Mathematical Literacy Grade 12 P2 Eastern Cape Mock 2018 QP

NATIONAL SENIOR CERTIFICATE GRADE 12 SEPTEMBER 2018 MATHEMATICAL LITERACY P2 MARKS: 150 TIME: 3 hours This question paper consists of 12 pages including a 5-page addendum (with 1-page answer sheet attached).

2 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2018) 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. Use the ADDENDUM with ANNEXURES for the following questions: ANNEXURE A for QUESTION 2.2.1 ANNEXURE B for QUESTION 2.3 ANNEXURE C for QUESTION 3.1 ANNEXURE D for QUESTION 3.3 ANSWER SHEET 1 for QUESTION 2.3.5 Write your name in the spaces provided on the ANSWER SHEET and hand in the ANSWER SHEET 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. Show ALL calculations clearly. 6. Maps and diagrams are NOT drawn to scale, unless otherwise stated. 7. Indicate units of measurement, where applicable. 8. Round off ALL final answers appropriately accordingly to the given context, unless stated otherwise. 9. Start EACH question on a NEW page. 10. Write neatly and legibly. Copyright reserved Please turn over

(EC/SEPTEMBER 2018) MATHEMATICAL LITERACY P2 3 QUESTION 1 1.1 A family with five people are living in a water-restricted area in Johannesburg where they can use 87 litres of water per person per day from the municipality. They have decided to install eco-water storage tanks to be able to use 250 litres per person per day. The family uses 87 litres per person of water from the municipality and uses the extra amount from the water tanks. They have two water tanks with dimensions as shown in TABLE 1 below. TABLE 1: Dimensions of the two water tanks TANK Diameter in millimetres Height in millimetres A 1 050 1 420 B 1 800 2 100 NOTE: Two tanks with dimensions as shown have been installed at their house. 1.1.1 How many litres of water in total do they use per month (30 days) from the municipality and from the tanks? (5) 1.1.2 Use TABLE 2, the water tariff charges, below to answer the question. TABLE 2: [NORMAL WATER TARIFF CHARGES FOR JOHANNESBURG IN 2016/2017] Tariff Summary Tariff (in kilolitre) Rand per kilolitre (without VAT) 0 – 6 kℓ Free 7 – 10 kℓ R7,14 11 – 15 kℓ R12,07 16 – 20 kℓ R17,65 21 – 30 kℓ R24,03 31 – 40 kℓ R25,81 > than 40 R32,27 [Source: www.johannesburgwater.co.za] Conversion: 1 kℓ = 1 000 litres The family states that, if the water per person (number of litres) used from the water tank were charged using the normal municipality tariffs, they would be paying more than R300 including VAT (14%) for the water bill. Verify, with the necessary calculations, whether their statement is valid or not. (9) Copyright reserved Please turn over

4 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2018) 1.1.3 Verify, with the necessary calculations, whether they will have enough water for 30 days with both tanks full, even if it does not rain. NOTE: Amount of the water in a full tank is equal to the volume of the tank, rounded to the nearest thousand. You may use the formula: Volume of cylindrical tank = π × radius x radius × height; where π = 3,142 Conversion: 1 000 cm3 = 1 litre (9) 1.2 In a no fee school, book packs (stationary) are supplied to Grade 10, 11 and 12 learners in the ratio 5 : 3 : 2. There are different stickers for each of these grades; blue for Grade 10, beige for Grade 11 and green for Grade 12. Each book pack cost R320,00 including VAT (15%). 1.2.1 The Grade 10 learners received 250 book packs. How many packs were supplied for the whole school? (5) 1.2.2 A government official states that the 15% VAT charged on the total number of book packs is more than the total cost of 50 book packs. Verify, with calculations to show whether the statement is valid or not. (7) 1.2.3 Determine the probability of randomly choosing a book pack belonging to either Grade 11 or Grade 12. Give your final answer as a percentage. (4) [39] Copyright reserved Please turn over

(EC/SEPTEMBER 2018) MATHEMATICAL LITERACY P2 5 QUESTION 2 2.1 The two sets of data below represent the percentage passes in 11 chosen subjects for 2015 and 2016. 2015 59,6; 76,9; 75,7; 68,2; 97,1; 77,0; 84,0; 70,4; 71,4; 49,1; 58,6 2016 69,5; 75,4; 73,7; 65,3; 97,4; 76,5; 84,0; 70,5; 71,3; 51,1; 52,0 2.1.1 Study the data sets for 2015 and 2016 and answer the following questions. (a) Calculate the mean for the 2015 data set. (3) (b) An educator stated that, if only the mean was considered, the 2016 learners performed better than the 2015 learners did. Verify the statement by showing all calculations. (3) 2.1.2 The box and whisker diagrams below are representing the two sets of data for the percentage passes in 11 chosen subjects. Some information has been omitted. 2015 49,1 59,6 71,4 A 97,1 2016 51,1 B 71,3 76,5 97,4 An educator claimed that the 2015 results were better than the 2016 results when comparing the two box and whisker diagrams. Verify this statement by commenting on the interquartile range. (6) Copyright reserved Please turn over

6 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2018) 2.2 Use the tax table in ANNEXURE A to answer the following questions. 2.2.1 A 56-year-old woman is earning R31 625 taxable income per month. She is not contributing to any medical aid. She claims that with her monthly tax she can pay old age grants for two old age people and ten child support grants. Prove, with calculations, whether her statement is valid or not. NOTE: Child support grant is R380 and old age grant is R1 600. (10) 2.2.2 She is working for a company offering 5,8% increment for the first year and 6,8% for the following year. Calculate her total annual income after two years. (5) 2.3 The table in ANNEXURE B shows a statistical summary of social grants in South Africa. Answer the questions based on the table. 2.3.1 Calculate the difference in the total of the old age grant and child support grant for KwaZulu-Natal and Western Cape. (4) 2.3.2 Identify the province with the lowest number of social grants, excluding war veteran grants and grant in aid. (2) 2.3.3 The following table represents the War Veteran grants for 2017 and 2018 for the different provinces. EC FS GP KZN LP MP NC NW WC 2017 23 1 51 22 6 4 4 2 46 2018 21 1 48 15 3 3 3 2 42 Give a possible reason why the number of the War Veteran grants for Gauteng and North West provinces differ from one another. (2) 2.3.4 Describe the trend of the number of War Veteran Grants between the two years. (4) 2.3.5 Draw a compound bar graph on ANSWER SHEET 1 to represent the total number of War Veterans’ grants for the Eastern Cape, KwaZulu-Natal, Northern Cape and Limpopo for the two years. (4) [43] Copyright reserved Please turn over

(EC/SEPTEMBER 2018) MATHEMATICAL LITERACY P2 7 QUESTION 3 3.1 Two families are travelling from Cape Town to Durban for a holiday. The first family leaves Cape Town at 08:00 and the second family leaves 30 minutes later. Both families have one and a half hour rest during their trip. The arrival time in Durban for both families was 21:00. Use the map of Southern Africa with the given scale in ANNEXURE C to answer the questions below. 3.1.1 The first family claims that the second family might have been travelling at a greater speed. Verify, with the necessary calculations, whether their claim is valid. You may use the following formula: 𝑫𝒊𝒔𝒕𝒂𝒏𝒄𝒆 𝒊𝒏 𝒌𝒊𝒍𝒐𝒎𝒆𝒕𝒓𝒆𝒔 Speed = (10) 𝑻𝒊𝒎𝒆 𝒊𝒏 𝒉𝒐𝒖𝒓𝒔 3.1.2 Identify the country on the map, which is situated northwest of Zimbabwe. (2) 3.2 A Mathematical Literacy educator is teaching measurement to her class. She prepares shapes on a page as shown below. Learners must paste it in their books with dimensions as shown below. 28 cm 2 cm 12 cm 10 cm 6 cm 20 cm 2 cm 6 cm 4 cm Dimensions of page: Length = 28 cm Breadth = 20 cm You may use the following formula: Area of rectangle = Length × Breadth Area of square = Side × Side 3.2.1 A learner uses string to measure the perimeter of the shaded figure. What is the length of the string needed? (4) Copyright reserved Please turn over

8 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2018) 3.2.2 Calculate the area of the unshaded part in square centimetres (cm2). (7) 3.3 ANNEXURE D represents the gates and camp distances for the Kruger National Park. 3.3.1 Tourists in Kruger National Park state that travelling from Satara to Olifants will take them half the time from N’wanetsi to Lower Sabi. By considering the distances, explain whether their statement is valid or not. NOTE: They are not travelling at the same speed. (4) 3.3.2 The distance from Punda Maria to Paul Kruger via Mopani is 30 km less than the distance from Skukuza to Pafuri. Verify, showing all calculations, whether this statement is true. (4) [31] Copyright reserved Please turn over

(EC/SEPTEMBER 2018) MATHEMATICAL LITERACY P2 9 QUESTION 4 4.1 TABLE 3 below shows information for fees payable for undergraduate studies in Australia. It shows 3 faculties at 10 selected universities. Study the table below and answer the questions. TABLE 3: UNIVERSITY FEES Bachelor’s Degree (Undergraduate) – Fees University Business Engineering Arts Australian Catholic $23 800 $21 000 University Australian National $39 024 $41 040 $36 720 University Bond University $33 640 $33 640 $33 640 CQ University $23 760 $30 240 $21 120 Charles Darwin University $20 440 $26 000 $18 520 Charles Sturt University $22 800 $18 400 Curtin University $30 000 $34 000 $30 000 Deakin University $28 952 $33 000 $25 088 Edith Cowan University $27 600 $25 760 $27 200 Federation University $24 700 $28 800 $23 300 Australia 4.1.1 Give a possible explanation for no fees payable in Engineering at certain universities. (2) 4.1.2 Calculate the total amount (fees) payable in Rand, if two students are studying Business and Engineering at Bond and Edith Cowan Universities respectively. Given that the exchange rate was the following on 30 January 2018: 1 Australian dollar (AUSD) = R9,68. (4) 4.1.3 Determine the probability to randomly choose a university where the fees for Arts is greater than $15 000 but less than $30 000. Give your final answer as a decimal fraction. (3) Copyright reserved Please turn over

10 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2018) 4.2 The table below represents the sales in Europe for all models of Mercedes Benz from July to December for three consecutive years. TABLE 4: MERCEDES-BENZ SALES IN EUROPE Month Mercedes Benz sales 2014 2015 2016 July 29 406 29 689 31 795 August 28 958 30 633 31 556 September 29 523 29 678 32 470 October 30 733 31 749 31 383 November 37 110 32 813 32 927 December 37 297 38 249 35 871 [Source: www.carsalesbase.com] 4.2.1 Calculate the percentage increase in Mercedes-Benz sales from September 2015 to December 2015. (4) 4.2.2 Which month shows the highest Mercedes-Benz sales for all the years? Give a possible reason for these high Mercedes-Benz sales. (3) 4.2.3 Calculate the difference in sales for August 2015 and August 2016 if a car is sold at an average price of R550 000. Give your final answer in Euro. Given that 1 Euro = R14,81 (5) Copyright reserved Please turn over

(EC/SEPTEMBER 2018) MATHEMATICAL LITERACY P2 11 4.3 A construction company has employed people for a project to be done in 14 days. There are 3 different levels of employees with different rates of payments. There are two Level 3 employees paid at a rate of R248 per hour, six Level 2 employees at a rate of R218,24 per hour and thirty-two Level 1 employees at a rate of R163,68 per hour. They work from 14:00 until 20:00 on the first day, with an hour mealtime in-between. For the other days, they work from 08:00–20:00 with 2 hours mealtime in-between. On the last day, Level 1 employees work for four hours while Level 2 and 3 employees work for eight hours. Employees are staying 14 km from the construction site and are transported by bus daily to and from the construction site at a rate of R3,18 per kilometre per person. NOTE:  The construction company is paying the bus company for transport.  Employees are not paid for any breaks. 4.3.1 The chief financial officer of the construction company states that the amount needed for the employees without transport cost is R800 000. Verify, with the necessary calculations, whether his statement is valid or not. (10) 4.3.2 The chief financial officer reported to the board of managers that the total amount the construction company is paying for transport cost as a decimal fraction of the total amount for employees, is less than 0,5. Verify, with the necessary calculations, whether the report is valid or not. (6) [37] TOTAL: 150 Copyright reserved Please turn over

12 MATHEMATICAL LITERACY P2 (EC/SEPTEMBER 2018) ANSWER SHEET for QUESTION 2.3.5 Name and Surname: ……………………………………………………….. Grade 12: ……. War Veteran grant for the EC, KZN, NC and LP for 2017 and 2018 25 20 15 Provinces 10 5 0 OK KZN NK LP Number of WVG Copyright reserved Please turn over