $e$. Eliminating two answer choices is enough to take a guess on the SAT and not risk too much with a wrong answer penalty, but we might be able to narrow it down even further. Even without knowing that a straight line has a degree measure of 180, we can logically deduce that a straight line must measure some amount and that all straight lines will be the same. The unknown angle attached to a given angle in a straight line (the supplementary angle) will therefore measure the remaining amount of the full measure of the line (whatever that measure may be). To visualize this, let's say that you have two buckets full of tennis balls. Each bucket contains the exact same amount of tennis balls, even though you don't know how many that is. You remove two tennis balls from the first bucket and one tennis ball from the second. Even though you didn't know how many tennis balls there were to begin with in each bucket, we know that the second bucket must have more tennis balls remaining than the first. This means that the angle attached (supplementary) to the larger given angle on a line will be smaller than the angle supplementary to the smaller given angle on a line. In other words,angle $e$ will be smaller than angle $b$, because $e$ is attached to a larger angle on a line. This means we can eliminate angle $e$ from the group. This leaves us with two answer choices, $b$ and $d$, all without the use of any formulas whatsoever. By guessing now, we have a 50-50 shot of getting it right! [Note: the correct answer is D, angle $d$.] And, as a last resort, you can always skip the problem entirely. Remember: if you cannot eliminate any answer choices, then you’re better off skipping the problem and simply moving on. Pick up points where you can and cut your lossesa question here and there that you have to skip won’t affect your score as much as you may think. Ready to test out your formula skills? SAT Math Practice Using Formulas Now let’s test your formula knowledge against real SAT math problems, all of which require formulas (both given and not given) to solve. 1) 2) 3) 4) Answers: D, D, C, 8 Answer Explanations: 1) If we remember our solid geometry formulas, we know that the volume of a rectangular prism is found by: $a = lwh$ So we can find the volume of our smaller rectangular blocks by multiplying the height, length, and width. $3 * 2 * 1$ $6$ inches. We can also find the volume of our larger prism the same way. We are told that the box is a cube, which means that the height, length, and width are all equal. If one side of the cube measures 6 inches, the volume of the cube will be: $6 * 6 * 6$ $216$ inches. Now we can simply divide the larger box by the smaller blocks. $216/6$ $36$ 36 smaller rectangular blocks will be able to fit into the larger box. Our final answer is D, 36. 2) This is another problem we can pretty much eyeball and work through logically, without knowing much about circles. We can also work through it using our formulas properly, so let's look at both techniques. Let's start by estimating. We are told that the larger circle has a circumference of 36 and that the radius of the smaller circle is half the radius of the larger circle. We also know that the figure is to scale, since we are not told otherwise. Even without knowing anything about circles, we can see that the cut out of 80 ° looks to be a little less than a quarter of both the larger and the smaller circle. As you can see, the red lines would divide the circle into proper quarters, and 80 ° is a little less than this. So if we know that the larger circumference is 36, we can divide this by 4 to find the approximate length of the larger arc. $36/4 = 9$ We know that the arc of the larger circle must besmaller than 9 (remember80 ° is a little less than a quarter), so the arc of the smaller circle must be even smaller than this. We can safely eliminate answer options A and B. Now we can eyeball the difference between the arc measures and guess that, if the larger arc is close to 9, the smaller arc is probably larger than 2. This leaves us with two answer choices, C and D, which gives us a 50-50 chance of getting the right answer. It is a safe time to make our best guess. Alternatively, we can solve the question by using our knowledge of circle formulas and angles. We are told that the larger circle has a circumference of 36 and we know that, to find the circumference of a circle, we use the formula: $c =À2r$ If the circumference is 36, then the radius must be $36/2 = 18$ This means that the radius of the smaller circle (which we were told is half the radius of the larger) must be 9. Now, to find the circumference of an arc, we use the formula: $c_{arc} =À2r(\angle/360)$ $18(80/360)$ $4$ Our final answer is D, 4. 3) We know that the area of a triangle is: $a = {1/2}bh$ Imagine, then, that we are working with a right triangle. This way, we can use one of our leg measures as our height to get our maximum area. We also know that the hypotenuse of a right triangle will be the side opposite the 90 degree angle. So if 10 is the longest side (the hypotenuse), the base or the height would have to be smaller. If, however, 10 acted as either the base or the height, the 7 would act as the other piece. This would mean our area was: $a = {1/2}(10)(7)$ $a = 35$ The largest possible area for our triangle is 35. Our final answer is C, 35. 4) For this problem, let us first fill in our given information. Now, we know that triangle APC is a right triangle, which means we can use either the Pythagorean Theorem (or our triangle shortcuts) to find the length of AP. $a^2 + b^2 = c^2$ $a^2 + 3^2 = 5^2$ $a^2 + 9 = 25$ $a^2 = 16$ $a = 4$ AP = 4 Now triangle ABP is also a right triangle, because it is connected on a line to the right triangle APC. In other words, angles BPA and APC are supplementary. This means we can find the measure of leg BA by using the Pythagorean Theorem one more time. $a^2 + b^2 = c^2$ $(4√3)^2 + 4^2 = c^2$ $16(3) + 16 = c^2$ $48 + 16 = c^2$ $64 = c^2$ $c = 8$ BA = 8. Our final answer is 8. You did it! It's done, yay! Image: Travis Nep Smith/Flickr The Take-Aways Don’t underestimate the value of needing to both know and understand your SAT formulas, but don’t get too fixated on them either. Though problems that require formulas account for 20-25% of your overall SAT math questions, that still leaves 75-80% of all SAT math questions that DON’T require formulas at all. So make sure that you know your formulas, but don’t think that knowing your formulas is the only hurdle to pass to do well on your SAT math test. Formula knowledge is just one step (though an important step) for doing well on the SAT math section as a whole. But a knowledge of your formulas, a balanced study plan, and a brush-up on any SAT math topic in which you might be rusty will definitely help get you to get where you need to be by test-day. What’s Next? Need to brush up on a particular SAT math topic?Check out ourindividual math topic guidesfor all your SAT math needs. Running out of time on the SAT math section?We'll show youhow to beat the clock and maximize your scorebefore time runs out. Been procrastinating in your SAT math study?Our guide willhelp you balance out your study time and beat back the urge to procrastinate. Aiming for a perfect score?Check out ourguide to getting an 800 on the SAT math section, written by a perfect-scorer. Want to improve your SAT score by 160 points? Check out our best-in-class online SAT prep program. We guarantee your money back if you don't improve your SAT score by 160 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math strategy guide, you'll love our program.Along with more detailed lessons, you'll get thousands ofpractice problems organized by individual skills so you learn most effectively. We'll also give you a step-by-step program to follow so you'll never be confused about what to study next. 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