CXC Math Topic: RELATIONS FUNCTIONS AND GRAPHS (2010)



CXC math topic: Relations Functions and Graphs (2010)



CXC General Proficiency Math Topic: 

RELATIONS, FUNCTIONS AND GRAPHS (2010)

 

GENERAL OBJECTIVES

On completion of this section, students should:

1. appreciate the importance of relations im Mathematics;

2. appreciate that many mathematical relations may be represented in symbolic form, tabular or pictoral form;

3. appreciate the usefulness of concepts in relations, fuunctions and graphs to sovle real-world problems.

 

SPECIFIC OBJECTIVES:

Students should be able to:

 

CONTENT
1. explain concepts associated with relations;

Concept of a relation, types of relation, examples and non-examples of relations, domain, range, image, co-domain.

 

2.

represent a relation in various ways;

Set of ordered pairs, arrow diagrams, graphically, algebraically.

 

3.

state the characteristics that define a function;

Concept of a function, examples and non-examples of functions.

 

4.

use functional notation;

 

For example f: xx 2; or f(x)= x2 as well as y = f(x) for given domains.

 

5.

distinguish between a relation and a function;

Ordered pairs, arrow diagram, graphically (vertical line test).

 

6. draw and interpret graphs of linear functions;

Concept of linear function, types of linear function

(y = c; x = k; y = mx + c; where m, c and k are real numbers)

7.

determine the intercepts of graphs of linear functions;

x-intercepts and y-intercepts, graphically and algebraically.

8.

determine the gradient of a straight line;

 

Concept of a slope.

9.

detemine the equation of a straight line;

The graph of the line.

The co-ordinates of two points on the line.

The gradient and one point on the line.

The gradient on the line and its relationship to another line.

10

solve problems involving the gradient of parallel and perpendicular lines;

 

 

11

determine from co-ordinates on a line segment:

(a) the length;

(b) the co-ordinates of the                  midpoint;

 

The concept of magnitude or length, concept of midpoint.
12

solve graphically a system of two linear equations in two variables;

 

 
13

represent the solution of linear inequalities in one variable using:

(a) set notaton;

(b) the number line

(c) graph;

 

 
14

draw a graph to represent a linear inequality in two variables;

 

15

use linear programming techniques to solve problems involving two variables;

 

Optional Specific Objective
16

derive composite functions;

 

Composite function, for example, fg, f2 given f and g.

Non-commutativity of composite functions (fg ≠ gf)

 

17

state the relationship between a function and its inverse;

 

The concept of the inverse of a function.
18

derive the inverse of a function;

 

f -1, (fg)-1
19

evaluate f(a), f -1(a), fg(a), (fg)-1(a), fg(a), (fg)-1(a);

 

Where a ∈ℜ
20

use the relationship (fg)-1 = g-1f -1;

 

The concept of the inverse of a function, detemining the inverse of a given function.

 

21

draw and interpret graphs of a quadratic function to determine:

(a) the elements of the domain that have a given image;

(b) the image of a given element in the domain;

(c) the maximum or minimum value of the function;

(d) the equation of the axis of symmetry;

(e) the interval of the domain for which the elements of the range may be greater than or less than a given point;

(f) an estimate of the value of the gradient at a given point;

(g) intercepts of the function;

 

Concepts of gradient of a curve at a point, tangent, turning point. Roots of the equation.
22

determine the axis of symmetry, maximum or minimum value of a quadratic function expressed in the form a(x+h)2 + k;

 

Optional Specific Objective
23

sketch graph of quadratic function expressed in the form a(x+h)2 + k and determine the number of roots;

 

Optional Specific Objective
24 draw and interpret the graphs of other non-linear functions;

Optional Specific Objective

y=ax2 where n = -1, -2, and +3.

 

25

draw and interpret distance-time graphs and speed-time graphs (straight line only) to detemine:

(a) distance

(b) time

(c) speed

(d) magnitude of acceleration.

 

Optional Specific Objective

Here are our relations, functions and graphs tutorials to help you prepare for this section of the CXC math exam


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A summary is a shortened version of a much longer piece of writing and it must include the vital information contained in the original. It must be clear, precise, and the emphasis of the original information must not be altered.
¶ Important Points for Preparing Summaries
• Make sure you understand the original passage. You will be able to do this if you read, and possibly re-read, the information which is to be summarised.
• Identify the main ideas. (In the exam, you could underline them on the exam paper.) Be on the lookout for information which only serves to expand or explain the main ideas — for example, figures of speech and illustrations. These must not be included in your final draft.
• Only information given in the original passage must be used. Your personal opinion does not matter and should never be included.
• Focus on the question asked. Once you are sure that you have identified all the main points which will be required in your answer, organise them logically so that the ideas will flow and your summary will not seem incoherent.
• Even if you are summarising a piece of writing which consists of several paragraphs, your summary must be written in one paragraph.
• Write in your own words, using Standard English.
• You may be asked to present your summary in different ways. If it is to be done in a given number of words, count the number you have used and indicate this at the end of your answer. Do not cheat! Simply stick to the word limit or you may be penalised. If you are asked to use a numbered list of sentences, then be sure to do just that.
• It is important that the language you use be simple, clear and concise.
¶ Writing a Telegram
Although we may not often write telegrams today, the e-mail message could, with profit, be approached in much the same way as a telegram or cablegram.
For the telegrams/cablegrams, you are expected to extract information from a given situation. Since you pay for each word in the telegrams/cablegrams, you need to make your message as brief as possible. The following guidelines, along with those stated above, must be observed:
• No punctuation mark is transmitted so you have to ensure that the words you use create a clear message. The word "Stop" is used instead of a full-stop and should not be overused. In fact, "Stop" is counted as a word.
• It is better to write out figures if there is a need for them.
• Instead of sentences, you should use clear, precise phrases. Verbs play an important part. "Advise" is one of those words you will find useful, as it says much without the use of other words.
• Addresses must be accurate to avoid delay. Depending on the situation, the sender may include his/her address, but only if it is absolutely necessary.
• The sender may or may not use his full name. Again, this depends on the situation. Naturally, if you are sending a telegram/cablegram to your parents or a close relative or friend, you would not need to indicate your full name. In fact, you could use your pet name, if you have one.
• Like the summary of a passage, watch your word limit. You will be advised if names and addresses are to be included in the word count.
• Revise the format for writing up telegrams. You may choose to use block letters.
In the exam, the telegram/cable may be tested by itself or it may be coupled with a letter.
¶ Practice Example
Your name is John Garcia. Your father is on three months' holiday in the USA. While he is away, an accident occurs in which his car is damaged. The following conversation describes what happened.
John: Look out!
Karl: Oh, hell! What a mess.
John: Didn't you see the curb, you idiot?
Karl: Of course not. Would I have run into it if I had?
John: Don't yell at me. You've just crashed my father's car.
Karl: OK, relax. Have you got a cigarette?
John: Here.
Karl: Thanks. Let's see what the damage is.
John: I still can't see how you did that on a perfectly straight road.
Karl: I'm sorry. I'll ask my dad to pay for the damages. But the road isn't straight; it's winding, it's quite late, and the lighting is very bad.
John: It's OK. I'm just upset.
Karl: Well, you are not the only one. Let's see what happened to the car.
John: Can we move it?
Karl: I think so. The wheels are all right. We've just got to pull this front fender away from the wheel. Help me do it.
John: I don't think I should. I strained my back last week.
Karl: Well, you are not much help. How about trying to stop another car?
John: Not much chance of that at this time — it's after midnight.
Karl: Let me see. (Pulls at fender) Oh — it's broken off.
John: At least we can move on.
Karl: That's the spirit. Tomorrow we'll laugh about this.
1. Prepare a summary which will include the necessary information derived from this conversation.
2. Write a cablegram to your father. Provide him with just enough information on the cause of the accident, the nature of it and what steps you have taken. Your cable should not exceed 30 words (excluding names and addresses).
Basic components of all computers
¶ The computer
The computer is an electronic device designed to operate under the control of stored programmed instructions, accept data (input), process or manipulate (processing) that data and store (storage) the result for future use or output it in a meaningful form for the user.
¶ Control Unit
The Control Unit (CU) is the circuitry that controls the flow of information through the processor, and coordinates the activities of the other units within the processor. It is the "brain within the brain", as it controls what happens inside the processor, which in turn controls the rest of the PC.
¶ ALU
The arithmetic logic unit (ALU) is a digital circuit that calculates an arithmetic operation (addition, subtraction, etc.) or a logic operation (exclusive OR, AND, etc.) between two numbers. The ALU is a fundamental building block of the central processing unit of a computer.
¶ Main memory/immediate access storage
The memory within the central processor. Also referred to as internal use or main store.
¶ Backing store/disc storage
Memory external to the computer used for storage of large quantities of data or large programs. Backing store is also known as secondary store, auxiliary store or external store.
¶ Peripheral device
In computer hardware, a peripheral device is any device attached to a computer in order to expand its functionality. Some of the more common peripheral devices are printers, scanners, disc drives, tape drives, microphones, speakers, and cameras. A peripheral device can also refer to a non-physical item, such as a pseudo-tty, a RAM drive, or a network adapter.
Primary storage devices and media
¶ Bistable device
A device which can exist in two distinct stable states.
¶ PROM
Short for Programmable Read-Only memory, a memory chip on which data can be written only once. Once a program has been written onto a PROM, it remains there forever. Unlike RAM (Random Access Memory), PROMs retain their contents when the computer is turned off.
The difference between a PROM and a ROM (Read-Only Memory) is that a PROM is manufactured as blank memory, whereas a ROM is programmed during the manufacturing process. To write data onto a PROM chip, you need a special device called a PROM programmer or PROM burner. The process of programming a PROM is sometimes called burning the PROM.
¶ EPROM
An EPROM (Erasable Programmable Read-Only Memory) is a special type of PROM that can be erased by exposing it to ultraviolet light. Once it is erased, it can be reprogrammed.
¶ RAM
Random Access Memory (usually known by its acronym, RAM) is a type of data storage used in computers. It takes the form of integrated circuits that allow the stored data to be accessed in any order — that is, at random and without the physical movement of the storage medium or a physical reading head.
¶ ROM
Acronym for Read-Only Memory, computer memory on which data has been prerecorded. Once data has been written onto a ROM chip, it cannot be removed and can only be read.
Unlike main memory (RAM), ROM retains its contents even when the computer is turned off. ROM is referred to as being nonvolatile, whereas RAM is volatile.
Most personal computers contain a small amount of ROM that stores critical programs such as the program that boots the computer. In addition, ROMs are used extensively in calculators and peripheral devices such as laser printers, whose fonts are often stored in ROMs.
Characteristics and uses of secondary storage devices and media
¶ Magnetic tape
A storage medium consisting of a flexible plastic strip of tape covered with magnetic material on one side, used to store data. It is available in spools or cassettes.
¶ Floppy disc
A flexible magnetic coated disc, commonly used with microcomputers on which data can be stored magnetically.
¶ Micro-floppy disc
Refers to 3.5 inch floppy discs. They are housed in a rigid plastic casing having a sliding shutter which automatically closes when the disc is removed from the disc drive.
¶ Hard disc/fixed disc
A rigid disc used for storing data magnetically. Its rigid construction allows for higher storage densities. Access times for a hard disc are much faster than for a floppy disc.
¶ Optical disc — CD
Known by its abbreviation, CD, a Compact Disc is a polycarbonate with one or more metal layers capable of storing digital information. The most prevalent types of compact discs are those used by the music industry to store digital recordings and CD-ROMs used to store computer data. Both of these types of compact disc are read-only, which means that once the data has been recorded onto them, they can only be read, or played.
¶ Optical disc — DVD
Digital Video Disc or Digital Versatile Disc. A high-density compact disc for storing large amounts of data, especially high-resolution audio-visual material.
Terms associated with backing storage devices and media
¶ Read/write head
The mechanism that reads data from or writes data to a magnetic disc or tape. If the head becomes dirty, it will not work properly.
¶ Sector
A pie-shaped division of each track.
¶ Track
The path on a tape, disc or drum on which data are stored. On a disc these paths are concentric circles; on a tape there are several tracks parallel to the edge of the tape; on a drum there are bands of equal size along the circumference of the drum.
¶ Buffer
A temporary storage area, usually in RAM. The purpose of most buffers is to act as a holding area, enabling the CPU to manipulate data before transferring it to a device.
Because the processes of reading and writing data to a disc are relatively slow, many programs keep track of data changes in a buffer and then copy the buffer to a disc. For example, word processors employ a buffer to keep track of changes to files. Then when you save the file, the word processor updates the disc file with the contents of the buffer. This is much more efficient than accessing the file on the disc each time you make a change to the file.
¶ Cylinder
A single track location on all the platters making up a hard disc. For example, if a hard disc has four platters, each with 600 tracks, then there will be 600 cylinders, and each cylinder will consist of 8 tracks (assuming that each platter has tracks on both sides).
¶ Access time
The time a program or device takes to locate a single piece of information and make it available to the computer for processing. DRAM (Dynamic Random Access Memory) chips for personal computers have access times of 50 to 150 nanoseconds (billionths of a second). Static RAM (SRAM) has access times as low as 10 nanoseconds. Ideally, the access time of memory should be fast enough to keep up with the CPU. If not, the CPU will waste a certain number of clock cycles, which makes it slower.
¶ Sequential access
Refers to reading or writing data records in sequential order, that is, one record after the other. To read record 10, for example, you would first need to read records 1 through 9. This differs from random access, in which you can read and write records in any order.
Some programming languages and operating systems distinguish between sequential-access data files and random-access data files, allowing you to choose between the two types. Sequential-access files are faster if you always access records in the same order. Random-access files are faster if you need to read or write records in a random order.
Devices can also be classified as sequential-access or random-access. For example, a tape drive is a sequential-access device because to get to point q on the tape, the drive needs to pass through points a through p. A disc drive, on the other hand, is a random-access device because the drive can access any point on the disc without passing through all intervening points.
¶ Random access
Refers to the ability to access data at random. The opposite of random access is sequential access. To go from point A to point Z in a sequential-access system, you must pass through all intervening points. In a random-access system, you can jump directly to point Z. discs are random-access media, whereas tapes are sequential-access media.
The terms random-access and sequential-access are often used to describe data files. A random-access data file enables you to read or write information anywhere in the file. In a sequential-access file, you can only read and write information sequentially, starting from the beginning of the file.
Both types of files have advantages and disadvantages. If you are always accessing information in the same order, a sequential-access file is faster. If you tend to access information randomly, random access is better.
Random access is sometimes called direct access.
Input devices and media
¶ OMR
Short for Optical Mark Recognition, the technology of electronically extracting intended data from marked fields, such as checkboxes and fill-in fields, on printed forms. OMR technology scans a printed form and reads predefined positions and records where marks are made on the form. This technology is useful for applications in which large numbers of hand-filled forms need to be processed quickly and with great accuracy, such as surveys, reply cards, questionnaires and ballots. A common OMR application is the use of "bubble sheets" for multiple-choice tests used by schools. The student indicates the answer on the test by filling in the corresponding bubble, and the form is fed through an optical mark reader (also abbreviated as OMR, a device that scans the document and reads the data from the marked fields). The error rate for OMR technology is less than 1%.
¶ OCR
Often abbreviated OCR, Optical Character Recognition refers to the branch of computer science that involves reading text from paper and translating the images into a form that the computer can manipulate (for example, into ASCII codes). An OCR system enables you to take a book or a magazine article, feed it directly into an electronic computer file, and then edit the file using a word processor.
All OCR systems include an optical scanner for reading text, and sophisticated software for analyzing images. Most OCR systems use a combination of hardware (specialized circuit boards) and software to recognize characters, although some inexpensive systems do it entirely through software. Advanced OCR systems can read text in a large variety of fonts, but they still have difficulty with handwritten text.
¶ MICR
Magnetic Ink Character Recognition is a character recognition system that uses special ink and characters. When a document that contains this ink needs to be read, it passes through a machine, which magnetizes the ink and then translates the magnetic information into characters.
MICR technology is used by banks. Numbers and characters found on the bottom of checks (usually containing the check number, sort number, and account number) are printed using Magnetic Ink. To print with Magnetic Ink, you need a laser printer that accepts MICR toner.
MICR provides a secure, high-speed method of scanning and processing information.
¶ Mouse
A device that controls the movement of the cursor or pointer on a display screen. A mouse is a small object you can roll along a hard, flat surface. Its name is derived from its shape, which looks a bit like a mouse, its connecting wire that one can imagine to be the mouse's tail, and the fact that one must make it scurry along a surface. As you move the mouse, the pointer on the display screen moves in the same direction. Mice contain at least one button and sometimes as many as three, which have different functions depending on what program is running. Some newer mice also include a scroll wheel for scrolling through long documents.
¶ Joystick
A lever that moves in all directions and controls the movement of a pointer or some other display symbol. A joystick is similar to a mouse, except that with a mouse the cursor stops moving as soon as you stop moving the mouse. With a joystick, the pointer continues moving in the direction the joystick is pointing. To stop the pointer, you must return the joystick to its upright position. Most joysticks include two buttons called triggers.
Joysticks are used mostly for computer games, but they are also used occasionally for CAD/CAM systems and other applications.
¶ Light pen
An input device that utilises a light-sensitive detector to select objects on a display screen. A light pen is similar to a mouse, except that with a light pen you can move the pointer and select objects on the display screen by directly pointing to the objects with the pen.
¶ Touch terminal
Also called a touch screen. A device that allows data to be input by touching a screen with the finger or other object. The surface of the screen consists of a number of programmed touch points each of which may trigger a different action when selected by the user.
¶ Voice recognition
The field of computer science that deals with designing computer systems that can recognize spoken words.
A number of voice recognition systems are available on the market. The most powerful can recognize thousands of words. However, they generally require an extended training session during which the computer system becomes accustomed to a particular voice and accent. Such systems are said to be speaker-dependent.
Because of their limitations and high cost, voice recognition systems have traditionally been used only in a few specialised situations. For example, such systems are useful in instances when the user is unable to use a keyboard to enter data because his or her hands are occupied or disabled. Instead of typing commands, the user can simply speak into a headset. Increasingly, however, as the cost decreases and performance improves, speech recognition systems are entering the mainstream and are being used as an alternative to keyboards.
¶ POS
Point Of Sale, or POS as it is more commonly abbreviated, refers to the capturing of data and customer payment information at a physical location when goods or services are bought and sold. The POS transaction is captured using a variety of devices including computers, cash registers, optical and bar code scanners, magnetic card readers, or any combination of these devices.
¶ Bar code
A series of thick and thin black bars separated by spaces of varying widths representing data.
¶ Keyboard
The main input device on most PCs. It consists of a "board" with a set of buttons on it that represent all the letters in the alphabet, the numbers 0 through 9, and any extra keys, like cursor keys and function keys, that enable some keys to represent additional characters.
¶ Key-to-disc
Keyboard entry of data directly to magnetic disc without previous preparation on another medium.
¶ Scanners
A device that can read text or illustrations printed on paper and translate the information into a form the computer can use. A scanner works by digitizing an image — dividing it into a grid of boxes and representing each box with either a zero or a one, depending on whether the box is filled in. (For color and gray scaling, the same principle applies, but each box is then represented by up to 24 bits.) The resulting matrix of bits, called a bit map, can then be stored in a file, displayed on a screen, and manipulated by programs.
Optical scanners do not distinguish text from illustrations; they represent all images as bit maps. Therefore, you cannot directly edit text that has been scanned. To edit text read by an optical scanner, you need an optical character recognition (OCR ) system to translate the image into ASCII characters. Most optical scanners sold today come with OCR packages.
Output devices and media
¶ Monitor
A monitor is a display device that consists of a screen housed in a plastic metal case. A colour monitor displays text, graphics and video information in colour. The image on a screen is viewed by pixels, which are also known as dots. A pixel is a single point in an electronic image. A monitor consists of hundreds, thousands or millions of pixels arranged in rows and columns that can be used to create images. The pixels are so close together that they appear connected. The monitor is said to output "soft copy" of data because it is temporary output that is lost once electricity is removed from the device.
¶ Resolution
The resolution of a monitor indicates how densely packed the pixels are. In general, the more pixels (often expressed in dots per inch), the sharper the image. Most modern monitors can display 1024 by 768 pixels, the SVGA standard. Some high-end models can display 1280 by 1024, or even 1600 by 1200.
¶ Printer
A printer is an output device that produces text and graphics on a physical medium such as paper or transparency film. Printed information is called hard copy because the information exists physically and is a more permanent form of output than that presented on a display device (soft copy), for example, a monitor.
Printers can be grouped into two categories:
1. Impact printers
2. Non-impact printers
Impact printers
An impact printer forms graphics and characters on paper by striking a mechanism against an ink ribbon that physically contacts the paper. Impact printers are generally noisy. The print quality is not the best. These printers are ideal for printing mailing labels, envelopes or invoices, and multipart forms because they can easily print through many layers of paper. Impact printers are also used in many factories, hardware stores, etc., because they can withstand dusty environment, vibrations and extreme temperatures.
Two commonly used types of impact printers are the character printer and the line printer.
Character Printer. A character printer prints one character at a time. The typical character printer is the dot matrix printer.
This is an impact printer that produces printed images when tiny wire pins on a print head mechanism strike an inked ribbon. When the ribbon presses against the paper, it creates dots that form characters and graphics.
The speed of a dot-matrix printer is measured by the number of characters per second (cps) it can print. The speed of dot-matrix printers ranges from 50-700 characters per second.
Line Printer. A line printer is a high speed impact printer that prints an entire line at a time. The speed of line printers is measured by the number of lines per minute (lpm) it can print. A line printer is capable of printing 3000 lines per minute.
Non-impact printers
A non-impact printer forms characters or graphics on a piece of paper without actually striking the paper. Some spray ink while others use heat and pressure to create images. Because there is no striking on the paper, these printers tend to be quiet. Common types of non-impact printers are inkjet printers, laser printers and thermal printers.
Inkjet Printer. An inkjet printer is a non-impact printer that forms characters and graphics by spraying tiny drops of liquid ink onto a piece of paper. The print quality is usually high. These printers are ideal for printing on T-shirts, transparencies, labels, envelopes, banners and greeting cards.
One factor that determines the quality of an inkjet printer is its resolution or sharpness and clarity. Printer resolution is measured by the number of dots per inch (dpi) a printer can output. The higher the dpi and the better the print quality the more costly the printer will be. The speed of an inkjet printer is measured by the number of pages it can print per minute (ppm). Most inkjet printers print one to 12 pages per minute.
Laser Printer. A laser printer is a high-speed, high-quality, non-impact printer. These printers can print text and graphics in very high-quality resolutions ranging from 600 dpi to 1200 dpi. The print speeds are four to 30 pages per minute. Laser printers are mainly used with mainframe computers. Laser printers are sometimes called page printers. A laser printer creates images using a laser beam and toner.
¶ Plotter
Like printers, plotters are devices that can produce output on paper. Instead of producing images and text using print heads, ink ribbons or lasers, they use a row of charged wires called styli as in the case of an electrostatic plotter to draw an electrostatic pattern on specifically coated paper and then they fuse toner to the pattern. Plotters are used in specialised fields, such as engineering, drafting and graphic art. They are also used to print maps and blueprints.
¶ Microfiche
An output medium consisting of microfilm sheets. Very high-density storage can be attained using this method of storage.
¶ Permanent copy (hard copy)
Information printed on paper in contrast to being electronically displayed on a computer screen. This term is now used by many people to represent all paper documents, including memos, order forms, letters, print advertisements, books, catalogs, and so on. Hard copy has the advantage of being accessible to everyone everywhere, without the expense or inconvenience of a computer. In addition, even the best electronic images cannot duplicate an original image as well as a printed image can. However, hard copy is not easily modified or transmitted over distances and takes space and time to store and retrieve.
¶ Temporary copy (soft copy)
A soft copy (sometimes spelt "softcopy") is an electronic copy of some type of data, such as a file viewed on a computer's display or transmitted as an e-mail attachment.

Keys to Success in English
¶ Levels of Usage
There are two levels of usage: Standard English and Colloquial English.
Standard English
This is used when we are writing or speaking in a formal situation — for example, when you invite your Guidance Counsellor to address your class on Correct Study Habits or Opportunities for Young School Leavers. Standard English is free from slang and follows the basic rules of grammar.
Colloquial English
This is more informal. It is used in informal conversations and in certain circumstances only. The use of the slang is therefore permitted, but it should not be overused. When you ask your parents for permission to attend a classmate's sweet sixteen party, or when you ask your friend to tell you about a show you missed on television, you may choose to use colloquial language.
In the CXC examination, you may use English at either level, the choice of level depending upon the nature of the question you are answering.
¶ The Examination Papers
You are by now aware that there are two proficiencies on the exam: Basic and General. The examination consists of two papers: Paper One (Multiple Choice) and Paper Two (Free Response). Paper One has sixty items which test how well a student has mastered such areas as usage, spelling, grammar, sentence completion, sentence reconstruction, and comprehension of prose passages, poems and advertisements.
Paper Two is the paper students ought to enjoy as it gives you a chance to use the English language in many ways. You will use the language to inform, entertain, persuade, and to respond to the words of poets and/or prose writers. On this paper there are four sections, each with suggested times. If you adhere to these times, you will complete the examination paper.
• Sections One and Two — Report writing, analysis of prose passages and/or poems, summary.
• Section Three — Descriptive writing, story writing.
• Section Four — Persuasive writing; for example, letters, speeches, and expository writing.
¶ Tips on Being Prepared
Many skills are tested in the examination. These include summary skills, the ability to organise material, skills of understanding, comprehension, and analysing. Therefore, it is important for you to prepare wisely. The following suggestions are offered for your success:
• It is very important to read. Read the newspaper — the Editorial page is particularly recommended. Also read letters to the Editor, as these will help you to gather ideas and sharpen your skills of analysis. In addition, you may read texts on the English B Syllabus, or ask for suggestions from your teachers.
• Practise to write stories, reports, speeches, and letters to the Editor.
• Practise to speak properly.
• Become close friends with a good dictionary.
• If you identify a weakness you have with a particular area of the syllabus, spend more time on it and ask your teacher for assistance.
• Use your textbooks on your own.
• Should you encounter any difficulty, ask your teacher for assistance.
¶ Reference Material
A Comprehensive English Course, CXC English — A Roy Narinesingh and Uriel Narinesingh
English: A Study Guide and Exercises — Keith Noel, Sheilah Garcia Bisnott, Milton Drepaul
Mastering English for CXC — Clive Borely, Hollis Knight

Writing a Summary
A summary is a shortened version of a much longer piece of writing and it must include the vital information contained in the original. It must be clear, precise, and the emphasis of the original information must not be altered.
¶ Important Points for Preparing Summaries
• Make sure you understand the original passage. You will be able to do this if you read, and possibly re-read, the information which is to be summarised.
• Identify the main ideas. (In the exam, you could underline them on the exam paper.) Be on the lookout for information which only serves to expand or explain the main ideas — for example, figures of speech and illustrations. These must not be included in your final draft.
• Only information given in the original passage must be used. Your personal opinion does not matter and should never be included.
• Focus on the question asked. Once you are sure that you have identified all the main points which will be required in your answer, organise them logically so that the ideas will flow and your summary will not seem incoherent.
• Even if you are summarising a piece of writing which consists of several paragraphs, your summary must be written in one paragraph.
• Write in your own words, using Standard English.
• You may be asked to present your summary in different ways. If it is to be done in a given number of words, count the number you have used and indicate this at the end of your answer. Do not cheat! Simply stick to the word limit or you may be penalised. If you are asked to use a numbered list of sentences, then be sure to do just that.
• It is important that the language you use be simple, clear and concise.
¶ Writing a Telegram
Although we may not often write telegrams today, the e-mail message could, with profit, be approached in much the same way as a telegram or cablegram.
For the telegrams/cablegrams, you are expected to extract information from a given situation. Since you pay for each word in the telegrams/cablegrams, you need to make your message as brief as possible. The following guidelines, along with those stated above, must be observed:
• No punctuation mark is transmitted so you have to ensure that the words you use create a clear message. The word "Stop" is used instead of a full-stop and should not be overused. In fact, "Stop" is counted as a word.
• It is better to write out figures if there is a need for them.
• Instead of sentences, you should use clear, precise phrases. Verbs play an important part. "Advise" is one of those words you will find useful, as it says much without the use of other words.
• Addresses must be accurate to avoid delay. Depending on the situation, the sender may include his/her address, but only if it is absolutely necessary.
• The sender may or may not use his full name. Again, this depends on the situation. Naturally, if you are sending a telegram/cablegram to your parents or a close relative or friend, you would not need to indicate your full name. In fact, you could use your pet name, if you have one.
• Like the summary of a passage, watch your word limit. You will be advised if names and addresses are to be included in the word count.
• Revise the format for writing up telegrams. You may choose to use block letters.
In the exam, the telegram/cable may be tested by itself or it may be coupled with a letter.
¶ Practice Example
Your name is John Garcia. Your father is on three months' holiday in the USA. While he is away, an accident occurs in which his car is damaged. The following conversation describes what happened.
John: Look out!
Karl: Oh, hell! What a mess.
John: Didn't you see the curb, you idiot?
Karl: Of course not. Would I have run into it if I had?
John: Don't yell at me. You've just crashed my father's car.
Karl: OK, relax. Have you got a cigarette?
John: Here.
Karl: Thanks. Let's see what the damage is.
John: I still can't see how you did that on a perfectly straight road.
Karl: I'm sorry. I'll ask my dad to pay for the damages. But the road isn't straight; it's winding, it's quite late, and the lighting is very bad.
John: It's OK. I'm just upset.
Karl: Well, you are not the only one. Let's see what happened to the car.
John: Can we move it?
Karl: I think so. The wheels are all right. We've just got to pull this front fender away from the wheel. Help me do it.
John: I don't think I should. I strained my back last week.
Karl: Well, you are not much help. How about trying to stop another car?
John: Not much chance of that at this time — it's after midnight.
Karl: Let me see. (Pulls at fender) Oh — it's broken off.
John: At least we can move on.
Karl: That's the spirit. Tomorrow we'll laugh about this.
1. Prepare a summary which will include the necessary information derived from this conversation.
2. Write a cablegram to your father. Provide him with just enough information on the cause of the accident, the nature of it and what steps you have taken. Your cable should not exceed 30 words (excluding names and addresses).
¶ Finding the Subject
To find the subject, we first identify the finite verb and then ask who or what is before this verb. Consider these examples:
• "We baked the cake for the party."
The finite verb in the sentence is "baked". We then ask, "Who/what baked?" The answer is "we".
• "For some strange reason, only the box of books was stolen."
"Was stolen" is the finite verb. Who/what was stolen? "Only the box of books." Note that, in this case, the sentence does not begin with the subject.
When the sentence is a command, and no-one is specifically addressed, report the subject as "(you)", where the parentheses indicate that it is implied rather than being explicitly present in the sentence. (You may have heard this referred to as "'you' understood".) Consider these examples:
• "Please turn off the stove for your father."
The subject is "(you)".
• "Listen! I am not misleading you."
Since the sentence is a command, the subject is "(you)".
When the sentence is a question, change it into a statement and report the subject of the result. Consider this example:
• "Did Mary buy the book?"
Change the sentence to the statement: "Mary did buy the book." Since the subject of this statement is "Mary", that is also the subject of the original question.
As is already apparent from an example above, the subject does not have to be a single word. Sometimes it may be a group of words. Consider this additional example:
• "What Peggy did was unthinkable."
What was unthinkable? It is what Peggy did. So, the subject of the sentence is "what Peggy did".
¶ Agreement of Subject and Verb
The verb must agree with its subject. Examine these sentences:
1. "The boy in the red shirt lives in Kingston."
2. "After every Literature class, Marsha rereads her texts."
3. "One of the students is doing the art work for the magazine."
4. "The Principal always assists in preparing the school's debating team for competitions."
5. "From which poem is he quoting?"
If you look at the subject in each sentence, you will notice that each one is singular. So, they must each take a singular verb. Please note carefully the verb used in each sentence. Pay particular attention to the third sentence where the main word in the subject is "one" and not "students". The tendency to misidentify the subject in such a sentence is common. It is not always the noun nearest the verb that governs it.
Now examine these sentences:
1. "The books and the bags are on the table."
2. "Have the boys completed the game?"
3. "Among the passengers were the members of the Drama Club and their teacher."
4. "The stories in the magazine were written by the fourth formers."
In each sentence, identify the subject and the verb which goes along with it. This time, each sentence has a plural subject. Consequently, the verbs are in the plural form. The simple rule is:
• A singular subject takes a singular verb.
• A plural subject takes a plural verb.
Take special care with sentences that include such phrases as: along with, together with, in addition to, as well as, either … or, not only … but also. If any of these joins two singular subjects, the verb remains singular. For example:
1. "David, as well as Stephen, is in Sixth Form."
2. "Paying attention in class, in addition to reading ahead, prepares us for success."
Be careful, too, with words that end in "s" and yet are singular — for example, "mathematics", "news", and "measles". Then there are certain words ending in "s" that may be singular or plural depending on usage — for example, "politics" and "statistics".
1. "Today, politics appeals to both young and old."
Here, "politics" is a singular noun.
2. "The politics of the situation are interesting."
In this case, "politics" is plural.
¶ Activity
Choose the correct verb in each of the following sentences:
• The children of today (is, are) the hope of tomorrow.
• In the evenings, Mother (read, reads) the newspaper before she (supervise, supervises) our homework.
• There (goes, go) the teachers from India.
• Merle, as well as her grandchildren, (is, are) in Atlanta .
• (Has, have) the men gone hunting?
Reading, Writing, Speaking and Listening
Reading not only enriches your experience, but it also widens your vocabulary, and provides hours of fun and entertainment. Here are some texts which lend themselves to hours of delightful reading. These have been chosen from the reading list given at the end of the CXC English A syllabus; they cover a wide selection from novels, poetry, short stories, and drama pieces.
• Achebe, Chinua — Things Fall Apart
• Austen, Jane — Pride and Prejudice
• Brontë, Charlotte — Jane Eyre
• Lee, Harper — To Kill a Mockingbird
• Salkey, Andrew — West Indian Stories
• Walcott, Derek-Ti — Jean and His Brothers
• Stewart Brown — Caribbean Poetry Now
Practice becomes perfect. You may look at a passage from one of your favourite writers and then, later, have fun by imitating his/her style. Try to write stories, poetry, skits, and/or articles for your journal class or school magazine/newspaper.
Do a variety of pieces! Do not discard the pieces you have written. Share them with your friends and ask your teacher to look at them.
Consider also the benefits of writing, speaking, and listening.
¶ Sentences
We write in sentences so that what is written flows smoothly and is correct. The sentence is a group of words which makes sense and can stand by itself. The sentence consists of at least one subject and one predicate.
Sentences are classified in two ways — according to their purpose or according to their structure.
¶ The Purpose of the Sentence
There are four purposes:
To make a statement
the declarative sentence — for example, "English Language is a really important subject".
To issue a command or to make a request
the imperative sentence — for example, "Close the door, please."
To ask a question
the interrogative sentence — for example, "Do you know where I can buy a good dictionary?"
To exclaim
the exclamatory sentence — for example, "What a beautiful dress!"
The same words can convey different meanings by being used with different purposes in mind. For example:
• He kicked the ball. — declarative
• He kicked the ball! — exclamatory
• He kicked the ball? — interrogative
Note that the punctuation of each sentence assists the reader with its intended purpose and therefore with its meaning.
¶ Subject and Predicate
The subject is a noun or a pronoun; it is that which the sentence speaks about. Look at these two sentences:
1. Her son is now a university student.
2. I went to see the play, Old Story Time.
The subjects of these sentences are "Her son" (sentence 1) and "I" (sentence 2). You can see clearly that each of these sentences speaks about "someone". In the same way, a sentence can speak about "something". For example:
3. Down the hill rolled the stone.
4. Above all, laziness will not be tolerated.
These two sentences also illustrate the fact that the subject is not always found at the beginning of a sentence.
The predicate tells us about what is happening to the subject or what the subject is doing. The predicate in sentence 1 above is "is now a university student" and, in sentence 2, it is "went to see the play, Old Story Time".
The most important part of the predicate is the finite verb (the action word). This is a verb that can take a subject, one that can be conjugated. A verb we use frequently is 'to be'. Here is its conjugation in the present tense:
Singular Plural
I am we are
you are you are
he is
she is
it is they are
Remember that verbs have other tenses too — for example, the past, present, future, and perfect tenses.
Verbs that are not conjugated are called infinitives. For example: "to cry", "to achieve", or "to put out". Auxiliaries (helping words) are added to another form of the infinitive — for example, "crying" — to convert it to a finite verb ("am crying", "is crying", "would cry", "has been crying", etc.).
¶ Common Way to Find the Subject
Find the finite verb first, and then look for the noun/pronoun being spoken about by asking "Who" or "What" before the verb.

Kathy-ann Daniel's picture
Kathy-ann Daniel
Offline
Joined: 24 Aug 2007
Thanks for the study notes

Hi Chetram,
Thanks for the study notes! I am sure that many of out members and guests will benefit greatly from having these notes available to them.

Thanks a lot choosing to add your notes to our library, and, in doing so, help your fellow CXC candidates. We appreciate your co-operative actions.

Kathy-ann Daniel-Gittens

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Challengea2009 (not verified)
english

can u please help me with some english always failing , and i am willing to work Challengea2000@yahoo.com

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tammyg (not verified)
math &english

i need help in math esecieally

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dejanya (not verified)
Re: math &english

hay im going to this class... and even thou i need a little help. maybe i can teach what i know so far...btw thats if you want

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