RADIAL – (adjective) means coming from the centre like the radii of a circle. “The wheel of an ox wagon has radial spokes.” See diagram 51.

RADIAN – (noun) A radian is a measure of angle. A radian is equal to about 57 degrees. A radian is the angle at the centre of a circle subtended by an arc that is 1 radius long. See diagram 34 & SUBTEND.

RADIUS – (noun) The radius of a circle is a line from the centre to the circumference. See diagram 16.

RANGE – (noun) 1. Range means the distance a gun can fire a bullet. “When we get to the first trees we will be in range so you must be careful to take cover. “ 2. Range also means the distance between two limits. “In summer the temperature range is from 15 degrees to 30 degrees.” 3. Distance from a gun to the object aimed at. “He hit the animal with his first shot at a range of 1000 metres.” 4. The greatest distance an aircraft – (or any other vehicle) can travel on a full load of fuel. “This aircraft has a range of 2500 km so it can easily fly to Johannesburg without stopping for refueling. “ 5. Range also means a series of articles for sale. “She went to town to look at the summer range of clothes. “ As a verb range means: 1. To vary between two limits. 2. To wander.

RANK – (noun 1. Rank means a row. “The children lined up in 3 ranks. “ 2. It also means a level of command in an organization. For example in an army the rank of colonel is senior to the rank of captain. In a business the rank of manager is senior to that of secretary.

RATE – (noun) 1. rate is another word for amount. See AMOUNT. It is often used when talking about money and interest. See INVEST. “He moved his money to another bank because they will give him a higher rate of interest. The rate of interest is 10 per cent. “2. Rate also means speed. “ He was going at too fast a rate when he had the accident. ” 3. One also talks about the rate that something changes.” His rate of growth was greater when he was 10 years old than when he was 20. See diagram 19.

RATES & TAXES – (nouns) When someone owns a piece of ground one has to pay taxes to the local township committee or to the local municipality. See MUNICIPALITY. This money is used for running the township or municipality which allows it to provide services like water supply pipes, road repairs, dirt collection, sewage disposal. This kind of tax on the ownership of property is usually called Rates & Taxes. The amount that one must pay depends on the value of the property. Electricity and water usage are usually billed separately to the rates. One usually pays more for a plot with a house on it than for an empty plot.

RATIO – (noun) A ratio is a comparison between two quantities. See COMPARE. The comparison is made by dividing one quantity by the other. I am 20 years old and he is 10 years old so the ratio of our ages is 20/10 = 2. You can also say the ratio between our ages is 10/20 = 1/2. It depends on the view point. Both answers are correct: 2 and 1/2. In geometry you often talk about the ratio between one side of a figure and another side. For example in a triangle ABC the ratio of the side AB to the side BC is AB/B

RATIONAL NUMBER – (noun) A rational number is a number which can be written as a fraction made up of whole numbers. 3/4 or 22/7 or 121/13 are all rational numbers. 1/4,13 or 2,45/3 or 7,34/5,89 are all not rational numbers.

READY 1. Ready means prepared for action or use at once. “This car is full of petrol and ready for a long journey. The soldiers are trained and ready to fight. ” 2. It also means willing. “ The loyal soldiers are ready to die for their king. ” 3. Ready also means likely. “ That teacher is ready to find fault with the children. “4. It also means immediately available. “ Do you have any ready money?

REAL – (adjective) 1. Real means existing in fact and not in one’s imagination. The earth, your body and your shoes are examples of things that are real. What happened today at school is real. What you may have dreamed last night is not real, nor is what you would like to be, when you grow up, real. 2. In maths a real number is a rational number or an irrational number. See RATIONAL & IRRATIONAL NUMBERS.

REALITY – (noun) is the word used to describe the things around us that are real. “As a little girl she imagined what it would be like to have her own baby. When she got married and had her own baby she found that reality was very different to what she imagined it would be.

REASON – (noun) 1. Reason means the cause for something. “What is the reason you did not go to school yesterday? The reason is that I was sick. “2. Reason also means what is sensible. It is the same thing as common sense.” Reason demands that one learn to read and write and do arithmetic before one tries to get a job in an office. If you use reason you will do well if you don’t you will fail. ” 3. Reason also means to use your powers of thought. “ You must reason it out before you can answer the question. “4. If you reason with someone it means you discuss something with someone and ask them to see reason. “ When the boy wanted to run away I reasoned with him and got him to change his mind and stay.

RECIPROCAL – (noun) The reciprocal of a number is 1 divided by that number. For example the reciprocal of 4 is 1/4 and the reciprocal of 5437 is 1/5437. The reciprocal of 0,2 is 1/0,2 = 5. The reciprocal of 100 is 1/100 = 0,01. What is the reciprocal of 10000 and what is the reciprocal of 0.1?

RECORD – (noun) 1. A record is a putting of information in writing so that information is there for future use. “The secretary made a record of what was decided at the meeting”. 2. Record also means putting something in a permanent form like on a tape or disc “The record of this song has been made on both disc and tape.” 3. Record also means the best that has been done. “The record time for running 100 meters is less than 10 seconds. Next year someone may break the record.

RECORDING – (noun) is another word for record. “He made a recording of his song.

RECTANGLE – (noun) A rectangle is like a square, but two of the sides are longer than the other two. See diagram 7.

RECTANGULAR CO-ORDINATES – (noun) are co-ordinates which are at right angles to each other. See CO-ORDINATE & RIGHT ANGLE. See diagram 18.

RECTILINEAR – (adjective) means in a straight line. Motion that is in a straight line is called rectilinear motion.

RECURRING – (adjective) 1. Recurring means happening over and over again. “That is a recurring mistake; if you don’t stop making it you may fail your exam. “ 2. In maths one talks about a recurring decimal. In some division sums when one uses decimals you never get a final answer. For example if you divide 1 by 3 you get an answer of 0,3 with one to carry, but if you continue dividing you will continue getting a 3 with one to carry and this will go on as long as you care to continue. This is what is called a recurring decimal. It is written as 0,3+ . If you try dividing 22 by 7 you will find that this division also goes on and on without coming to an end. Try it!

REDUCE – (verb) 1. Reduce means to make smaller. “By working harder he reduced his losses to nothing and then started to make a profit.” See PROFIT & LOSS. 2. In maths reduce means to express everything in a smaller unit. If you are asked to reduce 2 metres and 20 centimetres to centimetres the answer will be 220 centimetres, but if you were asked to reduce it to millimetres the answer would be 2200 millimetres. The noun from reduce is reduction. 

REDUCING BALANCE – (noun) If one owes money and is making regular payments to pay it back then the amount of money one owes becomes less and less. The balance that is left over is called the reducing balance. If one is paying interest on the reducing balance then one can reduce the amount of interest one is paying by getting the balance down as fast as possible. “ He paid an extra amount of R500 off his loan with his bonus; as he was paying interest only on the reducing balance this has reduced his interest repayments.

REGARDLESS – (adverb) means not to take into account, not to pay attention to. “Regardless of my warning he stepped into the street and the bicycle bumped into him. She went to the party regardless of her mother telling her not to.

REGION – (noun) 1. Region means a large part of the surface of the earth. “Namibia is a dry region. The Free State is the region where most of the mealies are grown. “2. Region can also mean any part or area. “ The upstairs region of the building. She has a pain in the region of the stomach.

REGULAR – (adjective) 1. Regular means following the usual rule. “The regular time for starting work was 8 am. “ 2. It also means happening again and again at the same time.” While he waited he heard the regular ticking of the clock. ““When he fell asleep his breathing was regular. 3” “. “ Regular also means doing something again and again but not necessarily at the same time. “He was a regular watcher of TV sport. He always watched the football matches. ” 4. In maths regular means symmetrical. See SYMMETRICAL. See diagram 9.

RELATE – (verb) 1. Relate means to have a relationship with. John and Jane relate well because they like the same things. See RELATIONSHIP. 2. Relate also means to tell a story or give some information. “When he returned from his travels he related all the interesting things he did. “ RELATED – (adjective) 1. Related means to be of the same family. “I am related to him because he is my uncle’s son.” 2. Related means connected in some way. “His problem is related to him not being able to hear properly.

RELATION – (noun) 1. Relation has the same meaning as relationship. See RELATIONSHIP. “There is a relation between driving fast and the number of accidents that happen.” 2. Relation also means a person who is connected to you by blood or marriage. “She comes from big family and has many relations.

RELATIONSHIP – (noun) means being connected in some way. One can be connected by family. “My relationship to him is that he is my sister’s son.” It can be in business. “They are not friends, but they know each other because of a business relationship.” It can be about anything. “What is the relationship between cats and dogs?” The answer is they are both animals with four feet and are found in people’s homes.

RELATIVE – (noun) 1. Relative means the same as a family relation. “Because her father had 10 brothers and sisters who have all married and had children she has many relatives. “ 2. Relative also means in relationship to. “Yours is a big apple relative to the one I got.” This means that although your apple may not be a very big apple it is bigger than the one I got. The two apples are being compared to each other in relationship to their size. 3. Relative is also used in grammar. See RELATIVE PRONOUN, RELATIVE ADVERB and RELATIVE CLAUSE.

RELATIVE ADVERB – (noun) A relative adverb is a word which introduces a relative clause that acts as an adverb in relation to a verb. The following words are relative adverbs: Where, when, why. In the sentence: This girl only studies when she wants to, so she does not do well in class – ‘when she wants to’ is a relative adverbial clause. It relates to the verb ‘studies’ because it modifies it. See MODIFY.

RELATIVE CLAUSE – (noun) A relative clause is a clause which acts as an adverb or an adjective. One which acts as an adjective is relative to the noun which it qualifies. One which acts as an adverb is relative to the verb which it modifies. See MODIF Y. The man who I saw was my uncle. ‘who I saw’ is an adjectival relative clause because it qualifies the noun ‘man’. The boy spoke when he was told to. ‘when he was told to’ is an adverbial relative clause which modifies the verb ‘spoke’. See RELATIVE PRONO UN & RELATIVE ADVERB.

RELATIVE PRONOUN – (noun) A relative pronoun is a word which introduces a relative clause and also stands for a noun. The following words are relative pronouns: Who, whose, whom, which, that. In the sentence: The boy who is very clever will come top o f the class, ‘who’ stands for the boy and so is a pronoun and also introduces the relative clause ‘who is very clever’ which relates to the noun ‘boy’ because it acts as an adjective describing the noun ‘boy’.

RELIABLE – (adjective) means that it can be relied upon. See RELY.” He is a reliable worker. He always comes to work on time and his work is always good.

RELY – (verb) means to have confidence on something or someone to always do what is needed. “When he climbs on the high roof he will rely on this rope to stop him from falling if he slips. I always rely on him to help me when I get very busy. It is no good relying on him because he is not trustworthy.

REMAIN – (verb) means to continue in the same way. “Although it was dangerous the captain told the soldiers to remain calm. Half of us left and the other half remained behind.

REMAINDER – (noun) 1. The remainder is what is left over after some has been taken away. “Most of the sailors were drowned in the storm. The remainder swam onto the beach”. 2. In arithmetic the remainder is what is left over after a subtraction. For example: What is the remainder when you take 10 away from 15? The remainder will be 5. 3. Also in arithmetic when you divide one number by another number which does not go into the first number an exact number of times what is left over is called the remainder. For example: When you divide 10 by 5 you find that 5 goes into 10 exactly 2 times – (10 – 2 x 5 = 0) so the remainder is 0, but if you divide 13 by 5 you find that 5 goes into 13 only 2 times with a remainder of 3 – (13 – 2 x 5 = 3). In division the remainder is always less than the number you are dividing by. For example if you divide 11 b y 3 the correct answer is not 2 with a remainder of 5 – (11 – 2 x 3 = 5) because 3 will go another time into 5. The correct answer is 3 with a remainder of 2 – (11 – 3 x 3 = 2) See DIVIDE.

REMOVE – (verb) means to take away by moving from one place to another.” He removed the furniture from the room to make space for more people.

RENT – (noun) is what a person pays the owner of a building or room to be able to use that building or room. Rent is usually payable every month at the beginning of the month.” The monthly rent for that house is R500. ” Rental means the same as rent.” What rental are you paying for that house?” See LET.

REPAYMENT – (noun) A repayment is an amount of money paid back to someone who is owed money. “He is worried because he is behind with his repayments on his house, but he will be able to catch up when he gets his bonus. “ See BONUS.

REPEAT – (verb) means to do another time. “The drum beat repeated over and over. Repeat after me what I say. Because the students did not understand what she taught she said she would repeat the lesson.

REPEATING – (present participle) means happening again and again. “The repeating noise of the drums kept us awake.

REPRESENT – (verb) 1. Represent means to act for someone else. “Because the headmaster was sick he was represented by the assistant headmaster at the end of the year ceremony”. See CEREMONY. 2. Represent also means to be a symbol for something else. See SYMBOL. A red triangle represents danger. “Each letter of the alphabet represents a sound.”

RESERVE BANK – (noun) The Reserve Bank is the Central Bank of the country. The Reserve Bank is responsible for printing money and making coins. Interest rates and the supply of money are controlled by the Reserve Bank. All the other banks in the country have to work by the rules made by the Reserve Bank.

RESIST 1. Resist – (verb) means to act against. He resists all attempts to get him to study. The soldiers resisted the attack and pushed the enemy back. 2. The noun is resistance. “After they were beaten for the third time they gave up all resistance.” Resistance has a special meaning to do with electricity. See your physics text book.

RESPECT – (verb) 1. Respect means to have a good opinion of someone or something. “ The children in this teacher’s class always do well, so the school has respect for his knowledge and good methods of teaching. “ 2. You can also say “the school respects this teacher.” 3. Respect as a noun means good opinion or admiration. “That teacher gained the respect of the children.” 4. If you say something is good in all respects then you mean it is good in all ways. “This car is good in all respects: it has a good engine, excellent brakes, it uses little petrol and is comfortable.

RESPECTIVE – (adjective) 1. Respective means belonging to each. “After the lunch break the children went to their respective class rooms. “ 2. In geometry respective has a special meaning. See diagram 14.

RESULT – (noun) 1. Result means what happens because of some action. “The result of his hard work is that he got an increase in pay.” “The result of the fire was that his furniture was burned.” 2. Result is often used when speaking about how well a person did in an exam. “I am expecting a good exam result. We will see when the results come out.

RETIREMENT ANNUITY – (noun) When a person reaches the age when he stops work – (usually 65) he is said to retire. One of the things that you can get from an Insurance Company is called a Retirement Annuity. See ANNUITY. You can buy an annuity when you retire or you can have been paying for it month by month over a long period while you were still working. Depending on how much you have paid and at what age you retire the Insurance Company will pay you an amount of money every month until you die. It is similar to a pension. See Pension.

RETRIEVE – (verb) means to do whatever is necessary to get something back. “He retrieved his hat from the lake by using a long pole with a hook on the end. He retrieved his book which had fallen between the back of the chair and the wall. ” Retrieve and recover mean the same in this sense.

RETURN – (verb) means to come back or to go back. “After the holidays we will return to school. He did not like Johannesburg so he returned to Cape Town.

REVERSE – (verb) 1. Reverse means to go backwards. “He reversed the car into a pole because he could not see it easily. “ 2. The reverse – (noun) of something is the opposite of that thing. See OPPOSITE. “I asked him not to touch the wet paint, but he did the reverse”. 3. In reverse means backwards. “This time he did it in reverse; he started at the end and worked his way back to the beginning. “ 4. In reverse – (adjective) order means starting from the end and coming back to the beginning. “He did it in reverse” “order starting at step 10 and working his way back to step 1.

REVISE – (verb) 1. Revise means to go over your work again to learn what you still do not know. “Because he had time to revise all his subjects he did well in the exams. “ 2. Revise also means to read through carefully to correct and improve. “Every year he revises his book on motorcars to keep up with the latest models. 3. “It also means to change one’s opinion about something after some time has passed.” After John scored 5 goals in one match I had to revise my ideas on whether he should be dropped to the second team.

REVISION – (noun) is the action of revising something.

REVOLUTION – (noun) 1. A revolution is one complete turn – (360 degrees – See diagram 4) of a wheel or anything that rotates or revolves. “The top was spinning so fast that it did many revolutions before it fell over. When the car is going as fast as it can its engine is rotating at 7000 revolutions per minute. ” See ROTATE & PER. 2. A revolution is also when the people rise up and try to overthrow the government. “In the French revolution the people took over the government from the King of France.

REVOLVE – (verb) means to turn on an axis. See AXIS. “A wheel revolves on its axle”. See AXLE.

RHOMBUS – (noun) A rhombus is a parallelogram with 4 equal sides. See Diagram 7. See PARALLEL.

RIGHT – (adjective) 1. Right has several meanings. Firstly it means correct. Because I got all the sums right I got full marks. 2. It means agreeing with what is good. “It is not right to steal. It is right to help an old person across a busy street. “3. It means the opposite of left. “ Most people write with their right hands. “4. In geometry it means something to do with a right angle. See RIGHT ANGLE. See diagrams 14IV & 21 for a Right Triangle and a Right Cone.

RIGHT ANGLE – (noun) Four right angles make up a circle. See diagram 4. Two right angles make up a straight line. The angle between an upright wall and a level floor is a right angle. See diagrams 5 & 4.

RIGHT CIRCULAR CONE – (noun) This is a cone with a circular base and with its axis at 90 degrees to its base. See diagram 21.

RIGID – (adjective) 1. Rigid means not easily bent. “You need a rigid pole to lever up that heavy rock. “ See LEVER. 2. Rigid also means not easily moved. “The little boy tried to escape, but the man held him rigid. “ 3. Rigid rules mean rules that are not easily changed.

ROOT – (noun) 1. A root is that part of the tree which grows underground. Roots are like underground branches. “The wind blew the tree over because its roots did not go deep into the ground.” 2. The part of a tooth that grows in the gum is also called a root. That part of a hair that grows below the skin is also called a root. 3. The root of a number also has a special meaning in maths. See SQUARE ROOT & CUBE ROOT. 4. Also in maths the roots of an expression like – (x – 2)(x + 1) = 0 are the values of x that solve the equation. When the values of the terms in either of the brackets are equal to 0 the equation is solved. So the roots of this equation are x = 2 and x = -1. In the expression – (2x + 3)(x – 5)(x + 2) = 0 the roots are -2/3, +5 and -2 – (each of these values for x makes the value of one of the brackets equal to 0).

ROTATE – (verb) 1. Rotate means the same as revolve. See REVOLVE. 2. It also means to change on a regular basis. “We rotate shifts each week”. “One week I do the morning shift and he does the afternoon shift. The following week we rotate and he does the morning one and I the afternoon shift. “See SHIFT. “

ROTATION is the noun from rotate. “The moon does one rotation around the earth about every 28 days.

ROUND – (adjective) 1. Round means the shape of a circle or the shape of a sphere. “The shape of a ball is round. The shape of a record is round. “2. It also means a section in a game like a round of golf or a round in a boxing match. “ He was knocked out in the third round” – (noun). 3. It also means a bullet for a gun. “He fired four rounds at the thief.” 4. To round means to go around. “The car rounded” – (verb)” the corner at great speed. ” 5. To round also means to make round. “ He rounded the corners of the wood with a plane. ” See PLANE. 6. In maths you round off a figure. If you round off 659 823 497 – (spaces have been put after each 3 digits to make it easier to read the number) to the thousands you will get 659 823 0 00, and if you round it off to the 10 thousands you will get 659 820 000 and if you round it off to the millions you will get 659 000 000.

RUMOUR – (noun) means a story that is passed from person to person that may not be true. “ There is a rumour going around that John is the one who stole the missing books, but I don’t believe that it is true. “ “It is easy to start a rumour, but not so easy to stop it.