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NCERT Books Free Download for Class 10 Maths Chapter 4 - Quadratic Equations

All the solutions are available in Video Ch 4 maths class 10 pdf viewer also, in which each question is described properly. After going through PDF solutions, student can take help from videos if required. If still someone is facing problem, please contact us for help. It is clqss linear equation. So, it will not be considered as a quadratic equation.

Visit to Discussion Forum to ask your doubts and answer the questions asked by other users. Class 10 Maths Exercise 4. If the difference of their perimeters is 16 cm, find the sides of two odf.

If the second number viswer one clas than twice the first number, find the numbers. Find its base. Four years hence the product of their ages in years will be Find their present age. Find the speed of the stream. When 18 is ch 4 maths class 10 pdf viewer to the number, the digits interchanged their places. Find the number. Find the original fraction.

Find the numbers. Questions for Practice on 10th Maths Chapter 4 A natural number, when increased by 12 equals times its reciprocal. Eight years hence, the age of the man will be 4 years more than three times the age of his son. Find their present ages. Had he got vieder marks more in Mathematics and 4 marks less in Science, the product of his marks, would have been Find the marks in the two subjects.

What is meant by a quadratic equation? Exercise 4.

Abstract:

There have been the lot of additives which have been enclosed in a paint in sequence which it can be used upon a fiberglass. Yet mother-and-pop accommodations as well as oppulance resorts dot a island sequencenonetheless it is not elementary as cake.

North Milan is situated in Erie County north of Norwalk along SR-113.

NA49 has generated an impressive amount of data, around 10 Terabytes per run. This rate provided the ideal environment to develop and test the next generation data analysis. It means a liberal, informal development style that heavily relies on the diverse and deep talent of the user community. The result is that physicists developed ROOT for themselves; this made it specific, appropriate, useful, and over time refined and very powerful.

The development of ROOT is a continuous conversation between users and developers with the line between the two blurring at times and the users becoming co-developers. When it comes to storing and mining large amount of data, physics plows the way with its Terabytes, but other fields and industry follow close behind as they acquiring more and more data over time. They are ready to use the true and tested technologies physics has invented.

In this way, other fields and industries have found ROOT useful and they have started to use it also. In the bazaar view, software is released early and frequently to expose it to thousands of eager co-developers to pound on, report bugs, and contribute possible fixes.

More users find more bugs, because they stress the program in different ways. By now, after ten years, the age of ROOT is quite mature. Most likely, you will find the features you are looking for, and if you have found a hole, you are encouraged to participate in the dialog and post your suggestion or even implementation on the ROOT forum.

Please use the search engine to see if your question has already been answered before posting a topic in the Forum. We felt we could accept this in order to have the expert explain what they know best. If you would like to contribute a chapter or add to a section, please contact rootdoc cern. We count on you to send us suggestions on additional topics or on the topics that need more documentation.

Please send your comments, corrections, questions, and suggestions to the rootdoc list: rootdoc cern. We attempt to give the user insight into the many capabilities of ROOT. The book begins with the elementary functionality and progresses in complexity reaching the specialized topics at the end.

We tried to follow a style convention for the sake of clarity. The styles in used are described below. In the interactive system, the ROOT prompt has a line number root[12] ; for the sake of simplicity, the line numbers are left off. Italic bold monotype font indicates a global variable, for example gDirectory. When a variable term is used, it is shown between angled brackets.

ROOT is an object-oriented framework aimed at solving the data analysis challenges of high-energy physics. There are two key words in this definition, object oriented and framework.

First, we explain what we mean by a framework and then why it is an object-oriented framework. Programming inside a framework is a little like living in a city. Plumbing, electricity, telephone, and transportation are services provided by the city. In your house, you have interfaces to the services such as light switches, electrical outlets, and telephones. The details, for example, the routing algorithm of the phone switching system, are transparent to you as the user.

You do not care; you are only interested in using the phone to communicate with your collaborators to solve your domain specific problems. Programming outside of a framework may be compared to living in the country. In order to have transportation and water, you will have to build a road and dig a well.

To have services like telephone and electricity you will need to route the wires to your home. In addition, you cannot build some things yourself. For example, you cannot build a commercial airport on your patch of land. From a global perspective, it would make no sense for everyone to build their own airport. You see you will be very busy building the infrastructure or framework before you can use the phone to communicate with your collaborators and have a drink of water at the same time.

In software engineering, it is much the same way. The drawback of a framework is that you are constrained to it, as you are constraint to use the routing algorithm provided by your telephone service. You also have to learn the framework interfaces, which in this analogy is the same as learning how to use a telephone.

If you are interested in doing physics, a good HEP framework will save you much work. Less code to write - the programmer should be able to use and reuse the majority of the existing code.

Basic functionality, such as fitting and histogramming are implemented and ready to use and customize. More reliable and robust code - the code inherited from a framework has already been tested and integrated with the rest of the framework. More consistent and modular code - the code reuse provides consistency and common capabilities between programs, no matter who writes them. Frameworks make it easier to break programs into smaller pieces.

More focus on areas of expertise - users can concentrate on their particular problem domain. They do not have to be experts at writing user interfaces, graphics, or networking to use the frameworks that provide those services.

Object-Oriented Programming offers considerable benefits compared to Procedure-Oriented Programming:. Class hierarchies and containment containment hierarchies provide a flexible mechanism for modeling real-world objects and the relationships among them.

Complexity is reduced because there is little growth of the global state, the state is contained within each object, rather than scattered through the program in the form of global variables. Objects may come and go, but the basic structure of the program remains relatively static, increases opportunity for reuse of design.

You have a choice to download the binaries or the source. You can download the binaries, or the source. Before downloading a binary version make sure your machine contains the right run-time environment.

In most cases it is not possible to run a version compiled with, e. Now after we know in abstract terms what the ROOT framework is, let us look at the physical directories and files that come with the ROOT installation. You may work on a platform where your system administrator has already installed ROOT.

You will need to follow the specific development environment for your setup and you may not have write access to the directories. In the ROOTSYS directory are examples, executables, tutorials, header tutorials files, and, if you opted to download it, the source is here. The directories of special interest to us are bin , tutorials , lib , test , and include. The next figure shows the contents of these directories.

The libraries are designed and organized to minimize dependencies, such that you can load just enough code for the task at hand rather than having to load all libraries or one monolithic chunk. The core library libCore. In the Figure you see that libCore. The Cling library libCling. A program referencing only TObject only needs libCore ; libCling will be opened automatically. As one would expect, none of that depends on graphics or the GUI.

Library dependencies have different consequences; depending on whether you try to build a binary, or you just try to access a class that is defined in a library. When building your own executable you will have to link against the libraries that contain the classes you use. The ROOT reference guide states the library a class is reference guide defined in. Almost all relevant classes can be found in libraries returned by root-config -glibs ; the graphics libraries are retuned by root-config --libs.

These commands are commonly used in Makefiles. Using root-config instead of enumerating the libraries by hand allows you to link them in a platform independent way. A batch program that does not have a graphic display, which creates, fills, and saves histograms and trees, only needs to link the core libraries libCore , libRIO , libHist and libTree.

If ROOT needs access to other libraries, it loads them dynamically. The difference between reference guide libHist and libHistPainter is that the former needs to be explicitly linked and the latter will be loaded automatically at runtime when ROOT needs it, by means of the Plugin Manager. In the Figure , the libraries represented by green boxes outside of the core are loaded via the plugin manager plugin manager or equivalent techniques, while the white ones are not.

Of course, if one wants to access a plugin library directly, it has to be explicitly linked. An example of a plugin library is libMinuit. To create and fill histograms you need to link libHist. Non-plugins will need to be linked, and are thus loaded at start-up. Plugins are defined by a base class e. TFile that will be implemented in a plugin, a tag used to identify the plugin e. This can be specified in the.

When using a class in Cling, e. On start-up, ROOT parses all files ending on. They contain class names and the library names that the class depends on. After reading them, ROOT knows which classes are available, and which libraries to load for them.

It will load these libraries first. Otherwise, loading the requested library could cause a system dynamic loader error due to unresolved symbols. Several tutorials create new files. If you have write access to the tutorials directory, the new files will be created in the tutorials directory, otherwise they will be created in the user directory.

The test directory contains a set of examples example that represent all areas of the framework. The include directory contains all header files. It is especially important because the header files contain the class definitions. The directories we explored above are available when downloading the binaries. When downloading the source you also get a directory for each library with the corresponding header and source files, located in the inc and src subdirectories.

For example, the physics library libPhysics. The ROOT source code automatically generates this documentation, so each class is explicitly documented on its own web page, which is always up to date with the latest official release of ROOT. Each page contains a class description, and an explanation of each method. It shows the class inheritance tree and lets you jump to the parent class page by clicking on the class name. If you want more details, you can even see the source.

There is a help page available in the little box on the upper right hand side of each class documentation page. You can see on the next page what a typical class documentation web page looks like. The top of any class reference page lets you jump to different parts of the documentation. The first line links to the class index and the index for the current module a group of classes, often a library.

The second line links to the ROOT homepage and the class overviews. The last line links the different parts of the current pages.

We begin by showing you how to use ROOT interactively. There are two examples to click through and learn how to use the GUI. We continue by using the command line, and explaining the coding conventions, global variables and the environment setup.

Please note: the syntax is for bash , if you are running tcsh you will have to use setenv instead of export. To run the program just type: root. To start ROOT you can type root at the system prompt.

This option prevents the execution of these two scripts. One simply adds the name of the script s after the ROOT command. Be warned: after finishing the execution of the script, ROOT will normally enter a new session. For example if you would like to run a script myMacro.

C in the background, redirect the output into a file myMacro. You can build a shared library with ACLiC and then use this shared library on the command line for a quicker execution i.

For example:. Every object in the canvas is a graphical object in the sense that you can grab it, resize it, and change some characteristics using the mouse.

The canvas area can be divided in several sub areas, so-called pads the class TPad. A pad is a canvas sub area that can contain other pads or graphical objects.

At any one time, just one pad is the so-called active pad. Any object at the moment of drawing will be drawn in the active pad. The obvious question is: what is the relation between a canvas and a pad? In fact, a canvas is a pad that spans through an entire window. This is nothing else than the notion of inheritance. The TPad class is the parent of the TCanvas class.

If several canvases are defined, there is only one active at a time. One draws an object in the active canvas by using the statement:. In the next example, the first statement defines a function and the second one draws it. A default canvas is created since there was no opened one. You should see the picture as shown in the next figure. Menu bar - contains main menus for global operations with files, print, clear canvas, inspect, etc.

Tool bar - has buttons for global and drawing operations; such as arrow, ellipse, latex, pad, etc. Editor frame - responds dynamically and presents the user interface according to the selected object in the canvas. Save : save the drawing of the current canvas in a format selectable from the submenu.

There is only one active menu entry in the Edit menu. The others menu entries will be implemented and will become active in the near future. Editor : toggles the view of the editor. If it is selected activates and shows up the editor on the left side of the canvas window. Toolbar : toggles the view of the toolbar.

If it is selected activates and shows up the toolbar. It contains buttons for easy and fast access to most frequently used commands and for graphics primitive drawing. Tool tips are provided for helping users. Status Bar : toggles the view of the status bar. If it is selected, the status bar below the canvas window shows up. View With� : If the last selected pad contains a 3-d structure, a new canvas is created with a 3-D picture according to the selection made from the cascaded menu: X3D or OpenGL.

The 3-D image can be interactively rotated, zoomed in wire-frame, solid, hidden line or stereo mode. Move Opaque : if selected, graphics objects are moved in opaque mode; otherwise, only the outline of objects is drawn when moving them. The option opaque produces the best effect but it requires a reasonably fast workstation or response time.

Resize Opaque : if selected, graphics objects are resized in opaque mode; otherwise, only the outline of objects is drawn when resizing them. Pad Auto Exec : executes the list of TExecs in the current pad. Inspect the gROOT object. You can create the following graphical objects using the toolbar buttons for primitive drawing. Tool tips are provided for helping your choice. An Arc or circle : Click on the center of the arc, and then move the mouse.

A rubber band circle is shown. Click again with the left button to freeze the arc. A Line : Click with the left button at the point where you want to start the line, then move the mouse and click again with the left button to freeze the line. An Arrow: Click with the left button at the point where you want to start the arrow, then move the mouse and click again with the left button to freeze the arrow. A Diamond : Click with the left button and freeze again with the left button.

The editor draws a rubber band box to suggest the outline of the diamond. An Ellipse : Proceed like for an arc. They are highlighted. You can move the ellipse by clicking on the ellipse, but not on the sensitive points. If, with the ellipse context menu, you have selected a fill area color, you can move a filled-ellipse by pointing inside the ellipse and dragging it to its new position. A Pad : Click with the left button and freeze again with the left button.

The editor draws a rubber band box to suggest the outline of the pad. A PaveLabel : Proceed like for a pad. Type the text of label and finish with a carriage return. The text will appear in the box.

A Pave Text : Proceed like for a pad. You can then click on the TPaveText object with the right mouse button and select the option InsertText. A Poly Line : Click with the left button for the first point, move the moose, click again with the left button for a new point.

Close the poly-line with a double click. To edit one vertex point, pick it with the left button and drag to the new point position. A Curly Line : Proceed as for the arrow or line. Once done, click with the third button to change the characteristics of the curly line, like transform it to wave, change the wavelength, etc.

A Curly Arc : Proceed like for an ellipse. The first click is located at the position of the center, the second click at the position of the arc beginning.

Once done, one obtains a curly ellipse, for which one can click with the third button to change the characteristics, like transform it to wavy, change the wavelength, set the minimum and maximum angle to make an arc that is not closed, etc.

All TLatex expressions are valid. To move the text or formula, point on it keeping the left mouse button pressed and drag the text to its new position. If you position the mouse near the bottom-end of the text, you can rotate it. A Marker : Click with the left button where to place the marker. A Graphical Cut : Click with the left button on each point of a polygon delimiting the selected area.

Close the cut by double clicking on the last point. A TCutG object is created. It can be used as a selection for a TTree ::Draw.

You can get a pointer to this object with:. Once you are happy with your picture, you can select the Save as canvas. C item in the canvas File menu. This facility also works if you have other objects not drawn with the graphics editor histograms for example. The ROOT graphics editor loads the corresponding object editor objEditor according to the selected object obj in the canvas respecting the class inheritance.

An object in the canvas is selected after the left mouse click on it. For example, if the selected object is TAxis , the TAxisEditor will shows up in the editor frame giving the possibility for changing different axis attributes. The graphics editor can be:. It appears on the left side if the canvas window allowing users to edit the attributes of the selected object via provided user interface.

The name of the selected object is displayed on the top of the editor frame in red color. If the user interface needs more space then the height of the canvas window, a vertical scroll bar appears for easer navigation. Global - has own application window and can be connected to any created canvas in a ROOT session. It can be activated via the context menu entries for setting line, fill, text and marker attributes for backward compatibility, but there will be a unique entry in the near future.

The user interface for the following classes is available since ROOT v. Object oriented programming introduces objects, which have data members and methods. The next line creates an object named f1 of the class TF1 that is a one-dimensional function. The type of an object is called a class. The object itself is called an instance of a class.

When a method builds an object, it is called a constructor. The first parameter, func1 is the name of the object f1. Most objects in ROOT have a name. ROOT maintains a list of objects that can be searched to find any object by its given name in our example func1. So now, we understand the two lines of code that allowed us to draw our function. Other methods can be applied to the object f1 of the class TF1.

For example, the evaluating and calculating the derivative and the integral are what one would expect from a function. By default the method TFPaint , that draws the function, computes equidistant points to draw it.

The number of points can be set to a higher value with:. Note that while the ROOT framework is an object-oriented framework, this does not prevent the user from calling plain functions. Now we will look at some interactive capabilities. Every object in a window which is called a canvas is, in fact, a graphical object in the sense that you can grab it, resize it, and change its characteristics with a mouse click.

For example, bring the cursor over the x-axis. The cursor changes to a hand with a pointing finger when it is over the axis. Now, left click and drag the mouse along the axis to the right. You have a very simple zoom. When you move the mouse over any object, you can get access to selected methods by pressing the right mouse button and obtaining a context menu. If you try this on the function TF1 , you will get a menu showing available methods.

Try clicking on these and observe the context menu with their methods. For example try selecting the SetRange method and putting , 10 in the dialog box fields.

This is equivalent to executing f1. SetRange ,10 from the command line, followed by f1. Here are some other options you can try. Once the picture suits your wishes, you may want to see the code you should put in a script to obtain the same result.

C entry of the File menu. This will generate a script showing the options set in the current canvas. Another interesting possibility is to save your canvas into the native ROOT format.

This will enable you to open it again and to change whatever you like. All objects associated to the canvas histograms, graphs are saved at the same time. Once again, we call the constructor of a class, this time the class TCanvas. The difference between this and the previous constructor call TF1 is that here we are creating a pointer to an object.

Next, we call the method Divide of the TCanvas class that is TCanvas::Divide , which divides the canvas into four zones and sets up a pad in each of them. We set the first pad as the active one and than draw the function f1 there. All objects will be drawn in that pad because it is the active one. The ways for changing the active pad are:. Pads are numbered from left to right and from top to bottom.

To apply the method cd to the third pad, you would write:. Please note that saving the canvas this way will overwrite the file with the same name without a warning.

The user choice is saved for the next time the Save As� dialog shows up. The Print command in the canvas File menu pops-up a print dialog where the user can specify a preferred print command and the printer name. Both print parameters can be set via the new Print. Command and Print. Printer rootrc resources as follows:. All other parameters will be kept as they are written.

You can use the command line to execute multi-line commands. It is more convenient to edit a script than the command line, and if your multi line commands are getting unmanageable, you may want to start with a script instead. The Cling interpreter has several extensions. The interpreter knows all the classes, functions, variables, and user defined types.

This enables ROOT to help users to complete the command line. Its special treatment allows the easy matching of pathnames. The class TRegexp can be used to create a regular expression from an input string.

If wildcard is true then the input string contains a wildcard expression. The method finds the first occurrence of the regular expression in the string and returns its position.

From the first days of ROOT development, it was decided to use a set of coding conventions. This allows a consistency throughout the source code. Learning these will help you identify what type of information you are dealing with and enable you to understand the code better and quicker. Of course, you can use whatever convention you want but if you are going to submit some code for inclusion into the ROOT sources, you will need to use these.

Constants begin with k : kInitialSize , kRed. Global variables begin with g : gEnv. Different machines may have different lengths for the same type. The most famous example is the int type. It may be 16 bits on some old machines and 32 bits on some newer ones.

To ensure the size of your variables, use these pre defined types in ROOT:. This kind of architecture is also used in the Java language.

The main advantage of this approach is that it enforces the common behavior of the derived classes and consequently it ensures the consistency of the whole system. ROOT has a set of global variables that apply to the session.

For example, gDirectory always holds the current directory, and gStyle holds the current style. These methods return a TSeqCollection , meaning a collection of objects, and they can be used to do list operations such as finding an object, or traversing the list and calling a method for each of the members.

See the TCollection class description for the full set of methods supported for a collection. For example, to find a canvas called c1 you can do :.

A graphic object is always drawn on the active pad. It is convenient to access the active pad, no matter what it is. For that, we have gPad that is always pointing to the active pad. For example, if you want to change the fill color of the active pad to blue, but you do not know its name, you can use gPad.

This generator is very fast and has very good random proprieties a very long period of 10 Any other value will be used as a constant. The following basic random distributions are provided: Rndm or Uniform min,max , Gaus mean,sigma , Exp tau , BreitWigner mean,sigma , Landau mean,sigma , Poisson mean , Binomial ntot,prob. You can customize your ROOT session by replacing the random number generator.

You can delete gRandom and recreate it with your own. TRandom2 is another generator, which is also very fast and uses only three words for its state. This variable is set by reading the contents of a. See Environment Setup below for more information. The behavior of a ROOT session can be tailored with the options in the. At start-up, ROOT looks for a. If more than one. While in a session, to see current settings, you can do:.

For example, if the flag to use true type fonts is set to true in the system. Removing the UseTTFonts statement in the local. ROOT looks for scripts in the path specified in the.

Path variable. You can expand this path to hold your own directories. The rootlogon. C and rootlogoff. C files are scripts loaded and executed at start-up and shutdown. The rootalias.

C file is loaded but not executed. It typically contains small utility functions. For example, the rootalias. This allows the user to call the editor from the command line. You can use the up and down arrow at the command line, to access the previous and next command.

It is a text file, and you can edit, cut, and paste from it. You can specify the history file in the system. History option. You can also turn off the command logging in the system. History: -. The first value defines the maximum of lines kept; once it is reached all, the last HistSave lines will be removed. One can set HistSize to 0 to disable history line management. You can track memory usage and detect leaks by monitoring the number of objects that are created and deleted see TObjectTable.

This line will print the list of all active classes and the number of instances for each class. By comparing consecutive print outs, you can see objects that you forgot to delete. Note that this method cannot show leaks coming from the allocation of non-objects or classes unknown to ROOT. A memory checking system was developed by D.

Bertini and M. Ivanov and added in ROOT version 3. To activate the memory checker you can set the resource Root. MemCheck to 1 e. MemCheck: 1 in the. You also have to link with libNew. You can also set the resource Root. MemCheckFile to the name of a file.

Twentieth-century French philosopher Alain Badiou claims that ontology is mathematics. In some cases, natural philosophers and other scientists who have made extensive use of mathematics have made leaps of inference between beauty and physical truth in ways that turned out to be erroneous.

For example, at one stage in his life, Johannes Kepler believed that the proportions of the orbits of the then-known planets in the Solar System have been arranged by God to correspond to a concentric arrangement of the five Platonic solids , each orbit lying on the circumsphere of one polyhedron and the insphere of another. As there are exactly five Platonic solids, Kepler's hypothesis could only accommodate six planetary orbits and was disproved by the subsequent discovery of Uranus.

In the s, Abraham Moles and Frieder Nake analyzed links between beauty, information processing , and information theory. The latter corresponds to the first derivative of subjectively perceived beauty: the observer continually tries to improve the predictability and compressibility of the observations by discovering regularities such as repetitions and symmetries and fractal self-similarity. Whenever the observer's learning process possibly a predictive artificial neural network leads to improved data compression such that the observation sequence can be described by fewer bits than before, the temporary interesting-ness of the data corresponds to the compression progress, and is proportional to the observer's internal curiosity reward.

Examples of the use of mathematics in music include the stochastic music of Iannis Xenakis , Fibonacci in Tool 's Lateralus , counterpoint of Johann Sebastian Bach , polyrhythmic structures as in Igor Stravinsky 's The Rite of Spring , the Metric modulation of Elliott Carter , permutation theory in serialism beginning with Arnold Schoenberg , and application of Shepard tones in Karlheinz Stockhausen 's Hymnen.

Examples of the use of mathematics in the visual arts include applications of chaos theory and fractal geometry to computer-generated art , symmetry studies of Leonardo da Vinci , projective geometries in development of the perspective theory of Renaissance art, grids in Op art , optical geometry in the camera obscura of Giambattista della Porta , and multiple perspective in analytic cubism and futurism.

The Dutch graphic designer M. Escher created mathematically inspired woodcuts , lithographs , and mezzotints. These feature impossible constructions, explorations of infinity , architecture , visual paradoxes and tessellations.

British constructionist artist John Ernest created reliefs and paintings inspired by group theory. From Wikipedia, the free encyclopedia. Notion that some mathematicians may derive aesthetic pleasure from mathematics. This section's tone or style may not reflect the encyclopedic tone used on Wikipedia.

See Wikipedia's guide to writing better articles for suggestions. March Learn how and when to remove this template message. Main articles: Mathematics and art , Mathematics and music , and Mathematics and architecture. Argument from beauty Cellular automaton Descriptive science Fluency heuristic Golden ratio Mathematics and architecture Neuroesthetics Normative science Philosophy of mathematics Processing fluency theory of aesthetic pleasure Pythagoreanism Theory of everything.

Math Vault. Retrieved Mysticism and Logic: And Other Essays. Mathematics rightly viewed possesses not only truth but supreme beauty a beauty cold and austere like that of sculpture without appeal to any part of our weaker nature without the gorgeous trappings Russell. Basic Books.

ISBN BBC News online. Retrieved 13 February The Feynman Lectures on Physics. A Mathematician's Apology. Mathematics Is Not a Spectator Sport. Happily, mathematicians are all doers , not spectators. Journal for Research in Mathematics Education. JSTOR Ceasefire Magazine. Aesthetics as information processing.

Low-complexity art. Also in Proc. Curious model-building control systems. Aigner, Martin , and Ziegler, Gunter M. Hardy, G. Reprinted, C. A speaking programme for foreign students IntroductionIn this proposal I shall give reasons for designing a special programme to help foreign students at our university to become more proficient in their oral language skills.

Reasons for developing a programmeForeign students coming to our university to study need to have a high level of proficiency in our language. Most of these students have passed the relevant language examinations and encounter few problems. They have often, however, had little opportunity to use the language for speaking.

Although their current skills help them with their studies, they need to integrate into the general student popUlation and speaking the language fluentl y would help this. A possible speaking programmeA speaking programme should encourage foreign students to interact with native speakers.

The programme should have a systematic element which ensures regular sessions outside their academic study time, as well as the provision of opportunities to sociali se with native speakers on a less organised basis.

RecommendationsMy recommendations for setting up a programme would be:A member of staff should be appointed to run the scheme. Foreign students and general students should be invited to a series of organised social events such as cinema trips, walks and parties. I strongly believe that a programme like this would benefit the foreign students and allow them to get maximum profit from their time here.

There is an example at the beginning 0. To sell or not to sell? You may think selling your house is easy but everyone wants to get the O. Cb", deal. Unfortunately, the housing market is Word formation Part 3 For questions , read the text below. Use the word given in capita ls at the end of some of the lines to form a word that fits the gap in the same line.

There is an example at the beginning 0 o Barnes clearLy enjoys being around smaLL chiLdren and is sympathetic to the deeper phiLosophical implications of their way of thinking. Her book is absorbing and educative, despite sometimes feeling as if she is spending too much time simply confirming what parents and pre-schooL teachers have Long known.

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She suggests that aduLts are more like the production and marketing section, focusing on a project and following it through to its logical conclusion. B To have a good re lationship with your grandparents it is important. El Rewrite the sentences using the introductory it. Example:That re lationsh ips often b reak down is sad. It's sad that relationships often break down. To think how d ifferent genera tions could help each other is heartwarm ing.

S Having a ro le model is important for teenagers. You have several points to consider during your d iscuss ion, which are related to the question.

The question and related points will be g iven to you as a mind map. After two minutes, the examiner will stop your discussion and ask a question where you need t o make some kind of decision.

You have another minute to d iscu ss this. Strategy:Spend time discussing each point. So I decided to 6 ahead. Some people ha ted me, others were angry, bu t my real friends va lued my honesty.

In Writing Part 2 you may have the choice of writing a report The purpose of a report is to give information and make recommendations using an impersonal style. Strategy:Use headings for the different sections of your report.

This ma kes it easier for the target read er and also en sures t hat you org anise and present your info rm ation clearly. Use an impersona l styl e. The use of the passive is quit e common in re port writin g.

Make sure yo u give both an introduction where you outline the aim of the report and a conclu sion w here you summarise t he main points. Which plan do you think is best? Your college wa nts to give more assistance to new stu dents w ho are coming here to study. You ha ve agreed to w rite a report describing th e problems that new studen ts at the college often encounter and recom mending ways to help them.

Write your report in words in an appropria te style. The educa tion authorities in your area want to assess how usefu l the provisions at schools an d colleges are fo r equipping students with ski lls fo r dealing with a working life after they leave full t ime education.

You have agreed to write a report describing and evaluating the current programmes and recommending improvements. Write your report in words in an appropria te styl e.

Give cl ear examples of what you were taught and how you profited from t his. In this re port I am planning to describe what schools do at the moment to prepare their students for when th ey leave. Here are a few of them. But It'S not a good thing -we should force ourselves It.

Procrastmators are less wealthy, less healthy and regret their inability So why are so many of us like thiS? What IS It that prevents us from Are we attempting 7. The latter is untrue, as work done at the last minute contains more mistakes than that done on time.

Our procrasti nating behaviour inconveni ences others and leaves us something perfect or boredom With the task? Apparently, knOWing the reason means we can deal With It. As for me, I'm off to have a rest and think about it all! There are mistakes in six of the sentences. S It's people who dare trying new things that inspire others to do the same. B ensure employees know their place in a company.

C record the development of each employee. D reward good performance of their employees. B promotion that is too rapid. C an acceptance of poor performers at high levels. D chan ging the recruiting strategy of a company. Secret to success:M ost of us have been on the receiving end of an inspirational speech. Usually it is delivered by a former Olympian at a company conference and is all about the big M: motivation.

It is sometimes eloquently delivered and often fun to hsten to but most people leave the room wondering how thirty minutes of biographical information about a rowing champion is going to help them back in the office.

Nobody would dispute that motivation is a key driver of performance but thIs knowledge does not help many of us understand where it comes froID. Listening to a sportsperson speaking about their own personal journey may be uplifting but how is it going to leave a lasting and usable legacy in terms of how you approach your job?

It is almost insulting 10 think it could. It is not anecdotes we need, so much as a science of performance, underlying principles that help unlock the questlOn of why some people work hard and excel while others don't; why some are committed to what they are doing while others exist in a state of semi-detachment.

It is a question with ramifications not just for business but for education. To see how, we need to take a step back and ask a deeper question: where does excellence come from? For a long time, it was thought that the answer hinged, in large part, upon talent. Hard work may be important but if you don't have the abihty, you are never going to become top class.

It is the notion that high-level performers have excellence encoded in their DNA It turns out that this point of view is mistaken. Dozens of studIes have found that high flyers across all disciplines learn no faster than those who reach lower levels of attainment -hour after hour, they improve at almost identical rates.

The difference is simply that high achievers practise for more hours. Further research has shown that when students seem to possess a particular gift, it is often because they have been given extra tuition at home. But it is much more than that. It influences the way we think and feel, and the way we engage with our world. And it determines our motivation. To see how, consider an employee who believes success is all about talent -this is known as the 'fixed mindset'.

Why would they bother to work hard? If they have the right genes, won't they just cruise 10 the top' And if they lack talent, well, why bother at alF And who can blame someone for having this kind of attitude, given the underlying premise' If.

They will see failure as an opportunity to adapt and grow. And if they are right, they will eventually excel. What we decide about the nature of talent, then, could scarcely be more important. So, how to create a growth mindset within an organisation? Interventions which have presented participants with the powerful evidence of how excellence derived from perseverancewhich explains the possibility of personal transformationhave had a dramatic impact on motivation and performance.

When this is allied with clearly identifiable pathways from shop floor to top floor, so that employees can see the route ahead, these results are strengthened further. Businesses that focus on recruiting external 'talent' with 'the nght stuff' on the other hand, and who neglect the cultivation of existing personnel, foster the fixed mindset. A rankand-yank appraisal system is also damaging because it suggests that the abilities of those ranked the lowest cannot be developed.

In short, an ethos constructed upon the potential for personal transformation is the underlying psychological principle driving high performance. It is an insight that is not merely deeply relevant to business but to any organisation interested in unlocking human potential. Which speaker below shows a 'fixed mindset' and which shows a 'growth mindset'?

Match the underlined words in the article with their synonyms. There's no point pushing for promotion because I'd be out of my depth:2 'I've never tackled anything like that before but I guess I can learn as I go along Which two points do they discuss? Here are some areas of life where people want to be successful and a question for you to discuss. Now you have about a minute to decide which two areas you think it is most rewarding to succeed in.

Wri te an essay for your tutor discussing two of the suggestions in your notes. You should explain which suggestion is better, giving reasons to support your opinion. You may, if you Wish, make use of the opinions expressed in t he discussion but you should use you r own words as far as possible.

I lelt sChool, I clicl You should explain which types of people have more influence, giving reasons to support your opin ion. You may, if you Wish, make use of the opinions expressed in the discussion but you shou ld use your own words as fa r as possible. One way 5choo! ThiS' can benefit mal Y S'tudentS'. There are mal Y WhO fai] al d are humiliated by their failure.

Where is' the leHon in thiS'? What is' importal t is' for them to learn to work t0gether il al enjoyable way. There is an example at the beginning 0 Open doze Part 2 For questions , read the text below and think of the word which best fits each gap. Use only one word in each gap. Word formation Part 3 For questions , read the text below. Use the word given in capitals at the end of some of the lines to form a word that fits the gap in the same line.

Decide which two pictures you would choose to ta lk about. Then listen to a candidate doing t he task. Did she choose t he same pict ures? The route to perfection Use of EnglishLook at the pictures. They show people experiencing very special moments. Compare two of the pictures and say why these moments might be special for the people and how memorable these moments might be.

El Read the candidate's answer. Ignore t he gaps. Does t he candidate complete all parts of the task? I'd like to talk abou t these two pictures.

In my opinion the people in both pictures are experiencing a feelgood moment. It's special for all of them but, obviously, for different reas ons. The people are in contrasting locations, too. One looks as Janet's interest in stand-up comedy started because A she was dissatisfied With normal acting roles.

B she enjoyed wnting her own jokes and scripts. C she knew it would fulfil her desire for a challenge. D she feels it linked to her primary acting interest. A They hesitated about supporting her. B They wished she had been more studious. C They were pleased she was doing something she loved. D They were concerned about the insecurity. A frustrated by an unresponsive audience B privileged to be able to make people happy C tired by the stress involved in entertaining others D upset when an audience doesn't like her 4 Janet thin ks a successful comedian must A be a charismatic presence on stage.

B have the opportunity to win awards. C be able to ignore any criticism. D feel confident about growing as a performer. B mig ht accept other work for financial reasons. C has to work on a better stage presence. D lacks opportunities to develop in other areas. If Find and correct the mistakes in t he sentences. There are mistakes in six of t he sentences. About the exam:In Reading and Use of English Part 8, you match questions or statements to sections of one text or several short texts.

Strategy:Read the text s quickly to get a general idea of the topic. Read through t he questions and underline key word s and phrases that may help you. Scan the text s to find parts with a similar meaning to what you have underlined. Remember that the words will not be the same. D Read the article. Match the titles with the sections A-D. If Read[ s O talk about films that make us renect on life?

The Brits were pioneers of the form. What distinguished it was the tempo. The film-makers used cross-cutting to crank up the tension, which is only finally released when the baby is found.

The film 'marks a key stage in the medium's development from an amusing novelty to the "seventh art," able to hold its own alongside literature, theatre, painting, music and other more traditional forms: claims the British Film Institute's Screenonline website.

Film historians today continue to study Hepworth's storytelling abilities but that wasn't what interested the audiences who flocked to see it. They went because it was a feel-good film. BThere has long been a tendency to sneer at feel-good films. Serious, self-conscious auteurs are often too busy trying to express their innermost feelings about art and politics to worry about keeping audiences happy.

However, as Preston Sturges famously showed in his comedy Sullivan 's Travels , if you're stuck on a prison chain gang, you don't necessarily want to watch Battleship Potemkin.

Sullivan's Travels is about John L Sullivan, a glib and successful young Hollywood director of comedies, who yearns to be taken seriously. Sullivan dresses up as a hobo and sets off across America to learn more about the plight of the common man. He ends up sentenced to six years in prison. One of the prisoners' few escapes from drudgery is watching cartoons. As he sits among his fellow cons and sees their faces convulsed with laughter at a piece of what he regards as throwaway Disney animation, he rapidly revises his own priorities.

We had films about gUilt, Atonement about the all-American dream coming apart at the seams Revolutionary Road and even a very long account of a very long life lived backwards the deeply morbid The Curious Case Of Benjamin Buttonl. Deep-dish, feel-bad films have plenty to recommend them.

If you're not a teenager and you don't just want to see the next summer tentpole blockbuster, you'll welcome movies that pay attention to characterisation and dialogue and don't just rely on CGI or the posturing of comic book heroes. However, as film-make rs from Preston Sturges to Danny Boyle have discovered, there is no reason that a feel-good movie needs to be dumb.

You can touch on social deprivation and political injustice: the trick is to do so lithely and, if possible, with a little leavening humour. D Historically, the best feel-good movies have often been made at the darkest times. The war years and their immediate aftermath saw the British turning out some invigorating, entertaining fare alongside all the propaganda.

The Age of Austerity was also the age of the classic Ealing comedies, perfect examples of feelgood film-making. In the best of these films like Passport To Pimlico or Whisky Galore, a community of eccentric and mildly anarchic characters would invariably come together to thwart the big, bad, interfering bureaucrats.

Stories about hiding away a hoard of whisky or setting up a nation state in centrallondon were lapped up by audiences. To really work, feel-good movies must have energy and spontaneity -a reckless quality that no amount of script tinkering from studio development executives can guarantee.

The best take you by surprise. What makes the perfect feel-good movie? That remains as hard to quantify as ever -you only know one when you see one. Search More than just a petTwo of my friends recently adopted a dog. By 1 adopting a dog they have given me an insight into how animals can promote well -being. It's unsurpris ing that greater health and happiness can come from caring for a pet. One research study tra cked peo ple working in stressful jobs who adopted a cat or dog; caring for 3 their new cat or dog lowered the person's blood pressure more effectively than medicine.

People who own dogs tend to get more exercise than people without 4 a dog, and 5 exercise is a guaranteed way of boosting your health and happiness. Having said 6 exercise is a guaranteed way to boost health and happiness.

I would never suggest that families with young children should get a puppy or any similar pet; not because 7 getting a puppy is problematic in itself, but parents nowadays lead such busy lives that looking after a young animal is the last thing 8 parents wan t to worry about. But families can still benefit from the love of animals by adopting lower-maintenance pets such as fish or by helping out with other people's animal s.

Add it in the right place. A: Are you going to buy th at car' B: No, I can't afford at the moment. B: I expect because it's always busy on a Friday. B: Really? So I' Maybe we'll be there at the same time. S A: Please tell Sue that I'll be late for the meeting. B: Of course I. What tim e will you get here? B: I suppose means yo u ca n stay nea r your family, so that's good.

One of these options may be a review. It coul d be a review of a book, film, new p rod uct, theatrical performance or something el se t hat you have experience of.

You w rite bet w een an d words. Strategy:Incl ude so me information about wha t you are revi ewing but do n't go into a lot of detail about one element.

Give yo ur reactions, whether positive or nega tive or both , and include reco m mendatio ns. Use an informa l style to en gage readers. Then decide which paragraph opening sentence A-E best fits each gap. You see this an nouncement on a website.

When we're feel ing a bit low, watching somethi ng funny on TV can 11ft our spirits. We'd like to post some reviews of TV series that give us a good giggle. Send us a review of a TV series which you think will cheer us all up, giving reasons for your choice. Write yo ur review in words in an appropriate style.

A The script is wi tty and the characterisations are superb. B The seri es is based on the works of PG. Wodehouse, of Jeeves and Wooster fame. C It happens to all of us. D It is refreshing to watch a comedy series where the j okes are innocent but extremely funny.

S How does the writer persuad e us to watch the series? It is set in and it revolves around the lives of an aristocratic but hugely eccentric family who reside at a wonderful minor stately home called Blandings Castle. Timothy Spall plays the forgetful but lovable lord of the manor and the very talented Jennifer Saunders is his sharp' voiced sister who wants him to face up to his duties as a pillar of the local community.

Unfortunately, this is a role he detests. However, what makes it so amusing is the way it pokes mild fun at a bygone age where money, title and class ruled society. We see the British at their best and at their worst, and it is an excellent example of how the British can laugh at themselves.

Channel 2, 7 p. You won't regret it. IJ Read the exam task again and plan your own review. Think about the questions below. Then write you r review. Searching For a KingYou wouldn't expect to find a dead king under a city car park. Always a I.. Richard was The skeleton exhibited similar injuries to those recorded after rhe battle and scientists carried out carbon daring, which placed the skeleton in the fifteenth century.

The laSl missing king of England had been found. Extract 1You hear part of a discussion about keeping mementos and things from the past 1 The man feels that keeping things from the past is A important for people to maintain a sense of identity.

B necessary to preserve certain things for posterity. C a way of making good use of old things. A Some things are on ly signifi cant for those directly involved. B People need to feel a lin k to their ancestors. C It's essential to help older re latives retain their memories. Extract 2You hear part of a radio discussion about the role of museu ms in modern life.

A explaining why mu seums are not viable today B describing what is involved in running a museum C outlining reasons why museums are irrelevant nowadays 4 The speakers agree that museums A can be expen sive to maintain.

B have potenti al for educational use. C are popular with certain types of people. Extract 3You hear two people talking about a historical film they have seen. B often contain incorrect facts for dramatic effect C make history more interesting for many people. Look at th e pictures. They show people recording events and information for the future.

Compa re two of t he pictures and say why these records might be important to people in the future and how accurate th e recording needs to be. If Listen to a candidate doing the task. Tick v' the things in Activity 1 that he does. C ask an expert to diagnose Vasoulla's condition. D find ways to persuade Vasoulla to part with some possessions.

During the documentary, VasoullaA managed to recover from her obsession. B overcame her frustra t ion with her messy house. C recognised t he value of Jasmine's help. D foun d important things she had long forgotten. C He hoped to make money from his possessions. D He was determined to make life easier for his family.

Her grown-up sons remembered thinking it normal for dinner to be served in a bedroom; it was the only room that could accommodate the whole family. The hoarding had evidently been especially hard on Jasmine.

In contrast to Vasoulla, Jasmine 'vacuums everything, sofas, chairs, even the kitchen worktops: Over the course of the documentary, which followed the family over several months, Jasmine coaxed and cajoled Vasoulla to jettison at least some of her junk.

It was a slow, painful process -Vasoulla had been known to buy back her own possessions just hours after donating them to charity. In Stratford-on-Avon, Shakespeare's birthplace and the town where he is buried, a dig is taking place in the grounds of New Place, the house he owned in his later life. This has already turned up evidence providing Archaeologists have found pottery and animal remains in the this is 6 advantage!

You should explain which you think has the most influence on how historical events are described, giving reasons to support your opinion. You may. Write your essay in words in an appro priate style. El The phrases in italics in the sentences below can be used to give an impersonal introduction to a fact or opinion.

Complete them with the words in the box. To bake or not to bake? As a child I was captivated by the idea of being a baker -it was the 0 Or, at least, I do but only for a moment. After that comes guilt and more often than. Was Hamlet just one of us? One of the biggest issues many of us have to deal with in the modern worldis We're all experts at putting off things we're Keyword transformations Part 4 For questions , complete the second sentence so that it has a similar meaning to the first sentence, using the word given.

Do not change the word given. You must use between three and six words, including the word given. Here is an example 0.

Hype, advertising created by the company itself, is the sales 7 o One of the illustrations she will include is a 1; Example Use of Englishphotograph of a bus proceeding towards Selfridge's with an advertisement for 'self-denial week' on the side. For many of those in the crowds on the pavement, self-denial was a given. They could n"t afford to spend.

E The big department store continues to uphold the tradition of presenting lavish and eye-catching window displays today and uses the best artists and designers to create and dress them. Advam;es in technology have meant that the displays grow ever more spectacular.

F 'He was trying to aestheticise retailing. The glamour attracted attention and lifted people's spirits at a difficult time, Windows ofetail otreet theatre was all the rage in the As a show, it made any production of Chekhov seem action-packed by comparison.

Yet Gonion Selfridge. I 1 IAs Britain struggled to regain economic stability after the war, the importance of the ncw mass commerce to thl'" country's recovery was recognised,' says Rebecca. The new style of window dressing that came into its own after the armistice took inspiration from the theatre and the fine and decorative arts. It involved flambovant design and drew huge crowds. The s saw a big growth in major department stores in the main cities and they would all have had a budget for window dressing.

At her feel are swathes of ruffled material and posi tioned around her any number of ad ornments. Retailers complain about falling sales. But are they doing enough to seduce the passing customer? Scragg thinks not. I 6 ISo, although retail theatre may have been in its infancy, retail as leisure or therapy for a mass market was still a long way in the future.

Here are some issues that concern people today and a question for you to discuss. A new shopping centre opened recently in your town. The developers have asked you to write a report on the popularity of the centre and also to make recommendations on any improvements that need to be implemented. This is to be ba sed on the responses to a survey. Write your report in words in an appropriate style. El Choose the correct alternatives to complete the comments about the survey.

Peter uses the word 2. Peter thought he was 3. Pete r chose to write 4. Peter is most concerned about the lack of 5 when he starLed writing for a living.

A blogger might have an axe to grind and write negatively, which can be 7. It used to be necessary to read travel brochures before booking a holiday. These agencies charge the volunteers a fee but the volunteers themselves are unpaid. Most of these paying volunteers do have a sincere desire to do good.

But how much good they actually do may depend on the extent to which the trips are organised with the needs of the target communities in mind, rather than those of the volunteers. For example, on average, volunteers only stay two weeks, which is not enough time for them to make their mark on the community they work with.

It is easy to criticise this system and the hypocrisy of an industry that sells the experience of helping others while developing its own interests. Ultimately, however, voluntourism creates important links to sources of funding for needy communities. These links could be impossible to make without the physical presence of volunteers. BOver the years, many students have chosen to do voluntary work overseas but now this has become far more complicated.

The reason may be the growth of 'voluntourism ' agencies which are driven by an underlying commercial agenda. This is not the only complication, however. The relationship between different countries is complex and many emerging market countries are booming. Some are arguably better run than so-called developed countries and, consequently, the view that help is a one-way gift is old-fashioned.

In this case, agencies do have a part to play. Voluntourism should be seen as a two-way exchange which is as good for the giver as the receiver. Your college would like to give foreign students who are th inking about coming t o your country to study better information about the college and surrounding area. Students have been asked to submit proposa ls for different ways of providing this information and outline how best to proceed with the idea.

A decision will then be made on which proposa l to implement. Write your proposal in words in an appropriate style. Complete the proposal with the words in the box. Providing information about the college to foreign students IntroductionThe 1 of this proposa l is to e xp lain why I believe t ha t making a DVD would be a good way t o give foreign students additional informati o n about our college and the surrounding a r ea.

I sha ll also 2 aspec ts that could be focused on in the DV D. The benefits of ma k ing a DVD 11 3 sending more printed information would be a comprehensive way of giving foreign students add i tional information , a purpose-made DVD would be more attractive and entertaining.

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