NATIONAL SENIOR CERTIFICATE GRADE 12

Transcription

1 NATIONAL SENI CERTIFICATE GRADE 12 MATHEMATICAL LITERACY P1 NOVEMBER 2012 MARKS: 150 TIME: 3 hours This question paper consists of 16 pages and 3 annexures.

2 Mathematical Literacy/P1 2 DBE/November 2012 NSC INSTRUCTIONS AND INFMATION 1. This question paper consists of SIX questions. Answer ALL the questions. 2. Answer QUESTION 4.1.7, QUESTION and QUESTION on the attached ANNEXURES. Write your centre number and examination number in the spaces on the ANNEXURES and hand in the ANNEXURES with your ANSWER BOOK. 3. Number the answers correctly according to the numbering system used in this question paper. 4. Start EACH question on a NEW page. 5. You may use an approved calculator (non-programmable and non-graphical), unless stated otherwise. 6. Show ALL the calculations clearly. 7. Round off ALL the final answers to TWO decimal places, unless stated otherwise. 8. Indicate units of measurement, where applicable. 9. Maps and diagrams are NOT necessarily drawn to scale, unless stated otherwise. 10. Write neatly and legibly.

3 Mathematical Literacy/P1 3 DBE/November 2012 NSC QUESTION Simplify: 1 441,62 8,7 2 13, Write 0,0528 as a common fraction in simplified form Convert 23,005 litres to millilitres Determine the total price of 2,5 kilograms of meat costing R63,99 per kilogram Shameeg had to attend a meeting that was scheduled to start at 13:15. At what time did he arrive at the meeting if he arrived 1 hour 18 minutes early? Convert R3 850 to euros ( ) if the exchange rate is 1 = R10, State whether the following event is CERTAIN, MOST LIKELY or IMPOSSIBLE: Christmas Day is on 25 December in South Africa The price per litre of diesel at nine different garages is: R9,97 R9,97 R10,12 R10,17 R10,29 R10,79 R10,79 R10,79 R10,95 Determine the median price per litre of diesel. 1.2 Miss Lena asked all the learners in her class what their favourite fruit juice was. She illustrated the data in the bar graph below. FAVOURITE FRUIT JUICE Types of juice Pineapple Orange Mango Number of learners How many learners does she have in her class? (3)

4 Mathematical Literacy/P1 4 DBE/November 2012 NSC 1.3 Mrs Rose received a cash-sale slip after she bought some goods at CT-Haven at the Cape Town International Airport. Below is a copy of the cash-sale slip with some of the details omitted. NOTE: VAT is value-added tax. CT-HAVEN Cape Town International Airport Domestic Departures, Opposite Gate 8 Tel: (+2721) VAT Reg# TAX INVOICE Reg 1 ID 41 14:54 01/11/11 CHOCOLATE SLAB 14,95 13,95 97,65 JOY MAGAZINE 24,95 24,95 SUBTOTAL 167,45 TOTAL (EXCLUDING VAT)... TOTAL (INCLUDING VAT) 167,45 CASH PAYMENT 167,45 AMOUNT TENDERED 200,00 CHANGE 32,55 Receipt total includes 14% VAT RETAIN AS PROOF OF PURCHASE How much did Mrs Rose pay in total for the THREE slabs of chocolate? How many bangles did Mrs Rose buy? A Joy magazine costs R21,89 excluding VAT. Calculate the amount of VAT paid on the Joy magazine Calculate the total (excluding VAT) for the goods bought. (3)

5 Mathematical Literacy/P1 5 DBE/November 2012 NSC 1.4 South Africa imports crude oil from different countries. TABLE 1 below shows crude oil imports during 2010 and TABLE 1: Crude oil imports during 2010 and 2011 COUNTRY AMOUNT OF CRUDE OIL (IN MILLIONS OF TONS) Angola 3,409 1,948 Iran 5,528 4,874 Nigeria 3,594 3,755 Saudi Arabia 4,584 4,793 Other countries 2,139 2,264 [Source: Business Times, 1 April 2012] Calculate the total amount of crude oil imported during From which country did South Africa import most of its crude oil during 2010 and 2011? Which country showed the largest increase in the amount of crude oil exported to South Africa between 2010 and 2011? [34]

6 Mathematical Literacy/P1 6 DBE/November 2012 NSC QUESTION Didi is a contestant in a game show where they spin a wheel. She can win a prize if the arrow points to a specific colour after she spins the wheel and it stops. The diagram below shows a spin wheel that is divided into 24 equal parts called sectors. When someone spins the wheel, it is equally likely for the arrow to point to any one of the sectors when the wheel stops. One half of the sectors are grey, one third of the sectors are white, 8 1 of the sectors are 1 black and 24 of the sectors are spotted. Pointer (arrow) How many white sectors are there on the spin wheel? Didi spins the wheel. Which sector is the arrow LEAST likely to be pointing at when the wheel stops? The wheel has a radius of 60 cm. (a) Calculate the circumference of the wheel. Use the formula: Circumference of a circle = 2 (b) Calculate the area of ONE of the sectors of the wheel. Use the formula: 2 π (radius) Area of a sector of a circle = n π radius, using π = 3,14 where π = 3,14 and n = number of sectors (3)

7 Mathematical Literacy/P1 7 DBE/November 2012 NSC 2.2 South Africa's Road Traffic Management Corporation reported that sending an SMS (short message service) from a cellphone while driving, increases the reaction time needed to stop a vehicle in an emergency from 1,2 seconds to 1,56 seconds Calculate the percentage increase in the reaction time it takes to stop a vehicle when sending an SMS while driving. Use the formula: difference in time Percentage increase in reaction time = 100% original time (3) Calculate the distance (in metres) that a car will travel in 1,36 seconds if it is travelling at an average speed of 27,95 m/s. Use the formula: Distance = average speed time 2.3 Two businessmen, Mr Nobi and Mr Khoza, travel from their home towns to Pretoria. The distance from Pretoria and the time is indicated in the graph below: 300 TRAVELLING TO PRETIA Distance from Pretoria (in km) Mr Khoza Mr Nobi 0 07:30 08:30 09:30 10:30 11:30 Time At what time did Mr Khoza leave his home town? Which ONE of the two businessmen lives closer to Pretoria? (1) How long did Mr Nobi take to travel to Pretoria? Estimate Mr Khoza's arrival time in Pretoria At what time were the two businessmen exactly 100 km apart?

8 Mathematical Literacy/P1 8 DBE/November 2012 NSC 2.4 Kedibone has a cheque account with Iziko Bank. The bank charges a service fee up to a maximum of R31,50 (VAT included) on all transaction amounts. TABLE 2 below shows five different transactions on Kedibone's cheque account. TABLE 2: Transactions on Kedibone's cheque account NO. DESCRIPTION OF TRANSACTION TRANSACTION AMOUNT SERVICE FEE (IN R) (IN R) 1 Debit order for car repayment 4 250,00 31,50 2 Debit order for cellphone contract 344,50 A 3 Personal loan repayment 924,00 14,59 4 Vehicle and household insurance B 11,85 5 Cheque payment 403,46 8, Calculate the missing value A, using the following formula: Service fee (in rand) = 3,50 + 1,20% of the transaction amount (3) Calculate the missing value B, using the following formula: service fee Amount (in rand) = 1,20% 3,50 (3) [29]

9 Mathematical Literacy/P1 9 DBE/November 2012 NSC QUESTION Mr De Haan and his family live in Mossel Bay and he intends buying a new car. He sees the advertisement below for one of the cars that he is interested in. R cash or R deposit + R3 599,85 60 months on hire purchase Calculate the total cost of the car in the advertisement if it is bought on hire purchase Mr De Haan decides to buy a new car in two years' time instead. He will then sell his current car and use that money as the deposit for the new car. Currently the value of his car is R The value of the car depreciates at a rate of 13,5% per annum. Calculate (rounded off to the nearest R100) the depreciated value of his car in TWO years' time. Use the formula: A = P(1 i ) n where A = depreciated value P = current value i = annual depreciation rate n = number of years (3) 3.2 Petrol consumption can be calculated using the following formula: distance covered Petrol consumption (in litres per 100 km) = 12, How many litres of petrol will Mr De Haan's car use to travel 100 km? (1) Calculate the petrol consumption (in litres per 100 km) if Mr De Haan covered a distance of 325 km.

10 Mathematical Literacy/P1 10 DBE/November 2012 NSC 3.3 Below is a street map of a part of the area where Mr De Haan lives Give the grid reference of the Van Riebeeck Sport Stadium Write down the names of the streets on either side of the City Hall Complex Mr De Haan drives out of the parking area of the Van Riebeeck Sports Stadium and then turns right into George Street. He then turns left into Montague Street and continues driving until he reaches Marsh Street. In which direction must he turn if he wants to go directly to the entrance of the police station? The distance measured on the map from Mr De Haan's house to the entrance of the Bayview Hospital is 8,9 cm. Calculate the actual distance (in km) if 1 cm on the map represents 0,3 km. [16]

11 Mathematical Literacy/P1 11 DBE/November 2012 NSC QUESTION Lunje's dog gave birth to 9 puppies (6 males and 3 females). Lunje's dog with her puppies Lunje collected data from 10 of his friends whose dogs had puppies and summarised the data (including his own) in the table below. TABLE 3: Number of puppies in a litter* NAME OF DOG A B C D E F G H I J K Litter size Number of males Number of females *A litter is the number of puppies born at one birth Arrange the litter sizes in ascending order Which dog had seven more females than males? Give the modal litter size Determine the range of the number of females Calculate the mean (average) number of males. (3) Determine the ratio (in simplified form) of males to females for dog E Use the information in TABLE 3 to complete the compound bar graph on ANNEXURE A. (7)

12 Mathematical Literacy/P1 12 DBE/November 2012 NSC 4.2 Lunje made a rectangular box for his dog to sleep in. This helps to keep the puppies safe and comfortable. The dimensions of the box are as follows: The width is the same as the length of the dog. The length is 125% of the length of the dog. The height is 6 inches. Lunje's dog is 105 centimetres long. Give the following dimensions in centimetres: The length of the box The height of the box if 1 inch = 2,5 cm [24]

13 Mathematical Literacy/P1 13 DBE/November 2012 NSC QUESTION Maria has a house in Qwaqwa. The floor plan of Maria's house showing the actual exterior measurements is given below: mm N Bathroom Bedroom Kitchen mm Window Living Living room Area Front door Step mm How many windows does Maria's house have? (1) On the floor plan the exterior length of the northern wall is 70 mm. Determine the scale of the floor plan in the form 1 : Calculate the exterior side length of the house excluding the step section The area of the kitchen is 72% less than the area of the living room. Calculate the area (in m 2 ) of the kitchen if the area of the living room is 39,54 m 2. (3)

14 Mathematical Literacy/P1 14 DBE/November 2012 NSC 5.2 The step at the front door of Maria's house is in the shape of a symmetrical trapezium based prism as shown below. The step is made of concrete. The top (A) and sides (B and C) will be tiled. h B s A B C f The dimensions of the step are as follows: f = length of the front of the step = 1,3 m s = length of the slanting side = 1,6 m h = height of the step = 0,12 m A = Area of the trapezium = 2,52 m 2 B = Area of the slanting side of the step C = Area of the front of the step Concrete is made by adding water to a mixture of cement, sand and stone in the ratio: cement : sand : stone = 1 : 2 : 4 1 How many wheelbarrows of stone will Maria need for 1 2 bags of cement if one bag of cement equals one wheelbarrow of cement? (3) Calculate the volume of concrete (in m 3 ) required for the step. Use the formula: Volume of the step = area of the trapezium height of the step Maria wants to tile the top and side surfaces of the step. Calculate, rounded off to ONE decimal place, the total area that will be tiled. Use the formula: Total tiled area (in m 2 ) of the step = A + (2s + f) h (4) Maria decides to put a metal strip on the top edge of the step. Calculate the length of the strip. Use the formula: Total length of the strip = f + 2s [19]

15 Mathematical Literacy/P1 15 DBE/November 2012 NSC QUESTION Gracia is an athlete and is training for a 42,2 km standard marathon to be held in four weeks' time. She wants to finish the race in less than 3 hours. Gracia's training schedule involves endurance training and speed training. To build muscle strength she does strength exercises and long-distance running at a slow pace. Gracia runs 450 metres in 4 minutes at a constant pace. Calculate the distance she will cover in 9 minutes if she runs at the same constant pace. 6.2 Other preparation for the race involves 'carbo-loading'. Carbo-loading means following a special diet that will increase the amount of glycogen in your muscles so that the muscles can endure long periods of physical strain/activity. According to the Tips For Endurance Athletes ( an athlete requires between 1,4 and 2,27 grams of carbohydrates per kilogram of body mass per meal. Calculate the MAXIMUM number of grams of carbohydrates Gracia requires per meal if she weighs 65 kg. (3) 6.3 Gracia is sure that her training will allow her to finish the race in less than 3 hours. She doesn't want to start the race too fast and fade (grow tired and run slowly) at the end or start too slowly and then finish later than her targeted time. In order to plan her race, Gracia constructed a table showing the time (in minutes) and the required distance (in km) she needs to cover during the race. TABLE 4: Gracia's plan for the race Time after start of race (in minutes) Distance she needs to cover (in km) , Gracia managed to complete the race in her planned time. How many minutes did she take to finish the race? (1) Calculate the average pace (in kilometres per minute) she needs to maintain from the 60 th to the 90 th minute of the race. Use the formula: Average pace(in km per minute) = = change in distance change in time difference between the two distances difference between the two times (4) Use TABLE 4 to draw a line graph on ANNEXURE B representing Gracia's plan for the race. (8)

16 Mathematical Literacy/P1 16 DBE/November 2012 NSC 6.4 Titus, who was a marshal at the race, was stationed at the halfway point Titus kept the following record of the athletics clubs of the first 20 athletes who ran past him. Athletics Clubs: Liberty Striders Harmony Ramblers Striders Harmony Striders Ramblers Ramblers Harmony Liberty Harmony Liberty Liberty Striders Liberty Harmony Ramblers Striders Harmony Complete, on ANNEXURE C, the frequency table representing the athletic clubs of the first 20 athletes. (4) The data of the club membership of the top 300 athletes that finished the race is represented in the pie chart below. Club membership of the top 300 athletes A 8% E 29% B Key to the chart A Other B Striders C Harmony D Ramblers E Liberty D 12% C 35% (a) What percentage of the top 300 athletes belonged to the Striders Club? (b) Which club had the second largest number of athletes in the top 300? (c) Calculate the actual number of Ramblers athletes that finished in the top 300. [28] TOTAL: 150

17 Mathematical Literacy/P1 DBE/November 2012 NSC CENTRE NUMBER: EXAMINATION NUMBER: ANNEXURE A QUESTION TABLE 3: Number of puppies in a litter NAME OF DOG A B C D E F G H I J K Litter size Number of males Number of females THE LITTER SIZE OF 11 DOGS Number of puppies Females Males A B C D E F G H I J K Name of dog

18 Mathematical Literacy/P1 DBE/November 2012 NSC CENTRE NUMBER: EXAMINATION NUMBER: ANNEXURE B QUESTION TABLE 4: Gracia's plan for the race Time after start of race (in minutes) Distance she needs to cover (in km) ,2 GRACIA'S PLAN F THE RACE Distance (in km) Time (in minutes)

19 Mathematical Literacy/P1 DBE/November 2012 NSC CENTRE NUMBER: EXAMINATION NUMBER: ANNEXURE C QUESTION ATHLETICS CLUB Liberty Striders Ramblers Harmony FREQUENCY

20 NATIONAL SENI CERTIFICATE GRADE 12 MATHEMATICAL LITERACY P1 NOVEMBER 2012 FINAL MEMANDUM MARKS: 150 Symbol M M/A CA A C S RT/RG SF O P R Explanation Method Method with accuracy Consistent accuracy Accuracy Conversion Simplification Reading from a table/reading from a graph Correct substitution in a formula Opinion/Example Penalty, e.g. for no units, incorrect rounding off etc. Rounding off PLEASE NOTE: 1. If a candidate deletes a solution to a question without providing another solution, then the deleted solution must be marked. 2. If a candidate provides more than one solution to a question, then only the first solution must be marked and a line drawn through any other solutions to the question. This memorandum consists of 15 pages. EXTERNAL MODERAT EXTERNAL MODERAT INTERNAL MODERAT MR MA HENDRICKS MR RI SINGH MRS J SCHEIBER 15 NOVEMBER NOVEMBER NOVEMBER 2012

21 Mathematical Literacy/P1 2 DBE/November 2012 NSC Final Memorandum 13 November Rounding off penalty once only in question 5 QUESTION 1 [34 MARKS] Correct answer only: Full marks Ques Solution Explanation AS/L ,62 8,7 2 13, 26 L1 = 1441,62 62, 43 S 1S simplifying = 1441,62 7, = 1 433, ,72 CA L ,0528 = = ,005 = 23, m = m CA R63,99/kg 2,5 kg = R159,975 R159,98 CA h15 min 1h18 min = 11h57 min CA /A (accept R159,97 - no rounding penalty) /A /A 1A writing as a common fraction 1CA simplifying 1M/A multiplying by if multiplied by power of 10 1M/A multiplication to nearest cent 1M/A subtracting 1h18 min L L L Shameeg arrived at 11:57. CA 3 minutes to ,2584 /A 1CA arrival time (Accept 11H57) 1M/A dividing L2 = 375,30 CA CERTAIN 2A conclusion R10,29 2A median L L1

22 Mathematical Literacy/P1 3 DBE/November 2012 NSC Final Memorandum 13 November Ques Solution Explanation AS/L = 60 CA L1 (1) L2 (1) R14,95 /A 1A one correct reading from graph 1A correct reading of the other two values from graph 1CA total of the three (values within the range) (3) 1M/A multiplying L1 = R44,85 CA (CA only when using R14,95 or multiplying 3 with a price on the slip) R167,45 24,95 97,65 = R44, R24,95 R21,89 14% of R21,89 = R3,06 CA CA 97,65 /A 13,95 = 7 bangles CA /A /A 1M/A subtracting the values from the total 1CA the amount 1M/A dividing 1M/A subtracting/ calculating percentage to the nearest cent L L1 /A 14 R24,95 = R3, CA 1 M/A multiplying 1 CA simplification to the nearest cent

23 Mathematical Literacy/P1 4 DBE/November 2012 NSC Final Memorandum 13 November Ques Solution Explanation AS/L R167,45 114% = R 146,89 CA 1M dividing 1A correct values L2 100 R167, = R146,89 CA 14 VAT = R167,45 = R20, M dividing 1A correct values 1 M calculating VAT 1A correct values Total without VAT = R167,45 R20,56 = R146,89 CA /A (1, , , , ,264) millions of tons = 17,634 millions of tons CA tons (if 14% is calculated : 0 marks) (3) 1 M/A adding 1CA total ( if using the wrong data set: max 1 mark) Iran 2A correct country (extra country: 0 marks) Saudi Arabia 2A correct country (1) (1) L L L1 [34]

24 Mathematical Literacy/P1 5 DBE/November 2012 NSC Final Memorandum 13 November QUESTION 2 [29 MARKS] Ques Solution Explanation AS/L L = 8 3 1M multiplying 1A simplification Correct answer only: full marks Spotted sector 2A correct sector (accept dotted sector, black & white sector) (a) (b) Circumference = 2 3,14 60 cm = 376,8 cm (Using π: 376,99 cm) CA SF 2 3,14 60 Area of a sector of a circle = cm² = cm² 24 CA = 471 cm² (using π: 471,24 cm²) SF 1SF substitution 1SF substitution [refer to radius used in (a)] 1A square unit shown anywhere in solution L L L Difference in time Percentage increase in time = 100% original time 1,56 1,2 SF = 100% 1,2 SF = 30 % 0, Distance = (27,95 1,36) m SF = 38,012 m (any one) 38,01 m CA (3) 1SF difference in time 1SF substituting 1,2 ( no subtraction no CA) (3) 1SF substitution 1A simplification L L1

25 Mathematical Literacy/P1 6 DBE/November 2012 NSC Final Memorandum 13 November Ques Solution Explanation AS/L :00 or nine o' clock or 9 am RG 1RG reading from graph Mr Nobi RG 1RG reading from graph (1) hours or 3 hours RG 2RG reading from graph :47 RG (accept any time from 10:45 to 10:50) 2RG reading from graph :00 or nine o' clock or 9 am RG 2RG reading from graph Service fee (in rand) = 3,50 + 1,20% of the transaction amount = 3,50 + 1,20% 344,50 SF = 3,50 + 4,134 7,63 CA Service fee 3,50 Amount (in rand) = 1,20% 11,85 3,50 = 1,20% SF 8,35 = 0, ,83 CA 1SF substituting 344,50 1A simplification 1CA amount to the nearest cent Correct answer only if correctly rounded : full marks (3) 1SF substitution of 11,85 1A simplification 1CA amount to the nearest cent (3) L L L L L L1 L2 (1) L1 [29]

26 Mathematical Literacy/P1 7 DBE/November 2012 NSC Final Memorandum 13 November QUESTION 3 [16 MARKS] Ques Solution Explanation AS/L R deposit + R3 599,85 60 months L1 = R R S 1S simplification = R A = P(1 i ) n CA ( 1 13,5% ) = R = R38 608,41 CA R R 2 SF Correct answer only: full marks 1 SF correct substitution 1 R rounding to the nearest R100 Correct answer only: full marks (3) ,5 1A conclusion Petrol consumption (in litre per 100 km) distance covered = 12, = 12, 5 SF 100 = 40,625 CA (any one) 40,63 1SF substitution (1) L L L2 Petrol consumption (in litre per 100 km) = 12,5 3,25 SF = 40,625 CA (any one) 40,63 1SF substitution of factor 3,25 Correct answer only: full marks

27 Mathematical Literacy/P1 8 DBE/November 2012 NSC Final Memorandum 13 November Ques Solution Explanation AS/L C 4 4 C 1A C L2 1A Long Street and Marsh Street (or High Street) 2A any two correct (1 Penalty if other street names are given) Right (accept Easterly direction) 2A conclusion cm represents 0,3 km 8,9 cm represents 0,3 km 8,9 = 2,67 km 1M multiplying by 8,9 1 A simplification L L L2 1 : 0,3 8,9: 0,3 8,9 8,9 : 2,67 1M multiplying by 8,9 1 A simplification (If unit is incorrect: 1 mark) [16]

28 Mathematical Literacy/P1 9 DBE/November 2012 NSC Final Memorandum 13 November QUESTION 4 [24 MARKS] Ques Solution Explanation AS/L L M ascending order 1 A all correct (descending order: 1 mark, one number omitted: 1 mark, Using names of the dogs: 1 mark) Dog K 2A conclusion (Dog G: give 1 mark) A mode CA from Range = 9 1 = 8 CA Mean = = 11 = 6 CA : 4 = 5 : 2 CA 1M identifying 1 and 9 1CA range 1M sum of the values (no penalty for omitting 0) 1M dividing by 11 1CA mean Correct answer only: full marks (3) 1A correct ratio 1CA simplified ratio (unit ratio 1: 0,4 or 2,5 : 1 give 1 mark; written as a fraction 0 marks; Inverting the ratio 1 mark) Correct answer only: full marks (1) (1) L L L L (1) (1) L1

29 Mathematical Literacy/P1 10 DBE/November 2012 NSC Final Memorandum 13 November Ques Solution Explanation AS/L THE LITTER SIZE OF 11 DOGS L2 16 Number of puppies Female Male A B C D E F G H I J K Name of Dog 1A for each bar drawn correctly (correct litter size only, max 3 marks) cm 1, cm 100 1M multiplying (7) L1 = 131,25 cm = 131,25 cm 1A length Correct answer only: full marks ,5 cm 1M multiplying L2 = 15 cm 1A height Correct answer only: full marks [24]

30 Mathematical Literacy/P1 11 DBE/November 2012 NSC Final Memorandum 13 November QUESTION 5 [19 MARKS] Once off penalty for rounding off Ques Solution Explanation AS/L A 1A conclusion (1) L mm : mm /A 1M/A correct ratio = 1: 100 CA L1 Note: AFRIKAANS additional options mm mm = mm CA /A 1M/A subtraction L1 CA Perimeter = = mm % 39,54 m 2 28,47 m 2 area of the kitchen = 39,54 m 2 28,47 m 2 = 11,07 m 2 CA 100% 72% = 28% area of the kitchen =28% 39,54 m 2 11,07 m 2 CA 1 M finding perimeter 1 CA simplification (no penalty for units) 1M % concept 1M concept of decrease of area 1M concept of decrease of % 1M % concept (no penalty for units) (3) L2

31 Mathematical Literacy/P1 12 DBE/November 2012 NSC Final Memorandum 13 November Ques Solution Explanation AS/L cement : stone = 1 : 4 L2 1,5 bags of cement = 1,5 wheelbarrows of cement 1 For 1 2 wheelbarrows of cement, 1M concept she will need wheelbarrows of stone 1M multiply by 4 = 6 wheelbarrows of stone CA Correct answer only: full marks (3) Volume of the step = Area of the trapezium height of the step L2 = 2,52 m 2 0,12 m SF 1SF substitution = 0,3024 m 3 0,30 m 3 or 0,3 1A simplification (no penalty for units) Total tiled area (in m 2 ) = A + (2s+f) h = 2,52 + (2 1,6+1,3) 0,12 SF L2 = 3,06 3,1 CA R Total length of the strip = 1,3 m + 2 1,6 m = 4,5 m CA SF 1 SF substitution two correct 1 SF substitution another two correct 1R rounding (4) 1SF substitution L1 [19]

32 Mathematical Literacy/P1 13 DBE/November 2012 NSC Final Memorandum 13 November QUESTION 6 [28 MARKS] Ques Solution Explanation AS/L In 4 minutes she covers 450 m L minute she covers m = 112,5 m 4 1M working with ratio in 9 minutes she covers 112,5 9 m = 1 012,5 m CA 4 minutes: 450 m minutes: 4 m = 1012,5 m CA 1M working with ratio 6.2 Grams of carbohydrate = 2,27 65 = 147,55 CA 1A using 2,27 1M multiplying Correct answer only: full marks (3) minutes RT 1RT reading from table (1) L L SF Average pace (in km per minute) = SF 8 4 = = S ,27 CA 1SF distances 1SF times 1S simplification 1CA average pace (if inverted, max 2 marks; if using other values from the table, max 2 marks) (4) L1

33 Mathematical Literacy/P1 14 DBE/November 2012 NSC Final Memorandum 13 November Ques Solution Explanation AS/L GRACIA'S PLAN F THE RACE L Distance (in km) Time (in minutes) No penalty for omitting (0;0) and joining 6A any 6 points plotted correctly 1A all correct points joined 1M correct shape (not a straight line) If only a Bar graph is correctly drawn - max 4 marks (8)

34 Mathematical Literacy/P1 15 DBE/November 2012 NSC Final Memorandum 13 November Ques Solution Explanation AS/L ATHLETIC CLUB FREQUENCY Liberty 5 Striders 5 Ramblers 4 Harmony (a) (b) (c) Striders Club = 100% ( )% /A = 16% CA Liberty or club E or E Actual number of Ramblers athletes = 12% 300 /A = 36 CA 4A one mark for each correct frequency (just tallies or frequencies as fractions :MAX 2 marks) (4) 1M/A subtracting from 100% Correct answer only: full marks 2A correct club 1M/A calculating actual number TOTAL: L L L L1 [28]

35 GRAAD 12 NATIONAL SENI CERTIFICATE GRADE 12 MATHEMATICAL LITERACY P2 NOVEMBER 2012 MARKS: 150 TIME: 3 hours This question paper consists of 15 pages and 3 annexures.

36 Mathematical Literacy/P2 2 DBE/November 2012 NSC INSTRUCTIONS AND INFMATION 1. This question paper consists of FIVE questions. Answer ALL the questions. 2. Answer QUESTION 3.1.2(c), QUESTION and QUESTION on the attached ANNEXURES. Write your examination number and centre number in the spaces provided on the ANNEXURES and hand in the ANNEXURES with your ANSWER BOOK. 3. Number the answers correctly according to the numbering system used in this question paper. 4. Start EACH question on a NEW page. 5. You may use an approved calculator (non-programmable and non-graphical), unless stated otherwise. 6. Show ALL calculations clearly. 7. Round off ALL final answers to TWO decimal places, unless stated otherwise. 8. Indicate units of measurement, where applicable. 9. Maps and diagrams are NOT necessarily drawn to scale, unless stated otherwise. 10. Write neatly and legibly.

37 Mathematical Literacy/P2 3 DBE/November 2012 NSC QUESTION The Nel family lives in Klerksdorp in North West. They travelled by car to George in the Western Cape for a holiday. A map of South Africa is provided below. MAP OF SOUTH AFRICA SHOWING THE NATIONAL ROADS N KEY: N1 N12, N17 represent national roads. Use the map above to answer the following questions In which general direction is George from Klerksdorp? Identify the national road that passes through only ONE province The family travelled along the N12 to Kimberley. When they reached Kimberley, they took a wrong turn and found themselves travelling on the N8 towards Bloemfontein. Describe TWO possible routes, without turning back to Kimberley, that the family could follow to travel from Bloemfontein to George. Name the national roads and any relevant towns in the description of the two routes. (4)

38 Mathematical Literacy/P2 4 DBE/November 2012 NSC 1.2 The Nel family (two adults and two children) were on holiday for nearly one week. They left home after breakfast on Saturday morning and arrived at the guesthouse in time for supper. On Sunday and Wednesday they ate all their meals at the guesthouse. On Monday they visited a game park. On Tuesday they went on a nature walk. On Thursday they went on a boat cruise. They left George after breakfast on Friday and returned to Klerksdorp. TABLE 1: The Nel family's holiday costs ITEM COST * 1 Accommodation only R1 050 per day per family 2 Meals at the guesthouse: Breakfast R60 per person per day Lunch R90 per person per day Supper R120 per person per day 3 Travelling costs: Long distance driving (to and from Klerksdorp) and meal costs en route R1 602,86 for the return trip Local driving (in and around George) 4 Entertainment costs: Nature walk, including breakfast Visit to the game park, including lunch Boat cruise, including supper R513,60 for the duration of the holiday R120 per adult and R100 per child R200 per person R200 per adult and R150 per child Other entertainment R2 000 *All the costs above include value-added tax (VAT). Use the information above to answer the following questions Determine the total amount that they paid for accommodation (a) Write down an equation that could be used to calculate the total cost of meals eaten at the guesthouse in the form: Total cost (in rand) =... (3) (b) Use TABLE 1 and the equation obtained in QUESTION 1.2.2(a) to calculate the total cost of the meals that they ate at the guesthouse if they ate THREE meals daily. (4) Mr Nel stated that the total cost of the holiday was less than R Verify whether or not Mr Nel's statement is correct. ALL calculations must be shown. (9) [26]

39 Mathematical Literacy/P2 5 DBE/November 2012 NSC QUESTION On 14 February 2012 there was a queue of customers waiting to eat at Danny's Diner, a popular eating place in Matatiele. The time (in minutes) that 16 of Danny's customers had to wait in the queue is given below: A B B B is a value greater than The range of the waiting times was 37 minutes and the mean (average) waiting time was 34 minutes. (a) Calculate the missing value A, the longest waiting time. (b) Hence, calculate the value of B. (4) (c) Hence, determine the median waiting time. (3) The lower quartile and the upper quartile of the waiting times are 27 minutes and 41,5 minutes respectively. How many of the 16 customers had to wait in the queue for a shorter time than the lower quartile? Danny's previous records, for 16 customers on 7 February 2012, showed that the median, range and the mean (average) of the waiting times were 10 minutes, 5 minutes and 10 minutes respectively. Compare the statistical measures relating to the waiting times on 7 and 14 February and then identify TWO possible reasons to explain the difference in these waiting times. (4)

40 Mathematical Literacy/P2 6 DBE/November 2012 NSC 2.2 The pie chart below shows the percentage of customers who ordered different meals at Danny's Diner on 14 February Percentage of customers who ordered different meals Sausage 10% Chicken Lamb 25% Beef 20% Fish 30% If 40 customers ordered beef meals, determine how many customers ordered chicken meals. (4) A customer is randomly selected. What is the probability that the customer would NOT have ordered a lamb meal?

41 Mathematical Literacy/P2 7 DBE/November 2012 NSC 2.3 Danny bought a braai drum to cater for those customers who wanted 'shisanyama' or grilled meat. The braai drum is made by cutting a cylindrical drum in half and placing it on a stand, as shown in the picture below. The semi-cylindrical braai drum has a diameter of 572 mm and a volume of 108 l. A rectangular metal grid with dimensions 1% greater than the dimensions of the braai drum is fitted on top. H D H = Height of the drum D = Diameter of the drum The following formulae may be used: Volume of a cylinder = π (radius) 2 (height) where π = 3,14 Area of a rectangle = length breadth 1l = mm 3 = 0,001 m Danny filled 3 1 of the base of the drum with sand. Give TWO practical reasons why sand was placed in the braai drum. (4) Calculate the length (in mm) of the rectangular metal grid. Show ALL your calculations. (9) [34]

42 Mathematical Literacy/P2 8 DBE/November 2012 NSC QUESTION 3 Longhorn Heights High School needs R7 000,00 to buy a new computer. The finance committee decides to sell raffle tickets to raise funds. A food hamper donated by one of the school's suppliers will be the prize in the raffle. A raffle is a way of raising funds by selling numbered tickets. A ticket is randomly drawn and the lucky ticket holder wins a prize. 3.1 The committee decides to sell the raffle tickets at R2,00 each. The tickets will be divided evenly amongst a number of ticket sellers Write down a formula that can be used to calculate the number of tickets to be given to each ticket seller in the form: Number of R2,00 tickets per seller = TABLE 2 below shows the relationship between the number of ticket sellers and the number of tickets to be sold by each seller. TABLE 2: Sale of R2,00 raffle tickets Number of ticket P sellers Number of tickets Q 25 per seller (a) Identify the type of proportion represented in TABLE 2 above. (1) (b) Calculate the missing values P and Q. (4) (c) Use the information in TABLE 2 or the formula obtained in QUESTION to draw a curve on ANNEXURE A to represent the number of ticket sellers and the number of tickets sold by each seller. (4) 3.2 The finance committee changed their plan and decided to sell the tickets at R5,00 each instead Give a possible reason why they made this decision State ONE possible disadvantage of increasing the price of the tickets On ANNEXURE A, draw another curve representing the number of ticket sellers and the number of R5,00 tickets sold by each seller. Show ALL the necessary calculations. (8) Use your graph, or otherwise, to calculate the difference between the number of R2,00 and R5,00 tickets that must be sold by 70 ticket sellers, assuming the ticket sellers sell all their tickets. (3) [26]

43 Mathematical Literacy/P2 9 DBE/November 2012 NSC QUESTION 4 A local airline company uses three types of aircraft for its domestic and international flights, namely Jetstreams, Sukhois and Avros. Below is a picture of the Jetstream aircraft as well as a table showing information on the three types of aircraft. Length of the Jetstream TABLE 3: Information on the three types of aircraft TYPE OF AIRCRAFT JETSTREAM SUKHOI AVRO Maximum number of passengers Length 19,25 m 26,34 m 28,69 m Wing span* 18,29 m 20,04 m 21,21 m Height 5,74 m 6,75 m 8,61 m Fuel capacity (in kg)** kg kg kg Maximum operating altitude*** ft (feet) ft (feet) ft (feet) Maximum cruising speed**** 500 km/h 800 km/h 780 km/h [Source: Skyway, November 2011] * The distance from the tip of the left wing to the tip of the right wing ** The mass of the fuel in the tank *** The recommended maximum height that the aircraft should fly at for best fuel efficiency ****The maximum average speed that the aircraft flies at its maximum height 4.1 Use TABLE 3, which is also given on ANNEXURE B, to answer the following Mr September flew from Johannesburg to Polokwane along with 37 other passengers. In which aircraft was he travelling? Explain your answer. (3) The length of the Jetstream in the picture is 9,9 cm, while its actual length is 19,25 m. Determine the scale (rounded off to the nearest 10) of the picture in the form 1: (4)

44 Mathematical Literacy/P2 10 DBE/November 2012 NSC A nautical mile is a unit of measurement based on the circumference of the earth. 1 nautical mile = 1,1507 miles = feet = 1,852 kilometres Calculate the maximum operating altitude (to the nearest nautical mile) of the Jetstream. (3) Ms Bobe travelled in an aircraft that covered a distance of 510 km in 39 minutes. Determine, showing ALL calculations, in which ONE of the three aircraft she could have been travelling. The following formula may be used: Distance = average cruising speed time (4) Determine the fuel capacity (to the nearest litre) of the Avro aircraft. Use the formula: Fuel capacity (in litres) = fuel capacity (in kg) 820g (3)

45 Mathematical Literacy/P2 11 DBE/November 2012 NSC 4.2 The table below shows the schedule of flights between Johannesburg and Polokwane. TABLE 4: Schedule of South African Airways flights between Johannesburg and Polokwane FLIGHT ROUTE DEPARTURE ARRIVAL OPERATING DAYS NUMBER TIME TIME SA 8801 JNB POL 06:35 07: SA 8802 POL JNB 07:55 08: SA 8809 JNB POL 11:40 12: SA 8809 JNB POL 11:40 12:30 7 SA 8810 POL JNB 13:00 14: SA 8810 POL JNB 13:00 13:55 7 SA 8817 JNB POL 13:15 14: SA 8818 POL JNB 14:25 15: SA 8815 JNB POL 16:30 17: SA 8816 POL JNB 17:45 18: [Source: Skyways, November 2011] KEY: JNB = Johannesburg; POL = Polokwane 1 = Monday 2 = Tuesday 3 = Wednesday 4 = Thursday 5 = Friday 6 = Saturday 7 = Sunday Use TABLE 4 above to answer the following questions Mr Likobe has to fly from Johannesburg to Polokwane on a Thursday to attend a business meeting that starts at exactly 13:00 and finishes at exactly 15:30. He needs to be present for the full duration of the meeting. He has to attend a 1-hour meeting at 08:30 with a client in his office in Johannesburg before his flight. His office is 30 minutes' drive from the Tambo International Airport in Johannesburg. The meeting venue in Polokwane is a 5-minute drive from the airport. Passengers need to check in at the airport at least 1 hour before the departure time of their flight. Which flight numbers should he book for his trip if he has to return to Johannesburg on the same day? (3) On ANNEXURE B a line graph representing the number of flights available daily for the Johannesburg-to-Nelspruit route has been drawn. (a) Use ANNEXURE B and the information in TABLE 4 above to draw a line graph representing the number of flights available daily for the Johannesburg-to-Polokwane route. (4) (b) Use the line graphs on ANNEXURE B to determine on which day each route has the lowest number of flights available. Give ONE reason why there are fewer flights on this particular day. (3) [27]

46 Mathematical Literacy/P2 12 DBE/November 2012 NSC QUESTION Mr Stanford owns a company that sells health care products. The company pays R50 per item plus R3 500 for shipping and packaging. They sell the items at R120 each. The graph below shows the company's costs and income according to the number of items sold COSTS AND INCOME OF HEALTH CARE PRODUCTS Income Costs Amount (in rand) Number of items Use the graph above to determine the exact number of items sold that will give a loss of R (3) Mr Stanford stated that the company would break even if 40 items were sold at R137,50 each. Verify whether Mr Stanford's statement is correct or not. Show ALL the necessary calculations. (4)

47 Mathematical Literacy/P2 13 DBE/November 2012 NSC 5.2 Mr Stanford employed eight salespersons in his company. He budgeted R for bonuses at the end of 2010 for his salespersons. He allocated the bonuses according to each salesperson's contribution to the total sales for the year. TABLE 5 below shows the total annual sales of health care products for each salesperson during 2010 and 2011 with some information omitted. TABLE 5: Total annual sales of health care products during 2010 and NAME OF SALES AS A SALESPERSON PERCENTAGE SALES (IN THOUSANDS OF RANDS) SALES (IN THOUSANDS OF RANDS) SALES AS A PERCENTAGE Carl Themba 750 K Mabel Vanessa L Henry Vivesh 900 M Peter Cindy TOTAL N Use the information above to answer the following questions Calculate the missing values N, K and L. (7) Vivesh received a bonus of R in The other salespeople objected and claimed that he should have received less than this amount. Verify, showing ALL the necessary calculations, whether this objection was valid or not. (5)

48 Mathematical Literacy/P2 14 DBE/November 2012 NSC For 2011 Mr Stanford decided to allocate 6,5% of the total sales to bonuses and that each salesperson would be paid a basic bonus as shown in TABLE 6 below. The remaining budgeted amount for bonuses would then be shared equally amongst all the salespersons. TABLE 6: Basic bonus structure for 2011 CATEGY AMOUNT IN RAND Sales up to and including 10% Sales of more than 10% up to and including 20% Sales of more than 20% (a) Use TABLE 5 and TABLE 6 on ANNEXURE C to determine Henry's basic bonus. (b) Verify, showing ALL calculations, whether Mabel's total bonus is more than R (8)

49 Mathematical Literacy/P2 15 DBE/November 2012 NSC 5.3 Mr Stanford was given the following graph by his sales director showing the percentage sales for each salesperson in 2011 and PERCENTAGE SALES IN 2011 AND 2012 Cindy Peter Name of salesperson Vivesh Henry Vanessa Mabel Themba Carl Percentage sales Interpret the change in the percentage sales for Vivesh from 2011 to After he looked at the graph, Mr Stanford identified Henry and Mabel as the two top salespeople for 2012 with sales of 45% each. What errors did Mr Stanford make in his interpretation of the graph? Explain your answer. (4) Name TWO other types of graphs that the sales director could have used so that Mr Stanford would not misinterpret the graph so easily. [37] TOTAL: 150

50 Mathematical Literacy/P2 DBE/November 2012 NSC CENTRE NUMBER: EXAMINATION NUMBER: ANNEXURE A QUESTION 3.1.2(c) and QUESTION SALE OF RAFFLE TICKETS Number of tickets sold by each seller Number of ticket sellers

51 Mathematical Literacy/P2 DBE/November 2012 NSC CENTRE NUMBER: EXAMINATION NUMBER: ANNEXURE B QUESTION 4.1 TABLE 3: Information on the three types of aircraft TYPE OF AIRCRAFT JETSTREAM SUKHOI AVRO Maximum number of passengers Length 19,25 m 26,34 m 28,69 m Wingspan* 18,29 m 20,04 m 21,21 m Height 5,74 m 6,75 m 8,61 m Fuel capacity (in kg)** kg kg kg Maximum operating altitude*** ft (feet) ft (feet) ft (feet) Maximum cruising speed**** 500 km/h 800 km/h 780 km/h [Source: Skyway, November 2011] QUESTION NUMBER OF FLIGHTS AVAILABLE PER DAY 6 Number of flights 4 JNB - NEL 2 0 Monday Tuesday Wednesday Thursday Day Friday Saturday Sunday

52 Mathematical Literacy/P2 DBE/November 2012 NSC NOTE: THIS IS AN INFMATION SHEET ONLY. DO NOT ANSWER QUESTION 5.2 ON THIS ANNEXURE AND DO NOT HAND IT IN. ANNEXURE C: INFMATION SHEET QUESTION 5.2 TABLE 5: Total annual sales of health care products during 2010 and NAME OF SALESPERSON SALES (IN THOUSANDS SALES AS A PERCENTAGE SALES (IN THOUSANDS SALES AS A PERCENTAGE OF RANDS) OF RANDS) Carl Themba 750 K Mabel Vanessa L Henry Vivesh 900 M Peter Cindy TOTAL N QUESTION 5.2.3(a) TABLE 6: Basic bonus structure for 2011 CATEGY AMOUNT IN RAND Sales up to and including 10% Sales of more than 10% up to and including 20% Sales of more than 20%

53 NSC Final Memorandum + NATIONAL SENI CERTIFICATE GRADE 12 MATHEMATICAL LITERACY P2 NOVEMBER 2012 FINAL MEMANDUM MARKS: 150 Symbol M M/A CA A C S RT/RG SF O P R J Explanation Method Method with accuracy Consistent accuracy Accuracy Conversion Simplification Reading from a table/reading from a graph Correct substitution in a formula Opinion/Example Penalty, e.g. for no units, incorrect rounding off, etc. Rounding off Justification PLEASE NOTE: 1. If a candidate deletes a solution to a question without providing another solution, then the deleted solution must be marked. 2. If a candidate provides more than one solution to a question, then only the first solution must be marked and a line drawn through any other solutions to the question. This memorandum consists of 19 pages.

54 Mathematical Literacy/P2 2 DBE/November 2012 Final Memorandum QUESTION 1 [26 MARKS] Ques Solution Explanation AS South-westerly (accept abreviations for compass directions) N5 N17 A A One possible route: A From Bloemfontein turn onto the N1 and travel south until Beaufort West. Then turn onto the N12 until George. A A second possible route: A From Bloemfontein turn onto the N1 and travel south until the intersection with the N9. Then follow the N9 until George. A 2A correct direction 1A Southerly 1A Westerly 2A correct national road N17 accepted due to unclear provincial boundaries 1A N1 1A N12 and Beaufort West 1A N1 1A N L L L2 A third possible route: A From Bloemfontein turn onto the N1 and travel south until the intersection with N10. Then follow the N10 in a south easterly direction until the N2. Then follow the N2 in a westerly direction until George. A A fourth possible route: A From Bloemfontein turn onto the N1 and later turn onto the N6 to East London. Then follow the N2 in a westerly direction until George. A A fifth possible route: A From Bloemfontein turn north onto the N1, turn right unto N5, take a right unto N3 pass Pietermaritzburg to Durban. Then at Durban turn south unto the N2, pass East London, Port Elizabeth and continue until George. A NOTE: Follow the learners route. But leaners cannot go back to Kimberley (No N8 route). 1A N1 1A N10, N2 1A (N1) N6 and East London, 1A N2 1A N1; N5 and 1A N3 Durban; N2 (4)

55 Mathematical Literacy/P2 3 DBE/November 2012 Final Memorandum Ques Solution Explanation AS Total amount for accommodation = R = R6 300 CA (a) (due to language interpretation) Total amount for accommodation = R = R7 350 CA Total cost (in rand) = (60 4 number of breakfasts) + (90 4 number of lunches) + (120 4 number of suppers) 1A rate 6 Correct answer only full marks Note: Equation must have a variable 1M adding 1M multiplying cost 1M multiplying by 4 or number of people L L3 Total cost (in rand) = (60 x + 90 y z) 4 Where x = number of breakfasts y = number of lunches and z = number of suppers 1M adding 1M costs in terms of meals 1M variables explained Total cost (in rand) = (number of days n 60) + (number of days n 90) + (number of days n 120) Where n = number of people 1M adding 1M costs in terms of meals 1M variable explained (b) Total cost (in rand) = (Sat + Sun + Mon + Tues + Wed + Thurs + Fri) cost = 120n + 270n + 180n + 210n + 270n n + 60n) = n Where n = number of people Total cost (in rand) = (60 4 S 5) + (90 4 4) + (120 S 4 5) = CA CA = M adding 1M costs in terms of days 1M variable explained 270 number of people/meals - (1 mark only) (3) REFER TO CANDIDATE S FMULA Correct answer only full marks 1S correct substitution of number of people 1S correct substitution of number of meals 1CA total L3

56 Mathematical Literacy/P2 4 DBE/November 2012 Final Memorandum Ques Solution Explanation AS Total cost (in rand) = (60 x + 90 y z) 4 = ( ) 4 = CA = CA S S 1S correct subst. no. of people 1S correct subst. no. of meals 1CA total (using equation from (a) working with daily cost) Total cost (in rand) = S S = CA CA 2S substitution of no. of people 2CA total (calculating total daily costs) Cost of meals: Saturday = R120 4 = R480 Sunday = (R60 + R90 + R120) 4 = R1 080 Monday = (R60 + R120) 4 = R720 Tuesday = (R90 + R120) 4 = R840 Wednesday = (R60 + R90 + R120) 4 = R1 080 Thursday = (R60 + R90) 4 = R600 Friday = R60 4 = R240 Total cost (in rand) = = CA (calculating total cost of types of meals) S S CA 2S correct subst. daily cost 1CA total Total cost of breakfast = R = R1 200 Total cost of lunches = R = R1 440 Total cost of suppers = R = R2 400 S S 2S correct subst. meal cost Total cost (in rand) = CA = CA 1CA total (4)

57 Mathematical Literacy/P2 5 DBE/November 2012 Final Memorandum Ques Solution Explanation AS Cost for nature walk = (R120 2) +(R100 2) /A = R440 CA Cost for game park = R200 4 = R800 Cost for boat cruise = (R200 2) + (R150 2) /A = R700 CA Total entertainment cost = R440 + R800 + R700 + R2 000 = R3 940 CA Six day option: Total cost for the trip (accom. + meals + long dist. + local + ent) /A =R R R1 602,86 + R513,60 + R3 940 = R17 396,46 CA Seven day option: Total cost for the trip (accom. + meals + long dist. + local + ent) /A =R R R1 602,86 + R513,60 + R3 940 = R18 446,46 CA 1M/A expression for cost 1A cost for game park 1M/A expression for cost 1CA total cost 1M/A adding all costs 1CA total cost 1M/A adding all costs 1CA total cost L4 Mr Nel's estimate was CRECT J 1J verification (9) [26]

58 Mathematical Literacy/P2 6 DBE/November 2012 Final Memorandum QUESTION 2 [34 MARKS] Ques Solution Explanation AS 2.1.1(a) A 15 = 37 A = 52 A = = (b) The mean for 16 customers is 34 minutes total waiting time = = 544 Total of known waiting times = = 494 1M concept of range 1A simplification Correct answer only full marks Refer to value of A in 2.1.1(a) 1M total waiting time 1M total of known times L L3 Difference is = 50 S 2 customers have a total waiting time of 50 minutes 50 B = = 25 CA 2 Mean = B + B = 34 1S difference of the totals 1CA value of B 1M adding all the values 1M dividing by B = B = (34 16) 494 S = 50 B = 25 CA ( 34 16) 494 B = S 2 = 25 CA 1S simplification 1CA value of B (c) Waiting times are: /A 15; 25; 25; 26; 28; 30; 32; 34; 35; 36; 38; 40; 41; 42; 45; Median = 2 = 34,5 CA Correct answer only - full marks (4) (Using A and B values calculated above) 1M/A arranging 16 terms in ascending order 1M median concept (even number of terms) (3) L3

59 Mathematical Literacy/P2 7 DBE/November 2012 Final Memorandum Ques Solution Explanation AS CA The mean, median and range for 7 February are less than those for 14 February. O This means that his customers had to wait for a shorter time on 7 February than on 14 February. O Any two of the reasons below: It could be that more people came to eat at his eating place on 14 February, because of Valentine's Day. J He had less staff on the 14 th, J He had the same number of staff but did not anticipate the increased number of customers. J His equipment was faulty on the 14 th people had to wait longer to be served J The electicity was off for a while J The mean, median and range for 14 February are more than those for 7 February. O This means that his customers had to wait for a longer time on 14 February than on 7 February. O Any two of the reasons below: It could be that less people came to eat at his eating place on 7 February, because of Valentine's Day. J He had more staff on the 7 th, J He had the same number of staff but did not anticipate the difference in number of customers. J His equipment was working well on the 7 th people did not wait long to be served J No electicity problems on the 7 th J Any other valid, well thought out reason will be accepted 2CA correct number Note if B is greater than 27 answer can be 2 2O comparing the measures Accept a comparison table of correct values 2J conclusion (4) L4

60 Mathematical Literacy/P2 8 DBE/November 2012 Final Memorandum Ques Solution Explanation AS Percentage ordering chicken = 15% If 20% of the total = % of the total = = % of the total = 15 2 = 30 20% : 40 = 15% : x 15% x = 40 S 20% = 30 CA 20% of total = Total = 20% = % of 200 = 30 CA P(not lamb) = 1 25% = 75% 0,75 4 Percentage not ordering lamb = = 75 3 P(not lamb) = 75% 0,75 4 CA Number of people not ordering lamb = = 150 1A percentage ordering chicken 1M finding 1% 1A multiplying by 15 1M using proportion 1A percentage ordering chicken 1S expression for x 1M finding total no. of customers 1A total number of customers 1A percentage ordering chicken Correct answer only full marks 1M subtracting from100 % 1A simplification 1M adding percentages 1A simplification 1M adding actual numbers (4) L2 L P(not lamb) = = ,75 75% 1A simplification Correct answer only - Full marks

61 Mathematical Literacy/P2 9 DBE/November 2012 Final Memorandum Ques Solution Explanation AS Two of the following possible reasons: To protect the base of the drum from burning. To bring the fire closer to the grid. To spread the coals evenly. (Perfect the braaing) To use less coal. To stabilise the drum. To retain the heat of the burning coals. The sand can be used to put out the fire. Accept any two valid reasons. O O Volume of the braai drum = 108 l = mm 3 = mm 3 C 2O reason 2O reason 1C volume in mm 3 (4) L4 572 mm Radius of the braai drum = = 286 mm 2 Volume of the braai drum = 21 π (radius) 2 (height) SF mm 3 = 21 3,14 (286 mm) 2 (height) mm Height = 2 3,14 (286 mm) 3 = 840,99 mm CA (840,56... mm using π ) 841 mm 1A value of radius 1M using 2 1 cylinder 1SF substitution into formula 1M Finding expression for height 1CA for height only But length of grid = 1% more than height of drum 1% of 840,99 mm = 8,4099 CA Length of grid = 840,99 mm + 8,4099 = 849,41 mm Length of grid = 101% of 840,99 mm = 849,40 mm CA 1M calculation percentage 1M increasing by 1% 1CA length of grid 1M increasing by 1% 1M calculation percentage 1CA length of grid No penalty if answer is rounded to 850 mm (9) [34]

62 Mathematical Literacy/P2 10 DBE/November 2012 Final Memorandum QUESTION 3 [26 MARKS] Ques Solution Explanation AS Number of R2,00 tickets per seller = 3500 number of sellers Number of R2,00 ticket per seller = 2 number of sellers Number of R2,00 tickets per seller = = 2n n where n = number of sellers 1A using A dividing by number of sellers 1A using A dividing by number of sellers L (a) Indirect/Inverse proportion (b) 3500 P = P : 70 = 50 : CA CA 70 = 14 = 50 = A correct type of proportion two answers zero marks 1A finding the number of tickets 1M dividing by 250 1CA correct value of P (1) L L Q = 125 = 28 CA 1CA correct value of Q Correct answer only - Full marks (4)

63 Mathematical Literacy/P2 11 DBE/November 2012 Final Memorandum (c) L2 R2 Tickets CA 1A correct plotting of point (20;175) 1A correct plotting of point (140;25) 1A one other point plotted correctly 1CA joining the plotted points by a "smooth" curve (section from 20 ticket sellers to 100 ticket sellers) (4) Fewer tickets have to be sold. J To reduce the number of sellers. To raise the money faster (in a shorter time) To raise more money/to buy more computers J J J Fewer people can afford (too expensive) to buy the R5,00 tickets. Some of the sellers might not be able to sell all their tickets 2J reason for decision 2J disadvantage (1) (1) L (1) (1) L4

64 Mathematical Literacy/P2 12 DBE/November 2012 Final Memorandum Ques Solution Explanation AS R7 000,00 Number of tickets to be sold = R5 = Number of tickets per person = 1400 CA number of sellers The possible points learners can use: (other point values can be used) M dividing by R5 1A number of tickets to be sold 1CA formula Showing values in a table/co-ordinates - 3 marks (3) (5) L3 (4) L4 (4) R2 Tickets CA R5 Tickets 4CA any 4 points plotted correctly 1CA joining the plotted points by a smooth curve (8)

65 Mathematical Literacy/P2 13 DBE/November 2012 Final Memorandum Ques Solution Explanation AS At R2 per ticket 50 tickets must be sold At R5 per ticket 20 tickets must be sold Difference = = 30 tickets CA RG RG 1RG reading from graph 1RG reading from graph 1 CA difference in number of tickets (1) L Number of R2,00 tickets per person = 70 = Number of R5,00 tickets per person = 70 = 20 Difference = tickets = 30 tickets CA 1M calculating the number of R2,00 tickets 1M calculating the number of R5,00 tickets 1CA difference in number of tickets Answer only Full marks Accept values from 29 to 32. (refer to candidate's graph) (3) [26]

66 Mathematical Literacy/P2 14 DBE/November 2012 Final Memorandum QUESTION 4 [27 MARKS] Ques Solution Explanation AS Avro J It is the only one that can take ME than 37 passengers (himself plus 37 others) Scale is 9,9 cm to 19,25 m C or 9,9 cm to cm 0,099 m : 19,25 m 1925 Scale = 1 : CA 9,9 = 1 : 194,44 = 1 : 190 CA 1 : CA 19,25 0, Maximum Operating Altitude = feet RT = nautical miles = 4,1145 nautical miles 4 nautical miles CA Distance = average cruising speed time 510 km = average cruising speed 39 minutes SF 1A correct aircraft 2J justification (3) 1M scale concept 1C converting to the same unit 1CA dividing to bring to a unit ratio 1CA rounding off Reversed ratio maximum 2 marks No conversion maximum 2 marks Correct answer only- full marks (4) 1RT reading from the table 1M dividing by 6076 ft 1CA nearest nautical mile 1SF substitution (3) L (1) (3) L L L3 L4 510 km Average cruising speed = 39 minutes 510 km = 0,65 h C = 784,62 km/h CA 1C converting to hours 1CA average speed Ms Bobe was travelling in the SUKHOI J C 39 Distance (Jetstream) = (500 )km = 325 km SF Distance (Sukhoi) = (800 )km = 520 km CA 60 1J identification of Aircraft 1SF substitution 1C converting to hours 1CA distance travel 39 Distance (Avro) = (780 )km = 507 km 60 Ms Bobe was travelling in the SUKHOI J 1J identification of Aircraft

67 Mathematical Literacy/P2 15 DBE/November 2012 Final Memorandum Ques Solution AS Ques cont Comparing time distance Time = speed 510 SF CA C Time (Jetstream) = h = 1,02 hours = 61,2 minutes 500 1SF substitution 1CA time taken 510 Time (Sukhoi) = h = 0,6375 hours = 38,25 minutes 800 1C converting to minutes 510 Time (Avro) = h = 0, hours = 39,23 minutes 780 Ms Bobe was travelling in the SUKHOI J 1J identification of Aircraft (4) fuel capacity (in kg) Fuel capacity (in litres) = 820g 9362 kg = SF 820 g g = C 820g = , CA 1SF substitution 1C converting to grams 1CA nearest litre L2 L3 (1) fuel capacity (in kg) Fuel capacity (in litres) = 820g 9362 kg = SF 820 g 9362 kg = C 0,820 kg = , CA 1SF substitution 1C converting to kilograms 1CA nearest litre Johannesburg to Polokwane: SA 8809 Polokwane to Johannesburg: SA 8816 No conversion - maximum 2 marks (3) 2A correct flight number 1A correct flight number (3) L3

68 Mathematical Literacy/P2 16 DBE/November 2012 Final Memorandum Ques Solution AS 4.2.2(a) L3 CA 1A drawing the horizontal line at 4 1A plotting (Saturday; 2 ) 1A plotting (Sunday; 3) 1CA joining the plotted points (b) Saturday 1A correct day (4) L4 Not many people travel on Saturday, as most business meetings are scheduled during the week. O 2O own opinion based on candidates graph If people go away for the weekend on holiday, they travel there on a Friday and travel back on Sunday. O Possible religious reason O Any other valid reason O (3) [27]