Chapter 1/2 – Basics
1. Basic notations 1.1. Sum of: ∑ 1.2. Product of: ∏ 2. Sets A = {1,2,3} describes the set A containing members 1, 2, and 3. A={n | n is a whole number and 1≤n≤3} x A denotes that x is a member of set A S T denotes that S is a subset of T A B is the set whose members belong to either set A, set B or both i.e. A B = {x | x A or x B} A B is the intersection of 2 sets where A B = {x | x A and x B} denotes an empty set

3. Functions Given two sets A and B, a function from A to B is a rule which assigns to each member of A precisely one member of B.

A function is a one-way relationship: the function number, (x).

takes a number x as input and it returns another

An inverse function takes as input a number y and returns the number x such that ( ) ( ) Not all functions have an inverse. Ex. ( ) A composite function is one where two functions that; ( ) ( ( )) 4. Powers Rules ( )

is given by

are applied consecutively to obtain h such

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MT105a Study Notes – J.Fenech

Chapter 3 – Differentiation
1. Definition The derivative is a measure of the instantaneous rate of change of a function 1.1. Derivative from first principles ( ) ( )

1.2. Alternative notation ( ) 1.3. Standard Derivatives Table

2.4. Chain Rule or Composite function rule ( ) ( ( )) ( ) ( ( )) ( )

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MT105a Study Notes – J.Fenech 3. Differentiation by taking logarithms 4. Local Maxima and Minima Derivatives are very useful for finding the maximum and minimum values of a function In particular; If ’(x) > 0 then is increasing at x If ’(x) < 0 then is decreasing at x 4.1. First derivative test At a point c for which ’(c) =0, is neither increasing nor decreasing. C is the...

...How much is needed? 3. When is it needed?
Forecasting: 1.Techniques assume some underlying causal system that existed in the past will persist into the future 2. Forecasts are not perfect 3. Forecasts for groups of items are more accurate than those for individual items 4. Forecast accuracy decreases as the forecasting horizon increases
Strategic Capacity Planning• Goal • To achieve a match between the long-term supply capabilities of an organization and the predicted level of long-term demand • Overcapacity! operating costs that are too high • Undercapacity! strained resources and possible loss of customers
Decision Theory: A general approach to decision making that is suitable to a wide range of operations management decisions • Capacity planning • Product and service design • Equipment selection • Location planning
...

...of strategic management accounting was first coined by Simmonds (1981). Who defined it as the provision and analysis of information about a business and its competitors for use in developing and monitoring the business strategy? However, in the contemporary business environment, organizations are experiencing greater challenges, increased competition and rapid diffusion of knowledge. (2)
Traditionally management accounting has been characterised as providing information to aid managers internally in a firm and as such the focus of the management accounting systems has also tended to be internally orientated. During the 1980s and 1990s a growing number of academics (Johnson and Kaplan, 1987; Bromwich and Bhimani, 1989, 1996) began to recognise that management accounting was not adapting to changes in the modern business environment and as such was not fulfilling its function to aid managers. In a bid to improve the quality of management accounting information for managers it was necessary to focus more widely on the external environment of the firm and thus the concept of strategic management accounting evolved. Now (strategic) management accounting involves the provision of information, which is externally orientated, market-driven and customer-focused and provides managers with a range of techniques and tools to facilitate strategically-orientated decision making. (3)...

...UniversitiesLondon has the largest student population of any British city, although not the highest per capita. Universities in London may be divided into two groups:
First, the federal University of London, which, with over 120,000 students, is the largest contact teaching university in the United Kingdom (smaller only than the distance-education Open University) and one of the largest Universities in Europe. It comprises 19 colleges and 12 institutes, as well as a distance-learning External System. Constituent colleges have a high degree of autonomy, controlling their own admissions and degree programmes, and are effectively universities in their own right. The largest and most well-known University of London colleges include (in order of size) University College London, Birkbeck, King's College London, Queen Mary, the London School of Economics and Political Science, Royal Holloway, Goldsmiths, and the Institute of Education. Smaller schools and institutes (with fewer than 5,000 students) include the School of Oriental and African Studies, the London Business School, the School of Pharmacy, the London School of Hygiene and Tropical Medicine, St. George's Hospital Medical School and Central School of Speech and...

...Management 3200: Principles of Management
Spring 2012; Section 01; 12:10-1:30 TTH
Course Objective: The course objective is two-fold: 1) to acquire knowledge of the basic vocabulary and major facts, principles, and concepts of management and 2) to achieve an appreciation of the issues involved in managing people.
Required Text: Fundamentals of Management (7ed.) (2011) by Robbins, DeCenzo, &
Coulter; Prentice Hall.
Recommended: The Wall Street Journal http://subscribe.wsj.com/semester
Grading Components Final Grade
Exam 1 = 100 points (50 Questions x 2) A (90-100%) = 270-300 points
Exam 2 = 100 points (50 Questions x 2) B (80- 89%) = 240-269 points
Exam 3 (final) = 100 points (50 Questions x 2) C (70- 79%) = 210-239 points
Total 300 points D (60- 69%) = 180-209 points
F (00- 59%) = 000-179 points
Exams: The exams will cover material presented in the lectures, the textbook, and the assigned outside readings. Each of the three exams will consist of 50 multiple-choice questions. The final exam is not comprehensive.
If you must miss an exam, please contact me before the date of the exam. Make-up exams will be given in the week following the exam. The format of the make-up exam (multiple choice, short answer, or essay) is left to the discretion of the instructor.
NOTE: If you miss an exam and fail to contact me before the date of the exam,...

...Yr 10
Mathematics
Assignment
LCR Maths
By Adonis Chigeza
Understanding and Fluency Tasks
Task A
1. y = 1.2𝑥 + 2.57
2. Interpolation: y = -3.43
Extrapolation: y = -8.23
Task B
a) The equation for the path of the ball is h = -0.1t^2 + 0.9t + 1 (h = height, t = time)
b) The vertical height of the ball after 2. seconds2.664m
c) The maximum height reached by the ball is 3.025m
d) The time of with the ball is at maximum height of 3.025 is 4.5 seconds
e) The total time in which the ball was in the air is 10 seconds
f) The two times in which the ball was 1 metre above ground is 0 and 9
Adonis Chigeza 10C
LCR Mathematics
Problem Solving and Reasoning Task
1.
Equation: y = -1.2𝒙2 + 8.4𝒙
a. The bridge is 7 metres wides so therefore it will successfully span the river with 2
metres to spare.
b. If a yacht has a 15 metre mask it will be unable to pass safely under the bridge
because the bridge only has a vertical height 14.7 metres.
Adonis Chigeza 10C
LCR Mathematics
2. Equation: v= -0.2h2 + 2.4h
a. The horizontal distance covered by the rocket when it reached its maximum
height of 7.2 metres was 6 metres.
b. The maximum height reached by the rocket was 7.2 metres.
c. At the horizontal distance of 9 metres from the launch site, there is a 5.2 metre
wall and at that vertical distance, the rocket has a vertical distance 5.4 metre.
That is not taking to account the dimensions of the rocket, however the rocket
cannot have...

...• What were the most revolutionary social and economic developments of the last quarter of the nineteenth century?
• How did different groups of Americans respond to those changes and how effective were their responses?
• What role did government play in these developments?
In the late 1900s some of the most social and economic developments were railroads, steel oil, the type writer cash register, light bulb and agriculture. The development of the railroad made it easier for immigrant to come to this country for work. This meant that there were more group of different races and cultures in America. And in some states there became an over population and city workers like police and garbage men could not keep up with the demand of so many people. Some groups mover to open land for the Homestead Act. They had hope of farming and staying on the land for at least five years as agreed but the supply and demand of agriculture did sustain so many farmer moved off the land well before their five years. The government played many different role I deescalating some issues in American history. Women and children were being worked for long hours and getting paid a little bit of nothing in return for their hard work. So the government put labor laws into place that were to protect women and children. As oil, steel and railroad industries grew so did the levels of pollution. The government again put laws that were to protect animals and the earth so that there would not...

...block to overcome its state of inertia. A body travelling on an inclined plane due to its weight has an angle of repose, wherein it has a uniform sliding motion. There is no acceleration taking place when the block slides uniformly. No matter what vertical height or horizontal distance is used, the angle of repose will remain the same. The tangent of the angle of repose is always equal to the coefficient of friction of the block.
Coefficient of friction denoted by μ is determined the formula μ=FN f=Friction force, N=normal force. The value of μ has no units since it only serves as a factor between F and N. In order to obtain a constant value for the μ, one has to consider state of equilibrium for the object being experimented. We also took note of the fact that 0 < u < 1.
In cases which there is an angle of repose, all forces involved are being translated with accordance to the surface’s inclination. The weight will now have components that contribute to the sliding of the object. If we have the angle of repose as θ, the components of W contributed to the object in sliding motion are Wsinθ, parallel to the surface and Wcosθ, perpendicular to the surface. Since the system is in equilibrium, Wsinθ is also equaled by the frictional force, while Wcosθ is also equaled by the normal force. In determining μ, it would be μ=FN=WsinθWcosθ=tanθ. Since the θ for the value of μ is also the θ of inclination, therefore in correlation, we can relate μ as equal to the...

...
The case between Beauty and Stylish involves concept of a valid contract, pre-contractual statements, express term and misrepresentation.
A valid contract is established between Beauty and Stylish when an offer is accepted and there is intention for both parties to create legal relations. An offer refers to the expression of willingness of the offerer to be contractually bound by an agreement if his or her offer is properly accepted. It has to be clear and certain in terms. It must also be communicated to the offeree before it is being accepted. In addition, the acceptance has to be unqualified, unconditional and made by a positive act. In the case of Beauty and Stylish, a positive act refers to the signing of the contract. All terms of the offer must be accepted without any changes and cannot be subjected to any condition, taking effect only upon fulfillment of that condition. When Beauty and Stylish enter into the agreement, they must intend to bind and bound legally to each other by their agreement. This is the intention to create legal relations between two parties. In the meanwhile, this contract must possess consideration. A contract must therefore be a two-sided affair, with each side providing or promising to provide something of value in exchange for what the other is to provide.
Every contract, whether oral or written, contain terms. The terms of a contract set out the rights and duties of the parties. Terms are the promises and undertakings given by each...

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