Sequences on ACT Math Strategy Guide and Review

Sequences on ACT Math Strategy Guide and Review SAT / ACT Prep Online Guides and Tips Sequences are patterns of numbers that follow a particular set of rules. Whether new term in the sequence is found by an arithmetic constant or found by a ratio, each new number is found by a certain rule- the same rule- each time. There are several different ways to find the answers to the typical sequence questions- †What is the first term of the sequence?†, â€Å"What is the last term?†, â€Å"What is the sum of all the terms?†- and each has its benefits and drawbacks. We will go through each method, and the pros and cons of each, to help you find the right balance between memorization, longhand work, and time strategies. This will be your complete guide to ACT sequence problems- the various types of sequences there are, the typical sequence questions you’ll see on the ACT, and the best ways to solve these types of problems for your particular ACT test taking strategies. Before We Begin Take note that sequence problems are rare on the ACT, never appearing more than once per test. In fact, sequence questions do not even appear on every ACT, but instead show up approximately once every second or third test. What does this mean for you? Because you may not see a sequence at all when you go to take your test, make sure you prioritize your ACT math study time accordingly and save this guide for later studying. Only once you feel you have a solid handle on the more common types of math topics on the test- triangles (comng soon!), integers, ratios, angles, and slopes- should you turn your attention to the less common ACT math topics like sequences. Now let's talk definitions. What Are Sequences? For the purposes of the ACT, you will deal with two different types of sequences- arithmetic and geometric. An arithmetic sequence is a sequence in which each term is found by adding or subtracting the same value. The difference between each term- found by subtracting any two pairs of neighboring terms- is called $d$, the common difference. -5, -1, 3, 7, 11, 15†¦ is an arithmetic sequence with a common difference of 4. We can find the $d$ by subtracting any two pairs of numbers in the sequence- it doesn’t matter which pair we choose, so long as the numbers are next to one another. $-1 - -5 = 4$ $3 - -1 = 4$ $7 - 3 = 4$ And so on. 12.75, 9.5, 6.25, 3, -0.25... is an arithmetic sequence in which the common difference is -3.25. We can find this $d$ by again subtracting pairs of numbers in the sequence. $9.5 - 12.75 = -3.25$ $6.25 - 9.5 = -3.25$ And so on. A geometric sequence is a sequence of numbers in which each successive term is found by multiplying or dividing by the same amount each time. The difference between each term- found by dividing any neighboring pair of terms- is called $r$, the common ratio. 212, -106, 53, -26.5, 13.25†¦ is a geometric sequence in which the common ratio is $-{1/2}$. We can find the $r$ by dividing any pair of numbers in the sequence, so long as they are next to one another. ${-106}/212 = -{1/2}$ $53/{-106} = -{1/2}$ ${-26.5}/53 = -{1/2}$ And so on. Though sequence formulas are useful, they are not strictly necessary. Let's look at why. Sequence Formulas Because sequences are so regular, there are a few formulas we can use to find various pieces of them, such as the first term, the nth term, or the sum of all our terms. Do take note that there are pros and cons for memorizing formulas. Pros- formulas are a quick way to find your answers, without having to write out the full sequence by hand or spend your limited test-taking time tallying your numbers. Cons- it can be easy to remember a formula incorrectly, which would lead you to a wrong answer. It also is an expense of brainpower to memorize formulas that you may or may not even need come test day. If you are someone who prefers to use and memorize formulas, definitely go ahead and learn these! But if are not, then you are still in luck; most (though not all) ACT sequence problems can be solved longhand. So if you have the patience- and the time to spare- then don’t worry about memorizing formulas. That all being said, let’s take a look at our formulas so that those of you who want to memorize them can do so and so that those of you who don’t can still understand how they work. Arithmetic Sequence Formulas $$a_n = a_1 + (n - 1)d$$ $$\Sum \terms = (n/2)(a_1 + a_n)$$ These are our two important arithmetic sequence formulas and we will go through how each one works and when to use them. Terms Formula $a_n = a_1 + (n - 1)d$ If you need to find any individual piece of your arithmetic sequence, you can use this formula. First, let us talk about why it works and then we can look at some problems in action. $a_1$ is the first term in our sequence. Though the sequence can go on infinitely, we will always have a starting point at our first term. $a_n$ represents any missing term we want to isolate. For instance, this could be the 4th term, the 58th, or the 202nd. Why does this formula work? Well let’s say we wanted to find the 2nd term in the sequence. We find each new term by adding our common difference, or $d$, so the second term would be: $a_2 = a_1 + d$ And we would then find the 3rd term in the sequence by adding another $d$ to our existing $a_2$. So our 3rd term would be: $a_3 = (a_1 + d) + d$ Or, in other words: $a_3 = a_1 + 2d$ And the 4th term of the sequence, found by adding another $d$ to our existing third term, would continue this pattern: $a_4 = (a_1 + 2d) + d$ Or $a_4 = a_1 + 3d$ So, as you can see, each term in the sequence is found by adding the first term to $d$, multiplied by $n - 1$. (The 3rd term is $2d$, the 4th term is $3d$, etc.) So now that we know why the formula works, let’s look at it in action. What is the difference between each term in an arithmetic sequence, if the first term of the sequence is -6 and the 12th term is 126? 3 4 6 10 12 Now, there are two ways to solve this problem- using the formula, or finding the difference and dividing by the number of terms between each number. Let’s look at both methods. Method 1: Arithmetic Sequence Formula If we use our formula for arithmetic sequences, we can find our $d$. So let us simply plug in our numbers for $a_1$ and $a_n$. $a_n = a_1 + (n - 1)d$ $126 = -6 + (12 - 1)d$ $126 = -6 + 11d$ $132 = 11d$ $d = 12$ Our final answer is E, 12. Method 2: finding difference and dividing Because the difference between each term is regular, we can find that difference by finding the difference between our terms and then dividing by the number of terms in between them. Note: be very careful when you do this! Though we are trying to find the 12th term, there are NOT 12 terms between the first term and the 12th- there are actually 11. Why? Let’s look at a smaller scale sequence of 3 terms. 4, __, 8 If you wanted to find the difference between these terms, you would again find the difference between 4 and 8 and divide by the number of terms separating them. You can see that there are 3 total terms, but 2 terms separating 4 and 8. 1st: 4 to __ 2nd: __ to 8 When given $n$ terms, there will always be $n - 1$ terms between the first number and the last. So, if we turn back to our problem, now we know that our first term is -6 and our 12th is 126. That is a difference of: $126 - -6$ $126 + 6$ $132$ And we must divide this number by the number of terms between them, which in this case is 11. $132/11$ $12$ Again, the difference between each number is E, 12. As you can see, the second method is just another way of using the formula without actually having to memorize the formula. How you solve these types of questions completely depends on how you like to work and your own personal ACT math strategies. Sum Formula $\Sum \terms = (n/2)(a_1 + a_n)$ This formula tells us the sum of the terms in an arithmetic sequence, from the first term ($a_1$) to the nth term ($a_n$). Basically, we are multiplying the number of terms, $n$, by the average of the first term and the nth term. Why does this work? Well let’s look at an arithmetic sequence in action: 4, 7, 10, 13, 16, 19 This is an arithmetic sequence with a common difference, $d$, of 3. A neat trick you can do with any arithmetic sequence is to take the sum of the pairs of terms, starting from the outsides in. Each pair will have the same exact sum. So you can see that the sum of the sequence is $23 * 3 = 69$. In other words, we are taking the sum of our first term and our nth term (in this case, 19 is our 6th term) and multiplying it by half of $n$ (in this case $6/2 = 3$). Another way to think of it is to take the average of our first and nth terms- ${4 + 19}/2 = 11.5$ and then multiply that value by the number of terms in the sequence- $11.5 * 6 = 69$. Either way, you are using the same basic formula, so it just depends on how you like to think of it. Whether you prefer $(n/2)(a_1 + a_n)$ or $n({a_1 + a_n}/2)$ is completely up to you. Now let’s look at the formula in action. Andrea is selling boxes of cookies door-to-door. On her first day, she sells 12 boxes of cookies, and she intends to sell 5 more boxes per day than on the day previous. If she meets her goal and sells boxes of cookies for a total of 10 days, how many boxes total did she sell? 314 345 415 474 505 As with almost all sequence questions on the ACT, we have the choice to use our formulas or do the problem longhand. Let’s try both ways. Method 1: formulas We know that our formula for arithmetic sequence sums is: $\Sum = (n/2)(a_1 + a_n)$ In order to plug in our necessary numbers, we must find the value of our $a_n$. Once again, we can do this via our first formula, or we can find it by hand. As we are already using formulas, let us use our first formula. $a_n = a_1 + (n - 1)d$ We are told that the first term in our sequence is 12. We also know that she sells cookies for 10 days and that, each day, she sells 5 more boxes of cookies. This means we have all our pieces to complete this formula. $a_n = 12 + (10 - 1)5$ $a_10 = 12 + (9)5$ $a_10 = 12 + 45$ $a_10 = 57$ Now that we have our value for $a_n$ (in this case $a_10$), we can complete our sum formula. $(n/2)(a_1 + a_n)$ $(10/2)(12 + 57)$ $5(69)$ $345$ Our final answer is B, 345. Method 2: longhand Alternatively, we can solve this problem by doing it longhand. It will take a little longer, but this way also carries less risk of mis-remembering a formula. The decision is, as always, completely up to you on how you choose to solve these kinds of questions. First, let us write out our sequence, beginning with 12 and adding 5 to each subsequence number, until we find our nth (10th) term. 12, 17, 22, 27, 32, 37, 42, 47, 52, 57 Now, we can either add them up all by hand- $12 + 17 + 22 + 27 + 32 + 37 + 42 + 47 + 52 + 57 = 345$ Or we can use our arithmetic sequence sum trick and divide the sequence into pairs. We can see that there are 5 pairs of 69, so $5 * 69 = 345$. Again, our final answer is B, 345. Whoo! Only one more formula to go! Geometric Sequence Formulas $$a_n = a_1( r^{n - 1})$$ (Note: there is a formula to find the sum of a geometric sequence, but you will never be asked to find this on the ACT, and so it is not included in this guide.) This formula, as with the first arithmetic sequence formula, will help you find any number of missing pieces in your sequence. Given two pieces of information about your sequence ($a_n$ $a_1$, $a_1$ $r$, or $a_n$ $r$), you can find the third. And, as always with sequences, you have the choice of whether to solve your problem longhand or with a formula. What is the first term in a geometric sequence if each number is found by multiplying the previous term by -3 and the 8th term is 4,374? -0.222 0.667 -2 6 -18 Method 1: formula If you’re one for memorizing formulas, we can simply plug in our values into our equation in place of $a_n$, $n$, and $r$ in order to solve for $a_1$. $a_n = a_1( r^{n - 1})$ $4374 = a_1(-3^{8 - 1})$ $4374 = a_1(-3^7)$ $4374 = a_1(-2187)$ $-2 = a_1$ So our first term in the sequence is -2. Our final answer is C, -2. Method 2: longhand Alternatively, as always, we can take a little longer and solve them problem by hand. First, set out our number of terms in order to keep track of them, with our 8th term, 4374, last. ___, ___, ___, ___, ___, ___, ___, 4374 Now, let’s divide each number by -3 down the sequence until we reach the beginning. ___, ___, ___, ___, ___, ___, -1458, 4374 ___, ___, ___, ___, ___, 486, -1458, 4374 And, if we keep going thusly, we will eventually get: -2, 6, -18, 54, -162, 486, -1458, 4374 Which means that we can see that our first term is -2. Again, our final answer is C, -2. As with all sequence solving methods, there are benefits and drawbacks to solving the question in each way. If you choose to use formulas, make very sure you can remember them exactly. And if you solve the questions by hand, be very careful to find the exact number of terms in the sequence. The ACT will always provide bait answers for anyone who is one or two terms off the nth term- in this problem, if you had accidentally assigned 4374 as the 7th term or the 9th term, you would have chosen answer B or D. Once you find the strategy that works best for you, the pieces will all fall into place. Typical ACT Sequences Questions Because all sequence questions on the ACT can be solved (if sometimes arduously) without the use or knowledge of sequence formulas, the test-makers will only ever ask you for a limited number of terms or the sum of a small number of terms (usually less than 12). As we saw above, you may be asked to find the 1st term in a sequence, the nth term, the difference between your terms (whether a common difference, $d$, or a common ratio, $r$), or the sum of your terms in arithmetic sequences only. You also may be asked to find an unusual twist on a sequence question that combines your knowledge of sequences. For example: What is the sum of the first 5 terms of an arithmetic sequence in which the 6th term is 14 and the 11th term is 22? 2.2 6.0 12.4 32.6 46.0 Again, let us look at both formulaic and longhand methods for how to solve a problem like this. Method 1: formulas In order to find our common difference, we can use our main arithmetic sequence formula. But this time, instead of beginning with the actual $a_1$, we are beginning with our 6th term, as this is what we are given. Essentially, we are designating our 6th term as our 1st term and our 11th term as our 6th term and then plugging these values into our formula. $a_n = a_1 + (n - 1)d$ $22 = 14 + (6 - 1)d$ $22 = 14 + 5d$ $8 = 5d$ $1.6 = d$ Now, we can find our actual 1st term by using the $d$ we just found and our 11th term value of 22. $a_n = a_1 + (n - 1)d$ $22 = a_1 + (11 - 1)1.6$ $22 = a_1 + (10)1.6$ $22 = a_1 + 16$ $6 = a_1$ The 1st term of our sequence is 6. Now, we need to find the 5th term of our sequence in order to use our arithmetic sequence sum formula to find the sum of the first 5 terms. $a_n = a_1 + (n - 1)d$ $a_5 = 6 + (5 - 1)1.6$ $a_5 = 6 + (4)1.6$ $a_5 = 6 + 6.4$ $a_5 = 12.4$ And finally, we can find the sum of our first 5 terms by using our sum formula and plugging in the values we found. $(n/2)(a_1 + a_n)$ $5/2(6 + 12.4)$ $2.5(18.4)$ $46$ Our final answer is E, 46. As you can see, this problem still took a significant amount of time using our formulas because there were so many moving pieces. Let us look at this problem were we to solve it longhand instead. Method 2: longhand First, let us find our common difference by finding the difference between our 6th term and our 11th term and dividing by how many terms are in between them, which in this case is 5. (Why 5? There is one term between the 6th and 7th terms, another between the 7th and 8th, another between the 8th and 9th, another between the 9th and 10th, and the last between the 10th and 11th terms. This makes a total of 5 terms.) This gives us: $22 - 14 = 8$ $8/5 = 1.6$ Now, let us simply find all the numbers in our sequence by working backwards and subtracting 1.6 from each term. ___, ___, ___, ___, ___, 14, ___, ___, ___, ___, 22 ___, ___, ___, ___, ___, 14, ___, ___, ___, 20.4, 22 ___, ___, ___, ___, ___, 14, ___, ___, 18.8, 20.4, 22 And so on, until all the spaces are filled. 6, 7.6, 9.2, 10.8, 12.4, 14, 15. 6, 17.2, 18.8, 20.4, 22 Now, simply add up the first 5 terms. $6 + 7.6 + 9.2 + 10.8 + 12.4$ $46$ Our final answer is E, 46. Again, you always have the choice to use formulas or longhand to solve these questions and how you prioritize your time (and/or how careful you are with your calculations) will ultimately decide which method you use. You've seen the typical ACT sequence questions, so let's talk strategies. Tips For Solving Sequence Questions Sequence questions can be somewhat tricky and arduous to slog through, so keep in mind these ACT math tips on sequences as you go through your studies: 1: Decide before test day whether or not you will use the sequence formulas Before you go through the effort of committing your formulas to memory, think about the kind of test-taker you are. If you are someone who lives and breathes formulas, then go ahead and memorize them now. Most sequence questions (though, as we saw above, not all of them) will go much faster once you have the formulas down straight. If, however, you would rather dedicate your time and brainpower to other math topics or to the method of performing sequence questions longhand, then don’t worry about your formulas! Don’t even bother to try to remember them- just decide here and now not to use them and forget about the formulas entirely. Unless you can be sure to remember them correctly, a formula will hinder more than help you when it comes time to take your ACT, so make the decision now to either memorize them or forget about them. 2: Write your values down and keep your work organized Though many calculators can perform long strings of calculations, sequence questions by definition involve many different values and terms. Small errors in your work can cause a cascade effect. One mistyped digit in your calculator can throw off your work completely, and you won’t know where the error happened if you do not keep track of your values. Always remember to write down your values and label them in order to prevent a misstep somewhere down the line. 3: Keep careful track of your timing No matter how you solve a sequence question, these types of problems will generally take you more time than other math questions on the ACT. For this reason, most all sequence questions are located in the last third of the ACT math section, which means the test-makers think of sequences as a â€Å"high difficulty† level problem. Time is your most valuable asset on the ACT, so always make sure you are using yours wisely. If you can answer two other math questions in the time it takes you to answer one sequence question, then maximize your point gain by focusing on the other two questions. Always remember that each question on the ACT math section is worth the same amount of points, so prioritize quantity and don’t let your time run out trying to solve one problem. If you feel that you can answer a sequence problem quickly, go ahead! But if you feel it will take up too much time, move on and come back to it later. Ready to put your knowledge to the test? Test Your Knowledge Now let’s test your sequence knowledge with real ACT math problems. 1. What is the first term in the arithmetic sequence if terms 6 through 9 are shown below? ...196, 210, 224, 238 7 14 98 126 140 2. What is the sum of the first 8 terms in the arithmetic sequence that begins: 7, 10.5, 14,... 143.5 154 162.5 168 176.5 3. Answers: D, B, E Answer Explanations: 1. As always, we can solve this problem with formulas or via longhand. For the sake of brevity, we will only use one method per problem here. In this case, let us solve our problem via longhand. We are told this is an arithmetic sequence, so we can find our common difference by subtracting neighboring terms. Let us take a pair and subtract to find our $d$. $238 - 224 = 14$ $d = 14$ We know our common difference is 14, and 196 is our 6th term. Let us work backwards to find our 1st term. ___, ___, ___, ___, ___, 196, 210, 224, 238 ___, ___, ___, ___, 182, 196, 210, 224, 238 ___, ___, ___, 168, 182, 196, 210, 224, 238 And so on, until we reach our first term. 126, 140, 154, 168, 182, 196, 210, 224, 238 As long as we kept our work organized, we will find the first term in our sequence. In this case, it is 126. Our final answer is D, 126. 2. Again, we have many options for solving our problem. In this case, we can use a combination of longhand and formula (in addition to the standard options of using either method alone). First, we must find our common difference between our terms by subtracting any neighboring pair. $14 - 10.5 = 3.5$ $d = 3.5$ Now that we have found our $d$, let us finish our sequence until the 8th term by continuing to add 3.5 to each successive term. 7, 10.5, 14, 17.5, 21, 24.5, 28, 31.5 And finally, we can plug in our values into our sum formula to find the sum of all our terms. $(n/2)(a_1 + a_n)$ $(8/2)(7 + 31.5)$ $(4)(38.5)$ $154$ The sum of the first 8 terms in the sequence is 154. Our final answer is B, 154. 3. Again, we can use multiple methods to solve our problem. In this case, let us use our formula for geometric sequences. First, we need to find our common ratio between terms, so let us divide any pair of neighboring terms to find our $r$. ${-27}/9 = -3$ $r = -3$ Now we can plug in our values into our formula. $a_n = a_1( r^{n - 1})$ $a_7 = 1(-3^{7 - 1})$ $a_7 = 1(-3^6)$ $a_7 = 1(-729)$ $a_7 = 729$ The 7th term of our sequence is 729. Our final answer is E, 729. You did it, you genius you! The Take Aways Sequence questions often take a little time and effort to get through, but they are usually made complicated by their number of terms and values rather than being actually difficult to solve. Just remember to keep all your work organized and decide before test-day whether you want to spend your study efforts memorizing, or if you would prefer to work out your sequence problems by hand. As long as you keep your values straight (and don’t get tricked by bait answers!), you will be able to grind through these problems without fail, using either method. What’s Next? Phew! You have officially mastered ACT sequence questions. So...now what? Well you're in luck because there are a lot more ACT math topics and guides to check out! Want to brush up on your ratios? How about your trigonometry? Coordinate geometry and slopes? No matter what ACT topic you want to master, we've got you covered. Feel like you're running out of time on ACT math? Check out our guide to help you beat the clock. Want to know the score you should aim for? Start by looking at how the scoring works and what that means for you. Looking to get a perfect score? Our guide to getting a 36 on ACT math (written by a perfect-scorer) will help you get to where you want to be! Want to improve your ACT score by 4 points? Check out our best-in-class online ACT prep program. We guarantee your money back if you don't improve your ACT score by 4 points or more. Our program is entirely online, and it customizes what you study to your strengths and weaknesses. If you liked this Math lesson, you'll love our program. Along with more detailed lessons, you'll get thousands of practice 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. Check out our 5-day free trial:

Mill on Repression Essay Example | Topics and Well Written Essays - 1000 words

Mill on Repression - Essay Example Moreover, his individuality must be nurtured instead of hampered. This idea greatly affects his belief that social repression must be thwarted. This paper intends to look deeper into the ideas of Mill in order to understand further why he is so against social repression and to examine further the differences between social and political repression. As mentioned earlier, Mill strongly believes in individuality. Consequently, he also has considerable confidence in diversity. As human beings, each of us have differences and such differences often make us differ in tastes, opinions, interests and other important characteristics and traits. For Mill, such differences should be encouraged instead of stopped. He is against uniformity because this thwarts the expression of one’s unique attributes. As a result, uniformity encourages a few people to stand out because they take courage in being different however, ultimately, the numbered few will rise to rule over the uniform others. Suc h system eventually leads to other social problems such as political repression, tyranny, racism and sexism. On the contrary, when individual attributes are to be encouraged, there would be no uniformity but diversity. Diversity results to individualism which in turn inspires being informed. Information is very important in improving one’s self. As they say, knowledge is power. ... Whereas when there is uniformity, those who are able to access important information tend to keep it to themselves so that they will be the only ones to benefit from the knowledge. In addition, the numbered few who tend to rise when there is uniformity often alter information fed on the bigger percentage of the population so that they are deceived to believe that they are well-informed. This leads to tyranny because the misinformed public tends to trust the stronger majority. Consequently, people can be transformed to puppets who will simply obey what is asked of them. People will be dictated by a few individuals who are able to control the information being told and they will in turn ‘mere industrious sheep’ who will simply obey orders without questioning. This again can lead to abuses such as what was witnessed in the relationship between the Black slaves and the White masters during the recent century. Through social repression, the Blacks were made to believe that th ey are mere objects who were supposed to serve their White masters. However, as social beings, the Blacks came to learn that they, too, can have the liberty the Whites are enjoying and that they can also have their own lands by doing lesser jobs compared to when they are yet slaves. For decades, there have been no Blacks who excelled in art, music or other professions because they have been deprived of opportunities and information. This is the very reason why Mill is against social repression. He is afraid that there will come a day when the talents and creativity of individuals will not be encouraged because they have been limited to some standards. He sees this as a dangerous end because when such circumstance happens, people will eventually become accustomed to an

Managing for results Essay Example | Topics and Well Written Essays - 2250 words

Managing for results - Essay Example The present day mangers believe in acting as a guide cum leader for the employees; they not just assist the subordinates to perform their task but also help them to move ahead in the career. Therefore, the managers must keep themselves updated with the activities taking place within the organisation. Apart from the internal factors, they also have to understand the external environment that is the economic condition, the government policies in the local as well as in other nations, changes taking place in customer’s behaviour and technology. The growing competition in the business sector demands high degree of efficiency from the managers; thus the company also motivates the mangers to update themselves by participating in different trainings sessions (seminars, conferences and off-job training). In the given project at first role of the manager in the prevailing globalised world will be discussed. Later on, different approaches will be discussed that needs to be followed by t he managers in achieving the organisational goal. Some real life examples will also be drawn to further explain different approaches followed by the managers in their organisations. ... Figure: The Managerial Grid by Blake & Mouton Source: Egner, 2009, p.10 According to Blake & Mouton, the manager’s attitude can be measured on basis of two distinct factors. These are concern for people and concern for production. Generally, the functional mangers (floor managers) are more concerned about the production; whereas the top level managers who have to manage group of highly efficient and self sufficient subordinates are more concerned about the people. The managers who are neither concerned about the people nor about the productions are considered as the inefficient one. Similarly, the one who is high in both the factors is the most effective one. Such a manager maintain close association with the subordinates and assist them to develop themselves (Miller, 2008, p.46-47). The attitude followed by the manager is influences by several factors. These can be summarised as the organisational culture, the leadership style of the top management, the nature of the subordin ates, the social norms of the society were the organisation is operating and finally the personality of the manager. Therefore, all these factors should be taken into consideration by the manager to modify his or her attitude so that organisational goal can be achieved. Role of a manager in the organisation In general, the role of a manger comprises of planning, organising, scheduling, and assisting the employees to accompany their task and evaluating the operations (Rothwell, 2001, p.7). All of these functions are quite essential and managers have to be careful while conducting them. The process of management starts with planning. At first the manager has to analyse the external as well as internal environment and then a plan should be developed that will guide the subordinates in

Organizational change typology of evolutionary and strategic changes

Organizational change typology of evolutionary and strategic changes Introduction: This assignment examines organizational change, focusing on the distinction of changes according to their scope and presenting a typology of evolutionary and strategic changes. Business in the new millennium will continue to increase in intricacy. More and more, this demanding environment forces executives and managers to deal with constant change. Globalisation, increased opposition, international development and reformation are just a few of the challenges faced daily. Success in dealing with these new challenges will depend to a great extent on the organisation’s ability to change and adapt. It will depend on how well these organisations can manage these situations by understanding the opportunities and challenges that accompany it. The organisations that will succeed are those that recognise and react the fastest to change. Therefore, the ability of an organisation’s staff to change can mean the difference between scraping just to get by or else becoming the industr y leader. In either case the results translates into millions of dollars in revenues, profits, or losses. It must therefore be accepted that change is an organisational reality. It is critical therefore for managers and executives in todays business environment to be equipped with the skills necessary to manage change. Ultimately it is people who make organisations, and if they do not change, then there is no organisational change. The challenge therefore is for managers and executives to not only know what to change but how to go about it especially in relation to people, products, processes and systems, marketing strategies etc. Just like the butterfly, organisations will have to change and undergo a metamorphosis before they can fly. If they do not, they will be doomed to live out their lives only as caterpillars, or worse still become dinosaurs. Litrature Review: Organizational change is an empirical observation in an organizational entity of variations in shape, quality or state over time (Van de Ven and Poole, 1995), after the deliberate introduction of new ways of thinking, acting and operating (Schalk, Campbell and Freese, 1998). The general aim of organizational change is an adaptation to the environment (Barr, Stimpert and Huff, 1992; Child and Smith, 1987; Leana and Barry, 2000) or an improvement in performance (Boeker, 1997; Keck and Tushman, 1993). This definition encompasses many situations that should be distinguished by applying certain dimensions to establish ‘typologies of change’. We will refer to the scope of change, because it is one of the most used variables in literature to design change typologies. That way, changes can be defined along a continuum starting in lowscope or evolutionary changes to high-scope or strategic ones. With the aim of making the use of this dimension (scope) easier, we will describe bot h extremes of the continuum, but we should always keep in mind that real changes are not a pure type but a mixture. First, we will describe evolutionary, incremental, or first order changes. These are small changes that alter certain small aspects, looking for an improvement in the present situation, but keeping the general working framework (Blumenthal and Haspeslagh, 1994; Goodstein and Burke, 1991; Greiner, 1972; Levy, 1986; Mezias and Glynn, 1993; Nadler and Tushman, 1989; 1990). The second type of changes arestrategic, transformational, revolutionary or second order ones. They are radical transformations, where the organization totally changes its essential framework (Blumenthal and Haspeslagh, 1994; Ghoshal and Bartlett, 1996; Goodstein and Burke, 1991; Marshak, 1993; Nadler and Tushman, 1989, 1990), looking generally for a new competitive advantage (Hutt, Walker and Frankwick, 1995) and affecting the basic capabilities of the organization (Ruiz and Lorenzo, 1999). Background to Change exits in HP Economic Movement: Managing change is one of the most important issues confronting information technology (IT) organizations today. By combining three powerful products—HP Service centre software, HP Change Control Management software and HP Universal Configuration Management Database (CMDB) software—HP Change Management Suite software gives IT managers, changer managers and change advisory boards (CABs) a complete solution for managing change within an IT environment. This tightly integrated solution enables IT departments to gain visibility into the IT environment and service dependencies, and manage the change process in a standardized manner to increase the number of effective, well-founded changes their companies undertake. It also provides decision support for the CAB by auto mating impact analysis to make change decisions based upon business impact and mitigates the risks inherent in instituting change. Strengths and Weaknesses of Change within an organisation in regards to HP: Strengths: Sole point of contact, high market consciousness, easier for customers to deal and cooperate. Easier to preserve functional skill, staffs tends to be more loyal to occupation, frequently has lower cost at the unit level. Highly combined work units, integrated functions, and backup skills. Easier harmonization, determined on the customer, more supple, minimal isolation, flatter, staff gain broader information of the business. Federal responsibility, higher quality, faster decision making, focused on the customer of each product/service group. Flexible resource planning, high practical knowledge exposed to diversity, forced collaboration service areas. Weaknesses: Less contribution/higher costs, more product or service changeability. Tends not to have end-to-end customer sight, practical priorities sometime are contradictory, more difficult to transform processes due to isolation of functions. Some laying-off of functions, lower sense of useful responsibility. Difficult to put into practice and maintain, requires cross functional expertise, long term management commitment. Comparison of alternative forms of organisational development: Digital change and organisational Development: It is been investigated the determinants of local governmental presence and the influence of organizational presence using econometric scrutiny, supported by qualitative information from the review. The variables included in these regressions and the hypotheses about the impacts of explanatory variables are discussed in a later section. In all regressions, the coefficients and standard errors were corrected for sampling weights, stratification, and the total number of communities in the central region (StataCorp 1997). The results are thus agent of the province as a whole. Standard mistakes were approximate using the Huber-White estimator, and are thus robust to general forms of heteroskedasticity (White 1980). A pathways of enlargement found in the region, were included as descriptive factors in the analysis (along with other factors).10 A development pathway is defined as a common prototype of change in livelihoods and resource management, and thus represents a particular set of ec onomic opportunities and constraints (Pender, Scherr, and Duron 1999). Using data on occupations and changes in profession and land use since the mid-1970s, six pathways of development were acknowledged. Basic grain (maize, beans and sorghum) production is the most or second most important profession in all but one of the sample communities. Other factors were therefore more determinate in characteristic the pathways. The pathways include villages where 1) basic grain production is the dominant economic activity and has been expanding during the past 20 years (basic grains expansion pathway), 2) basic grains production is the dominant economic activity though production has been sluggish or failing (basic grains stagnation pathway), 3) horticultural (mainly vegetable) production has amplified and has become the first or second most important activity (horticultural expansion pathway), 4) coffee production has increased and is the first or second most important activity (coffee expan sion pathway), 5) forestry performance are the first or second most important activity (forestry specialization pathway), and 6) non-farm employment has increased and become the first or second most important source of income (non-farm employment pathway). Involvement of Stakeholders in the Introduction of Change in an Organisation: Stakeholders, including NGOs, investors, and activists, as well as communities, labour, and consumers, are playing an increasingly important role in improving corporate behaviour. Some NGOs are using tactics of direct confrontation. Others have been working for years to create partnerships with companies in order to help them green their production, often in ways that actually save them money. As well, the investor community is taking an increasingly active role in encouraging corporations to consider not just the next quarter’s earnings but also the long-term financial risks of failing to address broader social and environmental issues. Together, these are proving key strategies in compelling corporations to internalize the environmental and social costs that are often ignored in the mad race for profit. Analysis and Evaluation of the Strategies: Corporate managers face many daily pressures, and improving social and environmental records (often in ways that don’t directly enhance the bottom line) is not generally their highest priority—until their corporations suddenly become the targets of bad publicity from a coordinated group of activists. With corporations spending a half trillion dollars each year to create positive images through advertising, a sudden storm of negative publicity from the actions of thousands of coordinated activists can swiftly raise environmental issues to the top of managers’ action-item lists. This fear of public shaming—and the connected loss of profit and stock value—are what makes these â€Å"corporate campaigns† so successful. Unlike traditional campaigns against companies, such as boycotts, labour strikes, and litigation (which remain important but often have limited objectives), corporate campaigns treat the targeted company more as a lever of change th an as an end in itself. When a coalition of NGOs and investors led by the Rainforest Action Network (RAN) targeted Citigroup, the goal was to reduce overall exploitation of natural resources. But RAN didn’t target mining and logging companies—which are not in the public eye and depend on continued extraction to survive—pouncing instead on the financial institutions that capitalize the mining and logging companies. Unlike them, banks spend billions to maintain strong brands and customer bases. These assets are essential, and thus exploitable vulnerabilities.And exploit RAN did. In 2000, RAN asked Citigroup to adopt a green lending policy.While the company initially refused, after more than three years of protests, shareholder actions, and other irritating tactics, Citigroup finally recognized that lending to unsustainable industries would be more costly than profitable, while not lending to them would be worth its weight in free advertising. Once Citigroup yielde d, its antagonistic relationship with RAN evolved into a collaboration to ensure adherence to its new standards—a partnership that provided much free publicity to Citigroup. Meanwhile, RAN quietly drafted a letter to Bank of America asking managers to adopt a similar policy. Bank of America, having witnessed the disruption that committed activists can cause by chaining themselves to bank doors, quickly realized that it was better to join the ranks of ecofriendly banks. Bank of America’s capitulation then left JPMorgan Chase as the next target, and it soon followed suit. Conclusion: It can be argued that the booming management of change is vital to any organisation in order to endure and succeed in the present highly economical and endlessly evolving business environment. However, theories and approaches to change management currently available to academics and practitioners are often clashing, mostly deficient pragmatic evidence and supported by undisguised hypotheses concerning the nature of fashionable organisational change management. The reason of this assignment was, therefore, to provide a significant review of some of the main concepts and methodologies to organisational change management as an important initial step towards implementing a new framework for managing change. Reference: Boeker, W. (1997) â€Å"Strategic change: The influence of managerial characteristics and organizational growth†, Academy of Management Journal, 40 (1), pp. 152-170. Blumenthal, B. and Haspeslagh, P. (1994) â€Å"Toward a Definition of Corporate Transformation†, Sloan Management Review, 35 (3), pp. 101-106. Ghoshal, S. and Bartlett, C.A. (1996) â€Å"Rebuilding Behavioral Context: A Blueprint for Corporate Renewal†, Sloan Management Review, 37 (2), pp. 23-36. Goldstein, J. (1988) â€Å"A Far-from-Equilibrium Systems Approach to Resistance to Change†, Organizational Dynamics, (Autumn), pp. 16-26. Goodstein, L.D. and Burke, W.W. (1991) â€Å"Creating Successful Organization Change†, Organizational Dynamics, 19 (4), pp. 5-17. Greiner, L.E. (1972) â€Å"Evolution and revolution as organizations grow†, Harvard Business Review, (July/Aug.), pp. 37-46. Hutt, M.D., Walker, B.A. and Frankwick, G.L. (1995) â€Å"Hurdle the Cross-Functional Barriers to Strategic Change†, Sloan Management Review, 36 (3), pp. 22-30. Leana, C.R. and Barry, B. (2000) â€Å"Stability and Change as Simultaneous Experiences in Organizational Life†, Academy of Management Review, 25 (4), pp. 753-759. Levy, A. (1986) â€Å"Second-Order Planned Change: Definition and Conceptualization†, Organizational Dynamics, (Summer), pp. 5-20. Mezias, S.J. and Glynn, M.A. (1993) â€Å"The three faces of corporate renewal: institution, revolution, and evolution†, Strategic Management Journal, 14, pp. 77-101. Nadler, D.A. and Tushman, M.L. (1989) â€Å"Organizational Frame Bending: Principles for Managing Reorientation†, Academy of Management Executive, 3, pp. 194-204. Nadler, D.A. and Tushman, M.L. (1990) â€Å"Beyond the Charismatic Leader: Leadership and Organizational Change†, California Management Review, 32 (2), pp. 77-97. Pender, J., S.J. Scherr, and G. Durà ³n. 1999. Pathways of development in the hillsides of Honduras: Causes and implications for agricultural production, poverty, and sustainable resource use. Environment and Production Technology Division Discussion Paper No. 45. Washington, D.C.: International Food Policy Research Institute. Ruiz, J. and Lorenzo, J.D. (1999) â€Å"Cambio estratà ©gico y renovacià ³n organizativa: utilizacià ³n de las capacidades latentes y perifà ©ricas†, Revista Europea de Direccià ³n y Economà ­a de la Empresa, 8 (4), pp. 71-82. Schalk, R., Campbell, J.W. and Freese, C. (1998) â€Å"Change and employee behaviour†, Leadership Organization Development Journal, 19 (3), pp. 157-163. StataCorp. 1997. Stata statistical software: Release 5.0. College Station, TX: Stata Corporation. Van de Ven, A.H. and Poole, M.S. (1995) â€Å"Explaining development and change in organizations†, Academy of Management Review, 20 (3), pp. 510-540. White, H. 1980. A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48: 817–838.

Dracula and Kenneth Essay

The high angle shot and extreme long shot looking down at Dracula and Harker crossing through the hall. This shot draws attention to Dracula’s extremely long red cape streaming out behind him like a trail of blood. The low angle shot shows Dracula looming over Harker and makes him look powerful, like he is in control. Many two shots are used to allow the audience to make comparisons between the two characters. The low angle shot is also used to emphasize the shadow’s movements. The low lighting helps with casting Dracula’s shadow which is again typical of horror. Dracula’s eerie shadow moving in the gloom is very effective for scaring the audience as the combination of shadow with candle light works exceptionally well for this scene. This candle light makes the gloomy aspect more present as the castle is immense and there are not very many candles so most of the entrance hallway would be beyond the reach of the light and in darkness, which makes it very scary as you do not know what lurks in the gloom. There is orchestral music played by the strings which go low and slow to create a sinister atmosphere. This music adds to the feeling of tension, the feeling that something is going to happen. The music gets louder and quicker when Harker offends Dracula by laughing and Dracula gets furious and pulls out a sword. This combined with the change of pace and volume of the music makes the audience become afraid, a typical trick of horror. There are many different sound effects in this scene from Dracula. There is the howling of the savage wolves, which scares the audience and makes the element of horror and wildness of the setting more clear. There was the thunder, which is typical of a horror movie. The clanging of the huge, metal gates emphasizes the feeling of the strength and inescapability of the castle and that Harker will not be able to escape and this will be his prison for the rest of his life. Harker’s costume is typical of a man of those times. He wears a suit and is very neatly presented. He has his hair combed very carefully. Dracula’s is very different. He wears a huge red robe which trails out behind him like blood. His hair is curled up high and is white and it mixes with the skin on the back of his neck which makes him look weird and scary. His skin is white and wrinkled like an old man and this creates the effect that he has been drained of all his blood and that helps you to understand his lust for blood and the way he talks about the preciousness of blood. It makes him look very scary and effective, almost dead in a way. It also makes him look exotic and abnormal. He would stand out in a crowd of normal people. There were quite a few similarities between the film extract and the text; both were set in a huge, Gothic castle with a vast courtyard. The stone was ‘massively carved’ and the door was old and studded. Both had creeping shadows and lanterns. In both the film extract and the text, Dracula is portrayed as having hairy palms (abnormal), profuse hair, an â€Å"extraordinary pallor† as he is very pale, he is portrayed as being an old man in both and he is also similarly portrayed as speaking with a ‘strange intonation’ (foreign accent). The similarities between the film extract and the text with Harker is that in both they portray his feelings of anxiety and his crossing of the threshold is made significant. The differences are that in the text, Dracula is described as having bushy eyebrows and a moustache whereas in the film extract he has a plain face. In the text, Dracula is dressed in all black while in the film he is dressed in white which emphasizes his paleness with a red cape that is more powerfully visual as looking like blood flowing behind him. Also in the text Dracula is portrayed as having a red mouth with protuberant, pointed teeth while in the film he is shown as having a pale mouth and normal teeth. The director uses this look in order to make Dracula look like a normal human, adding to the feeling of mystery surrounding him, and to make him different from the stereotypic image of Dracula. Summary These two films engage a modern audience in the way the films use clever tricks to give suspense, which can be overlooked in some of the newer horror films that rely on the amount of blood that comes out rather than clever filming and jumpy moments. In short, Dracula and Frankenstein were very similar in the way that they portrayed the typical horror tricks and consisted of similar camera angles to each other point out various bits. I thought that Dracula, both the written extract and the film extract fitted the horror genre a bit better than Frankenstein as it was more believable for me. I also thought that the film extract was much more scary, although Frankenstein wasn’t bad and had its moments of fright. My final views were that Dracula was on the whole filmed better than Frankenstein as it used the different camera angles more effectively in my opinion. Andrew Baillie 10ALB Show preview only The above preview is unformatted text This student written piece of work is one of many that can be found in our GCSE Mary Shelley section.

Animal Testing Should Be Banned - 1300 Words

In today’s cosmetics industry, many ordinary animals, such as dogs, cats, rabbits, and monkeys, are being subjected to animal testing on products that could potential benefit a person’s complexion. Such animals are often chosen, because their DNA is genetically very similar to humans, and thus could be used for testing. The extensive procedures to testing various merchandises could potentially harm the animals during the process, because there are multiple trials to see whether or not the product is safe to use on humans. Of these trials, many animals suffer from intensive allergic reactions that could have long-term affects on them or potentially kill them. American cosmetic industry today are harming innocent animals, specifically rabbits, through testing procedures and instead should be using human cells to make synthetic cells that could be tested on rather than on live animals. Laboratory rabbits are being abused to fit the needs of the cosmetic industry. In skin i rritation experiments, the rabbit’s back are shaven and cosmetic ingredients are applied to the raw skin. The rabbits are not given any pain relief to these toxic chemicals that will often burn the skin, and thus leading to tissue damaged. Once the experiment is over, the rabbits are killed. Also, rabbits are subject to eye irritation experiments. John H. Draize, Ph.D, is a scientist at the United States Food and Drug Administration (FDA). In 1944, Dr. Draize developed the Draize eye test to evaluate eyeShow MoreRelatedShould Animal Testing Be Banned?844 Words   |  3 PagesShould animal testing be banned? Nowadays, a lot of animals has been tested on a range of experiments over the world. You could be supporting animal teasing cruelty without knowing it. Have you ever check if there’s animal testing on the cosmetics before you buy it? 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Animals are often abused, suffer, and even die during laboratory testing for the benefits of people to make sure medications, household products, newest procedures, and cosmetics are safe and effective for human use. Humans have benefited from animal testing for years while these animals suffer consequences with no positive outcomes for themselves. Even if a product or procedure is deemed successful, these animals are frequentlyRead MoreAnimal Testing Should Be Banned Essay1632 Words   |  7 Pages Animal Testing Should Be Banned Throughout the decades, animals have been used in medical research to test the safety of cosmetics including makeup, hair products, soaps, perfume, and countless of other products. Animals have also been used to test antibiotics and other medicines to eliminate any potential risks that they could cause to humans. The number of animals worldwide that are used in laboratory experiments yearly exceeds 115 million animals. Unfortunately, only a small percentage of

My Future as an Electrical Engineer - 1008 Words

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