Grade 12 Maths Literacy CAPS Complete Syllabus – Revision



her great twelves my name is Annette stineman and I'm going to be taking you through all the mathematical literacy topics I just need to remind you that in your to exam papers you do all the different topics it's just the levels of the two papers that actually very okay so I'm going to take you through measurement through daughter handling probability you're also going to do a scale and with maps and then finally we are going to be doing graphs okay so let's start with measurement now two of our main things in measurement or conversions and Tom and I let's have a look at our measurement we have three different systems and that is our length mass and volume and it's important that you know these conversions of our heart it's the Imperial measurements that you will be given the conversions for okay so I have a ram that you can use for this for our length we go King Henry died a miserable death called measles for our mess we have the same exactly the same room except we change it from from miserable to gross so we're going to go King Henry died a gross death called measles and finally in our volume we say King Henry died a lousy death called measles now in our mess in our volume we only actually use the first one at the top are kilograms and killer litres are grams and liters are milligrams and are milliliters so converting from the one to the other there is quite easy okay so in the metric system when we convert from the top down the units are getting smaller and for each unit down you must multiply by ten however when we convert from the bottom up the units are getting bigger and you have to divide by ten so if we have a look at our system over here when you are going from the bottom up they are getting a bigger so you have to divide so you divide up and then coming down we have to multiply okay let's have a look at some of the units okay so he has our metric units and here are our Imperial ones so when we are talking about mass we've got our grams and milligrams and the imperial equivalents that we would use is your answers so our answers is the smallest imperial measurement then kilograms and pounds are the two that go together and then we have tons and we have tonnes and notice there is a different spelling in that one when it comes to our measurement we've got millimeters in the metric and inches which is i-n meters we equate to fit and kilometers we equate to miles and our hectares we equal area measurements we've got milliliters and fluid answers we've got liters and killer liters and gallons okay let's have a look when we can avert within the imperial system now the imperial system measurements you will always be given and you'll be given the easy conversions in the question where you actually need to use them okay so we're in our length over here twelve inches is one foot three feet is a yard 1769 yards is a mile as well as your volume conversions another conversion that we do as temperature conversions and how you often have to convert from degrees Celsius to Fahrenheit or vice versa and again the formula will be given to you when we have solids to liquids your volume can either be measured using different units so we can either use our cubic unit so for example a centimeters cubed or we could use liters okay so we've got the one in centimeters and then we've got the other ones in our different liter units now the conversions are as follows for solids to liquids and one of them should be given if it needs to be used so one milliliter is equal to one cubic centimeter that is a good one to actually memorize in case you are not given it and it's not a difficult one to remember Canha a liter is a thousand cubic centimeters and a kiloliter is one cubic meter at least thought with some examples so I want to write the ratio of two kilometers to 1500 meters in simplified form okay so let's have a look at that so what we going to do is we're going to do two kilometers to 1500 meters now the first thing when you have to go into a ratio these two units must be the same so we're going to use a conversion here and it's easier to change your kilometers to meters so from kilometers to meters if you go on your system looking Henry died a miserable so you're going to come down like this so we've got three jumps so you're going to have to multiply by a thousand so two kilometers becomes 2,000 meters and when you've got the two into the same units then you do not need to write the unit's in okay so now we're going to simplify this you can do this on your calculator or it's quite an easy one so we can cancel two 0s on each side and then five goes into both of those five goes into twenty four times and into 15 the three times okay so your simplified form the mass go down to four over three now remember you can actually use your calculator and on the calculator what you would do is you would actually do your duo divide something so you'd go to thousand you divide that by 1500 when you've got the same units and now you can see it is a 4 over 3 and remember that a fraction is just the same as a ratio just written in eight different formats ok let's move on to the next example yes in this example we're going to determine the number of 250 centimeter lengths that can be cut from a roll of material that is a hundred and twenty meters long okay so let's have a look so each of the pieces or 250 centimeters and the row that we've got is a hundred and twenty meters long and we want to know how many of these can be cut from this ok so again you can see our units are not the same so we're going to convert so we're going from meters to centimeters yes goes King Henry died a miserable death called measles we're now going from meters to centimeters it's two jumps are we going to multiply by a hundred so 120 meters becomes 12,000 centimeters so then for our number of legs you've got to take your 12,000 and you're going to divide that by 250 okay so let's do that on the calculator guess it's going to be 12,000 divided by 250 so it gives us exactly 48 okay so this is 48 pieces okay so the important thing to remember when you're doing ratio or measurements in any of the sections in fact if your units are not the same you must first convert to the same units let's have a look at the next example contaminated water can be made safe by adding a bleach to the water and leaving the mixture to stand for a minimum of two hours before use now one teaspoon of bleach can be added to 25 liters of water or five drops can be added to one liter of water okay so let's just write this down so you can get one teaspoon into 25 liters or we can use five drops and the five drops can go into one liter of water now the drinking water can then be stored in sealed water containers with taps now I want us to convert five liters to cubic centimeters and they tell us that one liter is equal to one thousand cubic centimeters okay so how are we going to do this well if you have a look over here going from five liters so we going the other way going from one liter up to five liters you would have to multiply by far so if you did that on this side you would have to do it on other side as well in other words five liters is five times 1,000 which gives you 5000 cubic centimeters now how many drops of bleach need to be added to 16 liters of water okay so for this one we're going to have to use this one that we've got over here so we're going to use five drops for one liter and how much do we need for 16 liters okay so from one liter to 16 you're multiplying by 16 so here we have to multiply by 16 as well and 5 times 16 you can do on your calculator it is 80 drops okay so you've got to add 80 drops to 16 liters of water to make the water tea yes so now we're going to do a conversion from metric to imperial convert five liters to gallons if one gallon is three comma eight liters and we're going to give the answer rounded off to one decimal place okay so they tell us that one gallon is equal to three comma eight liters and we want to know what 5 liters is inequivalent over here now we can use the little ratio here I always find it the easiest to do it that way so we want to know what X is so what I'm going to do is we're going to take X and divide it by 1 and then so we're going to divide these two as well so X divided by one gallon is five liters divided by three comma 8 liters okay so now on our calculator we go a five divided by three point eight we change it to a decimal and it gives us 1 comma 3 1 5 1 comma 3 1 5 okay now they tell us that we must round off to one decimal place so to one decimal place you're going to look at the second is at the second decimal here it's a 1 so the stays are 3 so this is 1 comma 3 liters something that I need to remind you of is that you must please always in to always make certain that you put your units in otherwise you're going to get penalized for that now let's have a look at our next example a person suffering from cholera Mart become dehydrated now a rehydration mixture can be made at home to be bring someone from becoming dehydrated a rehydration mixture is one liter of clean water with 8 level teaspoons of sugar and half a level teaspoon of salt as we have 1 liter of water and to that you've got got to add 8 teaspoons of sugar and then you have to have half a teaspoon of salt just take note that I have used teaspoon yeah and it is a little tea a capital T normally means a tablespoon okay so you're going to take those three you're going to mix it together and then to help somebody not become hydrated they are going to drink that mixture let's have a look at a question how much salts in milliliters will you need when preparing six liters of the rehydration mixture and they tell us that five milliliters is equal to one teaspoon okay so let's have a look at now we want six liters okay and this is for one liter over here so if we want six liters it means that we're going to have six times 1/2 a teaspoon of salt so our total salt is going to be three teaspoons there then give us a conversion that 5 milliliters is equal to one teaspoon so to convert our 3t space into milliliters you're going to multiply by 5 so 3 teaspoons is 5 times 3 and that gives you 15 milliliters ok so now we're going to have a look at a graph question okay so the graph below illustrates John's trip to the bicycle shop which is 3,000 meters away from his home and is going to collect his bicycle which was sent in for a piece now he first walked to the post office to bar steps and then he went to collect his bicycle and he rode the bicycle back home please remember to always read everything that you have preceding a thing like a growth so that you know exactly what information you are being given now let's have a look at the graph okay so remember our graph must always have headings so here we've got John's trip to collect his bicycle on the horizontal scale over here remember this is our independent variable okay we've got time in minutes these little divisions that we've got here each of these represent one minute we've got the distance from her and it is in meters remember that on this axis over here this one depends on this one over here how many minutes was John away from home this thing over here is showing us the time in minutes and this is our distance at zero meters from home then he went to the post office and over here he is home again so here we've got 30 minutes took him 33 minutes altogether now how long did John take to reach the post office which asazin deters away from his home case he'll be going post office and they tell us it's a thousand two meters okay so if we look here again Casey has our distance a thousand meters and he has the post office over here let's see how many minutes that is guess if we come down over here so it took him six minutes to get to the post office how far was John away from home after twenty-one minutes so we need to go back to our graph and I we've got to find 21 minutes so he has 20 21 takes us up to there now you've got to do a vertical line up to up to thee and you can see that we're two blocks along with a solid one over here okay so if we now have a look at our distance on the side here the distance between two of these is 1,000 meters and we've got four little blocks there which means one of these blocks over here represents 250 meters and over here we are two blocks above which means that at this point 2500 meters okay let's have a look at another question okay after how many minutes did John begin his journey back home okay so he started his journey home if you have a look over yes he started at zero we into a thousand meters and then he was stationed was there for a while at the post office and then he continued walking at this point over here he was at the maximum distance so we need to know how many minutes are you gonna go 25 + 2 so after 27 minutes he began his journey home hey let's have a look at an example involving Tom okay so John took 12 minutes to walk from the post office to the bicycle shop if he left the post office at 10:55 at what time did he arrive at the bicycle shop okay so what we've got to do is we've got to take our 10:55 which was the time that he lived okay and we've got to add 12 minutes on to that okay so if you add a 12 on to this we need 5 minutes he's going to make it 11 o'clock and that means it's going to be another 7 left this it's going to be 1107 okay so it takes him 1107 you must remember that if you go past the hour you need to take that portion off and then you're going to change your hour and you're going to have your minutes afterwards okay one final question on the Schroth question and this is one to do with speed distance and Tom now if the trip from the bicycle shop to his home took six minutes calculate the average speed in meters per minute at which John cycled okay so now there are likely to tell you what the actual formula is and your speed is distance divided by Tom okay so we trying to find his average speed so what was the distance that he covered he covered a distance of 3000 meters and they're telling us that it took him six minutes to get home so we can't revise this by a six minute please remember that when you are writing down six minutes you have to write bright mi in four minutes you can't just use a name because I aim is our meters okay so now if we do this calculation get six is going to thirty five times and we're going to have our 2-0 so it's 500 meters per minute you can use either the line or you can actually write out the word per let's have a look at our next section on measurement now this section involves length perimeter area weight of volume and temperature again so let's have a look at our example a church congregation in Ha Tinh decided that they wanted to contribute to the building of a church hall in an informal settlement and they visited the site where the church hall is to be built after studying the plans they decided that they would donate two thousand one hundred towards the painting of the walls and members of the congregation would paint the walls in their free time at no cost the wall has four walls which face north south east and west okay so that's what the church hall looks like you can see over here here is our direction pointing north okay so in other words this wall at the back is facing north this wall that we can see at the front is our South wall and then we've got the west wall over on this side over here on the left of the door and this one over here is going to be our east wall now we can ask quite a lot of different questions on this particular one so let's go on to the first one now the wall facing south has a door and four windows and the height of the door is 2 comma five meters and each window has a heart of 1 comma 2 meters and a width of 0 comma 4 5 meters you must remember that these questions often have a lot of detail and as you get the information if it is an honor diagram you should write it on ok let's move on now calculate the width of the door in meters if the area of the door is 2 comma 2 5 square meters okay so they tell us that our area is 2 comma 2 5 square meters now the area of a rectangle issue is usually length x britt but yeah we've got a door and they spoke about the heart and the width so we're going to use those two okay now they tell us that the heart of the door is 2 comma 5 meters and it's the width that we are trying to determine so we're solving an equation over here and if you want to get your W by itself we're going to divide both sides by 2 comma 5 yeah so if you go and do that on your calculator your width is going to be 0 comma 9 meters and the zero comma 9 meters is actually a standard door width okay let's have a look at the next question yeah there are no windows in the Western and the eastern walls and I want us to calculate the total area of the two walls and they tell us to use the formula that the area is equal to the width of the wall and then we're going to multiply that by the sum of the heart of the front and the heart of the back wall okay so we need to have a look at our diagram again too heavily to see what those measurements are okay so we can see that the width is 8 meters and the height of the front wall is 3 meters and the height of the back wall is a 2 comma 8 meters okay so here we're going to have 8 multiplied Hatta front is 3 and the height of the back is 2 comma 8 so this is going to be 8 x 5 comma 8 guess if we did it on the calculator 8 times 5 point 8 and that gives us 46 comma 4 so it's 46 comma 4 our units are meters so this is going to be meters Quade okay let's have a look at the next question now the northern wall has three circular windows and each window has a radius of 1 comma 2 5 meters okay so that's what our diagram looks like ok so here you can see the hottest 2 comma 8 the width is 24 meters and here you can see a radius of the circle is 1 comma 2 5 now want us to calculate the circumference of one of the windows and they tell us to use the formula circumference is equal to 2 PI multiplied by the radius so it's going to be 2 times pi and they gave us the radius it was 1 comma 2 5 guess if we can do that on the calculator so it's 2 pi x 1.25 okay and that gives us 7 comma 8 5 remember that your default number of decimal places is always 2 so if they haven't specified anything else then you do it to 2 so this is going to be 7 comma 8 or 5 and so this is meters it's only circumference so it's only meters only our area is in square units let's look at the next question calculate the area of all three windows and our formula that we're going to use is PI R squared okay so it's going to be pi our radius is 1 comma 2 5 and we're going to square that okay so we're going to go pi times 1.25 we're going to square that can we get 4 comma 9 0 8 I'm not going to round it off now because I still have to work out what three windows is so for three windows we're going to take the answer that we've got and we're going to multiply that by 3 so you use your answer that's on the calculator you go times 3 equals get it to a decimal so now we can round it off to 14 comma 7 3 so it's 14 comma 7 3 meters squared because we are working with area Z all right let's have a look at our next one now the leader of the church prove calculated that the total area of the inside walls is 184 comma 8 3 square meters and total area of the outside walls is 201 comma 3 0 square meters one litre of PVA paint will cover six square meters of the inside walls they want us to now calculate the number of liters of PVA paint that must be bought to paint the inside walls of the church and they want us to run off the answer to the nearest whole number okay so to calculate the amount of paint we need we're going to have to take the amount that has to be painted by PVA and we're going to divide that by the coverage okay so mount of paint that we need is going to be the total area and we're going to divide that by the actual coverage so our total area is a hundred and eighty four comma eight three square meters and one liter covers six six square meters okay so let's have a look at that so it's one eighty four point eight three and we're dividing that past six okay and that gives us 30 comma 8:05 30 comma 8:05 and this is the number of liters now they said we must run off to the nearest hole so this is going to be 31 liters okay now total of 49 liters of whether God paint was used to paint the outside walls of the church hall determine the area covered by one liter of paint okay so now we're going to do the opposite of what we have just done and we're going to say that our area is the total area and now we're going to divide by the number of liters search was 201 comma three zero square metres of whether God and it was 49 liters used all together so that gives us a coverage of let's have a look – oh 1.3 and we're dividing that by 49 and that gives 4 comma 1 0 8 4 comma 1 0 8 so we're going to round this off to nearest whole number which is going to be 4 meter squid so that's what one liter actually covers okay let's have a look at another question the paint is sold in 20 liters and five liter containers the PVA paint costs two hundred and eighty grand for 20 liters and a hundred and six rent for five liters the weather god costs 499 ran 99 for 20 litres and 250 rent for five liters as you can see that is a lot of information so you need to read through a twice before you actually get to the answer now the church group estimated that they'd need 1/2 liter and 3/5 liter containers of PVA and that would need 320 liter containers of whether God so now what do they want us to do they want us to calculate the total cost of the paint that is needed yeah so total cost is going to be the cost of the PVA plus the weather god ok so our cost is going to be PVA plus the weather god ok so for our PVA it was 280 rent for the 20 litres and 306 rent for each of the 5 liter containers and then the whether God was three containers and that is 499 rent and 99 cents okay so we need to do this whole thing on the cat on the calculator and when you do that we'll end up with a total of two thousand and ninety seven rent and 97 cents here now let's have a look at the surface area of a solid object mister Berta owns a restaurant called the grill and he has a three-dimensional model of a hamburger as his restaurant son the model consists of equal hemispheres which are Hoffs fears with a radius of 50 centimeters the hemispheres are joined by a cylinder with a hat of 20 centimeters okay so you can see this looks like a hamburger Kathy is the banner in the bottom and that's the shape of a hemisphere and in the middle we've got a cylinder okay so there are different dimensions of the of the cylinders the cylinder and the two hemispheres now he wants to paint the outside of the model of the hamburger with one coat of silver enamel paint and the coverage of the paint is 12 liters per square meter now we want to calculate how much paint mr. butter will need to paint the model and they're telling giving us the formula please remember that with the moment we work with volume and surface area they will give you the formulas that you need to use and sometimes in the exam papers they tell you to use a PI as a 3 comma 1 4 however when I do the quick calculations I will be using PI on the calculator ok so let's have a look at our answer so here we've got our dimensions now remember that the what they told us just now they told us that it uses 12 liters per one square meter so the first thing that we need to do is we need to convert these two meters so 50 centimeters is 0 comma 5 meters and 20 centimeters is 0 comma 2 meters okay so now let's start with the outer surface area of the hemisphere now they tell us that the surface area of the hemisphere is 2 pi or squid yes so that's going to be 2 times pi and our radius is 0 comma 5 meters and we've got to square that ok so if we do that let's see what our answer is so it's going to be 2 times pi times 0.5 and we're going to square that ok and that gives us 1 comma 5 7 yes this is going to be 1 comma 5 7 now we've got now we've got to do the cylinder ok so the surface area of the cylinder they tell us that it's two pi multiplied by the radius multiplied by the heart so it's two pi our radius is fifty centimeters that's also a zero comma five meters and our heart is 0 comma 2 meters yeah so let's see what that is so it's two times pi and you got to multiply that by 0.5 and we have to multiply that by another point two okay so that gives us zero comma six to eight okay so now our total surface area is going to be two of these over here so it's R 2 times 1 comma 5 7 plus zero comma 6 to 8 okay so let's do that so 2 times one point five seven plus point six to eight yeah and that gives us 3 comma 7 6 8 okay now we need to run this off to two decimal places so this is going to be 3 comma seven seven now remember this is the area that is going to be covered we still have to calculate how much paint we actually need to buy now the paint is 12 liters per square meters okay so the number of liters of paint is going to be our three comma you know I think to our calculation that's probably better to use our three decimals we've got over here so it's three comma seven six eight multiplied by 12 and then we'll round it off generally your rules for rounding off is you must work with as many decimal places as you can and only round off in your final answer okay so let's see what that gives us so we've got three point seven six eight we multiply that by 12 and that gives us 45 comma two one six which is going to become 45 comma 2 2 liters so that was quite a complex problem so you need you look at it and say hey what do I have I've got the two hemispheres plus a cylinder and make certain that you add all of them up okay let's have a look at another question now mister Berta believes in recycling and catches the rainwater in a tank and the restaurant kitchen uses the recycled water to wash the dishes a rectangular metal plate measuring 250 centimeters by 300 centimeters was used to construct a cylindrical tank fixed onto a circular concrete base okay so let's have a look what we mean okay so here we've got the rectangular piece okay you can see these our heart is our two 50 centimeters so they took this and they bent it into the cylinder that we've got over here now if the 300 centimeter side of the rectangular metal plate is being to form a circle determine the diameter of the cylindrical tank and they want us to use the formula that circumference is pi times diameter case our circumference is pi times diameter now what do we know we know that the circumference is 300 that's the part of the rectangle that was turned into the circle so this is going to be part times diameter now whenever you're solving an equation you always have to do the opposite operation so we're going to divide here by PI and we're going to divide this side by PI as well okay so let's see what that gives us so we're going to go 300 and we're going to divide by PI and that gives us 90 5 comma 4 and now when we round off the two decimal places 95 comma 4 9 and our unit here is meters when I want to calculate the volume of water that the tank can hold in liters here and they tell us that thousand cubic centimeters is equal to one liter remember I told you earlier that when you have to do certain conversions they will actually give you the conversions okay so they tell us that one liter is a thousand cubic centimeters they also tell us that the volume is pi times radius squared times your heart okay so it's part x right so we've just worked at the diameter in the previous question and our diameter was ninety five comma four none so we need to take that answer and we need to divide that by two to get our radius so please make certain that you don't go and use your diameter dimension okay so it's ninety five point four nine we're going to divide that by two and it's forty seven comma seven five when we round it off so this is our diameter and radius is going to be forty seven comma seven five okay so here we're going to get forty seven comma seven five squared and our height is three hundred okay so let's do that whole calculation so it's going to be pi multiplied by forty seven point seven five squared multiplied by 300 and that gives you 2 1 4 8 9 8 comma two eight those odds of ours is in cubic centimeters but now they wanted us to convert it to liters gets a little conversion they gave us they say that one liter is equal to a thousand cubic centimeters okay so this one up here is cubic centimeters so we've got to take this answer and divided by 1,000 to turn it into liters now when you divide by a thousand we can just move our decimal place three positions so it's going to be two thousand one hundred and forty eight comma nine will run off the two decimal places so it becomes nine one liters and a favorite type of question that they like to ask is to give you a certain area that has to be paved or tiled and the size of the tile that you're going to use and then you have to calculate how many tiles you actually need so let's have a look at how we're going to do a question like that mr. Ravi decided to pave the driveway in front of his garage the length of the driveway is 10 comma 3 5 meters and the width is 2 comma and 9 9 meters and here they've given you a nice diagram showing you exactly what's happening so he has the driveway that's been paved he has our width and here is our length now a rectangular paving brick has a length of 23 centimeters and a width of 11 comma 5 centimeters okay so let's write those ones done okay so first of all a driveway is too common 9 9 meters but 10 comma 3 5 okay and then we have our brick and brick is 23 centimeters by 11 comma 5 centimeters remember our driveway here was given in meters which means that there we going to have to use our conversions yeah what else do they tell us they tell us that paving bricks are sold in pellets of 354 and on the diagram here you can see that there is a picture of what a pellet looks like so it's on a wooden wood piece like this and the bricks are stacked on top and then they are tied together with both thicker plastic sheeting okay so now let's see what they want us to do they want us to calculate the minimum number of pellets that's important that you read that because that is going to affect how we actually going to round the answer off okay so the minimum number of pellets that must be purchased in order to pave the driveway in one pellet we have three hundred and fifty-four bricks ok so now we need to know the number of pellets so the first thing we're going to do now is we're going to calculate the area of the driveway so we're going to multiply these 2 so it is 2 Anana x 10.35 okay so that gives us 30 comma nine four six five and I'm not going to round that answer off right until I get right up to the end okay so now we need the area of the brick but now the first thing is this one this is in centimeters and this one here is in meters and the easiest thing to do if you have to work with the area or volume and you have to give your answer in a different unit first go and convert your dimensions and your foil is likely to make a mistake then okay so now we've got to do 23 times 11 points five okay oh I didn't convert them okay we've got to convert them otherwise this is difficult to convert so it's going to be 0 comma 2 3 x 0 comma double 1 5 okay now it is possible to go from square centimeters to square meters but the thing is then instead of dividing by 10 for each jump you have to divide by 100 because as you can see on here two of these dimensions we have had to divide by hundred so you would have to go and do it twice to get to your area in square meter so it's easier to do it like this so it's going to be point two three times point double 1/5 let's see what that gives us gives us zero comma zero two six four five and this is also in meters oh this is meter squared okay yeah we've got me two squid okay so let's just go over that again so we've got the area of the driveway which our answer was in square meters we then had to take our brick the dimensions were given in centimeter so we had to convert them into meters and then we got the area of the face of a brick so now to find the number of bricks we're going to take the area of the driveway and we're going to divide that by the area of one brick okay so here we've got a number of bricks it's going to be 30 comma and nine four six five and we've got to divide that by our zero comma zero two six four five okay so we've got the two zero comma two six four five and I calculator so I'm going to go 30 point nine four six five I'm going to divide it remember you can use your answer button okay or you've got to put it in again and that gives us one thousand one hundred and seventy bricks now the question was how many food pellets do we need to order okay so now for our number of pellets you've got to take the total number of bricks and abide by the number of bricks in one pellet which was three hundred and fifty four case he has our double one seven AB divide that by three hundred and fifty four and that gives us 3 comma 3 is zero five okay so now the question was how many food pellets do we need now this is where you got to be careful in your math literacy if we look at this our normal rounding rules would be because this is a three we're going down to three but if we only order three pellets we are not going to have enough bricks so we have to go and round this answer up okay so therefore we in need of four pellets yes you must just be careful there because sometimes also depending on your context although your answer is three comma eight you may actually have to go down to three rather than to four it all depends on the context that you have been given okay so we've finished everything on measurement we're now going to move on to daughter handling now daughter handling involves collecting classifying and organizing summarizing representing and analyzing a daughter now I'm going to cover all the different aspects of daughter handing her via our example so let's go straight on to the first one the marks below represents learners performance in a mathematical literacy test which was at of fifteen and the first thing to notice with these marks is that they are arranged from your lowest to your highest remember quite a few of our different values that we calculate do you need the sorted now our first question is is the data discrete or continuous okay let me remind you about the difference between those a discrete daughter is a counted daughter and very often the sections are what we call categorical yes sir for example you can have red blue and gray cause for example so that is your counter daughter a continuous daughter is daughter that is measured so anything in centimeters kilograms anything it has to be measured is a continuous daughter so to answer this question that the daughter is discrete the first thing we're going to do is begin to calculate the mean of the marks now mean is one of our three measures of central tendency we've got a mean we've got our merge and we've got our median mean is our normal average in other words what you get on your report at the end of term they've added up all your marks and they've divided by the number of subjects so that is what we're going to do here your median is your middle most so when your daughter is arranged you're going to select the middle number if they're odd values and if you've got an even number of values it's going to be the average of your middle two and our mode is our one that appears the most it's the one that is most popular yes so here I've got all the numbers written down on our piece of paper so for our mean and watching mr. years always go and show what it is that you're doing so we're going to go 10 plus 20 plus 23 now it's quite a lot of numbers so we don't need to write them all so we can go three dots plus 47 and then we've got a divided by the number we've got here so we've got 2 4 6 8 10 11 there are 11 pieces of data there okay so let's have a look what that totals going to be so it's going to be 10 and 20 gives us 30 and then we've got 23 33 34 35 37 40 43 45 and finally 47 okay so that turtle is three hundred and 67 and we're going to divide that by 11 now please remember you must show all your steps a show what you're going to do show that some and then go to your final step that way if you've made a mistake they can still follow up with your answers if you write down only the answer that's wrong you're going to get zero out of three instead of a possible two out of three okay see how we've got our three hundred and sixty-seven I'm going to divide that by eleven and that gives us thirty three comma 633 comma three six three six so we're going to round it off to approximately 33 comma three six okay let's see what the next thing is we can do with the start time when I going to Turman the median of the marks okay so for our median as I said it's the middle most one so what we've got to do is we've got to see how we're going to divide so we take I living so 11 is an odd number so we can share five numbers here five numbers here and the sixth value is going to be our median okay so let's go to our values and let's count one two three four five here's our sixth value and just to check one two three four five in other words our median is equal to 35 okay let's have a look at our next one then I want us to determine the range of the Mocs now a range is one of our measures of dispersion and it shows us how spread out the data is so our formula for our range is our highest value – your lowest value so it's going to be 47 minus 10 which gives us 37 next question the upper quartile is 43 what the center of the marks is greater than the upper quartile okay so let me remind you about that so we've got our daughter and our median divides it into half in other words we've got 50% on the one side and 50% on the other side your Chloe and your upper quartile divides each of those two sections into half so quartile is quarters so if you have a look at they've told us that this is our upper quartile so if you have a look at you can see that you've got two values there and you've got two values there so it's divided that part into two okay so what percentage is above here our percentage that is above me is 25% romão quartiles divides into four so each section is 25% now let's have a look at our next example two paragraphs in a book or compare and the first about in each word is recorded okay so yeah we've got our data that is recorded so our vowels are a e IOU and in paragraph a you've got 3 6 2 3 & 1 & 4 paragraph B they were 6 1 3 4 & 1 now we're going to use the daughter to draw a compound bar off okay so let's just remind ourselves as well we have bar graphs and we have histograms so our bar graph has spaces in between so it looks like that okay and it is used for discreet daughter whereas our histogram has no gaps in between the dots so it looks like that and that is used for continuous data so now they want us to draw a compound bar graph so compound bar graph is abused when we do more than one piece of data and comparing more than one okay so the first thing if you have a look at your graph it needs to have a heading okay so these are heading number of hours in each word in paragraphs a and B okay then along the bottom we've got our vowels a eio and U and here we've got our number of first parts going from 0 up to 7 okay so let's have a look when we've drawn a bar graph what it looks like okay so here you can see if paragraph a is the blue ones and paragraph B or the red ones compound you've got two side by side remember you can also get a stacked bar graph and Bhargav is when you have the two on top of each other let's have a look at the next question now what percentage of the letters of the alphabet is vowels now remember that percentages is just one of those things that comes up quite often and it could come up in any of your sections so how many of our letters of the alphabet or vowels there or five and our total number of letters are 26 to get your percentage you gotta multiply that by a hundred okay so we're going to get five over 26 multiply that by 100 and that gives us 19 comma 2 3 this is a percentage that please remember to use your percent son okay let's have a look at another example it's a little bit more complicated on the 14th of February 2012 there was a queue of customers waiting to eat a Denny's Donna a popular eating place in Makati all the time in minutes at 16 of Danny's diner customers had to wait in the queue is given below yes so it goes 30 and you can see these are not arranged in dots in these are not arranged in numerical order and they tell us that B is a value greater than 2 and you'll notice that we have got 2 B's as well now the range of waiting times was 37 minutes and the mean waiting time was a 34 minutes okay so we're going to need to write that down okay so our range is 37 and our mean was 34 minutes now we need to calculate the missing value a which they say is the longest waiting term okay so for longest waiting time we're going to be working with our range so our range is the highest value minus the lowest value and that is 37 so our highest value is a our lowest value we need to not go through these and it looks as though 15 is our lowest one so a minus 15 is equal to 37 so we're solving a little equation here our minus 15 we add 15 to both sides and that makes this 52 minutes now we are also going to calculate the value of B so this a over here is 52 okay so now for our mean we've got to add up all these values and divide by the 16 and the answer should be 34 so we're going to go here 30 plus 15 plus we're going to add all of them and we'll notice that we have got two beers okay so this is going to be plus 2b and that total is going to be 34 when this has been divided by 16 okay so what we've got here is a another equation which you're going to solve so the first thing is we need to do is to add all of these values up besides our two B's okay so if you do that you get 494 now please be careful when you do this calculation and add them up twice if necessary to make certain you haven't made a mistake all right now how do we solve an equation like this I guess I remember whenever we're solving an equation we do the opposite operation okay so we have to divide by 16 so we're going to multiply both sides by 16 okay so when we do that we're going to get our 494 plus 2b and you've got a multiplier at these two over here and this gives us 544 now the opposite operation we've got to get rid of our 494 so we're going to subtract it from that side over there and 544 divided by 494 gives us a 50 and then two beers 2 times B so in other words we're going to divide both sides by 2 and then B works out to be 25 minutes please remember to always add your units let's have a look at another question here the lower quartile and the upper quartile of the waiting times are 27 minutes and 41 comma 5 minutes respectively how many of the 16 customers had to wait in queue for a shorter time then a veal lower quartile okay so let's have a look on our sheet over here so they tell us that the lower quartile is 27 minutes remember that's your q1 and our upper quartile is q3 and that is 41 comma five minutes and they want to know how many of the 16 customers had to wait in the queue for a shorter time than the lower quartile so all we have to do is go and count how many values are less than 27 I guess if we have a look over here now we've got one two and less than 27 how much was Bibi was 25 so those are another two so we've got a total of four so in other words for customers waited less than 27 minutes and I let's move on to part shots now in an exam you're not going to be expected to be able to draw a path chart however you have to be able to tell them how the a particular Sciences the size of a sector has been calculated and the other thing is you have to be able to do interpretation of a pie chart so let's have a look at a pie chart the pie chart below shows the percentage of customers who ordered different meals at Denny's Donna on the 14th of February 2012 so there is a percentage of customers now remember a a part shot must have the percentages of the different ones you'll see that one has actually been left off here he has fish in this one over here here's our heading and let's have a look at some questions that we can be asked if 40 customers ordered beef meals determine how many customers ordered chicken meals ok so they tell us that 40 customers ordered a beef and they want to know how many customers ordered chicken yeah so let's go and have a look at our pass shot so the first thing we need to work out is how many actually ordered chicken what percentage okay so the percentage that ordered chicken is going to be a hundred percent – yes if we have a look we've got twenty percent beef 30 percent fish that gives us 50% Plus this 10 is 60 percent plus this 25 gives us 85 percent so in other words our chicken is 100 percent minus 85 percent and that gives us a 15 percent okay so now let's have a look 40 customers is equal to beef which is 20 percent okay so if we take this down a 15 we can divide by five three times if we divide this by a 4 it goes to five percent so now on this side over here we've divided this by four so on this side we must also divide by four so 40 divided by four gives us that 10 customers is equal to five percent in other words 15 percent is going to be 3 times 10 and that's going to give us 30 customers now an X example involves a box and whisker plot or a box and whisker cut whisker growth now our box and whisker basically has our five number summary on and it's a visual display of our different measures again let's have a look at the example Jolene has worked at a florist for nine months the box and whisker plot shows her sales of wedding bouquets okay so here we've got a value over here then you can see the box starts from here goes to thee and then here it ends so here we've got our different values so this one over here is our minimum value and it is our Q 0 then this first line over here represents our lower quartile which is q1 middle line represents our median which is q2 and then the 13 represents our upper quartile q3 and finally this value over here is our q4 or our maximum value let's have a look at some questions determine the five number summary for the number of wedding bouquets salt okay so here I've got a picture of the of the box and whisker plot so let's write them down so here's going to be our q1 value is 3 sorry I q0 value is 3 this is our minimum value okay then here we've got our lower quartile here we've got our median which is cutie or M okay so that's going to be a value 7 here we've got our upper quartile which is q3 and finally our maximum value which is a q4 yes sir lower quartile upper quartile and she has our median so this shows you nicely exactly how the daughter has been distributed let me just draw a histogram on this to see what it would look like if we actually drew this now if you have a look over here remember our median divides the daughter in two Hobbs we've got 50% that side and 50% beside so if we were to draw this a histogram for this the daughter would look more or less like that okay peaking over here so you can see that the distance on this side over here is much longer than the distance on the side and when that happens then we say this daughter is skewed and this daughter is skewed to the right okay your tail is longer on the right-hand side such skewed to the right you can also say that it is positively skewed so if they'll ask you to describe the distribution this is basically what you say so you could have normal if it was a hundred percent even although that very seldom happens so if you have a long tail on the right it's skewed to the right or positive if you have a long tail to the left it is skewed left or it is negative and the thing to remember is that the tail tells us oh yeah let's have a look at another question describe the distribution of the daughter that's what I've just explained to you okay so our final question for this is does the starter have an outlier now the it's not such a good question for this particular one because you can't really tell you can only tell if you have an outlier if you have a lot of data now in an outlier is something like blast outside of your main daughter so for example if we had a look at a scatter plot case if we had to put a scatter plot and say say our point sort of went like this okay and you had one way down over here then this one over here would be described as being an outlier but yeah you can't really tell that on a box-and-whisker plot okay let's have a look at another example the time spent valuing is that a clause writing an essay was recorded a histogram was drawn to represent the data and the midpoints of the class intervals have been given okay so there's a histogram notice that we have got an open space at the beginning and at the end and there are no gaps in between so let's have a look at some of the questions that can be asked on a histogram how many learners are they in the class okay so to determine how many learners they are we need to have a look at our frequency table at our frequency axis which is up on the side over here so now if we have a look in this one over here we've got seven learners here we've got fifteen learners on this one we've got ten here we've got seven and in this one here we have got one okay so what is our total we need to add that up okay so we've got 22 plus 10 is 30 to 39 40 so the total number of learners is of 40 let's have a look at another one what is the Moodle class interval okay so remember what is mode mode is our most popular so our Myrtle Cross interval is going to be the interval it was most popular okay so let's have a look at our graph and you can see that it's going to be this interval over here okay it's going to be this one over here so what we need to determine is what that value and this value over here are so first of all let's have a look at the difference between at least two 27 minus 22 gives you five in other words we've got to go to 1/2 minutes that direction and two and a half minutes of that direction so if we take 20 27 minus 2 no hot it gives us 24 comma 5 and 27 plus 2 and 1/2 gives us 29 comma 5 so in other words this class interval is between 20 comma 5 24 comma 5 and 29 comma 5 okay so and now we've done the daughter handling section or with representing and organizing and analyzing our daughter now we're going to move to the other part of that is probability now when the probability is a chance hey let's have a look at our first example the marks below represent learners performance in a mathematical literacy test which was at of 15 marks against a year I'm using the same daughter that we used in the daughter handling let's have a look at our question however determine the probability that our MOT if a mark is chosen at random from the sample the mark will be less than 25 okay so annotation the way that we write that is the probability of a mark being less than 25 okay so first let's have a look at our favorable art cup so all the ones that are less than 25 but this one this one and this one so it's only a three and our total number of marks that we've got here 4 2 4 6 8 10 11 so the probability of marks being less than 25 is 3 over 11 now remember that your probability can be written in three ways either is a fraction in simplest form like I've just done now it can also be converted to a decimal or it can be written as a percentage so percentage we're going to go from zero percent up to 100% being from not able to happen at all up to 100% possible chance of happening when we're talking about fractions and decimals they gave to between 0 & 1 and let's have a look at another example yet Tauber in ball share a pizza they each spin the spinner and decide that the first one to spin it to will pay for the Pizza what is the probability that the spinner will land on two okay so we can't have the probability of it landing on two so let's have a look so what we've got is how many favorable outcomes to behave there's only one favorable outcome is this two over here so that's going to be one and our total number of outcomes is four it can land on the numbers one two three or four so there's a quartet chance there's a quartet chance of the spinner landing on a – okay let's have a look at another example the part chart below shows the percentage of customers who ordered different meals at Denny's Donna on the 14th of February 2012 okay so these the part shot you should recognize that from the last section as well okay so we've got our chicken beef and lamb and our sausage a customer is randomly selected what is the probability that the customer would not have ordered a lamb meal okay so this time it's a probability of not lamb in other words it's going to be everything excepting for the lamb okay so let's go to our slide so let's have a look over here okay so here's our lamb over here which is 25% so if lamb is 25% it means that not lamb is going to be 75% ok so there we can go straight to our actual answer so 75% if you were to write this as a decimal it could be 0 comma 7-5 as a fraction it would be 3/4 it I recommend unless they ask otherwise just write it in a fraction in its simplest form and remember your calculator when you put it in will give you that simplest form let's have a look at another question mr. spear a laugh orientation teacher has seven blue socks and five Red Sox in his drawer it is dark in the morning as he gets dressed he blindly chooses two socks one after the other without replacement okay now that's the important thing to notice yet it's with art replacement so that means he reaches into the drawer he pulls out a sock and then he reaches in and he takes out another sock now they want us to draw a tree diagram to represent the scenario and we're going to indicate the probability of choosing a blue or red sock in each case yes and I remember a tree diagram looks like a tree lying on its side with the roots coming out so whenever you draw a tree diagram go and start in the middle of your page and use a lot of space otherwise it's going to be very squashed okay so at the first time that mr. Speer reaches into the drawer what his what can he draw at he can either get a red sock or he can get a blue sock okay then when he reaches in the second time he can either get a red sock or a blue sock and the same over here okay so that's what actually diagram looks like now what we're going to do is on each of the arms of the probability tree we're going to write down what the probability is so let's have a look at our numbers okay so he has five red socks and a seven blue socks okay so let's have a look so he starts with five and he starts with seven over there so in other words he's got a total of twelve socks so for the first one over here the probability of getting a red is going to be 5 divided by 12 and the probability of getting a blue is going to be 7 divided by 12 ok so now this is the first drawer now what about his second drawer okay so let's go into the red one over here first if he selected a red sock out of his draw it means that he's now only got four Reds left but he has still got seven blues so our total number of socks noisy living and the probability of getting a red one is going to be four over Levin and the probability of getting a blue one is going to be seven out of 11 on the other hand if we drew a blue sock first time then he's going to have only six blues left and he's still going to have the five Red Sox so now it's again a total of eleven so here we're going to have five over eleven and this is going to be six over eleven now something that I want you to notice is that when you take each of the branches the total of your probabilities is going to be one so if we have a look over here five over 12 plus seven over 12 gives us 12 over 12 which is one so we've got four plus seven is 11 over eleven and here we've got 5 plus 6 is 11 over 11 remember that your total of all the probabilities is always going to be one can now let's see what other question they want us to do with the probability tree okay so the example says determine the probability of mr. Speer choosing a pair of blue socks okay so we're gonna come to our tree diagram and they want a pair of blue socks so in other words it's this one and this one over here this is our outcome blue sock blue sock so that's going to be our P now when you find your probabilities at the end what do you have to do to these you have to multiply them okay so our probability of getting a blue and then a blue is going to be 7 over 12 multiplied by 6 over 11 yeah so if we do that on the calculator so it's going to be 7 over 12 multiplied by 6 over 11 yeah and that gives us 7 over 22 okay so that's the probability of him actually pick picking a pair of blue socks ok let's have a look at the next one determine the probability of mr. spera choosing an odd pair of socks ok so now let's look at our diagram and see which one's we need this time so where are our odd socks okay so odd sock would be a red and a blue or a blue and a red okay so it's these two together so what we do is we going to multiply these along two the probability of that outcome we multiply these ones and then those two there we actually going to add okay so this one is going to be 5 over 12 multiplied by 7 over 11 this one is 7 over 12 multiplied by 5 over 11 so let's have a look at our final the probability of getting an odds P is guess I'm going to do it in one step over here these two we're going to add K so it's going to be 5 over 12 multiplied by 7 over 11 and then we're going to add 7 / 12 multiplied by 5 over 11 okay so let's see all those values are correct just always check it you have got the right things in and that gives us 35 over 66 yeah so let's change it to a percentage and let's multiply that by 100 just to see what our percentage is so because of his combination there he's got a 53% chance of wearing an odd pair of socks to school that day okay let's have a look at a contingency table now in South Africa the number of cases of teenage pregnancy has risen exponentially mr. spear as the life orientation teacher decided to do a survey on how learners felt about abstinence now abstinence means not having sex at all so you abstain from the actual activity okay so let's have a look what the contingency table gives us okay here in the columns going downwards we've got all of those in favor and here's the total we've got those that are opposed and we've got the total those that are undecided and the total then going horizontally in our rows we've got the females and the males and they're also we have the totals for each of those so this has been divided in two lights males and females as well as in favor opposed or undecided and then we have a total here of 510 so in other words 510 learners were interviewed all together okay so let's have a look at our possible questions calculate the probability that a learner chosen at random will be in favor of abstinence okay so our notation probability of a learner chosen at random in favor now they say a learner which means that they're going to include the men and the woman okay so if we have a look at our table okay I total that are in favor gather or over here it's a 301 so this is going to be 301 and our total that we get from our table is 510 okay so we can do that on the calculator to check whether it's simplifies or not so it's three hundred and one divided by five hundred and ten it doesn't okay so that is how you're going to leave it you only need to change it to decimals or percentage if they tell it to give you in that format okay let's have a look at another question what is the ratio of female female learners in favor of abstinence in relation to female learners that are opposed okay so we're looking female that are in favor relative to the females that are opposed okay so again this is a table reading skill so let's go and have a look at our values they so the females that are in favour is 212 and they opposed a 78 so it's going to be 212 to 78 let's simplify that so 212 / 78 is 106 over 39 in other words 106 to 39 please remember that your ratios and fractions must always be in simplest of format now let's have a look at our last question now remember in your exam papers you may have a question that is what we call a level 4 which is reasoning and reductions so he has a question like that give two reasons why abstinence is important okay well I think the first and most obvious reason is going to be that you don't want to get pregnant case if you abstain you're not going to get pregnant and the other reason is that you will not get any STDs in other words sexually transmitted diseases such as HIV or AIDS and now we're going to move on to our next section and are we going on to our first of three finance sections in this section we're going to be covering a tariff systems income and expenditure profit and loss budgets cost and selling price and break-even analysis let's look at our first example determine the profit margin if a product that costs 350 rent is sold for six hundred and 250 rent okay and they tell us to use the formula that your profit margin is equal to your selling price minus your cost price divided by the selling price and we got a multiplier that about 100 okay so let's go back and get those values so our selling price is 650 red our cost price is a 350 red and you've got to divide that by the selling price which is 650 and multiply that by 100 to get to the percentage okay so let's have a look at the calculator so it's going to be is 650 – 350 that's quite easy you can go straight to the 300 if you see that or you can just rely on your calculator divide that by 650 multiplied by 100 for a percentage and we're going to do 2 decimal places which is our default so it's 46 comma 1 5% yeah let's have a look at our next question 2 small companies lad fitters a cupboard making company and mango computing a computer company each employ a general assistant mega computing Computex general assistant earns a 310 rent per day if I ever she is at work for less than one hour on a particular day then she earns a no salary for that day okay so manga computing general assistant gets a three hundred and ten rent per day and if she works at less than one hour she's going to get nothing okay let's have a look at life fighters now life fighters earns a basic daily wage of a hundred grand plus an additional 30 rent for each hour worked okay so this is a hundred rent per day plus a 30-round per hour for each additional hour that she's worked the formula used to calculate the daily wage of the general assistant of the last Vitor's is daily wage equals 100 plus 30 rent per hour 30 rank times I was worked you can see that's almost what I wrote over here okay so our daily wage it's going to be 100 red plus a 30 rent times the hours worked our table has been drawn up showing their daily wages yes our table gives us the wage for the bending on the number of hours worked per day so let's have a look at it okay so number of hours worked we go 0 1 4 there's a C we can obviously have to calculate that just now 7 & 8 hours now make a comp you ticket compute tech if you work nothing you get nothing and then as 310 rain doesn't matter whether you work anything from one hour up to eight hours if we have a look at lot fitters we're going to have to work out of these ones over here one hour is 130 we're going to have to work out what C is but for C you get 280 round seven hours is 310 and 8 hours is 340 okay so our first question is to calculate the missing values from the table okay so let's go and have a look now live fitters if you don't work you are going to get 0 so this air over here is 0 rent right 4b larvas are working for 4 hours so we're going to use our formula that we've got over here and we're going to say it's 100 red plus 30 times 4 okay so 30 times 4 is 120 plus 100 is 220 and that's the value of B now for C we're going to have to backwards okay so we know that the value is 280 rent so we're going to have 280 is 100 plus a 30 times the number of hours worked which was called C okay so he I was solving a equation so the first thing we do is we're going to subtract this 100 ran from both sides so – 80 – 100 gives us 180 V and we've got 30 times C which is 30 C doing the opposite operation we're going to divide both sides by 30 and 30 goes into 86 times in other words C is equal to 6 hours again notice that here I put in the rent sign and here I've put in the hours let's have a look at another question now the graph showing the daily wages earned by mango Computex general assistant has been drawn so let's have a look at it okay so here it is again here you can see your heading your daily wages earned by the two general assistance mango computing the compute occurs with a blue line yeah we've got number of hours work on our independent axis and our vertical is the daily wages yeah so now that we've got this graph let's see what question we're going to be asked it says on the same set of axes draw a labelled graph to illustrate the daily wages earned by the last live fitters general assistant okay so what you've got to do is you've got to go and put the different points on so one that we had to put on there was zero zero okay so let's have a look so we need a point there and then one hour was a hundred and thirty okay and we saw we got to keep putting the different values on let's have a look at our final graph okay so here it goes from 0 these are 130 so that goes up in a straight line there and then it has a pink thing and then it goes all the way up to here with 8 hours can I remember he must also go and add in your actual key that you've got over here for the color that you have chosen ok now this graph can be used to answer more questions let's have a look it says how many hours I shoot both assistants work to earn an equal equal amount on a particular day okay so we need to have a look at our graph now the equal amount occurs where the two graphs actually cross each other okay and at this point over here is called the break-even point we often draw one of these graphs when we are busy comparing because and the profits made by a business to determine exactly how many products have to be produced in this case it's how many hours do the assistants have to work to earn the same amount so if we have a look here's our number of hours worked on our horizontal axis so the answer is going to be seven hours now another question that would be good for this is which company would you rather work at so your answers going to be dependent on the number of hours if you're definitely going to be working eight hours a day or seven hours a day then you would go with the lot if you were going to work less than seven hours on any day then obviously your mango is going to give you a better value okay let's have a look at our next finance section okay let's have a look at an example with a tariff system okay in our third example we're going to have a look at the cost of water now a table showing the costing structure of water is given so let's have a look at how you can see we've got our water usage in kiloliters and here we've got the tariff and this is per kilo litre you will notice there is an asterisk over here if you look over here you can see it tells us that our tariffs exclude the 14% vet now if we have a look at our process over here if you use between zero and nine kiloliters then you are not going to have to pay any costs if you use between nine and twenty five for these kiloliters in this category over here you can see pain 9r and 27 now if we see how many kilolitres they are in this category if you go 25 and you subtract the nine that we've got before then this category over here it's got 16 kiloliters so between the first category and the second category you would have used a total of 25 in our third category over here if you go 30 – 25 then you're going to get five killer liters here and these five kilolitres will be charged at 12 and 36 per killer liter so you can see that the cost is going up now if we have a look at our next category 45 – 30 gives you 15 kilolitres and those 15 kilolitres would cost 19 Rand and 6 cents and then for any 40 for any amount about 45 kiloliter you will pay 20 around 96 cents of per killer liter now this is what we call a sliding scale the more water you use the more you're going to pay per killer liter but there's more to a tariff table than just that we have a look over here there are also fixed charges of per month and he has our tariffs and add si per kiloliter but it is in fact a fixed charge if you use from zero to 90 liters then you do not have to pay any fixed charges at all however anything from an on kiloliters and more you're going to have a fixed tariff of 83 R + 83 round and 43 cents okay so now let's have a look at our question mr. Wilson receives his monthly musical account and has used 46 killer litres of water with the use of the water tariff table calculate the cost of the water used and they give us reminder here as I remember to include the 14% vet in your answer I guess it's 46 kiloliters that we are going to be using okay so let's go back to our table and let's have a look what we've got Jenna okay so this is not going to be a total of 46 kiloliters okay so now we know that this is more than that which means our fixed tariffs is going to be 83 rent and 43 cents we're going to have to pay that amount okay so now if we have a look at our table we can see that for 0 to 99 liters we have got a no red okay so for our first non kilolitres you are not going to pay anything okay so then for our next lock let's have a look at those it's going to be 16 kilo liters at 9r + 27 case at 16 kilo liters and this we have to multiply by 9 and 27 okay and we're going to get that total over thee then back to our table we've got to do 5 kiloliters at 12 range 36 so far kilolitres at 12 and 36 yeah and then we're going to have to do pay for the next 15 kilo liters we're going to pay 19 rent and 6 cents okay now if we have a look at our running total if we have a look at our table again up till here we've got a total of 45 kilo liters and they are using 46 kiloliters in other words we've got to have one extra kiloliter at the threat of 20-round 96 so it's going to be one killer liter at 20-round and 96 cents okay so now let's do these calculations and then we can add them all up okay so we've got a 16 multiplied by nine point two seven and that gives us a hundred and forty eight rent and 32 cents okay then five kilolitres multiplied by 12 36 that gives us 61 r and 80 and then 15 multiplied by nineteen point zero six gives us 285 Monte and then our final one kiloliter 2096 is just going to be 20 r + 96 okay so now we're going to add all these values up okay so we've got to start at the top with our fixed rate of 83 Rand and 43 cents so it's 83 43 plus 1 48:32 plus 60 180 plus 2 85 and 90 remember on your calculator you don't have to go and put the zero that's at the end the calculator knows that that's what's supposed to be there and then plus twenty point nine six yeah and that gives us a total of six hundred range and forty one cents okay so now what we've got to do what I remember we have to add up that amount onto this and our vet amount is fourteen percent okay so let's see what that's going to be so we've got our six hundred run on our calculator so we're going to go times point one four okay and that gets a total of eighty for rent and six cents yes in other words the total the final total that has to be paid is going to be six hundred red and forty one cents plus 84 and and six cents and that gives us a total of six hundred and eighty for end and forty seven cents okay so I just want to tell you read carefully and when you think you finish the question go back and check to see that you have in fact calculated it okay let's have a look at our final finance section which is on taxation and exchange rates as our first example a clock working at the bureau de change is at our chamber international airport is assisting two tourists in exchanging their money the tourists from Japan needs to convert 500,000 yen to rents and the exchange rate is one yen is zero comma zero six red and the question is how much will he get in rents now the way I like to set up the finance questions with these exchange rates is to use ratios so what I do is this us go okay we need a wrench again on the side and we need our rent two yen on the side and this system that you use over here basically works for any of any ratios that you have to work out okay so they tell us that one yen okay so we've got to put that under the yen column is equal to zero comma zero six red and then on this side the question is how much will they get in red so I'm going to call that X and then my yen yeah of this 500 thousand okay so now we're going to set up a ratio so we start with the unknown which is going to be X so I'm going to put X divided by 500,000 and then on this side I'm going to put 0 comma 0 6 divided by 1 so you must always do the same thing on the left and the right notice I've got rent yen rent yen so here I go x over 500,000 so here must go 0 comma 6 over 1 now when we get to this point we're going to find the lowest common denominator and the quick way of doing that is doing what we find finding the lowest common dominant denominator let me just quickly IRA's illustrate it to you if for example we have got 1/2 is equal to 3 over 6 so we start here with a proportion which is equal if we cross multiply which is not very good maths terminology but it works so you go 1 times 6 and on this side we've got 3 times 2 now this answer is 6 and so is this one so you can see that when we do that we still end up with a statement which is true so when we've got a single fractions on either side like we've got over here we're going to cross multiply them okay let's do it so now I'm going to say 1 times X gives me X and you always start with the one that's got the variable and on this side it's 500 thousand times zero comma zero six okay so if we do that on the calculator 500 thousand times point zero six and that gives you 30 thousand and that answer is in red okay so now you may say but that seems to be a very long process when you know you just have to multiply but one of the questions that are often get is how do you know when to multiply and when to divide well the thing is if you follow this process it doesn't matter it automatically the right thing comes along so if you have to multiply that's after workout or you have to divide let me illustrate with the next example the tourists from South Africa needs to change two thousand seven hundred and seventy eight rent two euros and the exchange rate is one euro is 925 how much will she get in euros okay so now we're working rent and hero's and it really doesn't matter which one you put on the left or which one you put on the right so you can go around euro or you could go euro euro rent as long as you've got the same on both sides okay so now they tell us that non-round 25 is equal to one rent and on here they tell us she's got two thousand seven hundred and seventy eight rounds and we're trying to find the number of euros okay so let's call that X so now gang we're going to set up our proportion starting with our variable so we're going to go X divided by two thousand seven hundred and seventy eight so we've gone second over first so we're going to do the same thing here as well so that's 925 so now we could be cross multiply we're going to get nine comma five at times X so are we going to get nine comma to five times X and here we can shave one times two thousand seven hundred and seventy eight now we have to do the same thing on both sides so we're going to divide both sides by nine comma two five okay so in this one you can see that we've had to divide the amount by the exchange rate that we give it and in the previous one you had to multiply it but unless you really understand the different currencies it's not easy to know which one you have to do okay so here we're going to go x equals okay so we're going to do this so we've got two thousand seven hundred and seventy eight and we've got to divide that by nine point two five cats currencies we've got a run off to two decimals so this is going to be this is the number of euros and it's a three hundred comma three two euros okay let's move along to our next question Rebecca bought a small French are selling upwards at a local free more on weekends she imports 120 iPads at a cost of 95 dollars each for her first shipment from America okay so let's see we've got 120 airports and each of them cost $95 now if the exchange rate is one R and a zero comma zero nine seven dollars calculate the value of the are pods in Reds okay so now the first thing I would go and do is calculate the dollar value okay so the number of dollars that is going to cost is going to be 120 times 95 okay so it's 120 times 95 gives us 11400 okay so this is eleven thousand four hundred dollars so this is what we need the rent value of okay so now we're going to go around dollar and here we're going to have R and dollar okay so because want to know how many rains we going to the value is and this is eleven thousand four hundred dollars and here I exchange rate is one rent is zero comma zero nine seven dollars again it's going to go X divided by eleven thousand four hundred and here 1 divided by is zero comma zero nine seven we cross multiply so we're going to get zero comma zero nine seven X his 11,400 now we're going to divide both sides by a zero comma zero nine seven okay so here you're going to go x equals say leaven thousand four hundred is on the calculator divided by point two zero nine seven and that gives us a hundred and seventeen thousand five hundred and twenty five comma seven seven since okay so now the thing is when you're doing exchange rates and you're working with dollars very often you just know what I've got a multiple witness dollars but it depends on how the exchange rate has been given to you so in this particular instance here we were told that one round is zero comma zero nine seven so we landed up dividing if we been given $1 is our 10 rent or whatever the exchange rate is then it would have been a multiplication sum but fortunately if you set it up as a ratio like this then you don't have a problem yes sir just follow the system again Alice let's do an example involving income tax mr. Moyer is 55 years old and earns a gross salary of forty thousand six hundred rent per month now our gross salary is a salary earned before pension tax and medical aid etc have been deducted from his salary an amount of 3138 rent is deducted for his medical aid and four hundred and fifty rain for uif a further seven and a half percent of his gross salary is deducted to contribute towards his pension okay so let's write all of that down okay so we've got a 3138 read and that is his medical aid hey and then there's a four hundred and fifty rent for UI f and UI f of course stands for the unemployment insurance fund which is what you can claim if you become unemployed okay then seven and a half percent of his gross salary is deducted to contribute towards his pension okay so let's work that out okay so his pension is seven and a half point percent so it's seven and a half percent let's have a look his gross salary is a forty thousand the six hundred Rand a month okay so that gives us a 3045 rent okay let's have a look at the question now calculate mr. Moyers taxable income for the financial year 2012-2013 now the taxable income is the annual salary – the annual deductions okay so these are his three deductions so let's add these three up okay so we've got three thousand and forty front of on the calculator plus 450 plus three one three eight and that gives us six thousand 633 so this is the total of the deductions ok so now let's have a look at his at his income so he gets a forty thousand six hundred rent a month and we've got a deduct V deductions okay so it's going to be forty thousand six hundred minus six thousand six hundred and thirty three so that gives a total of thirty three thousand nine hundred and sixty-seven now this is per month okay so we are looking for the annual amount so the annular martes per year so we've got to take our answer and multiply that by 12 okay so here's our mud multiplied by 12 four hundred and seven thousand six hundred and four okay so the annual in annual amount is four hundred and seven thousand six hundred and four rent okay so this is what the amount that he's going to be taxed on it okay let's carry on now employees income tax payable is calculated according to a text table once it is calculated the the rebadge the employee qualities for qualifies for is deducted okay so a rebate is an amount that comes off via March that you have to actually pay and you see that you'll see there are three different rebates first let's look at the table okay so he has your tax table here from March 2012 to February 2013 now if we have a look at this yeah we've got the taxable income amount and you'll see that it's in different income brackets so you've got from zero to one hundred and sixty thousand and then you start at one hundred and sixty thousand and one up to two hundred and fifty thousand and each of them goes up okay so here's our rates of text for the first income tax bracket you pay 18% of every one red okay if you earn in the next tax bracket you're going to pay twenty eight thousand eight hundred grand plus twenty five percent of the amount over 160,000 read so what happens is this amount over here is the maximum text that you would pay if you were in this income tax bracket so if you work out 18 percent of a hundred and sixty thousand this is the amount that you pay okay then in your next text tax bracket from two hundred and fifty thousand and one red after three hundred and forty six thousand you pay fifty one thousand three hundred plus a thirty percent of the amount over two hundred and fifty thousand and so you can see each tax bracket increases until you get to six hundred and seventeen thousand and one read all amounts over that your basic tax is one hundred and seventy eight thousand nine hundred and forty and forty percent of the amount over six hundred and seventeen thousand and this tax table are the rates that are applicable to individuals okay now let's have a look at the rebates okay so there are three rebates there's the primary rebate which everybody gets which is eleven thousand four hundred and forty Rand then is a secondary rebate which you get if you are over 65 years of age that's an additional six thousand three hundred and ninety then there's a tertiary rebate which if you're over 75 years of age you get an additional amount of two thousand one hundred and thirty so if you for example are 78 years old you would get all three of these off your taxable amount okay let's look at our question calculate mr. Moyers a monthly income tax payable for the year 2012-2013 because if we have a look over here he has his taxable income and these his monthly amount here let's go back a slide now his 55 years old which means that he's only going to get the primary rebate get so let's write that dance that we don't forget to take that off remember the rebate is a deduction so that is eleven thousand four hundred and forty red okay let's see which income tax bracket he's in so now he owns four hundred and seven thousand so we're going to go down the table until we get to four hundred and seven thousand here it is in our what we call our fourth income tax bracket Cassidy has our basic amount that he has to pay okay so our basic tax is eighty thousand one hundred range now the next thing we need is a 35% of the march over three hundred and forty six thousand okay so let's calculate so our amount over three hundred and forty six thousand you're going to take your amount 476 over four and we're going to subtract three hundred and forty six thousand okay so let's have a look what that is so it's 407 604 minus three hundred and forty six thousand three hundred and forty six thousand you must be came from exit near at the right number of zeros on okay so this is going to be sixty one thousand

15 thoughts on “Grade 12 Maths Literacy CAPS Complete Syllabus – Revision”

  1. I love it when South Africans make videos. I did pure mathematics in matric but I'm interested in how mathematics literacy looks.

  2. I really do appreciate ur help dear mom, u have done something important to me for future. thanks you very much, I promise you that I will get distinction ❤❤❤💯

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