A is used before a noun. It means one. ‘A boy’ means one boy, but not any particular boy. For example you would say “I saw a boy when I got onto the train’ ” if you did not know that boy and had never seen him before, but you would say “Today I saw the boy that I saw yesterday on the train’ “because the boy is not any boy but the particular boy you saw before. A is not used with a plural noun so you would usually say “the boys’“because you are now talking about a group of boys. If it is not a particular group of boys then you can say “some boys’ ”. A is an adjective, but A and THE have special names. A is called the indefinite article. It is called indefinite because it is not referring to a definite thing or person. The is called the definite article because it is referring to a definite thing or person. If you are not clear about this then look at the examples at THE.

ABACUS – (noun) An abacus has beads that slide on rods. See diagram 41. They are used for counting. The beads in the diagram represent 70 000, 4000, 900, 50 and 4 or the number 74954.

ABBREVIATION  – (noun) means a shortened form or way of writing something. For example the abbreviation for Doctor Smith is Dr Smith and the abbreviation for Mister Jones is Mr Jones. The abbreviation for Street is St and the abbreviation for Road is Rd.

ABOVE – (preposition) means at a higher level. “He looked up and saw what was above him. The bird flew high above the earth.

ABSCISSCA – (noun) To understand abscissca you must first understand the meaning of co-ordinate so look up CO-ORDINATE. Look at diagram 18 and you will see that the abscissca is the name for the distance of the point A from the Y-axis. The ordinate is the distance of the point A from the X-axis.

ABSOLUTE 1. Absolute – (adjective) means complete or whole. “An honest man is expected to tell the absolute truth. To get 100% you must answer with absolute accuracy. “2. In Maths ‘absolute’ has a special meaning. See ABSOLUTE VALUE. 3. The adverb ABSOLUTELY means completely or without doubt.” He believed what she said absolutely because he trusted her. ““The clever boy got the answer absolutely correct.

ABSOLUTE VALUE – (noun) The absolute value of a number is the value of that number regardless of it being a positive or negative number.” For example the absolute value of -4 is 4 & the absolute value of + 6 is 6.

ABSTRACT – (adjective) means something that does not exist as an object in the world around us. For example he has the idea that he will be a doctor when he grows up. The idea that he will become a doctor is abstract. The idea of being able to fly in an aeroplane was abstract until the first aeroplane was built and someone flew in it. Qualities such as ‘beauty’, ‘honesty’ are also abstract things. The opposite of ABSTRACT is CONCRETE. See CONCRETE.

ACCELERATION – (noun) means how fast does something increase speed. “A rocket has a very big acceleration.” The verb is to accelerate.” The big heavy lorry could only accelerate slowly. The man in the sports car accelerated quickly and passed the lorry easily. The sports car has very good acceleration.

ACCENT – (noun) 1. In maths the symbol ‘ is called an accent. x’ is read as x prime and x” as x double prime. x, x’ and x” all represent different variables. See VARIABLE. ‘and ” are also used to represent minutes and seconds of an angle. 25 degrees 40 minutes and 33 seconds are written 25&>0 &> 40′ 33”. See MINUTE & SECOND. See ANGLE. 2. The way a person speaks is also called an accent. “She speaks English with a French accent.

ACCEPT – (verb) means to be willing to take or receive something as it is given.” He accepted the parcel when it was delivered. “See DELIVER.” She was very cross with him, but she accepted his apology for being so late. She accepted his invitation to go to the party with him. He accepted the position of head master.

ACCORDING TO – (preposition) means in agreement with or on the authority of. See AUTHORITY. “According to James maths is” “very easy. According to the dictionary the meaning of car is something, with 4 wheels and engine that you can ride in.

ACCOUNT – (noun) 1. An account is something written or spoken that gives the details about something or something that has happened. “He gave a true account of the accident to the policeman. When he got home very late the boy gave his father an account of what had happened. ” 2. Account has a more special meaning when used about money. It means a record of money transactions. See TRANSACTION. “He had an account of what money he had spent on his holiday.” See BANK. A bank account is a record of one’s money transactions with the bank. “You cannot run a business properly without keeping a set of accounts. “ See BOOK KEEPING.” When you owe someone they will send you an account of what is owed. He was very happy when he paid all his accounts. “

ACCOUNTANT – (noun) An accountant is a person who is trained to do accounting work. “His business has grown and he now needs a full time accountant.

ACCOUNTING – (noun) is the name of the subject that is to do with the keeping of accounts in a business.

ACCURATE – (adjective) 1. Accurate means without errors or mistakes because care is taken not to make them. See ERROR. For example -” The boy who rushed through his homework made lots of mistakes. Therefore his work was not accurate. He must make an accurate measurement of the wood so he can cut it to the correct size. ” See CORRECT. 2. Accurate to a number of decimal places. If you wish to express the number 1,43546 accurate to 4 decimal places then the answer is 1,4355; accurate to 3 decimal places is 1,436; to 2 places 1,44; to 1 place 1,4; to zero places 1. You will notice that with 5 to 9on the right hand side of the number that will become the last number that number is increased by 1. With 1 to 4 on the right hand side the number stays t he same. 0,35; 0,36; 0,37; 0,38; 0,39 will all be 0,4 accurate to 1 decimal place whereas 0,31; 0,32; 0,33; 0,34 will become 0,3 correct to 1 decimal place.

ACHIEVE (verb) means to get something done or reach your goal. “I achieved standard 10. I achieved my purpose of reaching Cape Town.

ACQUAINTANCE – (noun) 1. An acquaintance means someone who one knows, but who is not a close friend. “When he went to the city he made many acquaintances, but his best friend was back at home.” 2. Acquaintance also means some knowledge of something through experience. “For example you could say that you have some acquaintance of some other language.” This would mean that you can speak that language a little, but not very well.

ACROSS – (preposition) means from one side to the other. “He swam across the river. When he saw me he walked across the room to say hello. ” It also means over. “ He walked across the bridge. ”

ACT – (verb) 1. To act means to do something. “When he saw the car coming at him he saved his life by acting quickly.” “The medicine acted well and he is not sick any more.” 2. To act also means to take part in a play. 3. Act – (noun) also means something that is done. For example,” his act of jumping into the swimming pool was foolish because he could not swim. ” 4. Another meaning of act – (noun) is a law that is passed in parliament.

ACTION – (noun) also means something that is done. See ACT. “His quick action saved her life.

ACTIVE 1. Active – (adjective) means doing a lot of things. “An active child will tire out an old person. The small kitten was very active and then it went to sleep. “2. It also means being able to do things. “ That old motorcar is still active “- (meaning that although it is old it is still able to work).

ACTIVE VERB – (noun) an active verb is a verb in the active voice. See ACTIVE VOICE.

ACTIVE VOICE – (noun) the active voice of a verb is that voice when the subject is doing something to someone or something else. In “I kick the ball” kick’ is in the active voice. In “I am kicked” ‘am kicked’ is in the passive voice. See VOICE.

ACTIVITY – (noun) means the condition of being active. See ACTIVE. “ The activity of the children playing stopped when they heard the bell.

ACTUAL – (adjective) means what is in existence in the world around you. It is the opposite of imaginary. See IMAGINARY. “He thought he was very old and grown up and he tried to behave as if he was 20, but his actual age was 7. He thought there were 40 people in the room, but the actual number was found to be only 30 when they counted everyone.

ACTUALLY – (adverb) means in fact. If you say “tell me what actually happened” you mean you want that person to tell you what truly happened, what the facts were.

ACUTE – (adjective) in Maths refers to angles. An acute angle is an angle that is less than a right angle which is exactly the same as saying it is less than 90 degrees. See diagram 5. Acute also has several other meanings. 1. Quick thinking. “He tried to confuse me with his lies, but I was too acute for that. “ 2. Of short duration, but bad. This is usually used when describing a sickness. “He had an acute illness; he nearly died, but 2 weeks later he was well again.” This is the opposite of chronic that means going on for a long time. “He spent years in hospital with a chronic illness.” 3. Sharp. “The acute end of the stick hurt his hand. He cried out because of an acute pain. “4. Critical. “ Because it had not rained for a year there was an acute shortage of water. ” See CRITICAL.

ADD – (verb) Add means to put something with something else and then count it together. For example if you put 3 with 4 and count them together you get an answer of 7. The action of adding is called addition. When you say 1 plus 2 it is the same as saying 1 added to 2. In both cases the answer is 3. The short way of writing this is 1 + 2 = 3. + is called the plus sign. = is called the equals sign. Add also means just to put with. “You must add milk and sugar to your tea.

ADD UP – (verb) You use ‘up’ with ‘add’ in the following way.” Please add up these figures. When he added up the cost of the things he wanted to buy he found that he had just enough money. These numbers all add up to 100.

ADDEND – (noun) means any number that has to be added. In 1 + 2 + 3 = 6, 1 and 2 and 3 are all called addends.

ADDITION – (noun) is the action of adding numbers together. “He is good at addition because he can add up numbers fast and get the answers right.” See ADD. IN ADDITION means besides or also.” He is clever at school and in addition he is very good at football. ” See Appendix II.1 for addition in algebra.

ADDITIONAL – (adjective) means something extra.” Because he thought the weather would be very cold he took an additional jersey. Because the children would not attend the teacher gave then an additional sum to work out.

AD INFINITUM – (adverb) means going on and on without end. See INFINITY. “They talked ad infinitum about who was the best player. His speech to the students seemed to go on ad infinitum when at last after 2 hours he came to an end.

ADJACENT – (adjective) means next to.” He parked his car adjacent to a red kombi. The house adjacent to ours was sold. ” In Maths adjacent has the same meaning. See Diagrams 2, 3, 7, 8 & 20.

ADJECTIVE – (noun) A word is an adjective if it tells something about a noun. For example big, happy, sweet, and hot are adjectives.” He had a happy day at the big party, but he had too many sweet hot drinks. “See ADVERB & RELATIVE CLAUSE.

ADJUST – (verb) means to set something so that it works properly or so that it is in a better position.” Now that I have adjusted the brakes of my bicycle it stops very easily. When he had adjusted his position in his chair he felt more comfortable.

ADULT – (noun) means a grown up person. “People of 18 years old and more are called adults.

ADVANCE – (verb) has two main meanings. 1. It means to go forward. “The soldiers advanced towards the enemy so they could attack. He advanced until he was in front of everyone. “2. It also means to give something before it is due. “ His boss advanced him half of his weeks pay in the middle of the week. ” What is given like this is called ‘an advance’. “ He gave him an advance because his last weeks pay was stolen. “See ADVANCED.

ADVANCED – (adjective) 1. Advanced means some thing that has been advanced.” The advanced soldiers were first to fire their guns. ” 2. It also means the standard of those who have gone further in learning.” At University one has to study advanced courses. This clever girl is very advanced for her age. See ADVANCE.

ADVANTAGE – (noun) means something that helps you because it is better. “The big boy had an advantage over the small boy in the fight.

ADVERB – (noun) A word is called an adverb if it tells something about a verb. “He ran fast. She swims well. The children played happily”. The verbs here are ‘ran’, ‘swims’ & ‘played’. Some words can be used both as an adjective and as an adverb. In ‘“This is a fast car’ ”, ‘fast’ is an adjective. See ADJECTIVE.

ADVICE – (noun) is a suggestion from one person to another about what he should do. “Whenever the girl had a problem she went to her mother for advice. “ See SUGGESTION.

ADVISABLE – (adjective) means something that would be good or sensible to do. See SENSIBLE. “It is advisable to do your homework before coming to school. It is advisable to train well if you want to be in the football team.

AEROPLANE – (noun) An aeroplane has wings and a body in which the pilot and passengers sit. The wings going through the air give sufficient lift for it to fly. It is driven by a propeller or a jet engine.

AFFAIR – (noun) An affair is something that is being done or needs to be done. You can talk about business affairs or family affairs or any other sort of affairs. “He runs a big business and his affairs are quite complicated.” See COMPLICATED. “My family affairs are nothing to do with you.

AFFECT – (verb) means to act on something to cause a change. “If you put a plus sign instead of a minus sign in the sum it will affect the answer.” “If you pass your exams it will affect your ability to get a good job.” The noun is spelled effect. Affect means to have an effect on. See EFFECT.

AFTER – (preposition) is the opposite of before. It means coming behind in position or time. He walked after him means he walked behind him. He arrived after him means he came at a later time. “One comes before two. Two comes before three. Six comes after five. Nine comes after eight and so on.

AFTERNOON – (noun) means that part of the day which goes from 12 o’clock in the middle of the day until the sun goes down. p.m. – (post meridiem – from the Latin language) has the same meaning. For example 3 o’clock in the afternoon can also be written as 3 p.m. Times that are before the middle of the day are written with an ‘a.m.’ – (ante meridiem) after them. For example 10 o’clock in the morning can also be written as 10a.m. See NOON.

AFTERWARDS – (adverb) means later in time. “First you should do your homework, afterwards you can play. They went to the shop in the morning and afterwards they went to watch football.

AGAIN – (adverb) means another time. “He shouted again and again because he was frightened. Tomorrow I will come to see you again.

AGREE – (verb) has several meanings. Firstly it means to think or feel the same way about something. “They were good friends and always agreed on what they would do. They also agreed on what books they like to read. ” Agree also means that one will do something. “ When asked to clean the car he agreed. He has agreed to go for a run with me.

AGREEMENT – (noun) Agreement is the noun from agrees. When two people agree about something you say that they have come to an agreement. ““People can make a verbal agreement – (by the spoken word) or a written agreement when everything that has been agreed is written down and signed.

AIRMAIL – (noun) means that letters are sent in an aeroplane. “If you want to get that letter to Johannesburg by tomorrow you must send it by airmail.

ALBUM – (noun) 1. Album means a book with blank pages into which you can stick photographs or stamps and other things that you want to keep. 2. In music it means a collection of records or songs.

ALGEBRA – (noun) is the name of that part of Mathematics where letters are used in the place of numbers. For example when you write a + b = c it is the same as saying that a number called ‘a’ plus a number called ‘b’ are equal to another number called ‘c’. You will learn more about this in your algebra classes.

ALGEBRAIC is the adjective of ALGEBRA. x + y = z is an algebraic expression, but 6 + 7 = 13 is an arithmetic expression. See EXPRESSION.

ALIKE – (adjective) means similar or the same. “The twins look alike. They both had blue Ford cars that looked alike.

ALL – (pronoun) means everything or leaving nothing out.” She got good marks because she did all of her homework. They were very hungry so they ate all of the food. “All can also mean everyone. “ All went to the soccer match. ” As an adjective it has the same meaning.” All children should go to school.

ALLOW – (verb) means to let someone do something or to let something happen. “His father did not allow him to go out until he had done his homework. He allowed the food to burn because he went to sleep.

ALGORITHM – (noun) An algorithm is a method, for working out an answer, which repeats a calculation over and over to get the correct answer. It is the method that computers use to calculate answers.

ALONG – (preposition) means from one end towards the other. “He walked along the road. The train runs along the railway line.

ALONGSIDE – (adverb) means at the side of or next to. “Come and sit alongside me. The car was parked alongside the pavement.

288 ALPHA – (noun) is the first letter of the Greek alphabet. It is written like this: <:f240,QLetter Gothic – (Math8),0,0,0>a<:f> .

ALPHABET – (noun) is the name for all the letters that can be used to make words. They are usually in a definite order. The English alphabet is A, B, C, D, E, F, G, H, I, J, K, L, M, N, O, P, Q, R, S, T, U, V, W, X, Y, Z. Words in a dictionary are in the same order as the letters of the alphabet, so you need to know the alphabet well to be able to easily find a word in a dictionary.

ALREADY – (adverb) means before this time or by this time.” When I went to visit her she had already done her homework. He was late so the game had already begun when he arrived. “You must know that when you speak the two words ALL READY it sounds just the same as ALREADY. If you are not sure what ALL READY means look up these two words.

ALSO – (adverb) means in addition or besides; it gives the idea that there is something extra. “He did his homework and also swept the house. I brought food and also something to drink. ” See ADDITION.

ALTERNATE – (adjective) has a special meaning in Maths When used with angle. See diagram 6.

ALTERNATE – (verb) 1. Alternate means to change from one thing to another and then back again. “The weather alternates from hot in summer to cold in winter. He alternated 4 hours of work with one hour of rest. “2. – (Noun) Means a person or thing that alternates. “ He is my alternate because when I go on holiday he takes my place. The alternate for day is night. ” “The alternate” – (Adjective) “director took Bill’s place at the meeting because Bill was ill. “ See DIRECTOR. “I did not see him because I worked on the alternate shift that week. “ See SHIFT

ALTERNATING – (participle from the verb ‘to alternate’ See PARTICIPLE) means changing first from one thing to another and them back again. “The boxer hit his opponent many times with alternating left and right blows. “ See ALTERNATING CURRENT and ALTERNATING SERIES.

ALTERNATING ANGLES – (noun) See diagram 6.

ALTERNATING CURRENT – (noun) means an electric current which first flows in one direction and then changes to the other direction and then back again usually 50 times each second. See DIRECT CURRENT.

ALTERNATING SERIES – (noun) is a series in which each term – (See EXPRESSION) has the opposite sign. For example: “1 – 3 + 5 – 7 + 9 are an alternating series.

ALTERNATIVE – (noun) is a word that is used to mean a choice between two or more things. “He could stay and fight or run away. He was brave so he chose the first alternative. His first alternative was to read and his second was to watch TV.

ALTITUDE – (noun) 1. Altitude means height above something. It usually means height above sea level. For example “the altitude of Johannesburg is approximately 1850 metres. “ 2. In Geometry altitude has a special meaning. See diagrams 7 & 12.

ALTOGETHER – (adverb) 1. Altogether means counting everything in. “Altogether there were 20 people. “ 2. It also means completely. “The car was altogether destroyed because it caught alight after the accident and was completely burned.

ALWAYS – (adverb) means at all times or every time.” He always gets up at 6 o’clock.

AM – (verb) means to exist. I am means I exist. I am beautiful means I exist in a beautiful way. I AM changes to HE IS and WE ARE, YOU ARE and THEY ARE. You say he is clever and they are clever. AM, IS and ARE come from the verb TO BE. See your GRAM MAR BOOK or ask your teacher.

AMBIGUOUS – (adjective) 1. Ambiguous means something that has more than one meaning. It often also means that there is uncertainty what the real meaning is. For example if there are two men together and you say ‘He said goodbye when he left’ then on e does not know whether the man who left said goodbye or the man who stayed behind said goodbye. So what you said is an ambiguous statement. 2. In maths AMBIGUOUS simply means having more than one meaning or answer. For example in – (a x a) = 4 can be +2 or -2. – (when you multiply a minus number by another minus number the answer is a plus number)

AMONG – (preposition) means spread between a number of other things.” There were some houses among the trees. If you divide 10 apples equally among 5 people they will each get 2 apples.

AMOUNT – (noun) 1. An amount is a quantity of something. “There is a great amount of water in the sea. What amount of money did your house cost? “2. Amount can also be used as a verb. “ What does the cost of all this food amount to?

AMPLITUDE – (noun) 1. Amplitude means largeness. 2. In Mathematics it means the size of a wave. See diagram 24.

AN – (adjective) is the same as A but is used when it is difficult to say the next word. For example you do not say ‘a apple’. You say ‘“an apple’ ” or “an electric light ” not ‘a electric light’. The rule is that when ‘a’ is followed by a word beginning with a vowel you use ‘an’ instead of ‘a’. See VOWEL & A.


ANALYSE is the verb and ANALYSIS is the noun. See ANALYSIS.

ANALYSIS – (noun) means separation into parts so you can see what something is made of. It also means to examine carefully so as to find out more about something. “When he had completed his analysis of the subject he understood it better.” It also has a special meaning in more advanced maths.

ANALYTICAL GEOMETRY – (noun) same as CO-ORDINATE GEOMETRY. They both mean the use of co-ordinates to solve problems in geometry.

AND – (conjunction) means that one thing is taken with another or included with another. “Boys and girls go to school. He brought food and drink. She is pretty and she is clever.

ANGLE – (noun) An angle is the space between two lines that meet. An angle can be an ACUTE angle, a RIGHT angle or an OBTUSE angle. See diagrams 1 & 5.

ANNOUNCE – (verb) means to make something known usually to a lot of people. “The news was announced by television. He put an advertisement in the paper to announce his plan to open a new shop. The arrival of the aeroplane was announced.

ANNUAL – (adjective) means something that happens every year. For example “a birthday is an annual event. The annual accounts showed that the business made a good profit.

ANNUITY – (noun) An annuity is an amount of money that is paid to someone at fixed intervals for a definite period. Insurance companies are usually the organizations that pay annuities. For example if a person paid an insurance company some of his wages every month from the time he was 20 years old until he was 60 years old and then he stopped working, then the insurance company would pay him an amount of money each month for the rest of his life. The amount of money he would be paid would depend on ho w much he was paying each month while he was working and for how many years he made these payments. You can find out more information about annuities from an insurance company. See RETIREMENT.

ANNULUS – (noun) An annulus is the area between two concentric circles. See diagram 17.

ANOMALY – (noun) An anomaly is something that does not follow the normal rule. For example snow in Cape Town would be an anomaly or a nut with a left-hand thread would also be an anomaly. – (see ANTI-CLOCKWISE). “A left hand thread is an anomaly because threads are nearly always right-handed. “ See EXCEPTION.

ANOTHER – (adjective) means one more or an extra one.” Please have another apple. He took another step forward. ” It also means a different one”. I do not like this shirt please give me another.

ANSWER – (noun) An answer to a question is the information which correctly replies to what is asked for. For example if the question is ““How many fingers do you have?” “Ten fingers”“is the correct answer because it is the correct reply to what was asked for.

ANTARCTIC – (noun) See ARCTI Antarctic means the same thing for the South Pole as Arctic means for the North Pole. So Antarctic means at or near the South Pole or to do with the region of the South Pole. See diagram 44.

ANTARCTIC CIRCLE – (noun) This is an imaginary circle on the earth’s surface that is parallel to the equator and sixty six and a half degrees south of the equator. See diagram 44. The Antarctic region is all the area south of this circle. In the Antarctic region the sun never sets. You should ask your geography teacher to explain this to you. See diagram 44.

ANTI-CLOCKWISE – (adjective) means turning in the opposite direction to the hands of a clock. To open a tap you must turn it in an anti-clockwise direction. A thread is called a right-hand thread if the nut tightens when you turn it in a clockwise direction. ANTI-CLOCKWISE & COUNTER-CLOCKWISE – (adjective) means the same thing. See diagram 17.

ANTILOGARITHM – (noun) An antilogarithm is the number corresponding – (See CORRESPOND) to a logarithm. See LOGARITHM.

ANY – (adjective) means one out of many or some out of many. “Any of those apples will do for me. Come and see me any time. Have you any apples for sale?

APART – (adverb) 1. Apart means away from each other. “Please keep your distance apart.” 2. It means into pieces. “Please take the watch apart.” 3. It means to one side. “She set some money apart for her doctor’s bill.

APEX – (noun) means the highest or top point. “He climbed to the apex of the pyramid. “ See diagram 12.

APOLOGY – (noun) An apology is what you say to someone when you have done something wrong to that person and you now want to say you are sorry for what you have done. “As he would not apologise for being so rude the teacher sent him to see the headmaster”.

APOSTROPHE – (noun) This is the name of the sign ‘. 1. When something belongs to some one there are two ways you can write this. For example you can write “the dog of the boy” or you can write” the boy’s dog.” Both mean the dog belonging to the boy. Another example: “The girl’s father or the father of the girl.” 2. It is also used to show a plural. “How many 4’s and 5’s are there in this number: 4415545?

APPENDIX – (noun) 1. Appendix means something that is added at the end of a book. “He found the additional information he needed in the appendix. In this book you will find all the pictures in the appendix. “2”. ” Appendix is also the name for a small tube that everyone has in their bodies. It grows out of the large intestine. When it gets inflamed it usually has to be removed, otherwise it might burst and the person would eventually die.

APPLICATION – (noun) An application is a spoken or written request for something. For example “you make an application for a job that is advertised. She was very happy because her first application was accepted.

APPLIED MATHEMATICS – (noun) means that section of Mathematics which deals with a particular practical subject. For example one could have a branch of applied mathematics which deals with the design and construction of motor cars, or another branch which deals with the building of dams. At universities the subject Applied Mathematics usually is that branch of mathematics which deals with objects and forces that are either stationary or in motion. See MATHEMATICS.

APPOINT – (verb) means to choose for some position such as being on a committee.” He was appointed as a member of the committee. ” “He was appointed headmaster last year.

APPOINTMENT – (noun) 1. Appointment means a meeting with someone at a definite time and place. See DEFINITE.” He did not keep his appointment and I wasted one hour waiting for him. I have an appointment to see my doctor at 10 am. You make an appointment and then you should keep it. I made an appointment to see my doctor today and I intend to keep it. ” 2. An appointment also means the act of being given a definite job or position. “ Although the old headmaster died a year ago no appointment has yet been made for the position of headmaster.

APPROXIMATE – (verb) When one is asked in a maths problem to approximate an answer, it means one only needs to work out the answer in a way that will give nearly the right answer; it is not necessary to work out the exact answer. It also means close to the right answer – (adjective)

APPROXIMATELY – (adverb) means nearly correct. “He guessed the boy’s height to be 1,5 meters. He was approximately correct because the boy’s height was 1,4 meters.

APPROXIMATION – (noun) An approximation is something that is approximately correct. “You would say that his guess” – (see APPROXIMATELY) “was an approximation.

ARABIC NUMERALS – (noun) 1,2,3,4,5,6,7,8,9,0 are called Arabic Numerals or Arabic Numbers. I, II, III, IV, V, VI, VII, VIII, IX & X are Roman numerals.

ARBITRARY – (adjective) means chosen as one pleases. This is the opposite of something that is fixed by a rule or law. “Whether he does his homework in the afternoon or evening is his arbitrary decision. That school is open from Mondays to Fridays is not his arbitrary decision.

ARC – (noun) This means part of the circumference of a circle. See diagram 16. It also means part of any curve.

ARCTIC – (adjective) means at or near the North Pole. See diagram 44. It also means very cold because it is very cold at or near the North Pole. “There are very few living things in the arctic regions because it is so cold.” See ARCTIC CIRCLE & ANTARCTI

ARCTIC CIRCLE – (noun) This is an imaginary circle on the earth’s surface that is parallel to the equator and sixty six and a half degrees north of the equator. See diagram 44. The arctic region is all the area north of this circle. In the arctic region the sun never sets. You should ask your teacher to explain this to you.

ARE. – (verb) See AM.

AREA – (noun) 1. Area means the extent or amount of surface.” The area of water on this planet is greater than the area of land. ” To calculate the area of a field you multiply its length by its breadth. See Appendix II.12 for some formulae for areas. 2. Area also means range of activity or interest. “He is a civil engineer with large buildings being his area.

ARITHMETIC – (noun) is the name of the subject that deals with addition, subtraction, multiplication and division of numbers.” His arithmetic was good and he got all the answers right. ” It can also be used as an adjective.” His arithmetic boo k was very neat.

ARITHMETIC MEAN – (noun) This is the same as AVERAGE. To find the average of several amounts you add up the amounts and divide the answer by the number of amounts. To find the average of the 5 amounts 2, 1,10,9 & 3 first add up 2+1+10+9+3, which equals 25. Now divide 25 by 5 and you get an answer of 5 which is the arithmetic mean of these amounts. See AVERAGE & GEOMETRIC MEAN.

ARITHMETIC PROGRESSION – (noun) is the name for a particular sequence of numbers – (see SEQUENCE). Each number is the preceding – (see PRECEDING) number plus a fixed number. For example 2, 4, 6,8,10 are such a progression, the fixed number being 2. The fixed number can be a negative number. For example in 20, 16, 12,8,4,0 the fixed number is -4. The fixed number is called the COMMON DIFFERENCE.

AROUND – (preposition) has several meanings. Firstly it means on all sides of. “There is a garden around the house. There are trees all around the city. ” Secondly it means on the outside edge of. “ He ran around the field. She wore a blanket around her shoulders. ” Thirdly it means approximately. “ He is around 80 years old. I will see you around 6 o’clock.

ARRANGE – (verb) means to put things into a desired order. “She arranged the flowers in a vase so that they looked beautiful. He arranged the furniture in the room so everyone could easily find a seat”.

ARRANGEMENT – (noun) An arrangement is the way something is arranged.” That is a beautiful flower arrangement. “It also means an agreement. “ They made an arrangement to play at his house after school.

ARRAY – (noun) An array is another name for a table that has rows and columns. See COLUMN.

ARREARS – (noun) means money that is owed and is passed the date agreed for payment. “When I get my bonus at the end of the year I will pay all my arrears.

ARROW – (noun) An arrow consists of a line with an arrow head at one end. See ARROW HEAD. An arrow in maths is usually used to point to something. A line with an arrow head at each end is used to show the distance between the two points of the arrow heads. An arrow is also used to show a vector. See VECTOR. An arrow shows direction by which way it points and also can indicate size or amount by its length. See diagram 4.

ARROWHEAD – (noun) See diagram 4.

ARTICLE – (noun) 1. Article is a word which means something you buy or own.” He bought 5 articles of clothing in the shop. ““The shop is full of articles for sale.” 2. An article is the general name for any piece of goods. “How many articles are there in the basket? There are ten articles in it. “3. Article also means a piece of writing.” I read the article in the news paper about the football match. That was an interesting article in the magazine. See ITEM. ” 4. In grammar article is the name for the words ‘a’, ‘an’ or ‘the’.’A’ and ‘an’ are indefinite articles and ‘the’ is the definite article.

AS – (conjunction) has a number of different meanings. 1. AS means when or while. “I saw him as he came around the corner. He shouted as he ran away from the thief. ” 2. AS means in the same way that.” Do as I do. “3. ‘AS FOLLOWS’ is used when some examples of what you have been reading are the next thing to be read. 4. AS means because. “He did not buy it as he had too little money.” 5. AS …..AS mean to the same amount. “I can write as well as you can. He ate as much as he could.

ASCEND – (verb) means to go up. He ascended the stairs means he went up the stairs. Ascending numbers would be 8, 9, 10, 11 etc or 1, 2, 3,4,5,6. 19, 18, 17 are DESCENDING numbers.

ASCENDING ORDER – (noun) means in increasing amounts. It is the opposite of DESCENDING ORDER. The numbers 5, 6, 7, 8, 9, 10, 11, 12 are in ascending order. 99, 98, 97, 96 are in descending order. a, b, c, d, e, f are considered to be in ascending order and p, o, n, m in descending order.

ASK – (verb) 1. Ask means to use words to find out something. “When he could not find the way to the church he asked someone to show him. The teacher asked the class to write down the answers to the questions on the chalk board. ” 2. Ask also means to invite. “ She asked 10 girls to her birthday party. ” 3. Ask also means to say what price you want for something that you want to sell. “ No one would buy the shirts because he was asking too high a price.

ASSETS – (noun) means things that one owns that are of value. The usual assets that a man has are money, goods – (like a motor car & furniture) and property – (land & buildings). You can also speak of other things as an asset. For example, “beauty is an asset for an actress.

ASSISTANT – (noun) 1. Assistant means someone whose job it is to help someone else do something. “The motor mechanic got his assistant to help him lift the engine.” 2. A person whose job it is to help people decide what they want to buy in a shop and also to take the money is called a SHOP ASSISTANT.

ASSOCIATE – (verb) 1. Associate basically means to join together in some way. It means to connect in thought. “In South Africa we associate Xmas with summer holidays.” 2. It also means to join with in some way. “She is associated with her mother in a bakery business.” 3. It also means to be friendly with.” He associates with the other boys in his school class.

ASSUME – (verb) 1. Assume means to take for granted without proof. “I assume you are correct.” 2. Assume also means to take on. “When his brother died he assumed leadership. He assumed an air of confidence. ”

ASSURANCE – (noun) usually means Life Insurance. See INSURANCE. A person who takes out a Life Assurance Policy must pay an agreed amount every month. See POLICY. The bigger the amount the more money will be paid out. When he dies his family will get p aid a big sum of money. For example if he paid R50 per month and he died his wife would be paid something like R100000. There are many kinds of assurance policies. You can find out more by asking an insurance company.

ASTERISK – (noun) is the name of the symbol that looks like this *. It is used to call attention to something or show that some words or letters have been left out. “Fill in the missing letters at the asterisks. Please note the instructions marked with an asterisk.

ASYMPTOTE – (noun) This a word that is used in describing a curve on a graph that approaches an axis and gets closer and closer to it without ever reaching it. See diagram 27; see LIMIT

AT – (preposition) means: 1. by or near. “He is standing at the gate.” 2. It means in. “She is at school.” 3. It means toward. “He aimed the gun at me.” 4. It means near the time of. “At midnight it is very dark.” 5. It means in a place. “The pole was at right angles to the ground”. 6. It means doing. “Be careful, there are men at work.” 7. It means for. “There are sweets at 50c each.

ATOM – (noun) First see the last definition in ELEMENT. If you divide an element into its smallest particles then those particles are called atoms. For example if you have the element iron then the smallest particle of iron that you can get is an atom of iron. An atom of iron still has the property of iron. If you split up an atom of iron into smaller pieces then those pieces are no longer iron. Atoms are very small in size and cannot be seen unless you use very special microscopes. See diagram 38.

ATTEND – (verb) has two main meanings. Firstly it means to be there. “He attended the meeting. He attended school in the day time and worked at night time. ” Secondly it means to look at and listen to what is happening so you know what is going on. “ The children who don’t attend to what the teacher is saying will not do well in their exams. ”

ATTENTION – (noun) is the name for the action of looking and listening so you know what is going on. “Because the children were very interested in what the teacher was saying they gave him their full attention. “ If you say to someone “Pay attention”, it means that you want them to attend carefully.

ATTORNEY – (noun) An attorney is another name for a lawyer. See LAWYER.

ATTRACT – (verb) 1. Attract means to draw to oneself. “Iron is attracted by a magnet”. 2. It means to be pleasing to. “This play attracts many people.

 ATTRACTIVE – (adjective) means winning attention. “The film star is very attractive.

AUDITOR – (noun) An auditor is a person whose job it is to check accounts systematically. “You need to have your accounts audited by a good auditor before you can submit your tax return.

AUTHORITY – (noun) 1. Authority means the right to give instructions. “A good teacher will have authority over his pupils. The captain has the authority from the general to tell his soldiers to shoot on sight. “2. It also means an organisation which is responsible for local government.” According to the local authority all these roads will be tarred next year.

AUXILIARY VERB – (noun) An auxiliary verb is a verb that is used to form the tenses and moods and voices of other verbs – (auxiliary means giving help). The following are auxiliary verbs: be – (am, are), have, do, can, must, may, shall and will are all auxiliary verbs. “He will be coming soon. I am leaving now. We are playing cricket. I have gone. She does believe. They can come. The boy must be punished. I shall go and he will go. She may still come. ” See TENSE, MOOD & VOICE.

AVAILABLE – (adjective) means that can be used or got hold of. “There were many boys available for the team, but only 11 could get into the team. There are 20 text books available, but we have 22 students.

AVERAGE – (noun) The average is the answer you get when you add up a number of figures and divide the total by the number of figures. For example if the ages of the six children in a family are 3,10,8,5,6& 4 then their average age will be 6. – (Total = 36 divided by 6 = 6) See ARITHMETIC MEAN.

AVERAGES – (from the verb ‘to average’) means that the average of something is. When you say the car averages 60 kph you mean that the average speed it travelled over a particular distance was 60 kph. See ARITHMETIC MEAN.

AWARE – (verb) 1. To be aware of something means that you have knowledge of that thing. “Are you aware that it is very dangerous to play in the street? She was aware that she was beautiful and all the boys were looking at her. ” 2. To be aware also means that you are alive and awake and able to sense things around you by seeing, hearing, feeling or smelling. “ He was aware of the tremendous heat of the fire. She is a very aware person; she usually knows what people are thinking about her.

AWAY – (adverb) 1. Away means at a distance from a place or from a person. “Stay away from the water. He walked away from me. He is far away. 2. “It means out of one’s possession…” He gave his dog away. 3. “It means without stopping.” He worked away all day long.

AXIOM – (noun) An axiom means something that is basically true. One can see that an axiom is true from common sense – (See SENSE) or because it is obvious – (See OBVIOUS) that it is true. Sometimes axioms are called LAWS or BASIC PRINCIPLES. An axiom is true because it can be seen to be true or because it is obviously true. Here are some axioms: 1. One plus one equals two. – (If you put one apple on a table and then you put another apple on the same table you can see that you have two apples – you don’t have to prove it).

2. Something that is heavier than water will sink and something that is lighter than water will float.

3. Space has three dimensions – (see DIMENSION). It is obvious that space goes from left to right, up & down and from back to front. See diagram 11.

4. The shortest distance between two points is a straight line. This is obviously true. See diagram 45.

AXIS – (noun) has 3 important meanings in maths. Firstly it means the line about which an object rotates. For example “the axis of the earth is the line joining the north and south poles.” See Diagram 44. “The axis of a wheel is the line which passes through the centre of its axle”. Secondly it means a central line or plane – (see PLANE) about which parts are arranged in a regular way. “The axis of the body is the line from the top of the head to a point between the feet. This is also called the axis of symmetry. ” See diagram 35. Thirdly an axis is a line from which you take measurements to get the location of a point. Look at diagram 18. See SYMMETRICAL.

AXLE – (noun) An axle is a round piece of material on which a wheel turns. See diagram 40.