EARN – (verb) means to get in exchange for doing something. “He will earn R1000 for doing that job of work. People who always help others in difficulty earn their thanks. ” See EXCHANGE. Invested money earns interest. See INTEREST.

EAST – (noun) is the direction from where the sun rises.” If you look to the east you will see the sun rising. “When you face North, East is on your right hand side”. See diagram 39.

ECONOMICAL – (adjective) means to avoid waste and to use things so you get the most from them. “If you are economical your money will go a long way. An economical person does not waste things.

ECONOMICS – (noun) is the subject of production, distribution and consumption of goods and services. It deals with the problems of costs, prices, capital, labour, and wages. See PRODUCTION, CAPITAL, DISTRIBUTION & CONSUMPTION.

ECONOMY is the noun that relates to economical – (See RELATES & ECONOMICAL), but it also has another meaning when talking about a country. The economy of a country is the system of managing the production, distribution and consumption of goods and services. See ECONOMICS. If the economy of a country is well run then all the people who are educated and willing to work will have money and good jobs.

EDGE – (noun) An edge is the part on the side of something. A square piece of paper has 4 edges. A square box has 12 edges. A triangular piece of paper has 3 edges.” I bumped myself on the edge of the table.

ELECT – (verb) means choose someone by voting. One can cast one’s vote by a showing of a hands. Alternatively one can have a secret ballot where one marks one’s choice on a piece of paper and puts it into a ballot box. See VOTE.

ELECTRON – (noun) An electron is the smallest particle of electricity. An electric CURRENT consists of a stream of electrons that is flowing along an electric wire. Electrons are very small and cannot be seen by the eye. Electrons are also one of the things that an atom is composed of. See diagram 38. See PARTICLE, STREAM & FLOW.

ELECTRONIC – (adjective) means to do with the flow of electrons. ELECTRICITY is made up of electrons. Electrons are very small particles of electricity, so small that you cannot see them. In electronics the flow of electrons is controlled by TR ANSISTORS. See TRANSISTOR. All sorts of automatic things can be made to happen using electronics. For example all the wonderful things that can be done with computers depend on electronics. The following things also depend on electronics: radio, TV, calculators, some clocks and watches, tape recorders.

ELEMENT – (noun) 1. An element is one of the basic parts that something is made up of. “The main elements of a school are the teachers, the pupils, the classrooms and the school books.” 2. Element also means the most basic parts of a subject. “Before one can learn more advanced maths one must know the elements of arithmetic: addition, subtraction, multiplication and division. “ 3. An element is also the name of the part that gets hot in an electrical device. See DEVICE. An electric light bulb has an element, so does an electric heater. 4. In maths, element is the name for a member of a set. A hammer is one of the elements in my set of tools. In the set – (5, 6, 7, 8) 5 & 6 & 7 & 8 are all called elements of this set. See diagram 36. 5. Here is another use of the word element. Matter is composed of elements. The names of some of the elements are hydrogen, oxygen, nitrogen and carbon. See COMPOSED.

ELEVATE – (verb) means to raise up above the usual level or above the surrounding objects. “By standing on a chair the man elevated himself above the heads of those around him. The crane elevated the load onto the lorry. An elevator is another name for a lift.

ELEVATION – (noun) is another name for altitude. See ALTITUDE.

ELEVATOR – (noun) An elevator is the small room that carries people up and down in a building. It is also called a lift.

ELIMINATION – (noun) 1. Elimination means the action of getting rid of or removing something. For example “his team was eliminated from the contest in the first round. 2. “It can also mean getting rid of someone by killing them. “ The soldiers eliminated the two spies they discovered. ” 3. In maths it means getting rid of an UNKNOWN quantity in two or more EQUATIONS by combining them. To fully understand this, look at the examples in your maths text book and ask your teacher if necessary.

ELLIPSE – (noun) An ellipse has the shape of a flattened circle. See diagram 17. It is a Conic Section. See diagram 26.

EMBARRASS – (verb) means to cause a person to feel ashamed, uneasy and to have his attention on himself. See ATTENTION. People often feel like this when they have to stand up in front of a lot of people and do or say something.” She felt embarrassed when she had to ask a boy to take her to the party. He was embarrassed when he had to sing to the crowd.

EMPHASIZE – (verb) means to give something special importance. There are many ways that you can emphasize something. You can emphasize a word by speaking it louder than the other words or you can emphasize a written word by underlining it. “The teacher emphasized the important parts by saying them slowly, clearly and loudly.

EMPIRICAL – (adjective) means based on experiment and observation. See EXPERIMENT and OBSERVATION. It is an empirical fact that a stone is heavier than water because when you put a stone into water it sinks. If you have a glass of cold water and another glass of hot water you can tell which is which by putting a finger first into the one and then into the other. This is called an empirical test. THEORETICAL is the opposite of empirical. See THEORETICAL.

EMPLOY – (verb) means to give a job to. “This big firm” – (See FIRM) “employs many people. As his business grew bigger he was able to employ more people.

EMPLOYMENT is the noun from employ.” You need employment to get money.

EMPTY – (adjective) means having nothing in it. “He drank all the water so the glass was empty. I have spent all my money. My pockets are empty”. In maths empty has a special meaning. See SET.

ENDORSE – (verb) 1. Endorse means to support. When he got the committee to endorse his plan he knew he would succeed with it. 2. Endorse also means to sign your name on the back of a cheque. This is required in some cases by a bank before they will pay out the cheque. For example if a crossed cheque is made out to yourself and you do not wish to bank it, but use the same cheque to pay that amount of money to someone else, you must first sign the back of the cheque with your usual signature. This is called endorsing the cheque. See CHEQUE. See diagram 43.

ENERGY – (noun) 1. Energy means ability and willingness to do things.” He is full of energy. He plays football in the mornings and rugby in the afternoons. It takes a lot of energy to pick up that heavy box. You use up your energy doing that hard work. “2. In SCIENCE work and energy have special meanings. Look in your science text book for the definitions. 3. The conversion of matter into energy was worked out by a famous scientist called Albert Einstein. He worked out the formula for the conversion of matter into energy: E = mc&>2 &> where E = the energy of a certain object, m = the mass of that object and c = the speed of light. A small amount of mass produces a very large amount of energy – (as in an atomic bomb) because c is a very big figure.

ENFORCE – (verb) means to see that something is done.” The teacher enforced “- (by her authority)” the rule of not being late. The government enforced” – (by the rule of law) “the law that people who steal should be locked up.

ENTER – (verb) 1. Enter means to go in.” When you enter the house take off your hat. Do not enter because it is dangerous. “2. Enter has a special meaning in Bookkeeping. It means to write information into a book. “The book keeper entered the month’s sales figures into the Ledger. The cheques are entered into the Cash Book”. See ENTRY.

ENTRY – (noun) 1. Entry means a going in.” The king’s entry into the meeting was greeted with cheers. “2. In bookkeeping an entry is an amount of money that is written into one of the books. You say “you make an entry”. This means you write the amount into the book. See DOUBLE ENTRY.

EQUAL Equal means the same in size or in number. 1.” Two and two are equal” – (adjective) “to four.” “The two boxers were equal in weight. They both weighed 70 kilograms. “See EQUALS.

EQUALITIES – (noun) See Appendix II.7.

EQUALITY – (noun) means a condition of being equal. “Prove the equality of the two sides of the equation.

EQUALLY. Adverb of equal. “He spaced the fence posts equally. They were all 3 metres apart. They did equally well at school. Both got C passes.

EQUALS – (Verb) Equals means that one thing is equal to another. See EQUAL. Examples:” 4 plus 2 equals 6, 5 times 2 equals 10, 10 divided by 5 equals 2. ” The equals sign is =.

EQUATE – (verb) means to make equal or to consider to be equal. “He equated wealth with happiness and could not understand why he was not happy when he stole a lot of money.

EQUATION – (noun) An equation is a statement that two expressions are equal. He proved – (See PROVE) the equation to be true by showing that the LHS – (left hand side) was equal to the RHS – (right hand side). The following are examples of equations: a + b = c + d, x + y = z, 2x = 5y + 3. See STATEMENT & EXPRESSION.

EQUATOR – (noun) is the name of the imaginary line that goes around the earth half way between the North and South poles. It is an imaginary line. See diagram 44.

EQUIDISTANT – (adjective) means being at an equal distance from. When you stand in the centre of a room you will be equidistant from the four walls. All points on the circumference of a circle are equidistant from the centre. See diagram 16.

EQUILATERAL – (adjective) means having equal sides and equal angles. In an equilateral triangle each angle is 60 degrees. See TRIANGLE & diagram 13.

EQUIPMENT – (noun) is all that is needed to carry out some particular job. The usual equipment to build a house is: hammers, shovels, a concrete mixer, wheel barrows and things like that. Things like bricks, sand, cement, wood are not building equipment they are building materials. Equipment for working on a car would be things like spanners, screwdrivers, pliers and things like that.

EQUIVALENT – (adjective) is a word used to mean equal when you are speaking about things which cannot be measured exactly. “His advantage in weight is about equivalent to my advantage in speed. Running 5 kilometres gives you exercise equivalent to riding a bicycle 20 kilometres.

ERROR – (noun) 1. An error means a mistake. “He made an error because he said 2 plus 3 were equal to 6. “ 2. Error can also mean the difference between the wrong answer and the correct answer. In the above example the true answer is 5 so the error is 6 minus 5 which is 1. So the error is 1 in this example.

ESTIMATE – (verb) 1. To estimate means to work out by some method an answer which is not completely correct, but which is close to the correct answer. For example,” he estimated that it would take two hours to climb the mountain and one and a half hours to climb down again, a total of three and a half hours. He therefore decided to climb the mountain that afternoon. “2. The word estimate also means the price worked out by a builder to build a house. He estimates what the materials and the wages of the workmen will cost and then adds his profit. This is called a quotation which he gives to the person who wants the house. If that person is satisfied with the price he signs a contract with the builder who then will go ahead and build the house. This is called an estimate because the builder cannot be sure exactly how much material he will use and exactly how many hours his men will take. He will only know this for certain after the house is built and he can add up all the costs.

ETC is short for ETCETERA.

ETCETERA stands for ‘and so on’ which means the rest of a lot of similar things. For example: “the names of the boys in the class were John, James, Philip, Peter, Thomas etc”. This saves you from having to write down the names of all the boys in the class.

EVALUATE – (verb) means to find out or work out what the value of something is. “Before climbing the steep mountain he evaluated the danger.” “Evaluate the sum of 2 plus 3.” You will see that in the first example the answer was not an exact thing – just how dangerous he thought climbing that mountain would be. In the second case there is an exact answer. It is 5.

EVALUATION is the noun from EVALUATE.” He made a good evaluation of the runners and chose the boy who won the race.

EVEN has several meanings. 1. In mathematics it means that it can be DIVIDED by 2 without any REMAINDER. 2,4,6,8,10,12,14,16,18, 20,22, 242, 4896 etc are all even numbers because you will see that 2 goes exactly into all of these numbers. The opposite of EVEN is ODD. The odd numbers are the numbers which lie in between the even numbers. When you try to divide them by two you will see that there is a REMAINDER of 1. 1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 55, 179, 5467 etc are odd numbers. You will see that you only have to look at the last figure to decide if a number is odd or even. In 5467 you only look at the 7. It cannot be divided by 2 exactly so it is an odd number. In 4896 you only look at the 6. It can be divided by 2 without remainder so it is an even number. Secondly even means not rough. “You need an even surface to write on.” Thirdly it also means of the same height. “The country was not even because of the many hills.

EVEN NUMBER – (noun) See EVEN.

EVENTUALLY – (adverb) means after some time.” I waited for him and he eventually arrived after many hours.

EXACT – (adjective) means correct or without any error. “Because he paid the exact amount he did not get any change. The teacher asked for an exact answer and he would not accept a guess. ” See EXACTLY.

EXACTLY is the adverb from exact.” He answered all the questions exactly so he got 100 per cent. You must have exactly the right key to open the lock. “When you tell another person something and he answers with the word ‘exactly’ he means that he agrees exactly with what you are saying.

EXAGGERATE – (verb) 1. Exaggerate means to make something greater than it is. “He exaggerated the difficulty of his job to make him seem important. “ 2. It also means to go beyond the truth. “Don’t believe what he is saying because he always exaggerates.

EXAMPLE – (noun) 1. Example means one thing used to show what others are like.” Cape Town is an example of a city built between the sea and a mountain. ” 2. In maths it means something that shows the working out of a problem. 2 + 2 = 4 is an example of ADDITION. 4 x 3 = 12 is an example of MULTIPLICATION.

EXCEPT – (preposition) means leaving out. “All the boys except Peter can have the day off. We work every day except Sunday.

EXCEPTION – (noun) 1. An exception is something that does not follow the rule. For example a rule is that a year has 365 days, but a leap year has 366. So a leap year is an exception to the rule. Another rule is that men have deep voices. So if there was a man with a very high voice you would say he is an exception. 2. An exception is also something that is left out.” I like all my class mates with the exception of Bill.

EXCHANGE – (verb) means to give something for another thing. When a person buys something he exchanges money for the goods he wants. See GOODS. “The two little boys exchanged their toys. What will you give me in exchange “- (noun)” for this interesting book”?

EXCHANGE RATE – (noun) the exchange rate gives the number of Rand for a unit of foreign currency. For example “the exchange rate of Rand to US dollars was about R2,5 = 1 US$.” See FOREIGN EXCHANGE.

EXCLAMATION – (noun) An exclamation is something you say when you have a strong feeling about something. An exclamation is followed by an exclamation mark. Here are some examples. An exclamation of surprise – “Oh!” of disgust – “Oh no!”, of agreement -” Ah yes! “ , of surprise – “ Goodness me!

EXIST – (verb) means to be here in the world around us. If I say I exist then I mean that I am alive and am here. If I say plants exist I mean that there are plants in the world around us. When you talk about living things existing then you usually mean that they are still alive.

EXPAND – (verb) 1. Expand means to make bigger or become bigger. “The balloon expanded when he blew it up. He ate so much that his stomach expanded. “2. In maths it means to multiply out something. For example when you expand 2&>3 &> you get 2 x 2 x 2. When you expand – (a + b)(c + d) you get ac + ad + bc + bd.

EXPANSION is the NOUN from EXPAND. “The expansion of the balloon was so much that it burst. The expansion of 2&>3 &> is 2 x 2 x 2. ” &>

EXPENSE – (noun) An expense is something you get that costs you money. For example the expenses of running a business are: Rent, telephone, wages, materials and things like that. The expenses when you travel would be things like: railway ticket, hotel and food.

EXPENSIVE – (adjective) means costing a lot of money or costing more money than you would expect. “She wears expensive clothes; she buys only the very best clothes. That shop is expensive; everything costs more than at other shops.

EXPERIENCE – (noun) 1. An experience is something that you did or something that happened when you were there. “Going out in a small boat in the storm was a dangerous experience. His journey through the mountains was an interesting experience. ” 2. When you say ‘experience’ without ‘an’ or ‘the’ before it, it means something slightly different. It means all t he experiences you have had, particularly those experiences which have taught you things. “We need a man who has had experience before in this sort of work. Without experience it is difficult to get a good job. “3. Experience can also be used as a verb. “ He likes to experience exciting things.

EXPERIMENT – (verb) 1. To experiment means to try something out to see if it works. “Edison experimented with thousands of different materials before he discovered the element for the electric light bulb.” “The cook experimented with different kinds of food until he got the taste just right. “ 2. Experiment is also used as a NOUN. “He did an experiment to see if his idea would work.

EXPLAIN – (verb) means to tell someone about something so that he can clearly understand that thing. “Explain what the word ADD means. When the teacher had explained what the meaning of the words theorem and corollary meant the children could understand the example. ” See COROLLARY & THEOREM.

EXPLANATION – (noun) 1. An explanation is an explaining. See EXPLAIN. “Because the teacher gave the pupils a clear explanation they all understood the ““lesson. “ “2.” An explanation also means giving the reasons why something was done that should not have been done.” When he came home very late his mother asked him for an explanation. The manager was satisfied with his explanation of why the goods arrived late. 

EXPONENT – (noun) in maths means the number written to the right and a little above another number to show how many times that number must be multiplied by itself. 5&>1 &> = 1 x 5 = 5. 5&>2 &> = 5 x 5 = 25. 5&>3 &> = 5 x 5 x 5 = 125 and so on. 2&>5 &> = 2 x 2 x 2 x 2 x 2 = 32.

The number above and to the right is called the exponent, but when you read it out you say 5 to the first power; 5 squared; 5 cubed; 5 to the fourth power; 2 to the fifth power and so on. See SQUARE & CUBE. When you see a number written like this 4&>3 &> , then the number on the bottom is called the BASE and the small number on the top is called the exponent. See INDEX.

EXPONENTIAL CURVE – (noun) y = a&>x &> is another exponential equation. Its graph can be seen in diagram 32. This graph is an exponential curve.

EXPONENTIAL EQUATION – (noun) This is an equation where the unknown is an exponent. For example 3&>x &> + 2 = 11.

EXPRESS has 3 main meanings when used as a verb. 1. It can mean to put into words. “ He could express his ideas easily in Xhosa, but not in English. “ 2. It can mean to press out. “He expressed the juice from the lemon.” 3. And it can mean to send something by a quick method. “Because I needed the goods urgently he expressed them to me by air”. 4. Express is used as a noun to mean a fast method of transportation. “He sent it to me on the express” – (Usually meaning the express train). “ Air express is quick, but it is expensive.

EXPRESSION – (noun) 1. An expression means a way of saying something. “Come and sit beside me’ ” is an expression of friendliness.”Shut up’ ” is a rude expression telling someone to stop talking or making a noise. You can have as many kinds of expression as there are things you can say in words. 2. In maths, expression has a special meaning. It is any mathematical quantity wit h symbols and numbers in it. The following are all mathematical expressions: 3x + 7; ax + by + cz; x + y . A TERM is any one of the quantities which make up an expression. In ax + by + cz, ax is the first term, by is the second and cz is the third term. See COLLECT.

EXTEND – (verb) 1. Extend means to reach out. “He extended his arm to pick up the cup.” 2. It means to make longer. “The teacher told us to extend the line until it reached the edge of the paper. He extended his holiday for another 4 days. ” 3. To extend a line. See diagram 2.

EXTENT – (noun) means the amount to which a thing extends. “To what extent will you help us, “simply means how much help will you give us?

EXTERIOR – (noun) means that which is on the outside. “You should paint the exterior of your house when the walls are dry.” An exterior angle is an angle on the outside. See Diagram 13. Also see diagram 5.

EXTERNAL – (noun) means to do with the outside of something. It has a similar meaning to exterior. He gave the house an external coat of paint means that he painted the outside of the house.

EXTRA 1. Extra – (adjective) means in addition to what one would normally expect.” I did not expect the extra expense. She was generous; she gave all the children an extra helping of food. ” 2. – (noun) Extra can also be used as a noun to mean an extra thing. “ When he bought the car he got a seat cover thrown in as an extra.

EXTRACT – (verb) means to take something out of something else. “He extracted the juice from 4 oranges to make a nice drink. He extracted the information he needed out of the big book.

EXTRAPOLATE – (verb) means to use the information you know to predict what other information is likely to be. See PREDICT. “ He extrapolated from the fact that it rained every April for the last 3 years that April was not a good time for a holiday. “ Graphs are often used to help with extrapolation. See diagram 32.