GRADE 11 NOVEMBER 2015 MATHEMATICAL LITERACY P2

Transcription

1 NATIONAL SENIOR CERTIFICATE GRADE 11 NOVEMBER 2015 MATHEMATICAL LITERACY P2 MARKS: 100 TIME: 2 hours *imlit2* This question paper consists of 12 pages, including an annexure of 3 pages.

2 2 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2015) INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of FOUR questions. Answer ALL the questions. 2. QUESTION 1.1 must be answered with reference to ANNEXURE A, QUESTION must be answered on ANNEXURE B and QUESTION must be answered on ANNEXURE C. Write your NAME and CLASS GROUP on ANNEXURES B and C and hand in with your ANSWER BOOK. 3. Number the questions correctly according to the numbering system used in this question paper. 4. An approved calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 5. ALL calculations must be clearly shown. 6. Round off ALL final answers appropriately according to the given context, unless stated otherwise. 7. Start EACH question on a NEW page. 8. Write neatly and legibly.

3 (EC/NOVEMBER 2015) MATHEMATICAL LITERACY P2 3 QUESTION Study the floor plan of the Greenacres Shopping Centre in Port Elizabeth (ANNEXURE A) and answer the questions that follow How many entrances can you use to access the centre? (2) You get a call from your friend. The two of you lost each other in the centre. Your friend is at the Automatic Teller Machine (ATM) at Shop No. 40. You are waiting for your friend at Entrance No. 2. Explain to your friend the quickest way how to get to Entrance No.2. (3) 1.2 You and your friend want to watch the movie The Best of Me that is screened in Cinema 15 at The Bridge near the Greenacres Shopping Centre. The running time of the movie is 117 minutes. The show times of the movie are shown below for Sunday, 11 January Sun 11 Jan 10:00 12:15 14:45 17:45 20:15 22: Write the running time of the movie in hours and minutes. (2) You and your friend arrived at the centre at 11:20 and have to be at home by 17:30. It takes you two thirds of an hour from Greenacres Shopping Centre to your home. With your arrival at the centre, you and your friend spend three quarters of an hour at the Food Court. It will take you about 15 minutes to buy your tickets. Show with the necessary calculations which of the times will be most suitable for you to watch the movie. (6) Give TWO reasons why the movie for the next time slot is not exactly after the end of the previous screening. (2)

4 4 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2015) 1.3 The following table shows the prices of the movie tickets at The Bridge Cinemas: Kids (younger than 18 years) Adults (18 60 years) Seniors (older than 60 years) Table 1: Price of movie tickets at The Bridge Regular Pricing Adults Kids and Seniors 2D R 62,00 R43,00 3D R 75,00 R55,00 Mon, Tue, Thurs, Fri 2D R 38,00 3D R 55,00 Wowza Wednedays 2D R 37,00 3D R 45, Calculate the total price of the tickets for you and your friend. You are 18 years old and your friend 16 years; and you will be watching the movie in 3D. (3) Seeing that you and your friend are dependent on allowances from your parents, why do you think you and your friend chose the wrong day to watch movies? (2) [20]

5 (EC/NOVEMBER 2015) MATHEMATICAL LITERACY P2 5 QUESTION Mr. Gardner has a landline telephone. His service provider offers him a choice of their new call packages. Below is a table showing the two different call packages that they offer. Table 2: Two Landline call packages Call Package A Monthly rental of R100 First 100 minutes are free Calls cost 80 cents per minute Call Package B Monthly rental of R200 First 150 minutes are free Calls cost 60 cents per minute The total cost for Call package A is given by the following formula: Total cost (in Rand) = R100 + number of minutes more than 100 x R0,80 (a) (b) Write down a formula which can be used to calculate the total cost in Rand for Call package B. (3) If Call package B is used, determine the total cost in Rand, if Mr. Gardner and his family made calls with a total duration of 625 minutes. (4) The line graph illustrated in ANNEXURE B shows the total cost for Call package B. On the same set of axes, draw a line graph to illustrate the total cost for Call package A. (5) Briefly define what is meant by concept, break-even point, in the given context. (2) Write down the co-ordinates of the break-even point on the graph. (2) Show by means of calculation that Call Package A costs 20 cents more than Call Package B for using the minimum number of minutes after the break-even point. (4) Mr. Gardner wants to spend a maximum of R300 per month on one of the Call packages. Which Call package would you advise him to choose? Motivate your answer by showing all calculations. (5)

6 6 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2015) 2.2 The service providers have a major task on their hands. For Landline numbers they have to use a system where they make entirely sure that a number is not duplicated (repeated). Landline numbers consists of ten digits. The first three digits are for the area code followed by seven digits. The first three digits of the remaining seven digits for the area where Mr. Gardner lives, starts with 423 followed by the last four digits. The last four digits are numbers that can be repeated using the numbers 0 to 9. Show with calculations how many households in Mr. Gardner s area can be issued with a landline number starting with ? (3) [28] QUESTION As availability of water is becoming a major problem in South Africa, more people are intending to save water. Therefore some of them are investigating how they are billed and if the billing is correctly calculated. Mrs. Treace is one of those people and stays in Cape Town. She studied the water tariffs for carefully. Below is a table showing the water tariffs for Cape Town during Study the table carefully before answering the questions. Table 3 Water Tariff for Cape Town From To Rand per kl excluding VAT Including VAT > 0,0 kl 6,0 kl R 0,00 R0,00 > 6,0 kl 10,5 kl R7,60 R8,66 > 10,5 kl 20,0 kl R11,61 R13,24 > 20,0 kl 35,0 kl R17,20 A > 35,0 kl 50,0 kl R21,24 R24,22 > 50,0 kl B R31, Calculate the missing values for A and B respectively. (4) If Mrs. Treace uses on average 19,5 kl of water per month, will she be paying for the full 19,5 kl? Give a reason for your answer. (2) Hence, calculate how much Mrs. Treace will pay for using 19,5 kl of water including VAT. (4)

7 (EC/NOVEMBER 2015) MATHEMATICAL LITERACY P One of the ways to save water is to install a water tank. Mrs. Treace decided to investigate the different types of water tanks that is sold in order to make the best decision. Below are diagrams of a vertical, round water tank and a rectangular water tank. Study these diagrams and the information given and then answer the questions that follow. Vertical Round water tank Rectangular water tank Vertical Round water tank d = diameter h = height f = recommended filled height Rectangular water tank l = length w = width h = height f = recommended filled height Vertical Round Water Tanks Tank Volume in litres Diameter in mm Height in mm Rectangular Water Tanks Tank Volume in litres Depth in mm Height in mm Width in mm Show with the necessary calculations that the volume of the vertical round water tank numbered 1 is not exactly 1000 liters as indicated in the table. Use the formula: Volume of vertical round water tank = 3,142 x radius 2 x height of the water tank. Please Note: 1 m 3 = 1000 l (6) With reference to your answer in QUESTION 3.2.1, why do you think that there is a difference in the volume between what you have calculated and the given volume? Also explain how this given information can be misleading to consumers. (3) Briefly explain why the diagrams indicate a recommended filled height. (2)

8 8 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2015) In her backyard, Mrs. Treace has only one open area next to her house to install the water tank. The width of the area is 1,15 m. Which of the water tanks must she buy that will satisfy the requirement? (2) 3.3 Mrs. Treace will be using the water in her water tank for various purposes. If Mrs. Treace wants to illustrate her usage graphically, which graphical representations can Mrs. Treace use to illustrate how she is using the water? (2) [25] QUESTION The following table illustrates the weather forecast for George from Wednesday, 14 January 2015 to Tuesday, 20 January Study the weather forecast and answer the questions that follow. Table 4: Weather forecast for George Wed Thu Fri Sat Sun Mon Tue 26 C Partly Cloudy Wed 29 C Sunny Thu 22 C Windy Fri 23 C Partly Cloudy Sat 22 C Sunny Son 21 C Mostly Cloudy Mon 24 C Partly Cloudy Tue 21 C Mostly Clear 20 C Partly Cloudy 15 C 30% Chance Rain Shower 16 C Mostly Clear 17 C Partly Cloudy 17 C Mostly Cloudy 17 C Mostly Cloudy [ Calculate the mean day temperature for George for the forecasted period. Round your final answer to the nearest temperature in C. (4) Determine the range for the period. (2) Calculate the median for the night temperatures. (2) Briefly explain the trend of the night temperatures. (2) On which day was the difference in temperature the smallest? Write down this difference. (2) Write down the day where the day and night temperatures showed a decreasing trend. (2) Use the information in the table to draw a compound bar graph in ANNEXURE C. (6)

9 (EC/NOVEMBER 2015) MATHEMATICAL LITERACY P Explain what is meant by the forecast for Friday that states 30% chance of rain shower. (2) You want to travel from George to Knysna. The distance between George and Knysna is 64,7 km. Show with the necessary calculations how long it will take you from George to Knysna if you are driving at a speed of 90 km per hour. Give you answer to the nearest minute. You may use the formula: Distance = Speed x Time (3) If you experience problems with your car on the route, will it be possible that you will complete the trip in the time that you have calculated in QUESTION (2) [27] TOTAL: 100

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11 10 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2015) ANNEXURE A ATM (Automatic Teller Machine) OTM (Outomatiese Teller Masjien) Entrance Ingang

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13 (EC/NOVEMBER 2015) MATHEMATICAL LITERACY P2 11 ANNEXURE B QUESTION NAME: GRADE 11:

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15 12 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2015) ANNEXURE C QUESTION NAME: GRADE 11:

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17 NATIONAL SENIOR CERTIFICATE GRADE 11 NOVEMBER 2015 MATHEMATICAL LITERACY P2 MEMORANDUM MARKS: 100 Symbol M MA CA A C S RT/RG/RM F SF J P R Explanation Method Method with accuracy Consistent accuracy Accuracy Conversion Simplification Reading from a table/reading from a graph/read from map Choosing the correct formula Substitution in a formula Justification Penalty, e.g. for no units, incorrect rounding off, etc. Rounding Off/Reason This memorandum consists of 6 pages.

18 2 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2015) QUESTION Entrances 2A Identifying the number of Walk straight towards Shop No. 6 and turn left. Edgars will be on your left continue until you get to Shop No. 60 and turn right. Keep walking until Shop No and turn left where Entrance 2 is Accept any reasonable explanation entrances (2) 3A Explanation (3) h 57 minutes 1A Hours 1A Minutes (2) : min + 15 min = 12:20 It will be too late to watch the 12:15 screening 14:45 + 1:57 = 16: min = 17:22 min The only time slot will be the 14:45 screening and still be at home on time Cleaning of the cinema To prepare for the next showing OR Allow the cinema crew to take a break Accept any other relevant reasons 1M Adding 45 min and 15 min 1A 1O Opinion 1A Adding 1h57 and 40 min 1A Time to arrive at home 1O Conclusion (6) 1A First reason 1A Second reason Regular pricing = = R130 1A Identifying the correct values 1M Adding It is too expensive on a Sunday or weekends OR On other days its much cheaper Accept any other explanation (2) 1A (3) 2O Explanation (2) [20]

19 (EC/NOVEMBER 2015) MATHEMATICAL LITERACY P2 3 QUESTION (a) Total cost (in rand) = R200 + number of minutes more than 150 x R0, (b) OR Total cost (in rand) = R (number of minutes more than 150) x R0,60 OR Total cost (in rand) = R200 + (number of minutes 150) x R0,60 Total cost (in rand) = R200 + (number of minutes 150) x R0,60 = ( ) x 0,60 = (475 x 0,60) = = R485,00 Call package A Call package B For the same number of minutes used the same amount will be paid for both Call packages 1A Rental 1A Minutes more than 150 1A Multiply by 60 cents 1A Rental 1A Minutes more than 150 1A Multiply by 60 cents 1A Rental 1A Minutes more than 150 1A Multiply by 60 cents (3) CA from (a) 1SF 1S 1S 1A (4) 1 Mark for line minutes 1 Mark for the correct breakeven point 2 Marks for any other 3 points plotted correctly 1M Labelling Call Package A (5) 1A refer to minutes 1A refer to cost (2) Break-even point (450 ;380 ) CA from CA 450 minutes 1CA 380 rand If order incorrect 0 (2)

20 4 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2015) Call package A Total cost = ( ) x 0,80 = (351 x 0,80) = ,8 = R 380,80 Call package B Total cost = ( ) x 0,60 = (301 x 0,60) = ,60 = R 380,60 Difference = R 380,80 R 380,60 = R 0,20 OR Call package A - Call package B = ( ) x 0, ( ) x 0,60 = (351 x 0,80) (301 x 0,60) = , ,60 = R 380,80 R 380,60 = R 0, Would recommend that Mr. Gardner use Call Package A With R 300 on Call Package A he will get 350 minutes With R 300 on Call Package B he will get 316 minutes to 317 minutes 2.2 Number of households = 10 x 10 x 10 x 10 = SF 1CA 1CA 1CA Difference 1SF 1CA 1CA 1CA Difference (4) 1CA Choosing correct package 2 CA 2 A (5) 1A Identifying 10 1M Multiplying 10 four times 1CA (3) [28]

21 (EC/NOVEMBER 2015) MATHEMATICAL LITERACY P2 5 QUESTION A = 17,20 x 1,14 = R 19,61 OR A=17,20 + (17,20 x 0,14) = 17,20 + 2,41 = R 19,61 1M 1A B = 31,95 1,14 = R28,03 1M 1A (4) No, she will not pay for the first 6 kl 1A Payment for 19,5 kl = (6 x 0) + (4,5 x 7,60) + (9 x11,61) = R 0 + R 34,20 + R 104,49 = R 138,69 x 1,14 = R 158, Diameter = 750 mm, therefore radius = 375 mm = 0,375 m Height = 2230 mm = 2,230 m Volume = 3,142 x 0,375 m 2 x 2,230 m = 3,142 x 0, m 2 x 2,230 m = 0, m 3 x 1000 = 985, / Accept 985,312 1O (2) 1M 1S 1A 1A Including VAT (4) 1A Finding radius 1A Convert mm to m (both) 1SF 1S radius 2 1CA in litres 1A (6) Therefore; 1000 l 985, l OR 985, The given volume was rounded to the nearest O Consumers are under the impression that you buy a tank with a capacity of l, while it only has a tank capacity of 985 l. 2O (3) Tank can overflow if it is filled above the recommended filled height 2R (2) Any of the vertical round water tanks 2A (2) 3.3 Bar graph and Pie chart 1A Bar graph 1A Pie chart (2) [25]

22 6 MATHEMATICAL LITERACY P2 (EC/NOVEMBER 2015) QUESTION Mean = = = 23, = 24 ºC Range = 29 ºC 15 ºC = 14ºC Median = 15; 16; 17; 17; 17; 20; 21 = 17 ºC 1M adding all day temp 1M/7 1CA 1CA (4) 1M concept of range 1A (2) 1M Arrange values 1A (2) Night temperatures decreases from Wednesday to Friday and then increases on Saturday and then from Sunday remains constant until Tuesday 2O (2) Monday with 1RT Day 4 ºC 1A Difference (2) Friday 2RT (2) Temperature in C Day and night temperatures for George from 14 Jan - 20 Jan Wo Do Vr Sa So Ma Di Days Day temp Night temp Any 4 pairs correctly plotted 1Mark for legend 1 Mark correct graph (6) 4.2 It is highly unlikely that it will rain on Friday because it is only 30% which is small chance for rain to fall 2O (2) Time = Distance Speed = 64,7 km 90 km/h = 0,7188.hours x 60 = 43,133 = 43 minutes Your speed will decrease therefore it will take you longer to complete the trip 1M 1S 1A (3) 1A refer to speed 1A refer to time (2) [27] TOTAL: 100