NATIONAL SENIOR CERTIFICATE GRADE 11 MATHEMATICAL LITERACY PAPER HALF-YEARLY EXAMINATION MARKS: 75 TIME: 1 ½ HOUR This question paper consist of 11 pages with an Annexure
Mathematical Literacy P June 015 INSTRUCTIONS AND INFORMATION 1. This question paper consists of FOUR questions. Answer ALL the questions.. QUESTION 1. must be answered using ANNEXURE A and QUESTION 4.4 must be answered on ANNEXURE B. Write your name in the space provided and hand in the ANNEXURE with the ANSWERBOOK. 3. Number the answers correctly according to the numbering system used in this question paper. 4. Start EACH question on a NEW page. 5. A non- programmable and non-graphical calculator may be used, unless stated otherwise. 6. ALL the calculations must be clearly shown. 7. Round off AL FINAL answers appropriately according to the given context, unless stated otherwise 8. Write neatly and legibly
Mathematical Literacy P 3 June 015 QUESTION 1 NTT Group advertised their Toyota Yaris Hybrid Concept 014 model as follows: [Source: fotosearch.com] CASH PRICE R59 899 (14% VAT exclusive) 3,5% discount before December (after VAT) OR NO DEPOSIT AND LOW MONTHLY INSTALMENTS 8,5% interest rate Monthly installment - R5 860,05 Number of installments 59 months *Residual R85 766,67 Total repayment R351 684,96 Non- cash option also included a monthly service fee of R98,95 60 months. *The residual value is the amount you can buy the car for at the end of the lease, if you decide you want to purchase the car. 1.1 Mr. Govender was attracted to the CASH option and he quickly made his own calculations including VAT and the discount. His calculations come to: R58 914,89. 1.1.1 Verify whether Mr. Govender s calculations are correct (show all your calculations). (5)
Mathematical Literacy P 4 June 015 1.1. Upon Mr. Govender s arrival at key Delta dealers he was told about the following compulsory costs he had to add on the amount he had calculated: A once off initiation fee of R1 559,40 A pre-delivery cost of 0,65% on cash price (including VAT) calculated after any discount. Calculate the final cash price of the car, keeping in mind the discount and the additional costs. He bought the vehicle before December. (4) 1.1.3 Mr. Khumalo went for another option of no deposit and low installments. Calculate the total amount Mr. Khumalo will repay. (5) 1. The Abrahams is an American family of 5 members ( adults & 3 children) that planned a trip to the Kruger National Park. (See Map of part of Kruger National Park on Annexure A) 1..1 Use the scale provided (1,75 cm : 10 km) to determine the distance (in km) from the Phalaborwa Gate to the Letaba Restcamp if the Abrahams use the tarred road. (round off your answer to the nearest km) (3) 1.. In which general direction will the Abrahams travel from Phalaborwa to Letaba Rest camp? 1..3 The Abrahams start their journey from the Phaloborwa Gate at exactly 06:55 and hope to have breakfast at the Letaba Rest camp at 07:5. By use of accurate calculations determine the average speed they have to travel at, in order for them to have breakfast on time. Use formula : Distance = speed time (3)
Mathematical Literacy P 5 June 015 1..4 You are a game reserve ranger at the Kruger National Park and Mr Abraham asks you for the quickest route to the Bateleur Bushveld Camp from Letaba. Name at least places they should look out for in your directions to the Bateleur Bushveld Camp. 1..5 Mr. Abraham refuels his vehicle at a cost of R11,63 per liter of diesel. How much will the diesel cost, needed to travel 580 km. The vehicle s fuel consumption rate is 8,5 liters of diesel per 100km. (3) [7]
Mathematical Literacy P 6 June 015 QUESTION.1 Layla likes baking chocolate muffins at home. She wants to bake 5 muffins at once at 375 o F for the first 15 minutes and then a further 10 minutes at 5 0 F less than the initial temperature for 10. Ingredients (5 muffins) 1 kg snowflake chocolate muffin mix 4 extra-large eggs 310 ml (114) cup cooking oil 400 ml water [Source: fotosearch.com].1.1 How many grams of snowflake chocolate muffin mix will she need to bake 50 chocolate muffins?.1. Calculate the total baking time of the 5 chocolate muffins..1.3 Convert both temperatures to o C. Round your answer off to the nearest o C. Use the following formula: (5).1.4 If the oven temperature dial of the stove is marked in sections of 10 o C, what temperatures should be selected on the dial for QUESTION.3?
Mathematical Literacy P 7 June 015. Bushbuckridge local municipality charges a monthly water tariff on a sliding scale as shown in TABLE 1 below. TABLE 1: WATER TARIFF WATER USAGE FIXED CHARGE RATE PER KILOLITER 0 to 7 kl Nil Nil More than 7 kl up to 17 kl R44,8 R8, More than 17 kl up to 7 kl R44,8 R9,16 More than 7 kl R44,8 R1,50 Calculate the amount the school will pay at the end of the month, if they used 10 kl of water? (4) [15]
Mathematical Literacy P 8 June 015 QUESTION 3 Jabulani and his family have lived with his parents for many years. He has now saved enough money and wants to have a house built for himself and his family. He consults a draughtsman to draw plans for the house. A sketch of Jabulani s house Jabulani employs Simelane Contractors to do the building of his house. Jabulani and the contractors agree that the foundations of the house will be made out of a solid rectangular concrete slab. Concrete is made from cement, sand and crushed stone which are mixed with water. The following table gives the ratio of cement, sand and stone used when mixing the concrete. Table : Ratio of cement, sand and stone Number of bags of cement Number of wheelbarrows of sand Number of wheelbarrows of crushed stones Volume of the concrete in m 3 1 4 0, 4 8 0,4 3.1 How many bags of cement must the contractors use if they need 5 m 3 of concrete? (3)
Mathematical Literacy P 9 June 015 3. The contractors ordered bricks to build the walls of the house. They know that bricks usually get damaged during transportation. To make an allowance for this, he ordered 5% extra. Calculate the number of bricks that should be ordered, if 10 000 bricks are needed. (3) 3.3 Jabulani decides that he wants the outside of his house painted white. The total area of the outside walls that has to be painted is 55,84 m. One liter of white paint is needed to paint one coat of paint on 3 m 3 of the wall. Calculate how many liters of paint are required to paint two coats of paint on the outside of the house. (3) 3.4 White paint is sold in 1 liter, 5 liters, 10 liters and 0 liters tins. The paint is advertised as follows: SPECIALS ON WHITE PAINT 1 litre for R60 5 litres for R0 10 litres for R400 0 litres for R750 What combination of tins of paint would be the cheapest options to buy in order to paint the outside of the house? Show all the calculations. (5) [14]
Mathematical Literacy P 10 June 015 QUESTION 4 Rafique is a sales representative that sells bedding and curtains to shops. He uses his cellular phone to make business calls. He needs to upgrade his contract and must choose between two options; a business contract or pre-paid option. With the business contract he has to pay a monthly subscription fee of R190 and pay R1,50 per minute for phone calls during peak-time. With the pre-paid option he does not have a monthly subscription fee, but he pays R,50 per minute for phone calls during peak-time. BUSINESS CONTRACT PRE-PAID Free minutes NONE NONE Monthly subscription R190 per month NONE Call Tarrifs R1,50 per minute (or portion thereof) R,50 per minute (or portion thereof) 4.1 Explain why the equation C = 190 + 1,50 t represents the total monthly costs (C) in rand for calls made on the business contract for a given time (t) in minutes. 4. Write down a formula in the form: C = to represent Rafique s total monthly costs (C) in rand for calls made on the pre-paid option for a given amount of time (t) in minutes. 4.3 Calculate the costs of Rafique s phone calls with the pre-paid option if the calls comes to 7 minute and 1 seconds. (3)
Mathematical Literacy P 11 June 015 4.4 Table 3 below lists the cost (in rand) of the two cell phone options: TABLE 3 Number of minutes 0 50 100 150 00 50 Business Contract (A) 190 65 340 415 490 565 Pre-paid Option (B) 0 15 50 375 500 65 Use the table above to draw TWO graphs on the system of axes given on ANNEXURE B (attached). Label each of the graphs clearly. (5) 4.5 Use the graphs drawn in QUESTION 4.4 to answer the following questions: 4.5.1 Explain what break-even point means in this context. 4.5. Which option will be cheaper for Rafique to use? Give a reason for your answer. 4.6 Rafique and his colleague, James, draw graphs to illustrate their sales in 004, 005 and 006. TOTAL SALES MADE BY RAFIQUE IN 004, 005 and 006 TOTAL SALES MADE BY JAMES IN 004, 005 en 006 Profit (R in thousand) 6 5 4 3 1 004 005 006 Profit (R in thousand) 5 4 3 1 0 004 005 006 Year Year Which one of the two sales representatives achieved better sales in 004, 005 and 006? Give a reason for your answer. (3) [19] Total Marks: 75
Mathematical Literacy P 1 June 015 ANNEXURE A QUESTION 1. MAP OF THE KRUGER NATIONAL PARK
Mathematical Literacy P 13 June 015 ANNEXURE B NAME: COST OF CELL PHONE CALLS 600 550 500 450 400 Cost in rand 350 300 50 00 150 100 50 0 0 50 100 150 00 50 300 Time in minutes
NATIONAL SENIOR CERTIFICATE GRADE 11 MATHEMATICAL LITERACY PAPER HALF-YAERLY EXAMINATION MEMORANDUM SYMBOL A CA C J M MA P R RT/RG S SF O EXPLANATION Accuracy Consistent accuracy Conversion Justification (Reason/Opinion) Method Method with accuracy Penalty for no units, incorrect rounding off, etc. Rounding off Reading from a table/graph Simplification Correct substitution in a formula Own opinion This memorandum consists of 9 pages
Mathematical Literacy/P June 015 - MEMORANDUM QUESTION 1[7] QUES SOLUTION EXPLANATION TL 1.1.1 Cash price = R59 899,00 Add VAT = R59 899,00 + (14% of R59 899,00) = R59 899,00 + R36 385,86 = R 96 84,86 1M calculating % 1 CA answer Less 3,5% discount = R 96 84,86 3.5% x R 96 84,86 Mr. Govender was correct = R 96 84,86 R10 369,97 = R85 914,89 1M calculating % discount 1Subtracting discount 1J (5) 4 1.1. Cash after discount and VAT included = R85 914,89 Add once of inflation = R85 914,89 + R1 559,40 = R87 474,9 Add pre-delivery costs = R87 474,9 +( 0,0065 )of R85 914,89) = R87 474,9 + R 1 868,58 = R 89 34,87 1..3 Total repayment after 59 months = R5860,05x 59 = R345 74,96 Add monthly service fee = R345 74,96 + (R98,95 x 60 months) = R345 74,96 + R 5 937 = R 351 684,96 1M adding inflation 1 CA answer 1M calculating % 1 CA answer 1 M multiplying by 59 month (4) 1 M multiplying service fee by 60 1 CA answer 3 3 Add residual = R351 684,96 + R85 766,67 = R437 451,63 1 M adding residual 1 CA answer (5)
Mathematical Literacy/P 3 June 015 - MEMORANDUM 1..1 Distance on map = 90mm or 9cm Using given Scale bar on map: Distance = 5(10km) + 0,65km = 50,65km = 51km OR Using calculation: 1,75cm on map is approximately equal to 10km Map: ground 1,75cm : 10km 9cm : x : = 1:5,71 5,71 9 x= 51,43 = 51km 1M measurement A answer OR 1 M multiply by 5,71 km 1A answer (3) 3 1.. In an Easterly direction A answer 1..3 Time = 07h5 06h55 = 0h30 = ½ h Average speed = 51km 0,5h = 10 km/h 1 Subtract time 1 substitution 1A answer 1 Units (4) 3 1..4 They should drive in a northerly direction along the N4 highway and look out for: Mooiplaas Picnic Spot on their left and Tsendze Rustic Campsite approximately 36km from Letaba A fuel service station and Restcamp in Mopani on their left approximately 7,5km after Any
Mathematical Literacy/P 4 June 015 - MEMORANDUM Mooiplaas picnic sport Olifantsbad Pan lookout point on their right approximately 0km after Mopani petrol station Red Rocks waterholes where they turn left Tshanga Lookout Point along the dirt road 1..5 Amount of diesel needed for 580km 1 no. of litres = 580km= 49,3l Cost = R11,63/l 49,3l = R573,36 1 multiply by R11,63 1 Answer (3) 3
Mathematical Literacy/P 5 June 015 - MEMORANDUM QUESTION [15].1.1 1M simplification 1C converting to grams.1. Baking time = 15 min + 10 min = 5 min.1.3 Starting temperature 1M Adding time 1A 1SF 1A rounding to nearest Reduced temperature 1M Finding the reduced temperature 3 Celsius 1SF =176,666..1.4 Starting temperature = 00 ºC Reduced temperature = 180 ºC 1A rounding to nearest (5) 1A rounded to the nearest 10º C 1A rounded to the nearest 10ºC
Mathematical Literacy/P 6 June 015 - MEMORANDUM. 10kl 7kl = 113kl 0 7 kl R0,00 7,1 kl 17 kl (R8, 17,1 kl 7 kl (R9,16 >7,1 kl 10 kl ( R1,50 1A answer 1A answer 1A answer 1 CA total bill (4) 3 QUESTION 3[14] 3.1 0, m 3 concrete is made from 1 bag cement 5m 3 concrete is made from : = 5 bags of cement 1M proportion 1A substitution 1A answer (3) 3 3. 5% of 10 000 bricks 0,05 10 000 bricks 500 bricks Number of bricks to be ordered 10 000 500 10 500 bricks 3.3 Number of litres of paint for 1 coat 18,61 Total amount of paint 18,61 37,3 38 3.4 He needs 38 of paint. Option 1: Buy 0 litres paint and keep the extra litres Cost 0 litres R750 R1 500 Option 3 10 litres 1 5 litre 3 1 litre = 3 R400 1 R0 3 R60 = R100 R 0 R 180 = R 1600 1M calculating % 1A answer 1CA final solution (3) 1 M dividing 1A solution 1CA rounding up (3) 1M option 1 1CA total price 1M option 1CA total price 4
Mathematical Literacy/P 7 June 015 - MEMORANDUM Option 1 is better QUESTION 4[19] 4.1 The basic cost is R190 (constant) and the cost of each minute (t) is R1,50 1A correct option (5) 1 A R190 constant 1 A each minute 4. K=,50t A formula 4.3 7 minutes and 1 seconds 73 minutes Cost =R,50 73 =R 18,50 4.4 1M substitution 1M rounding up 1M CA solution (3) 3 Graph A A for plotting Graph B 1A point (0;0) A for plotting
Mathematical Literacy/P 8 June 015 - MEMORANDUM 4.5.1 The break-even point is the point where: the two graphs intersect. OR both packages cost the same OR there is no profit/gain or loss OR both situations are the same M description of break-even point 4.5. Option B will be cheaper if Rafique use less than 00 minutes but if not Option A will be cheaper if he uses more than 00 minutes. J motivation 4 4.6 Rafique s total sales R3 000 R4 000 R5 000 R1 000 1A addition James total sales R 000 R3 000 R4 000 1A final answer 4 = 9 000 Rafique s sales were higher. 1J Motivation (3) TOTAL : 75 MARKS
Mathematical Literacy/P 9 June 015 - MEMORANDUM TAXONOMY LEVEL GRID QUESTION NUMBER Taxonomy Levels TL1 TL TL3 TL4 1. 1.1.1 5 1.1. 4 1.1.3 5 1..1 3 1.. 1.3 4 1..4 1..5 3..1..3 5.4.5 4 3. 3.1.1 3.1. 3 3.1.3 3 3.1.4 5 4. 4.1 4. 4.3 3 4.4 5 4.5.1 4.5. 4.6 3 TOTAL 1 44 15 % 8% 5% 0%